TSTP Solution File: SYN476-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN476-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 23:55:45 EDT 2022
% Result : Unsatisfiable 1.52s 1.21s
% Output : Proof 1.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN476-1 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 04:16:11 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 1.52/1.21 % SZS status Unsatisfiable
% 1.52/1.21 % SZS output start Proof
% 1.52/1.21 tff(c1_1_type, type, (
% 1.52/1.21 c1_1: $i > $o)).
% 1.52/1.21 tff(a1100_type, type, (
% 1.52/1.21 a1100: $i)).
% 1.52/1.21 tff(c3_1_type, type, (
% 1.52/1.21 c3_1: $i > $o)).
% 1.52/1.21 tff(c0_1_type, type, (
% 1.52/1.21 c0_1: $i > $o)).
% 1.52/1.21 tff(c2_1_type, type, (
% 1.52/1.21 c2_1: $i > $o)).
% 1.52/1.21 tff(ndr1_0_type, type, (
% 1.52/1.21 ndr1_0: $o)).
% 1.52/1.21 tff(hskp5_type, type, (
% 1.52/1.21 hskp5: $o)).
% 1.52/1.21 tff(hskp2_type, type, (
% 1.52/1.21 hskp2: $o)).
% 1.52/1.21 tff(a1105_type, type, (
% 1.52/1.21 a1105: $i)).
% 1.52/1.21 tff(a1136_type, type, (
% 1.52/1.21 a1136: $i)).
% 1.52/1.21 tff(hskp30_type, type, (
% 1.52/1.21 hskp30: $o)).
% 1.52/1.21 tff(hskp0_type, type, (
% 1.52/1.21 hskp0: $o)).
% 1.52/1.21 tff(a1098_type, type, (
% 1.52/1.21 a1098: $i)).
% 1.52/1.21 tff(a1103_type, type, (
% 1.52/1.21 a1103: $i)).
% 1.52/1.21 tff(hskp21_type, type, (
% 1.52/1.21 hskp21: $o)).
% 1.52/1.21 tff(a1147_type, type, (
% 1.52/1.21 a1147: $i)).
% 1.52/1.21 tff(hskp23_type, type, (
% 1.52/1.21 hskp23: $o)).
% 1.52/1.21 tff(a1102_type, type, (
% 1.52/1.21 a1102: $i)).
% 1.52/1.21 tff(hskp4_type, type, (
% 1.52/1.21 hskp4: $o)).
% 1.52/1.21 tff(hskp7_type, type, (
% 1.52/1.21 hskp7: $o)).
% 1.52/1.21 tff(a1099_type, type, (
% 1.52/1.21 a1099: $i)).
% 1.52/1.21 tff(hskp1_type, type, (
% 1.52/1.21 hskp1: $o)).
% 1.52/1.21 tff(a1116_type, type, (
% 1.52/1.21 a1116: $i)).
% 1.52/1.21 tff(hskp29_type, type, (
% 1.52/1.21 hskp29: $o)).
% 1.52/1.21 tff(hskp13_type, type, (
% 1.52/1.21 hskp13: $o)).
% 1.52/1.21 tff(hskp27_type, type, (
% 1.52/1.21 hskp27: $o)).
% 1.52/1.21 tff(hskp16_type, type, (
% 1.52/1.21 hskp16: $o)).
% 1.52/1.21 tff(a1118_type, type, (
% 1.52/1.21 a1118: $i)).
% 1.52/1.21 tff(hskp14_type, type, (
% 1.52/1.21 hskp14: $o)).
% 1.52/1.21 tff(a1130_type, type, (
% 1.52/1.21 a1130: $i)).
% 1.52/1.21 tff(hskp20_type, type, (
% 1.52/1.21 hskp20: $o)).
% 1.52/1.21 tff(a1108_type, type, (
% 1.52/1.21 a1108: $i)).
% 1.52/1.21 tff(hskp9_type, type, (
% 1.52/1.21 hskp9: $o)).
% 1.52/1.21 tff(a1119_type, type, (
% 1.52/1.21 a1119: $i)).
% 1.52/1.21 tff(hskp15_type, type, (
% 1.52/1.21 hskp15: $o)).
% 1.52/1.21 tff(a1111_type, type, (
% 1.52/1.21 a1111: $i)).
% 1.52/1.21 tff(hskp28_type, type, (
% 1.52/1.21 hskp28: $o)).
% 1.52/1.21 tff(a1104_type, type, (
% 1.52/1.21 a1104: $i)).
% 1.52/1.21 tff(hskp6_type, type, (
% 1.52/1.21 hskp6: $o)).
% 1.52/1.21 tff(a1115_type, type, (
% 1.52/1.21 a1115: $i)).
% 1.52/1.21 tff(a1127_type, type, (
% 1.52/1.21 a1127: $i)).
% 1.52/1.21 tff(hskp19_type, type, (
% 1.52/1.21 hskp19: $o)).
% 1.52/1.21 tff(a1149_type, type, (
% 1.52/1.21 a1149: $i)).
% 1.52/1.21 tff(hskp24_type, type, (
% 1.52/1.21 hskp24: $o)).
% 1.52/1.21 tff(a1131_type, type, (
% 1.52/1.21 a1131: $i)).
% 1.52/1.21 tff(a1101_type, type, (
% 1.52/1.21 a1101: $i)).
% 1.52/1.21 tff(hskp3_type, type, (
% 1.52/1.21 hskp3: $o)).
% 1.52/1.21 tff(hskp8_type, type, (
% 1.52/1.21 hskp8: $o)).
% 1.52/1.21 tff(a1107_type, type, (
% 1.52/1.21 a1107: $i)).
% 1.52/1.21 tff(a1113_type, type, (
% 1.52/1.21 a1113: $i)).
% 1.52/1.21 tff(hskp11_type, type, (
% 1.52/1.21 hskp11: $o)).
% 1.52/1.21 tff(a1121_type, type, (
% 1.52/1.21 a1121: $i)).
% 1.52/1.21 tff(a1110_type, type, (
% 1.52/1.21 a1110: $i)).
% 1.52/1.21 tff(hskp10_type, type, (
% 1.52/1.21 hskp10: $o)).
% 1.52/1.21 tff(a1145_type, type, (
% 1.52/1.21 a1145: $i)).
% 1.52/1.21 tff(hskp22_type, type, (
% 1.52/1.21 hskp22: $o)).
% 1.52/1.21 tff(a1125_type, type, (
% 1.52/1.21 a1125: $i)).
% 1.52/1.21 tff(hskp18_type, type, (
% 1.52/1.21 hskp18: $o)).
% 1.52/1.21 tff(a1180_type, type, (
% 1.52/1.21 a1180: $i)).
% 1.52/1.21 tff(hskp26_type, type, (
% 1.52/1.21 hskp26: $o)).
% 1.52/1.21 tff(hskp12_type, type, (
% 1.52/1.21 hskp12: $o)).
% 1.52/1.21 tff(a1114_type, type, (
% 1.52/1.21 a1114: $i)).
% 1.52/1.21 tff(a1124_type, type, (
% 1.52/1.21 a1124: $i)).
% 1.52/1.21 tff(hskp17_type, type, (
% 1.52/1.21 hskp17: $o)).
% 1.52/1.21 tff(1,plain,
% 1.52/1.21 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.52/1.21 inference(bind,[status(th)],[])).
% 1.52/1.21 tff(2,plain,
% 1.52/1.21 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.52/1.21 inference(quant_intro,[status(thm)],[1])).
% 1.52/1.21 tff(3,plain,
% 1.52/1.21 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.52/1.21 inference(rewrite,[status(thm)],[])).
% 1.52/1.21 tff(4,plain,
% 1.52/1.21 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_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)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.52/1.21 inference(bind,[status(th)],[])).
% 1.52/1.21 tff(5,plain,
% 1.52/1.21 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.52/1.21 inference(quant_intro,[status(thm)],[4])).
% 1.52/1.21 tff(6,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.52/1.21 tff(7,plain,
% 1.52/1.21 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.52/1.21 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.52/1.21 tff(8,plain,
% 1.52/1.21 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.52/1.21 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.52/1.21 tff(9,plain,(
% 1.52/1.21 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.52/1.21 inference(skolemize,[status(sab)],[8])).
% 1.52/1.21 tff(10,plain,
% 1.52/1.21 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.52/1.21 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.52/1.21 tff(11,assumption,(hskp0), introduced(assumption)).
% 1.52/1.21 tff(12,plain,
% 1.52/1.21 (((~hskp0) | (~c1_1(a1098))) <=> ((~hskp0) | (~c1_1(a1098)))),
% 1.52/1.21 inference(rewrite,[status(thm)],[])).
% 1.52/1.21 tff(13,plain,
% 1.52/1.21 (((~c1_1(a1098)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a1098)))),
% 1.52/1.21 inference(rewrite,[status(thm)],[])).
% 1.52/1.21 tff(14,axiom,((~c1_1(a1098)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.52/1.21 tff(15,plain,
% 1.52/1.21 ((~hskp0) | (~c1_1(a1098))),
% 1.52/1.21 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.52/1.21 tff(16,plain,
% 1.52/1.21 ((~hskp0) | (~c1_1(a1098))),
% 1.52/1.21 inference(modus_ponens,[status(thm)],[15, 12])).
% 1.52/1.21 tff(17,plain,
% 1.52/1.21 (~c1_1(a1098)),
% 1.52/1.21 inference(unit_resolution,[status(thm)],[16, 11])).
% 1.52/1.21 tff(18,plain,
% 1.52/1.21 (((~hskp0) | (~c2_1(a1098))) <=> ((~hskp0) | (~c2_1(a1098)))),
% 1.52/1.21 inference(rewrite,[status(thm)],[])).
% 1.52/1.21 tff(19,plain,
% 1.52/1.21 (((~c2_1(a1098)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1098)))),
% 1.52/1.21 inference(rewrite,[status(thm)],[])).
% 1.52/1.21 tff(20,axiom,((~c2_1(a1098)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.52/1.21 tff(21,plain,
% 1.52/1.21 ((~hskp0) | (~c2_1(a1098))),
% 1.52/1.21 inference(modus_ponens,[status(thm)],[20, 19])).
% 1.52/1.21 tff(22,plain,
% 1.52/1.21 ((~hskp0) | (~c2_1(a1098))),
% 1.52/1.21 inference(modus_ponens,[status(thm)],[21, 18])).
% 1.52/1.21 tff(23,plain,
% 1.52/1.21 (~c2_1(a1098)),
% 1.52/1.21 inference(unit_resolution,[status(thm)],[22, 11])).
% 1.52/1.21 tff(24,plain,
% 1.52/1.21 (^[U: $i] : refl((hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.52/1.21 inference(bind,[status(th)],[])).
% 1.52/1.21 tff(25,plain,
% 1.52/1.21 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.52/1.21 inference(quant_intro,[status(thm)],[24])).
% 1.52/1.21 tff(26,plain,
% 1.52/1.21 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.52/1.21 inference(rewrite,[status(thm)],[])).
% 1.52/1.21 tff(27,plain,
% 1.52/1.21 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp21))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp0) <=> ((hskp21 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp0))), rewrite(((hskp21 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp0) <=> (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp0) <=> (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.52/1.21 inference(bind,[status(th)],[])).
% 1.52/1.21 tff(28,plain,
% 1.52/1.21 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp0) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.52/1.21 inference(quant_intro,[status(thm)],[27])).
% 1.52/1.21 tff(29,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 1.52/1.21 tff(30,plain,
% 1.52/1.21 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.52/1.21 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.52/1.21 tff(31,plain,
% 1.52/1.21 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.52/1.21 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.52/1.21 tff(32,plain,(
% 1.52/1.21 ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.52/1.21 inference(skolemize,[status(sab)],[31])).
% 1.52/1.21 tff(33,plain,
% 1.52/1.21 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.52/1.21 inference(modus_ponens,[status(thm)],[32, 25])).
% 1.52/1.21 tff(34,assumption,(~c1_1(a1098)), introduced(assumption)).
% 1.52/1.21 tff(35,assumption,(~c2_1(a1098)), introduced(assumption)).
% 1.52/1.21 tff(36,plain,
% 1.52/1.21 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))))),
% 1.52/1.21 inference(bind,[status(th)],[])).
% 1.52/1.21 tff(37,plain,
% 1.52/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.52/1.21 inference(quant_intro,[status(thm)],[36])).
% 1.52/1.21 tff(38,plain,
% 1.52/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.52/1.21 inference(rewrite,[status(thm)],[])).
% 1.52/1.21 tff(39,plain,
% 1.52/1.21 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_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)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))))),
% 1.52/1.21 inference(bind,[status(th)],[])).
% 1.52/1.21 tff(40,plain,
% 1.52/1.21 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.52/1.21 inference(quant_intro,[status(thm)],[39])).
% 1.52/1.21 tff(41,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 1.52/1.21 tff(42,plain,
% 1.52/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.52/1.21 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.52/1.21 tff(43,plain,
% 1.52/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.52/1.21 inference(modus_ponens,[status(thm)],[42, 38])).
% 1.52/1.21 tff(44,plain,(
% 1.52/1.21 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.52/1.21 inference(skolemize,[status(sab)],[43])).
% 1.52/1.21 tff(45,plain,
% 1.52/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.52/1.21 inference(modus_ponens,[status(thm)],[44, 37])).
% 1.52/1.21 tff(46,assumption,(~c0_1(a1136)), introduced(assumption)).
% 1.52/1.21 tff(47,assumption,(~c3_1(a1098)), introduced(assumption)).
% 1.52/1.21 tff(48,plain,
% 1.52/1.21 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 1.52/1.21 inference(bind,[status(th)],[])).
% 1.52/1.21 tff(49,plain,
% 1.52/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.52/1.21 inference(quant_intro,[status(thm)],[48])).
% 1.52/1.21 tff(50,plain,
% 1.52/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.52/1.21 inference(rewrite,[status(thm)],[])).
% 1.52/1.21 tff(51,plain,
% 1.52/1.21 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 1.52/1.21 inference(bind,[status(th)],[])).
% 1.52/1.21 tff(52,plain,
% 1.52/1.21 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.52/1.22 inference(quant_intro,[status(thm)],[51])).
% 1.52/1.22 tff(53,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 1.52/1.22 tff(54,plain,
% 1.52/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.52/1.22 tff(55,plain,
% 1.52/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[54, 50])).
% 1.52/1.22 tff(56,plain,(
% 1.52/1.22 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.52/1.22 inference(skolemize,[status(sab)],[55])).
% 1.52/1.22 tff(57,plain,
% 1.52/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[56, 49])).
% 1.52/1.22 tff(58,plain,
% 1.52/1.22 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.52/1.22 inference(bind,[status(th)],[])).
% 1.52/1.22 tff(59,plain,
% 1.52/1.22 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.22 inference(quant_intro,[status(thm)],[58])).
% 1.52/1.22 tff(60,plain,
% 1.52/1.22 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(61,plain,
% 1.52/1.22 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.52/1.22 inference(bind,[status(th)],[])).
% 1.52/1.22 tff(62,plain,
% 1.52/1.22 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.22 inference(quant_intro,[status(thm)],[61])).
% 1.52/1.22 tff(63,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 1.52/1.22 tff(64,plain,
% 1.52/1.22 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.52/1.22 tff(65,plain,
% 1.52/1.22 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.52/1.22 tff(66,plain,(
% 1.52/1.22 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.22 inference(skolemize,[status(sab)],[65])).
% 1.52/1.22 tff(67,plain,
% 1.52/1.22 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[66, 59])).
% 1.52/1.22 tff(68,assumption,(~hskp7), introduced(assumption)).
% 1.52/1.22 tff(69,plain,
% 1.52/1.22 (^[U: $i] : refl((hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 1.52/1.22 inference(bind,[status(th)],[])).
% 1.52/1.22 tff(70,plain,
% 1.52/1.22 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.52/1.22 inference(quant_intro,[status(thm)],[69])).
% 1.52/1.22 tff(71,plain,
% 1.52/1.22 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(72,plain,
% 1.52/1.22 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp5) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp5))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp5) <=> (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp5) <=> (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 1.52/1.22 inference(bind,[status(th)],[])).
% 1.52/1.22 tff(73,plain,
% 1.52/1.22 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp5) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.52/1.22 inference(quant_intro,[status(thm)],[72])).
% 1.52/1.22 tff(74,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 1.52/1.22 tff(75,plain,
% 1.52/1.22 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.52/1.22 tff(76,plain,
% 1.52/1.22 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[75, 71])).
% 1.52/1.22 tff(77,plain,(
% 1.52/1.22 ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.52/1.22 inference(skolemize,[status(sab)],[76])).
% 1.52/1.22 tff(78,plain,
% 1.52/1.22 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[77, 70])).
% 1.52/1.22 tff(79,assumption,(~ndr1_0), introduced(assumption)).
% 1.52/1.22 tff(80,plain,
% 1.52/1.22 ((ndr1_0 | (~hskp13)) <=> (ndr1_0 | (~hskp13))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(81,plain,
% 1.52/1.22 (((~hskp13) | ndr1_0) <=> (ndr1_0 | (~hskp13))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(82,axiom,((~hskp13) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause20')).
% 1.52/1.22 tff(83,plain,
% 1.52/1.22 (ndr1_0 | (~hskp13)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.52/1.22 tff(84,plain,
% 1.52/1.22 (ndr1_0 | (~hskp13)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[83, 80])).
% 1.52/1.22 tff(85,plain,
% 1.52/1.22 (~hskp13),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[84, 79])).
% 1.52/1.22 tff(86,plain,
% 1.52/1.22 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(87,plain,
% 1.52/1.22 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(88,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause6')).
% 1.52/1.22 tff(89,plain,
% 1.52/1.22 (ndr1_0 | (~hskp27)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[88, 87])).
% 1.52/1.22 tff(90,plain,
% 1.52/1.22 (ndr1_0 | (~hskp27)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[89, 86])).
% 1.52/1.22 tff(91,plain,
% 1.52/1.22 (~hskp27),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[90, 79])).
% 1.52/1.22 tff(92,plain,
% 1.52/1.22 ((ndr1_0 | (~hskp16)) <=> (ndr1_0 | (~hskp16))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(93,plain,
% 1.52/1.22 (((~hskp16) | ndr1_0) <=> (ndr1_0 | (~hskp16))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(94,axiom,((~hskp16) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause17')).
% 1.52/1.22 tff(95,plain,
% 1.52/1.22 (ndr1_0 | (~hskp16)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.52/1.22 tff(96,plain,
% 1.52/1.22 (ndr1_0 | (~hskp16)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[95, 92])).
% 1.52/1.22 tff(97,plain,
% 1.52/1.22 (~hskp16),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[96, 79])).
% 1.52/1.22 tff(98,plain,
% 1.52/1.22 ((hskp27 | hskp16 | hskp13) <=> (hskp27 | hskp16 | hskp13)),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(99,plain,
% 1.52/1.22 (((hskp16 | hskp13) | hskp27) <=> (hskp27 | hskp16 | hskp13)),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(100,plain,
% 1.52/1.22 ((hskp16 | hskp13) <=> (hskp16 | hskp13)),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(101,plain,
% 1.52/1.22 (((hskp16 | hskp13) | hskp27) <=> ((hskp16 | hskp13) | hskp27)),
% 1.52/1.22 inference(monotonicity,[status(thm)],[100])).
% 1.52/1.22 tff(102,plain,
% 1.52/1.22 (((hskp16 | hskp13) | hskp27) <=> (hskp27 | hskp16 | hskp13)),
% 1.52/1.22 inference(transitivity,[status(thm)],[101, 99])).
% 1.52/1.22 tff(103,axiom,((hskp16 | hskp13) | hskp27), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.52/1.22 tff(104,plain,
% 1.52/1.22 (hskp27 | hskp16 | hskp13),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[103, 102])).
% 1.52/1.22 tff(105,plain,
% 1.52/1.22 (hskp27 | hskp16 | hskp13),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[104, 98])).
% 1.52/1.22 tff(106,plain,
% 1.52/1.22 (hskp27 | hskp16 | hskp13),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[105, 98])).
% 1.52/1.22 tff(107,plain,
% 1.52/1.22 (hskp27 | hskp16 | hskp13),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[106, 98])).
% 1.52/1.22 tff(108,plain,
% 1.52/1.22 (hskp27 | hskp16 | hskp13),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[107, 98])).
% 1.52/1.22 tff(109,plain,
% 1.52/1.22 (hskp27 | hskp16 | hskp13),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[108, 98])).
% 1.52/1.22 tff(110,plain,
% 1.52/1.22 (hskp27 | hskp16 | hskp13),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[109, 98])).
% 1.52/1.22 tff(111,plain,
% 1.52/1.22 (hskp27 | hskp16 | hskp13),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[110, 98])).
% 1.52/1.22 tff(112,plain,
% 1.52/1.22 ($false),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[111, 97, 91, 85])).
% 1.52/1.22 tff(113,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.52/1.22 tff(114,plain,
% 1.52/1.22 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(115,plain,
% 1.52/1.22 ((hskp7 | hskp5 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098)) <=> (hskp7 | hskp5 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(116,plain,
% 1.52/1.22 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0)))),
% 1.52/1.22 inference(monotonicity,[status(thm)],[115])).
% 1.52/1.22 tff(117,plain,
% 1.52/1.22 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))),
% 1.52/1.22 inference(transitivity,[status(thm)],[116, 114])).
% 1.52/1.22 tff(118,plain,
% 1.52/1.22 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098))),
% 1.52/1.22 inference(quant_inst,[status(thm)],[])).
% 1.52/1.22 tff(119,plain,
% 1.52/1.22 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.52/1.22 tff(120,plain,
% 1.52/1.22 (hskp7 | hskp5 | c2_1(a1098) | c3_1(a1098)),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[119, 113, 34, 78])).
% 1.52/1.22 tff(121,plain,
% 1.52/1.22 (hskp5),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[120, 68, 35, 47])).
% 1.52/1.22 tff(122,plain,
% 1.52/1.22 (((~hskp5) | (~c2_1(a1103))) <=> ((~hskp5) | (~c2_1(a1103)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(123,plain,
% 1.52/1.22 (((~c2_1(a1103)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a1103)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(124,axiom,((~c2_1(a1103)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.52/1.22 tff(125,plain,
% 1.52/1.22 ((~hskp5) | (~c2_1(a1103))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.52/1.22 tff(126,plain,
% 1.52/1.22 ((~hskp5) | (~c2_1(a1103))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[125, 122])).
% 1.52/1.22 tff(127,plain,
% 1.52/1.22 (~c2_1(a1103)),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[126, 121])).
% 1.52/1.22 tff(128,plain,
% 1.52/1.22 (((~hskp5) | (~c0_1(a1103))) <=> ((~hskp5) | (~c0_1(a1103)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(129,plain,
% 1.52/1.22 (((~c0_1(a1103)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a1103)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(130,axiom,((~c0_1(a1103)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.52/1.22 tff(131,plain,
% 1.52/1.22 ((~hskp5) | (~c0_1(a1103))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[130, 129])).
% 1.52/1.22 tff(132,plain,
% 1.52/1.22 ((~hskp5) | (~c0_1(a1103))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[131, 128])).
% 1.52/1.22 tff(133,plain,
% 1.52/1.22 (~c0_1(a1103)),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[132, 121])).
% 1.52/1.22 tff(134,plain,
% 1.52/1.22 (^[U: $i] : refl((hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.52/1.22 inference(bind,[status(th)],[])).
% 1.52/1.22 tff(135,plain,
% 1.52/1.22 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.52/1.22 inference(quant_intro,[status(thm)],[134])).
% 1.52/1.22 tff(136,plain,
% 1.52/1.22 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(137,plain,
% 1.52/1.22 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp14) <=> ((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp14))), rewrite(((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp14) <=> (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp14) <=> (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.52/1.22 inference(bind,[status(th)],[])).
% 1.52/1.22 tff(138,plain,
% 1.52/1.22 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp14) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.52/1.22 inference(quant_intro,[status(thm)],[137])).
% 1.52/1.22 tff(139,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 1.52/1.22 tff(140,plain,
% 1.52/1.22 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.52/1.22 tff(141,plain,
% 1.52/1.22 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[140, 136])).
% 1.52/1.22 tff(142,plain,(
% 1.52/1.22 ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.52/1.22 inference(skolemize,[status(sab)],[141])).
% 1.52/1.22 tff(143,plain,
% 1.52/1.22 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[142, 135])).
% 1.52/1.22 tff(144,plain,
% 1.52/1.22 (((~hskp5) | c3_1(a1103)) <=> ((~hskp5) | c3_1(a1103))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(145,axiom,((~hskp5) | c3_1(a1103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.52/1.22 tff(146,plain,
% 1.52/1.22 ((~hskp5) | c3_1(a1103)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[145, 144])).
% 1.52/1.22 tff(147,plain,
% 1.52/1.22 ((~hskp5) | c3_1(a1103)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[146, 144])).
% 1.52/1.22 tff(148,plain,
% 1.52/1.22 ((~hskp5) | c3_1(a1103)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[147, 144])).
% 1.52/1.22 tff(149,plain,
% 1.52/1.22 ((~hskp5) | c3_1(a1103)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[148, 144])).
% 1.52/1.22 tff(150,plain,
% 1.52/1.22 ((~hskp5) | c3_1(a1103)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[149, 144])).
% 1.52/1.22 tff(151,plain,
% 1.52/1.22 ((~hskp5) | c3_1(a1103)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[150, 144])).
% 1.52/1.22 tff(152,plain,
% 1.52/1.22 ((~hskp5) | c3_1(a1103)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[151, 144])).
% 1.52/1.22 tff(153,plain,
% 1.52/1.22 ((~hskp5) | c3_1(a1103)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[152, 144])).
% 1.52/1.22 tff(154,plain,
% 1.52/1.22 (c3_1(a1103)),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[153, 121])).
% 1.52/1.22 tff(155,plain,
% 1.52/1.22 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(156,plain,
% 1.52/1.22 ((hskp14 | hskp7 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103))) <=> (hskp14 | hskp7 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(157,plain,
% 1.52/1.22 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103))))),
% 1.52/1.22 inference(monotonicity,[status(thm)],[156])).
% 1.52/1.22 tff(158,plain,
% 1.52/1.22 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)))),
% 1.52/1.22 inference(transitivity,[status(thm)],[157, 155])).
% 1.52/1.22 tff(159,plain,
% 1.52/1.22 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))),
% 1.52/1.22 inference(quant_inst,[status(thm)],[])).
% 1.52/1.22 tff(160,plain,
% 1.52/1.22 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[159, 158])).
% 1.52/1.22 tff(161,plain,
% 1.52/1.22 (hskp14),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[160, 113, 68, 154, 133, 127, 143])).
% 1.52/1.22 tff(162,plain,
% 1.52/1.22 (((~hskp14) | (~c3_1(a1118))) <=> ((~hskp14) | (~c3_1(a1118)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(163,plain,
% 1.52/1.22 (((~c3_1(a1118)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a1118)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(164,axiom,((~c3_1(a1118)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.52/1.22 tff(165,plain,
% 1.52/1.22 ((~hskp14) | (~c3_1(a1118))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[164, 163])).
% 1.52/1.22 tff(166,plain,
% 1.52/1.22 ((~hskp14) | (~c3_1(a1118))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[165, 162])).
% 1.52/1.22 tff(167,plain,
% 1.52/1.22 (~c3_1(a1118)),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[166, 161])).
% 1.52/1.22 tff(168,plain,
% 1.52/1.22 (((~hskp14) | (~c2_1(a1118))) <=> ((~hskp14) | (~c2_1(a1118)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(169,plain,
% 1.52/1.22 (((~c2_1(a1118)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a1118)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(170,axiom,((~c2_1(a1118)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.52/1.22 tff(171,plain,
% 1.52/1.22 ((~hskp14) | (~c2_1(a1118))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.52/1.22 tff(172,plain,
% 1.52/1.22 ((~hskp14) | (~c2_1(a1118))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[171, 168])).
% 1.52/1.22 tff(173,plain,
% 1.52/1.22 (~c2_1(a1118)),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[172, 161])).
% 1.52/1.22 tff(174,plain,
% 1.52/1.22 (((~hskp14) | c1_1(a1118)) <=> ((~hskp14) | c1_1(a1118))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(175,axiom,((~hskp14) | c1_1(a1118)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.52/1.22 tff(176,plain,
% 1.52/1.22 ((~hskp14) | c1_1(a1118)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.52/1.22 tff(177,plain,
% 1.52/1.22 ((~hskp14) | c1_1(a1118)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[176, 174])).
% 1.52/1.22 tff(178,plain,
% 1.52/1.22 ((~hskp14) | c1_1(a1118)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[177, 174])).
% 1.52/1.22 tff(179,plain,
% 1.52/1.22 ((~hskp14) | c1_1(a1118)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[178, 174])).
% 1.52/1.22 tff(180,plain,
% 1.52/1.22 ((~hskp14) | c1_1(a1118)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[179, 174])).
% 1.52/1.22 tff(181,plain,
% 1.52/1.22 ((~hskp14) | c1_1(a1118)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[180, 174])).
% 1.52/1.22 tff(182,plain,
% 1.52/1.22 ((~hskp14) | c1_1(a1118)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[181, 174])).
% 1.52/1.22 tff(183,plain,
% 1.52/1.22 ((~hskp14) | c1_1(a1118)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[182, 174])).
% 1.52/1.22 tff(184,plain,
% 1.52/1.22 (c1_1(a1118)),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[183, 161])).
% 1.52/1.22 tff(185,plain,
% 1.52/1.22 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1118) | c3_1(a1118) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1118) | c3_1(a1118) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1118)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(186,plain,
% 1.52/1.22 ((hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103))) <=> (hskp29 | c2_1(a1118) | c3_1(a1118) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1118)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(187,plain,
% 1.52/1.22 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1118) | c3_1(a1118) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1118))))),
% 1.52/1.22 inference(monotonicity,[status(thm)],[186])).
% 1.52/1.22 tff(188,plain,
% 1.52/1.22 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1118) | c3_1(a1118) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1118)))),
% 1.52/1.22 inference(transitivity,[status(thm)],[187, 185])).
% 1.52/1.22 tff(189,plain,
% 1.52/1.22 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))),
% 1.52/1.22 inference(quant_inst,[status(thm)],[])).
% 1.52/1.22 tff(190,plain,
% 1.52/1.22 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1118) | c3_1(a1118) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1118))),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[189, 188])).
% 1.52/1.22 tff(191,plain,
% 1.52/1.22 (hskp29),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[190, 113, 184, 154, 173, 167, 133, 127, 67])).
% 1.52/1.22 tff(192,plain,
% 1.52/1.22 (((~hskp29) | c3_1(a1116)) <=> ((~hskp29) | c3_1(a1116))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(193,axiom,((~hskp29) | c3_1(a1116)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.52/1.22 tff(194,plain,
% 1.52/1.22 ((~hskp29) | c3_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.52/1.22 tff(195,plain,
% 1.52/1.22 ((~hskp29) | c3_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[194, 192])).
% 1.52/1.22 tff(196,plain,
% 1.52/1.22 ((~hskp29) | c3_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[195, 192])).
% 1.52/1.22 tff(197,plain,
% 1.52/1.22 ((~hskp29) | c3_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[196, 192])).
% 1.52/1.22 tff(198,plain,
% 1.52/1.22 ((~hskp29) | c3_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[197, 192])).
% 1.52/1.22 tff(199,plain,
% 1.52/1.22 ((~hskp29) | c3_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[198, 192])).
% 1.52/1.22 tff(200,plain,
% 1.52/1.22 ((~hskp29) | c3_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[199, 192])).
% 1.52/1.22 tff(201,plain,
% 1.52/1.22 ((~hskp29) | c3_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[200, 192])).
% 1.52/1.22 tff(202,plain,
% 1.52/1.22 (c3_1(a1116)),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[201, 191])).
% 1.52/1.22 tff(203,plain,
% 1.52/1.22 (((~hskp29) | c2_1(a1116)) <=> ((~hskp29) | c2_1(a1116))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(204,axiom,((~hskp29) | c2_1(a1116)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 1.52/1.22 tff(205,plain,
% 1.52/1.22 ((~hskp29) | c2_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[204, 203])).
% 1.52/1.22 tff(206,plain,
% 1.52/1.22 ((~hskp29) | c2_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[205, 203])).
% 1.52/1.22 tff(207,plain,
% 1.52/1.22 ((~hskp29) | c2_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[206, 203])).
% 1.52/1.22 tff(208,plain,
% 1.52/1.22 ((~hskp29) | c2_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[207, 203])).
% 1.52/1.22 tff(209,plain,
% 1.52/1.22 ((~hskp29) | c2_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[208, 203])).
% 1.52/1.22 tff(210,plain,
% 1.52/1.22 ((~hskp29) | c2_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[209, 203])).
% 1.52/1.22 tff(211,plain,
% 1.52/1.22 ((~hskp29) | c2_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[210, 203])).
% 1.52/1.22 tff(212,plain,
% 1.52/1.22 ((~hskp29) | c2_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[211, 203])).
% 1.52/1.22 tff(213,plain,
% 1.52/1.22 (c2_1(a1116)),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[212, 191])).
% 1.52/1.22 tff(214,plain,
% 1.52/1.22 (((~hskp29) | c0_1(a1116)) <=> ((~hskp29) | c0_1(a1116))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(215,axiom,((~hskp29) | c0_1(a1116)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.52/1.22 tff(216,plain,
% 1.52/1.22 ((~hskp29) | c0_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.52/1.22 tff(217,plain,
% 1.52/1.22 ((~hskp29) | c0_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[216, 214])).
% 1.52/1.22 tff(218,plain,
% 1.52/1.22 ((~hskp29) | c0_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[217, 214])).
% 1.52/1.22 tff(219,plain,
% 1.52/1.22 ((~hskp29) | c0_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[218, 214])).
% 1.52/1.22 tff(220,plain,
% 1.52/1.22 ((~hskp29) | c0_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[219, 214])).
% 1.52/1.22 tff(221,plain,
% 1.52/1.22 ((~hskp29) | c0_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[220, 214])).
% 1.52/1.22 tff(222,plain,
% 1.52/1.22 ((~hskp29) | c0_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[221, 214])).
% 1.52/1.22 tff(223,plain,
% 1.52/1.22 ((~hskp29) | c0_1(a1116)),
% 1.52/1.22 inference(modus_ponens,[status(thm)],[222, 214])).
% 1.52/1.22 tff(224,plain,
% 1.52/1.22 (c0_1(a1116)),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[223, 191])).
% 1.52/1.22 tff(225,assumption,(~c0_1(a1103)), introduced(assumption)).
% 1.52/1.22 tff(226,assumption,(~c3_1(a1118)), introduced(assumption)).
% 1.52/1.22 tff(227,assumption,(c0_1(a1118)), introduced(assumption)).
% 1.52/1.22 tff(228,assumption,(c1_1(a1118)), introduced(assumption)).
% 1.52/1.22 tff(229,assumption,(~c2_1(a1103)), introduced(assumption)).
% 1.52/1.22 tff(230,assumption,(~c2_1(a1118)), introduced(assumption)).
% 1.52/1.22 tff(231,assumption,(c3_1(a1103)), introduced(assumption)).
% 1.52/1.22 tff(232,plain,
% 1.52/1.22 (hskp29),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[190, 113, 228, 231, 230, 226, 225, 229, 67])).
% 1.52/1.22 tff(233,plain,
% 1.52/1.22 (c0_1(a1116)),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[223, 232])).
% 1.52/1.22 tff(234,plain,
% 1.52/1.22 (c3_1(a1116)),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[201, 232])).
% 1.52/1.22 tff(235,plain,
% 1.52/1.22 (c2_1(a1116)),
% 1.52/1.22 inference(unit_resolution,[status(thm)],[212, 232])).
% 1.52/1.22 tff(236,assumption,(~c1_1(a1103)), introduced(assumption)).
% 1.52/1.22 tff(237,plain,
% 1.52/1.22 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.52/1.22 inference(bind,[status(th)],[])).
% 1.52/1.22 tff(238,plain,
% 1.52/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.52/1.22 inference(quant_intro,[status(thm)],[237])).
% 1.52/1.22 tff(239,plain,
% 1.52/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.52/1.22 inference(rewrite,[status(thm)],[])).
% 1.52/1.22 tff(240,plain,
% 1.52/1.22 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.52/1.22 inference(bind,[status(th)],[])).
% 1.52/1.22 tff(241,plain,
% 1.52/1.23 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.52/1.23 inference(quant_intro,[status(thm)],[240])).
% 1.52/1.23 tff(242,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 1.52/1.23 tff(243,plain,
% 1.52/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[242, 241])).
% 1.52/1.23 tff(244,plain,
% 1.52/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[243, 239])).
% 1.52/1.23 tff(245,plain,(
% 1.52/1.23 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.52/1.23 inference(skolemize,[status(sab)],[244])).
% 1.52/1.23 tff(246,plain,
% 1.52/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[245, 238])).
% 1.52/1.23 tff(247,assumption,(c3_1(a1116)), introduced(assumption)).
% 1.52/1.23 tff(248,assumption,(c2_1(a1116)), introduced(assumption)).
% 1.52/1.23 tff(249,assumption,(c0_1(a1116)), introduced(assumption)).
% 1.52/1.23 tff(250,plain,
% 1.52/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(251,plain,
% 1.52/1.23 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103))) <=> (c2_1(a1118) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(252,plain,
% 1.52/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 1.52/1.23 inference(monotonicity,[status(thm)],[251])).
% 1.52/1.23 tff(253,plain,
% 1.52/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.52/1.23 inference(transitivity,[status(thm)],[252, 250])).
% 1.52/1.23 tff(254,plain,
% 1.52/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))),
% 1.52/1.23 inference(quant_inst,[status(thm)],[])).
% 1.52/1.23 tff(255,plain,
% 1.52/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[254, 253])).
% 1.52/1.23 tff(256,plain,
% 1.52/1.23 ($false),
% 1.52/1.23 inference(unit_resolution,[status(thm)],[255, 113, 249, 248, 247, 228, 231, 230, 229, 246, 236, 227])).
% 1.52/1.23 tff(257,plain,(c1_1(a1103) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c1_1(a1118)) | (~c3_1(a1103)) | c2_1(a1118) | c2_1(a1103) | (~c0_1(a1118))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.23 tff(258,plain,
% 1.52/1.23 (c1_1(a1103)),
% 1.52/1.23 inference(unit_resolution,[status(thm)],[257, 227, 235, 234, 228, 231, 230, 229, 233])).
% 1.52/1.23 tff(259,plain,
% 1.52/1.23 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.52/1.23 inference(bind,[status(th)],[])).
% 1.52/1.23 tff(260,plain,
% 1.52/1.23 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(quant_intro,[status(thm)],[259])).
% 1.52/1.23 tff(261,plain,
% 1.52/1.23 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(262,plain,
% 1.52/1.23 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.52/1.23 inference(bind,[status(th)],[])).
% 1.52/1.23 tff(263,plain,
% 1.52/1.23 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(quant_intro,[status(thm)],[262])).
% 1.52/1.23 tff(264,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 1.52/1.23 tff(265,plain,
% 1.52/1.23 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[264, 263])).
% 1.52/1.23 tff(266,plain,
% 1.52/1.23 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[265, 261])).
% 1.52/1.23 tff(267,plain,(
% 1.52/1.23 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(skolemize,[status(sab)],[266])).
% 1.52/1.23 tff(268,plain,
% 1.52/1.23 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[267, 260])).
% 1.52/1.23 tff(269,plain,
% 1.52/1.23 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.52/1.23 inference(bind,[status(th)],[])).
% 1.52/1.23 tff(270,plain,
% 1.52/1.23 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(quant_intro,[status(thm)],[269])).
% 1.52/1.23 tff(271,plain,
% 1.52/1.23 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(272,plain,
% 1.52/1.23 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp2))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.52/1.23 inference(bind,[status(th)],[])).
% 1.52/1.23 tff(273,plain,
% 1.52/1.23 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(quant_intro,[status(thm)],[272])).
% 1.52/1.23 tff(274,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 1.52/1.23 tff(275,plain,
% 1.52/1.23 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[274, 273])).
% 1.52/1.23 tff(276,plain,
% 1.52/1.23 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[275, 271])).
% 1.52/1.23 tff(277,plain,(
% 1.52/1.23 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(skolemize,[status(sab)],[276])).
% 1.52/1.23 tff(278,plain,
% 1.52/1.23 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[277, 270])).
% 1.52/1.23 tff(279,plain,
% 1.52/1.23 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1103)) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(280,plain,
% 1.52/1.23 ((hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103))) <=> (hskp2 | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(281,plain,
% 1.52/1.23 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1103)) | (~c3_1(a1103))))),
% 1.52/1.23 inference(monotonicity,[status(thm)],[280])).
% 1.52/1.23 tff(282,plain,
% 1.52/1.23 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.52/1.23 inference(transitivity,[status(thm)],[281, 279])).
% 1.52/1.23 tff(283,plain,
% 1.52/1.23 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))),
% 1.52/1.23 inference(quant_inst,[status(thm)],[])).
% 1.52/1.23 tff(284,plain,
% 1.52/1.23 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1103)) | (~c3_1(a1103))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[283, 282])).
% 1.52/1.23 tff(285,plain,
% 1.52/1.23 (hskp2 | (~c1_1(a1103))),
% 1.52/1.23 inference(unit_resolution,[status(thm)],[284, 113, 233, 235, 234, 231, 229, 278])).
% 1.52/1.23 tff(286,plain,
% 1.52/1.23 (hskp2),
% 1.52/1.23 inference(unit_resolution,[status(thm)],[285, 258])).
% 1.52/1.23 tff(287,plain,
% 1.52/1.23 (((~hskp2) | (~c3_1(a1100))) <=> ((~hskp2) | (~c3_1(a1100)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(288,plain,
% 1.52/1.23 (((~c3_1(a1100)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a1100)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(289,axiom,((~c3_1(a1100)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.52/1.23 tff(290,plain,
% 1.52/1.23 ((~hskp2) | (~c3_1(a1100))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[289, 288])).
% 1.52/1.23 tff(291,plain,
% 1.52/1.23 ((~hskp2) | (~c3_1(a1100))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[290, 287])).
% 1.52/1.23 tff(292,plain,
% 1.52/1.23 (~c3_1(a1100)),
% 1.52/1.23 inference(unit_resolution,[status(thm)],[291, 286])).
% 1.52/1.23 tff(293,plain,
% 1.52/1.23 (((~hskp2) | c2_1(a1100)) <=> ((~hskp2) | c2_1(a1100))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(294,axiom,((~hskp2) | c2_1(a1100)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.52/1.23 tff(295,plain,
% 1.52/1.23 ((~hskp2) | c2_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[294, 293])).
% 1.52/1.23 tff(296,plain,
% 1.52/1.23 ((~hskp2) | c2_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[295, 293])).
% 1.52/1.23 tff(297,plain,
% 1.52/1.23 ((~hskp2) | c2_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[296, 293])).
% 1.52/1.23 tff(298,plain,
% 1.52/1.23 ((~hskp2) | c2_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[297, 293])).
% 1.52/1.23 tff(299,plain,
% 1.52/1.23 ((~hskp2) | c2_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[298, 293])).
% 1.52/1.23 tff(300,plain,
% 1.52/1.23 ((~hskp2) | c2_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[299, 293])).
% 1.52/1.23 tff(301,plain,
% 1.52/1.23 ((~hskp2) | c2_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[300, 293])).
% 1.52/1.23 tff(302,plain,
% 1.52/1.23 ((~hskp2) | c2_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[301, 293])).
% 1.52/1.23 tff(303,plain,
% 1.52/1.23 (c2_1(a1100)),
% 1.52/1.23 inference(unit_resolution,[status(thm)],[302, 286])).
% 1.52/1.23 tff(304,plain,
% 1.52/1.23 (((~hskp2) | c0_1(a1100)) <=> ((~hskp2) | c0_1(a1100))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(305,axiom,((~hskp2) | c0_1(a1100)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.52/1.23 tff(306,plain,
% 1.52/1.23 ((~hskp2) | c0_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[305, 304])).
% 1.52/1.23 tff(307,plain,
% 1.52/1.23 ((~hskp2) | c0_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[306, 304])).
% 1.52/1.23 tff(308,plain,
% 1.52/1.23 ((~hskp2) | c0_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[307, 304])).
% 1.52/1.23 tff(309,plain,
% 1.52/1.23 ((~hskp2) | c0_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[308, 304])).
% 1.52/1.23 tff(310,plain,
% 1.52/1.23 ((~hskp2) | c0_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[309, 304])).
% 1.52/1.23 tff(311,plain,
% 1.52/1.23 ((~hskp2) | c0_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[310, 304])).
% 1.52/1.23 tff(312,plain,
% 1.52/1.23 ((~hskp2) | c0_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[311, 304])).
% 1.52/1.23 tff(313,plain,
% 1.52/1.23 ((~hskp2) | c0_1(a1100)),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[312, 304])).
% 1.52/1.23 tff(314,plain,
% 1.52/1.23 (c0_1(a1100)),
% 1.52/1.23 inference(unit_resolution,[status(thm)],[313, 286])).
% 1.52/1.23 tff(315,plain,
% 1.52/1.23 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c0_1(a1103) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1103)) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c0_1(a1103) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(316,plain,
% 1.52/1.23 ((hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103))) <=> (hskp20 | c0_1(a1103) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(317,plain,
% 1.52/1.23 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c0_1(a1103) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1103)) | (~c3_1(a1103))))),
% 1.52/1.23 inference(monotonicity,[status(thm)],[316])).
% 1.52/1.23 tff(318,plain,
% 1.52/1.23 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c0_1(a1103) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.52/1.23 inference(transitivity,[status(thm)],[317, 315])).
% 1.52/1.23 tff(319,plain,
% 1.52/1.23 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))),
% 1.52/1.23 inference(quant_inst,[status(thm)],[])).
% 1.52/1.23 tff(320,plain,
% 1.52/1.23 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c0_1(a1103) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1103)) | (~c3_1(a1103))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[319, 318])).
% 1.52/1.23 tff(321,plain,
% 1.52/1.23 (hskp20),
% 1.52/1.23 inference(unit_resolution,[status(thm)],[320, 113, 231, 314, 303, 225, 292, 268, 258])).
% 1.52/1.23 tff(322,plain,
% 1.52/1.23 (((~hskp20) | (~c0_1(a1130))) <=> ((~hskp20) | (~c0_1(a1130)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(323,plain,
% 1.52/1.23 (((~c0_1(a1130)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a1130)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(324,axiom,((~c0_1(a1130)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.52/1.23 tff(325,plain,
% 1.52/1.23 ((~hskp20) | (~c0_1(a1130))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[324, 323])).
% 1.52/1.23 tff(326,plain,
% 1.52/1.23 ((~hskp20) | (~c0_1(a1130))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[325, 322])).
% 1.52/1.23 tff(327,plain,
% 1.52/1.23 (~c0_1(a1130)),
% 1.52/1.23 inference(unit_resolution,[status(thm)],[326, 321])).
% 1.52/1.23 tff(328,plain,
% 1.52/1.23 (((~hskp20) | (~c3_1(a1130))) <=> ((~hskp20) | (~c3_1(a1130)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(329,plain,
% 1.52/1.23 (((~c3_1(a1130)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a1130)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(330,axiom,((~c3_1(a1130)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.52/1.23 tff(331,plain,
% 1.52/1.23 ((~hskp20) | (~c3_1(a1130))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[330, 329])).
% 1.52/1.23 tff(332,plain,
% 1.52/1.23 ((~hskp20) | (~c3_1(a1130))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[331, 328])).
% 1.52/1.23 tff(333,plain,
% 1.52/1.23 (~c3_1(a1130)),
% 1.52/1.23 inference(unit_resolution,[status(thm)],[332, 321])).
% 1.52/1.23 tff(334,assumption,(~c0_1(a1130)), introduced(assumption)).
% 1.52/1.23 tff(335,plain,
% 1.52/1.23 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.52/1.23 inference(bind,[status(th)],[])).
% 1.52/1.23 tff(336,plain,
% 1.52/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.52/1.23 inference(quant_intro,[status(thm)],[335])).
% 1.52/1.23 tff(337,plain,
% 1.52/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(338,plain,
% 1.52/1.23 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.52/1.23 inference(bind,[status(th)],[])).
% 1.52/1.23 tff(339,plain,
% 1.52/1.23 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.52/1.23 inference(quant_intro,[status(thm)],[338])).
% 1.52/1.23 tff(340,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 1.52/1.23 tff(341,plain,
% 1.52/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[340, 339])).
% 1.52/1.23 tff(342,plain,
% 1.52/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[341, 337])).
% 1.52/1.23 tff(343,plain,(
% 1.52/1.23 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.52/1.23 inference(skolemize,[status(sab)],[342])).
% 1.52/1.23 tff(344,plain,
% 1.52/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.52/1.23 inference(modus_ponens,[status(thm)],[343, 336])).
% 1.52/1.23 tff(345,assumption,(~c3_1(a1130)), introduced(assumption)).
% 1.52/1.23 tff(346,plain,
% 1.52/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a1130) | c3_1(a1130) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1118)) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a1130) | c3_1(a1130) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1118)) | (~c1_1(a1130)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.52/1.23 tff(347,plain,
% 1.52/1.23 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | c3_1(a1118) | (~c0_1(a1118)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130))) <=> (c0_1(a1130) | c3_1(a1130) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1118)) | (~c1_1(a1130)))),
% 1.52/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(348,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | c3_1(a1118) | (~c0_1(a1118)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a1130) | c3_1(a1130) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1118)) | (~c1_1(a1130))))),
% 1.55/1.24 inference(monotonicity,[status(thm)],[347])).
% 1.55/1.24 tff(349,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | c3_1(a1118) | (~c0_1(a1118)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a1130) | c3_1(a1130) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1118)) | (~c1_1(a1130)))),
% 1.55/1.24 inference(transitivity,[status(thm)],[348, 346])).
% 1.55/1.24 tff(350,plain,
% 1.55/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | c3_1(a1118) | (~c0_1(a1118)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))),
% 1.55/1.24 inference(quant_inst,[status(thm)],[])).
% 1.55/1.24 tff(351,plain,
% 1.55/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a1130) | c3_1(a1130) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1118)) | (~c1_1(a1130))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[350, 349])).
% 1.55/1.24 tff(352,plain,
% 1.55/1.24 (c0_1(a1130) | (~c0_1(a1118)) | (~c1_1(a1130))),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[351, 113, 233, 235, 234, 345, 230, 226, 344])).
% 1.55/1.24 tff(353,plain,
% 1.55/1.24 (~c1_1(a1130)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[352, 227, 334])).
% 1.55/1.24 tff(354,plain,
% 1.55/1.24 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.55/1.24 inference(bind,[status(th)],[])).
% 1.55/1.24 tff(355,plain,
% 1.55/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.55/1.24 inference(quant_intro,[status(thm)],[354])).
% 1.55/1.24 tff(356,plain,
% 1.55/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(357,plain,
% 1.55/1.24 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.55/1.24 inference(bind,[status(th)],[])).
% 1.55/1.24 tff(358,plain,
% 1.55/1.24 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.55/1.24 inference(quant_intro,[status(thm)],[357])).
% 1.55/1.24 tff(359,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.55/1.24 tff(360,plain,
% 1.55/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.55/1.24 tff(361,plain,
% 1.55/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[360, 356])).
% 1.55/1.24 tff(362,plain,(
% 1.55/1.24 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.55/1.24 inference(skolemize,[status(sab)],[361])).
% 1.55/1.24 tff(363,plain,
% 1.55/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[362, 355])).
% 1.55/1.24 tff(364,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1130))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(365,plain,
% 1.55/1.24 (((~ndr1_0) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130)) <=> (c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1130))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(366,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1130)))),
% 1.55/1.24 inference(monotonicity,[status(thm)],[365])).
% 1.55/1.24 tff(367,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1130))),
% 1.55/1.24 inference(transitivity,[status(thm)],[366, 364])).
% 1.55/1.24 tff(368,plain,
% 1.55/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130))),
% 1.55/1.24 inference(quant_inst,[status(thm)],[])).
% 1.55/1.24 tff(369,plain,
% 1.55/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1130)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.55/1.24 tff(370,plain,
% 1.55/1.24 (c0_1(a1130) | (~c1_1(a1103)) | (~c0_1(a1118)) | c1_1(a1130)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[369, 113, 228, 231, 345, 226, 225, 363])).
% 1.55/1.24 tff(371,plain,
% 1.55/1.24 (~c1_1(a1103)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[370, 227, 334, 353])).
% 1.55/1.24 tff(372,plain,
% 1.55/1.24 ($false),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[255, 113, 233, 235, 234, 228, 231, 230, 229, 246, 371, 227])).
% 1.55/1.24 tff(373,plain,((~c0_1(a1118)) | (~c1_1(a1118)) | (~c3_1(a1103)) | c2_1(a1118) | c2_1(a1103) | c0_1(a1130) | c3_1(a1130) | c3_1(a1118) | c0_1(a1103)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.24 tff(374,plain,
% 1.55/1.24 ($false),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[373, 333, 327, 231, 230, 229, 228, 227, 226, 225])).
% 1.55/1.24 tff(375,plain,((~c0_1(a1118)) | (~c3_1(a1103)) | c2_1(a1118) | c2_1(a1103) | (~c1_1(a1118)) | c3_1(a1118) | c0_1(a1103)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.24 tff(376,plain,
% 1.55/1.24 (~c0_1(a1118)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[375, 154, 173, 127, 184, 167, 133])).
% 1.55/1.24 tff(377,assumption,(~hskp1), introduced(assumption)).
% 1.55/1.24 tff(378,assumption,(~c0_1(a1118)), introduced(assumption)).
% 1.55/1.24 tff(379,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a1118) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a1118) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(380,plain,
% 1.55/1.24 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118))) <=> (c3_1(a1118) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(381,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a1118) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1118)) | c0_1(a1118)))),
% 1.55/1.24 inference(monotonicity,[status(thm)],[380])).
% 1.55/1.24 tff(382,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a1118) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.55/1.24 inference(transitivity,[status(thm)],[381, 379])).
% 1.55/1.24 tff(383,plain,
% 1.55/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))),
% 1.55/1.24 inference(quant_inst,[status(thm)],[])).
% 1.55/1.24 tff(384,plain,
% 1.55/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a1118) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1118)) | c0_1(a1118)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[383, 382])).
% 1.55/1.24 tff(385,plain,
% 1.55/1.24 ((~c0_1(a1098)) | c0_1(a1118)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[384, 113, 249, 248, 247, 228, 226, 35, 47, 344])).
% 1.55/1.24 tff(386,plain,
% 1.55/1.24 (~c0_1(a1098)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[385, 378])).
% 1.55/1.24 tff(387,plain,
% 1.55/1.24 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.55/1.24 inference(bind,[status(th)],[])).
% 1.55/1.24 tff(388,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.24 inference(quant_intro,[status(thm)],[387])).
% 1.55/1.24 tff(389,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(390,plain,
% 1.55/1.24 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.55/1.24 inference(bind,[status(th)],[])).
% 1.55/1.24 tff(391,plain,
% 1.55/1.24 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.24 inference(quant_intro,[status(thm)],[390])).
% 1.55/1.24 tff(392,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.55/1.24 tff(393,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[392, 391])).
% 1.55/1.24 tff(394,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[393, 389])).
% 1.55/1.24 tff(395,plain,(
% 1.55/1.24 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.24 inference(skolemize,[status(sab)],[394])).
% 1.55/1.24 tff(396,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[395, 388])).
% 1.55/1.24 tff(397,plain,
% 1.55/1.24 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(398,plain,
% 1.55/1.24 ((hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098)) <=> (hskp1 | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(399,plain,
% 1.55/1.24 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c1_1(a1118)) | c0_1(a1118)))),
% 1.55/1.24 inference(monotonicity,[status(thm)],[398])).
% 1.55/1.24 tff(400,plain,
% 1.55/1.24 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.55/1.24 inference(transitivity,[status(thm)],[399, 397])).
% 1.55/1.24 tff(401,plain,
% 1.55/1.24 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))),
% 1.55/1.24 inference(quant_inst,[status(thm)],[])).
% 1.55/1.24 tff(402,plain,
% 1.55/1.24 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c1_1(a1118)) | c0_1(a1118)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[401, 400])).
% 1.55/1.24 tff(403,plain,
% 1.55/1.24 (hskp1 | c0_1(a1098) | c0_1(a1118)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[402, 113, 228, 226, 34, 47, 396])).
% 1.55/1.24 tff(404,plain,
% 1.55/1.24 ($false),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[403, 386, 378, 377])).
% 1.55/1.24 tff(405,plain,(c0_1(a1118) | hskp1 | (~c1_1(a1118)) | c3_1(a1118) | c1_1(a1098) | c3_1(a1098) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.24 tff(406,plain,
% 1.55/1.24 (hskp1),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[405, 376, 184, 167, 34, 47, 224, 213, 202, 35])).
% 1.55/1.24 tff(407,plain,
% 1.55/1.24 (((~hskp1) | (~c0_1(a1099))) <=> ((~hskp1) | (~c0_1(a1099)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(408,plain,
% 1.55/1.24 (((~c0_1(a1099)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a1099)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(409,axiom,((~c0_1(a1099)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.55/1.24 tff(410,plain,
% 1.55/1.24 ((~hskp1) | (~c0_1(a1099))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[409, 408])).
% 1.55/1.24 tff(411,plain,
% 1.55/1.24 ((~hskp1) | (~c0_1(a1099))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[410, 407])).
% 1.55/1.24 tff(412,plain,
% 1.55/1.24 (~c0_1(a1099)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[411, 406])).
% 1.55/1.24 tff(413,plain,
% 1.55/1.24 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.55/1.24 inference(bind,[status(th)],[])).
% 1.55/1.24 tff(414,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.24 inference(quant_intro,[status(thm)],[413])).
% 1.55/1.24 tff(415,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(416,plain,
% 1.55/1.24 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.55/1.24 inference(bind,[status(th)],[])).
% 1.55/1.24 tff(417,plain,
% 1.55/1.24 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.24 inference(quant_intro,[status(thm)],[416])).
% 1.55/1.24 tff(418,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 1.55/1.24 tff(419,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.55/1.24 tff(420,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[419, 415])).
% 1.55/1.24 tff(421,plain,(
% 1.55/1.24 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.24 inference(skolemize,[status(sab)],[420])).
% 1.55/1.24 tff(422,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[421, 414])).
% 1.55/1.24 tff(423,plain,
% 1.55/1.24 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.55/1.24 inference(bind,[status(th)],[])).
% 1.55/1.24 tff(424,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.24 inference(quant_intro,[status(thm)],[423])).
% 1.55/1.24 tff(425,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(426,plain,
% 1.55/1.24 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.55/1.25 inference(bind,[status(th)],[])).
% 1.55/1.25 tff(427,plain,
% 1.55/1.25 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.25 inference(quant_intro,[status(thm)],[426])).
% 1.55/1.25 tff(428,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 1.55/1.25 tff(429,plain,
% 1.55/1.25 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[428, 427])).
% 1.55/1.25 tff(430,plain,
% 1.55/1.25 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[429, 425])).
% 1.55/1.25 tff(431,plain,(
% 1.55/1.25 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.25 inference(skolemize,[status(sab)],[430])).
% 1.55/1.25 tff(432,plain,
% 1.55/1.25 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[431, 424])).
% 1.55/1.25 tff(433,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp15 | c3_1(a1118) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp15 | c3_1(a1118) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(434,plain,
% 1.55/1.25 ((hskp15 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098)) <=> (hskp15 | c3_1(a1118) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(435,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp15 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp15 | c3_1(a1118) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118)))),
% 1.55/1.25 inference(monotonicity,[status(thm)],[434])).
% 1.55/1.25 tff(436,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp15 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp15 | c3_1(a1118) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.55/1.25 inference(transitivity,[status(thm)],[435, 433])).
% 1.55/1.25 tff(437,plain,
% 1.55/1.25 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp15 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098))),
% 1.55/1.25 inference(quant_inst,[status(thm)],[])).
% 1.55/1.25 tff(438,plain,
% 1.55/1.25 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp15 | c3_1(a1118) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[437, 436])).
% 1.55/1.25 tff(439,plain,
% 1.55/1.25 (hskp15 | c0_1(a1118)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[438, 113, 184, 167, 34, 35, 47, 432])).
% 1.55/1.25 tff(440,plain,
% 1.55/1.25 (hskp15),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[439, 376])).
% 1.55/1.25 tff(441,plain,
% 1.55/1.25 (((~hskp15) | (~c2_1(a1119))) <=> ((~hskp15) | (~c2_1(a1119)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(442,plain,
% 1.55/1.25 (((~c2_1(a1119)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a1119)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(443,axiom,((~c2_1(a1119)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.55/1.25 tff(444,plain,
% 1.55/1.25 ((~hskp15) | (~c2_1(a1119))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[443, 442])).
% 1.55/1.25 tff(445,plain,
% 1.55/1.25 ((~hskp15) | (~c2_1(a1119))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[444, 441])).
% 1.55/1.25 tff(446,plain,
% 1.55/1.25 (~c2_1(a1119)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[445, 440])).
% 1.55/1.25 tff(447,plain,
% 1.55/1.25 (((~hskp15) | (~c0_1(a1119))) <=> ((~hskp15) | (~c0_1(a1119)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(448,plain,
% 1.55/1.25 (((~c0_1(a1119)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a1119)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(449,axiom,((~c0_1(a1119)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.55/1.25 tff(450,plain,
% 1.55/1.25 ((~hskp15) | (~c0_1(a1119))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[449, 448])).
% 1.55/1.25 tff(451,plain,
% 1.55/1.25 ((~hskp15) | (~c0_1(a1119))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[450, 447])).
% 1.55/1.25 tff(452,plain,
% 1.55/1.25 (~c0_1(a1119)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[451, 440])).
% 1.55/1.25 tff(453,plain,
% 1.55/1.25 (((~hskp1) | c2_1(a1099)) <=> ((~hskp1) | c2_1(a1099))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(454,axiom,((~hskp1) | c2_1(a1099)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.55/1.25 tff(455,plain,
% 1.55/1.25 ((~hskp1) | c2_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[454, 453])).
% 1.55/1.25 tff(456,plain,
% 1.55/1.25 ((~hskp1) | c2_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[455, 453])).
% 1.55/1.25 tff(457,plain,
% 1.55/1.25 ((~hskp1) | c2_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[456, 453])).
% 1.55/1.25 tff(458,plain,
% 1.55/1.25 ((~hskp1) | c2_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[457, 453])).
% 1.55/1.25 tff(459,plain,
% 1.55/1.25 ((~hskp1) | c2_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[458, 453])).
% 1.55/1.25 tff(460,plain,
% 1.55/1.25 ((~hskp1) | c2_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[459, 453])).
% 1.55/1.25 tff(461,plain,
% 1.55/1.25 ((~hskp1) | c2_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[460, 453])).
% 1.55/1.25 tff(462,plain,
% 1.55/1.25 ((~hskp1) | c2_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[461, 453])).
% 1.55/1.25 tff(463,plain,
% 1.55/1.25 (c2_1(a1099)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[462, 406])).
% 1.55/1.25 tff(464,plain,
% 1.55/1.25 (((~hskp1) | c1_1(a1099)) <=> ((~hskp1) | c1_1(a1099))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(465,axiom,((~hskp1) | c1_1(a1099)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 1.55/1.25 tff(466,plain,
% 1.55/1.25 ((~hskp1) | c1_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[465, 464])).
% 1.55/1.25 tff(467,plain,
% 1.55/1.25 ((~hskp1) | c1_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[466, 464])).
% 1.55/1.25 tff(468,plain,
% 1.55/1.25 ((~hskp1) | c1_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[467, 464])).
% 1.55/1.25 tff(469,plain,
% 1.55/1.25 ((~hskp1) | c1_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[468, 464])).
% 1.55/1.25 tff(470,plain,
% 1.55/1.25 ((~hskp1) | c1_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[469, 464])).
% 1.55/1.25 tff(471,plain,
% 1.55/1.25 ((~hskp1) | c1_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[470, 464])).
% 1.55/1.25 tff(472,plain,
% 1.55/1.25 ((~hskp1) | c1_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[471, 464])).
% 1.55/1.25 tff(473,plain,
% 1.55/1.25 ((~hskp1) | c1_1(a1099)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[472, 464])).
% 1.55/1.25 tff(474,plain,
% 1.55/1.25 (c1_1(a1099)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[473, 406])).
% 1.55/1.25 tff(475,plain,
% 1.55/1.25 (((~hskp15) | c1_1(a1119)) <=> ((~hskp15) | c1_1(a1119))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(476,axiom,((~hskp15) | c1_1(a1119)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.55/1.25 tff(477,plain,
% 1.55/1.25 ((~hskp15) | c1_1(a1119)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[476, 475])).
% 1.55/1.25 tff(478,plain,
% 1.55/1.25 ((~hskp15) | c1_1(a1119)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[477, 475])).
% 1.55/1.25 tff(479,plain,
% 1.55/1.25 ((~hskp15) | c1_1(a1119)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[478, 475])).
% 1.55/1.25 tff(480,plain,
% 1.55/1.25 ((~hskp15) | c1_1(a1119)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[479, 475])).
% 1.55/1.25 tff(481,plain,
% 1.55/1.25 ((~hskp15) | c1_1(a1119)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[480, 475])).
% 1.55/1.25 tff(482,plain,
% 1.55/1.25 ((~hskp15) | c1_1(a1119)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[481, 475])).
% 1.55/1.25 tff(483,plain,
% 1.55/1.25 ((~hskp15) | c1_1(a1119)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[482, 475])).
% 1.55/1.25 tff(484,plain,
% 1.55/1.25 ((~hskp15) | c1_1(a1119)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[483, 475])).
% 1.55/1.25 tff(485,plain,
% 1.55/1.25 (c1_1(a1119)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[484, 440])).
% 1.55/1.25 tff(486,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1119) | c2_1(a1119) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1119)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1119) | c2_1(a1119) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1119)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(487,plain,
% 1.55/1.25 ((hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1119) | c0_1(a1119) | (~c1_1(a1119))) <=> (hskp9 | c0_1(a1119) | c2_1(a1119) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1119)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(488,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1119) | c0_1(a1119) | (~c1_1(a1119)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1119) | c2_1(a1119) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1119))))),
% 1.55/1.25 inference(monotonicity,[status(thm)],[487])).
% 1.55/1.25 tff(489,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1119) | c0_1(a1119) | (~c1_1(a1119)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1119) | c2_1(a1119) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1119)))),
% 1.55/1.25 inference(transitivity,[status(thm)],[488, 486])).
% 1.55/1.25 tff(490,plain,
% 1.55/1.25 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1119) | c0_1(a1119) | (~c1_1(a1119)))),
% 1.55/1.25 inference(quant_inst,[status(thm)],[])).
% 1.55/1.25 tff(491,plain,
% 1.55/1.25 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1119) | c2_1(a1119) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1119))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[490, 489])).
% 1.55/1.25 tff(492,plain,
% 1.55/1.25 (hskp9),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[491, 113, 485, 474, 463, 452, 446, 412, 422])).
% 1.55/1.25 tff(493,plain,
% 1.55/1.25 (((~hskp9) | (~c3_1(a1108))) <=> ((~hskp9) | (~c3_1(a1108)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(494,plain,
% 1.55/1.25 (((~c3_1(a1108)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a1108)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(495,axiom,((~c3_1(a1108)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.55/1.25 tff(496,plain,
% 1.55/1.25 ((~hskp9) | (~c3_1(a1108))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[495, 494])).
% 1.55/1.25 tff(497,plain,
% 1.55/1.25 ((~hskp9) | (~c3_1(a1108))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[496, 493])).
% 1.55/1.25 tff(498,plain,
% 1.55/1.25 (~c3_1(a1108)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[497, 492])).
% 1.55/1.25 tff(499,plain,
% 1.55/1.25 (((~hskp9) | (~c1_1(a1108))) <=> ((~hskp9) | (~c1_1(a1108)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(500,plain,
% 1.55/1.25 (((~c1_1(a1108)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a1108)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(501,axiom,((~c1_1(a1108)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.55/1.25 tff(502,plain,
% 1.55/1.25 ((~hskp9) | (~c1_1(a1108))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[501, 500])).
% 1.55/1.25 tff(503,plain,
% 1.55/1.25 ((~hskp9) | (~c1_1(a1108))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[502, 499])).
% 1.55/1.25 tff(504,plain,
% 1.55/1.25 (~c1_1(a1108)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[503, 492])).
% 1.55/1.25 tff(505,plain,
% 1.55/1.25 (((~hskp9) | c0_1(a1108)) <=> ((~hskp9) | c0_1(a1108))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(506,axiom,((~hskp9) | c0_1(a1108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.55/1.25 tff(507,plain,
% 1.55/1.25 ((~hskp9) | c0_1(a1108)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[506, 505])).
% 1.55/1.25 tff(508,plain,
% 1.55/1.25 ((~hskp9) | c0_1(a1108)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[507, 505])).
% 1.55/1.25 tff(509,plain,
% 1.55/1.25 ((~hskp9) | c0_1(a1108)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[508, 505])).
% 1.55/1.25 tff(510,plain,
% 1.55/1.25 ((~hskp9) | c0_1(a1108)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[509, 505])).
% 1.55/1.25 tff(511,plain,
% 1.55/1.25 ((~hskp9) | c0_1(a1108)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[510, 505])).
% 1.55/1.25 tff(512,plain,
% 1.55/1.25 ((~hskp9) | c0_1(a1108)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[511, 505])).
% 1.55/1.25 tff(513,plain,
% 1.55/1.25 ((~hskp9) | c0_1(a1108)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[512, 505])).
% 1.55/1.25 tff(514,plain,
% 1.55/1.25 ((~hskp9) | c0_1(a1108)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[513, 505])).
% 1.55/1.25 tff(515,plain,
% 1.55/1.25 (c0_1(a1108)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[514, 492])).
% 1.55/1.25 tff(516,plain,
% 1.55/1.25 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))),
% 1.55/1.25 inference(bind,[status(th)],[])).
% 1.55/1.25 tff(517,plain,
% 1.55/1.25 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.25 inference(quant_intro,[status(thm)],[516])).
% 1.55/1.25 tff(518,plain,
% 1.55/1.25 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(519,plain,
% 1.55/1.25 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp7) <=> ((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))))),
% 1.55/1.25 inference(bind,[status(th)],[])).
% 1.55/1.25 tff(520,plain,
% 1.55/1.25 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.25 inference(quant_intro,[status(thm)],[519])).
% 1.55/1.25 tff(521,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 1.55/1.25 tff(522,plain,
% 1.55/1.25 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[521, 520])).
% 1.55/1.25 tff(523,plain,
% 1.55/1.25 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[522, 518])).
% 1.55/1.25 tff(524,plain,(
% 1.55/1.25 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.25 inference(skolemize,[status(sab)],[523])).
% 1.55/1.25 tff(525,plain,
% 1.55/1.25 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[524, 517])).
% 1.55/1.25 tff(526,plain,
% 1.55/1.25 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(527,plain,
% 1.55/1.25 ((hskp7 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118)) <=> (hskp7 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(528,plain,
% 1.55/1.25 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118)))),
% 1.55/1.25 inference(monotonicity,[status(thm)],[527])).
% 1.55/1.25 tff(529,plain,
% 1.55/1.25 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))),
% 1.55/1.25 inference(transitivity,[status(thm)],[528, 526])).
% 1.55/1.25 tff(530,plain,
% 1.55/1.25 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118))),
% 1.55/1.25 inference(quant_inst,[status(thm)],[])).
% 1.55/1.25 tff(531,plain,
% 1.55/1.25 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[530, 529])).
% 1.55/1.25 tff(532,plain,
% 1.55/1.25 (hskp6 | c0_1(a1118)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[531, 113, 68, 173, 167, 525])).
% 1.55/1.25 tff(533,plain,
% 1.55/1.25 (hskp6),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[532, 376])).
% 1.55/1.25 tff(534,plain,
% 1.55/1.25 (((~hskp6) | (~c2_1(a1104))) <=> ((~hskp6) | (~c2_1(a1104)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(535,plain,
% 1.55/1.25 (((~c2_1(a1104)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a1104)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(536,axiom,((~c2_1(a1104)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.55/1.25 tff(537,plain,
% 1.55/1.25 ((~hskp6) | (~c2_1(a1104))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[536, 535])).
% 1.55/1.25 tff(538,plain,
% 1.55/1.25 ((~hskp6) | (~c2_1(a1104))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[537, 534])).
% 1.55/1.25 tff(539,plain,
% 1.55/1.25 (~c2_1(a1104)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[538, 533])).
% 1.55/1.25 tff(540,plain,
% 1.55/1.25 (((~hskp6) | c0_1(a1104)) <=> ((~hskp6) | c0_1(a1104))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(541,axiom,((~hskp6) | c0_1(a1104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.55/1.25 tff(542,plain,
% 1.55/1.25 ((~hskp6) | c0_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[541, 540])).
% 1.55/1.25 tff(543,plain,
% 1.55/1.25 ((~hskp6) | c0_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[542, 540])).
% 1.55/1.25 tff(544,plain,
% 1.55/1.25 ((~hskp6) | c0_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[543, 540])).
% 1.55/1.25 tff(545,plain,
% 1.55/1.25 ((~hskp6) | c0_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[544, 540])).
% 1.55/1.25 tff(546,plain,
% 1.55/1.25 ((~hskp6) | c0_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[545, 540])).
% 1.55/1.25 tff(547,plain,
% 1.55/1.25 ((~hskp6) | c0_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[546, 540])).
% 1.55/1.25 tff(548,plain,
% 1.55/1.25 ((~hskp6) | c0_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[547, 540])).
% 1.55/1.25 tff(549,plain,
% 1.55/1.25 ((~hskp6) | c0_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[548, 540])).
% 1.55/1.25 tff(550,plain,
% 1.55/1.25 (c0_1(a1104)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[549, 533])).
% 1.55/1.25 tff(551,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a1118) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a1118) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(552,plain,
% 1.55/1.25 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | c3_1(a1104) | (~c0_1(a1104)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118))) <=> (c3_1(a1118) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(553,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | c3_1(a1104) | (~c0_1(a1104)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a1118) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1118)) | c0_1(a1118)))),
% 1.55/1.25 inference(monotonicity,[status(thm)],[552])).
% 1.55/1.25 tff(554,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | c3_1(a1104) | (~c0_1(a1104)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a1118) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.55/1.25 inference(transitivity,[status(thm)],[553, 551])).
% 1.55/1.25 tff(555,plain,
% 1.55/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | c3_1(a1104) | (~c0_1(a1104)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))),
% 1.55/1.25 inference(quant_inst,[status(thm)],[])).
% 1.55/1.25 tff(556,plain,
% 1.55/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a1118) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1118)) | c0_1(a1118)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[555, 554])).
% 1.55/1.25 tff(557,plain,
% 1.55/1.25 (c3_1(a1104)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[556, 113, 224, 213, 202, 184, 550, 167, 539, 344, 376])).
% 1.55/1.25 tff(558,plain,
% 1.55/1.25 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.55/1.25 inference(bind,[status(th)],[])).
% 1.55/1.25 tff(559,plain,
% 1.55/1.25 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.25 inference(quant_intro,[status(thm)],[558])).
% 1.55/1.25 tff(560,plain,
% 1.55/1.25 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(561,plain,
% 1.55/1.25 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.55/1.25 inference(bind,[status(th)],[])).
% 1.55/1.25 tff(562,plain,
% 1.55/1.25 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.25 inference(quant_intro,[status(thm)],[561])).
% 1.55/1.25 tff(563,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 1.55/1.25 tff(564,plain,
% 1.55/1.25 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[563, 562])).
% 1.55/1.25 tff(565,plain,
% 1.55/1.25 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[564, 560])).
% 1.55/1.25 tff(566,plain,(
% 1.55/1.25 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.25 inference(skolemize,[status(sab)],[565])).
% 1.55/1.25 tff(567,plain,
% 1.55/1.25 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[566, 559])).
% 1.55/1.25 tff(568,plain,
% 1.55/1.25 (((~hskp6) | c1_1(a1104)) <=> ((~hskp6) | c1_1(a1104))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(569,axiom,((~hskp6) | c1_1(a1104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.55/1.25 tff(570,plain,
% 1.55/1.25 ((~hskp6) | c1_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[569, 568])).
% 1.55/1.25 tff(571,plain,
% 1.55/1.25 ((~hskp6) | c1_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[570, 568])).
% 1.55/1.25 tff(572,plain,
% 1.55/1.25 ((~hskp6) | c1_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[571, 568])).
% 1.55/1.25 tff(573,plain,
% 1.55/1.25 ((~hskp6) | c1_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[572, 568])).
% 1.55/1.25 tff(574,plain,
% 1.55/1.25 ((~hskp6) | c1_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[573, 568])).
% 1.55/1.25 tff(575,plain,
% 1.55/1.25 ((~hskp6) | c1_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[574, 568])).
% 1.55/1.25 tff(576,plain,
% 1.55/1.25 ((~hskp6) | c1_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[575, 568])).
% 1.55/1.25 tff(577,plain,
% 1.55/1.25 ((~hskp6) | c1_1(a1104)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[576, 568])).
% 1.55/1.25 tff(578,plain,
% 1.55/1.25 (c1_1(a1104)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[577, 533])).
% 1.55/1.25 tff(579,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c2_1(a1104) | (~ndr1_0) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1104)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1104) | (~ndr1_0) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1104)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(580,plain,
% 1.55/1.25 ((hskp28 | (~ndr1_0) | (~c1_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1104)) | c2_1(a1104) | (~c3_1(a1104)) | (~c1_1(a1104))) <=> (hskp28 | c2_1(a1104) | (~ndr1_0) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1104)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(581,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1104)) | c2_1(a1104) | (~c3_1(a1104)) | (~c1_1(a1104)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c2_1(a1104) | (~ndr1_0) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1104))))),
% 1.55/1.25 inference(monotonicity,[status(thm)],[580])).
% 1.55/1.25 tff(582,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1104)) | c2_1(a1104) | (~c3_1(a1104)) | (~c1_1(a1104)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1104) | (~ndr1_0) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1104)))),
% 1.55/1.25 inference(transitivity,[status(thm)],[581, 579])).
% 1.55/1.25 tff(583,plain,
% 1.55/1.25 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1104)) | c2_1(a1104) | (~c3_1(a1104)) | (~c1_1(a1104)))),
% 1.55/1.26 inference(quant_inst,[status(thm)],[])).
% 1.55/1.26 tff(584,plain,
% 1.55/1.26 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1104) | (~ndr1_0) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1104))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[583, 582])).
% 1.55/1.26 tff(585,plain,
% 1.55/1.26 (hskp28 | (~c3_1(a1104))),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[584, 113, 550, 578, 539, 567])).
% 1.55/1.26 tff(586,plain,
% 1.55/1.26 (hskp28),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[585, 557])).
% 1.55/1.26 tff(587,plain,
% 1.55/1.26 (((~hskp28) | c2_1(a1111)) <=> ((~hskp28) | c2_1(a1111))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(588,axiom,((~hskp28) | c2_1(a1111)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.55/1.26 tff(589,plain,
% 1.55/1.26 ((~hskp28) | c2_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[588, 587])).
% 1.55/1.26 tff(590,plain,
% 1.55/1.26 ((~hskp28) | c2_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[589, 587])).
% 1.55/1.26 tff(591,plain,
% 1.55/1.26 ((~hskp28) | c2_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[590, 587])).
% 1.55/1.26 tff(592,plain,
% 1.55/1.26 ((~hskp28) | c2_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[591, 587])).
% 1.55/1.26 tff(593,plain,
% 1.55/1.26 ((~hskp28) | c2_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[592, 587])).
% 1.55/1.26 tff(594,plain,
% 1.55/1.26 ((~hskp28) | c2_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[593, 587])).
% 1.55/1.26 tff(595,plain,
% 1.55/1.26 ((~hskp28) | c2_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[594, 587])).
% 1.55/1.26 tff(596,plain,
% 1.55/1.26 ((~hskp28) | c2_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[595, 587])).
% 1.55/1.26 tff(597,plain,
% 1.55/1.26 (c2_1(a1111)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[596, 586])).
% 1.55/1.26 tff(598,plain,
% 1.55/1.26 (((~hskp28) | c1_1(a1111)) <=> ((~hskp28) | c1_1(a1111))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(599,axiom,((~hskp28) | c1_1(a1111)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.55/1.26 tff(600,plain,
% 1.55/1.26 ((~hskp28) | c1_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[599, 598])).
% 1.55/1.26 tff(601,plain,
% 1.55/1.26 ((~hskp28) | c1_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[600, 598])).
% 1.55/1.26 tff(602,plain,
% 1.55/1.26 ((~hskp28) | c1_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[601, 598])).
% 1.55/1.26 tff(603,plain,
% 1.55/1.26 ((~hskp28) | c1_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[602, 598])).
% 1.55/1.26 tff(604,plain,
% 1.55/1.26 ((~hskp28) | c1_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[603, 598])).
% 1.55/1.26 tff(605,plain,
% 1.55/1.26 ((~hskp28) | c1_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[604, 598])).
% 1.55/1.26 tff(606,plain,
% 1.55/1.26 ((~hskp28) | c1_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[605, 598])).
% 1.55/1.26 tff(607,plain,
% 1.55/1.26 ((~hskp28) | c1_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[606, 598])).
% 1.55/1.26 tff(608,plain,
% 1.55/1.26 (c1_1(a1111)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[607, 586])).
% 1.55/1.26 tff(609,plain,
% 1.55/1.26 (((~hskp28) | c0_1(a1111)) <=> ((~hskp28) | c0_1(a1111))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(610,axiom,((~hskp28) | c0_1(a1111)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 1.55/1.26 tff(611,plain,
% 1.55/1.26 ((~hskp28) | c0_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[610, 609])).
% 1.55/1.26 tff(612,plain,
% 1.55/1.26 ((~hskp28) | c0_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[611, 609])).
% 1.55/1.26 tff(613,plain,
% 1.55/1.26 ((~hskp28) | c0_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[612, 609])).
% 1.55/1.26 tff(614,plain,
% 1.55/1.26 ((~hskp28) | c0_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[613, 609])).
% 1.55/1.26 tff(615,plain,
% 1.55/1.26 ((~hskp28) | c0_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[614, 609])).
% 1.55/1.26 tff(616,plain,
% 1.55/1.26 ((~hskp28) | c0_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[615, 609])).
% 1.55/1.26 tff(617,plain,
% 1.55/1.26 ((~hskp28) | c0_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[616, 609])).
% 1.55/1.26 tff(618,plain,
% 1.55/1.26 ((~hskp28) | c0_1(a1111)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[617, 609])).
% 1.55/1.26 tff(619,plain,
% 1.55/1.26 (c0_1(a1111)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[618, 586])).
% 1.55/1.26 tff(620,plain,
% 1.55/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1108) | c3_1(a1108) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(621,plain,
% 1.55/1.26 (((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099))) <=> (c1_1(a1108) | c3_1(a1108) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(622,plain,
% 1.55/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1108) | c3_1(a1108) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111))))),
% 1.55/1.26 inference(monotonicity,[status(thm)],[621])).
% 1.55/1.26 tff(623,plain,
% 1.55/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.55/1.26 inference(transitivity,[status(thm)],[622, 620])).
% 1.55/1.26 tff(624,plain,
% 1.55/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))),
% 1.55/1.26 inference(quant_inst,[status(thm)],[])).
% 1.55/1.26 tff(625,plain,
% 1.55/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[624, 623])).
% 1.55/1.26 tff(626,plain,
% 1.55/1.26 ($false),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[625, 113, 619, 608, 597, 515, 474, 463, 504, 498, 412, 57])).
% 1.55/1.26 tff(627,plain,(hskp7 | c1_1(a1098) | c3_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.26 tff(628,plain,
% 1.55/1.26 (hskp7),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[627, 47, 34, 35])).
% 1.55/1.26 tff(629,plain,
% 1.55/1.26 (((~hskp7) | (~c1_1(a1105))) <=> ((~hskp7) | (~c1_1(a1105)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(630,plain,
% 1.55/1.26 (((~c1_1(a1105)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a1105)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(631,axiom,((~c1_1(a1105)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.55/1.26 tff(632,plain,
% 1.55/1.26 ((~hskp7) | (~c1_1(a1105))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[631, 630])).
% 1.55/1.26 tff(633,plain,
% 1.55/1.26 ((~hskp7) | (~c1_1(a1105))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[632, 629])).
% 1.55/1.26 tff(634,plain,
% 1.55/1.26 (~c1_1(a1105)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[633, 628])).
% 1.55/1.26 tff(635,assumption,(ndr1_0), introduced(assumption)).
% 1.55/1.26 tff(636,assumption,(hskp7), introduced(assumption)).
% 1.55/1.26 tff(637,plain,
% 1.55/1.26 (((~hskp7) | c0_1(a1105)) <=> ((~hskp7) | c0_1(a1105))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(638,axiom,((~hskp7) | c0_1(a1105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.55/1.26 tff(639,plain,
% 1.55/1.26 ((~hskp7) | c0_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[638, 637])).
% 1.55/1.26 tff(640,plain,
% 1.55/1.26 ((~hskp7) | c0_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[639, 637])).
% 1.55/1.26 tff(641,plain,
% 1.55/1.26 ((~hskp7) | c0_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[640, 637])).
% 1.55/1.26 tff(642,plain,
% 1.55/1.26 ((~hskp7) | c0_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[641, 637])).
% 1.55/1.26 tff(643,plain,
% 1.55/1.26 ((~hskp7) | c0_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[642, 637])).
% 1.55/1.26 tff(644,plain,
% 1.55/1.26 ((~hskp7) | c0_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[643, 637])).
% 1.55/1.26 tff(645,plain,
% 1.55/1.26 ((~hskp7) | c0_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[644, 637])).
% 1.55/1.26 tff(646,plain,
% 1.55/1.26 ((~hskp7) | c0_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[645, 637])).
% 1.55/1.26 tff(647,plain,
% 1.55/1.26 (c0_1(a1105)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[646, 636])).
% 1.55/1.26 tff(648,plain,
% 1.55/1.26 (((~hskp7) | c3_1(a1105)) <=> ((~hskp7) | c3_1(a1105))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(649,axiom,((~hskp7) | c3_1(a1105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.55/1.26 tff(650,plain,
% 1.55/1.26 ((~hskp7) | c3_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[649, 648])).
% 1.55/1.26 tff(651,plain,
% 1.55/1.26 ((~hskp7) | c3_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[650, 648])).
% 1.55/1.26 tff(652,plain,
% 1.55/1.26 ((~hskp7) | c3_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[651, 648])).
% 1.55/1.26 tff(653,plain,
% 1.55/1.26 ((~hskp7) | c3_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[652, 648])).
% 1.55/1.26 tff(654,plain,
% 1.55/1.26 ((~hskp7) | c3_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[653, 648])).
% 1.55/1.26 tff(655,plain,
% 1.55/1.26 ((~hskp7) | c3_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[654, 648])).
% 1.55/1.26 tff(656,plain,
% 1.55/1.26 ((~hskp7) | c3_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[655, 648])).
% 1.55/1.26 tff(657,plain,
% 1.55/1.26 ((~hskp7) | c3_1(a1105)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[656, 648])).
% 1.55/1.26 tff(658,plain,
% 1.55/1.26 (c3_1(a1105)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[657, 636])).
% 1.55/1.26 tff(659,plain,
% 1.55/1.26 (^[V: $i, U: $i] : refl((hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(660,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[659])).
% 1.55/1.26 tff(661,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(662,plain,
% 1.55/1.26 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(663,plain,
% 1.55/1.26 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp30) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[662])).
% 1.55/1.26 tff(664,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.55/1.26 tff(665,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[664, 663])).
% 1.55/1.26 tff(666,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[665, 661])).
% 1.55/1.26 tff(667,plain,(
% 1.55/1.26 ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.26 inference(skolemize,[status(sab)],[666])).
% 1.55/1.26 tff(668,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[667, 660])).
% 1.55/1.26 tff(669,assumption,(~c1_1(a1105)), introduced(assumption)).
% 1.55/1.26 tff(670,assumption,(~hskp30), introduced(assumption)).
% 1.55/1.26 tff(671,plain,
% 1.55/1.26 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(672,plain,
% 1.55/1.26 ((hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098)) <=> (hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(673,plain,
% 1.55/1.26 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105))))),
% 1.55/1.26 inference(monotonicity,[status(thm)],[672])).
% 1.55/1.26 tff(674,plain,
% 1.55/1.26 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))),
% 1.55/1.26 inference(transitivity,[status(thm)],[673, 671])).
% 1.55/1.26 tff(675,plain,
% 1.55/1.26 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1098) | c1_1(a1098) | c3_1(a1098))),
% 1.55/1.26 inference(quant_inst,[status(thm)],[])).
% 1.55/1.26 tff(676,plain,
% 1.55/1.26 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[675, 674])).
% 1.55/1.26 tff(677,plain,
% 1.55/1.26 ((~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105))),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[676, 670, 669, 34, 35, 47, 668])).
% 1.55/1.26 tff(678,plain,
% 1.55/1.26 ($false),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[677, 658, 647, 635])).
% 1.55/1.26 tff(679,plain,((~hskp7) | (~ndr1_0) | hskp30 | c1_1(a1105) | c1_1(a1098) | c2_1(a1098) | c3_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.26 tff(680,plain,
% 1.55/1.26 (hskp30),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[679, 628, 113, 634, 34, 35, 47])).
% 1.55/1.26 tff(681,plain,
% 1.55/1.26 (((~hskp30) | c1_1(a1136)) <=> ((~hskp30) | c1_1(a1136))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(682,axiom,((~hskp30) | c1_1(a1136)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.55/1.26 tff(683,plain,
% 1.55/1.26 ((~hskp30) | c1_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[682, 681])).
% 1.55/1.26 tff(684,plain,
% 1.55/1.26 ((~hskp30) | c1_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[683, 681])).
% 1.55/1.26 tff(685,plain,
% 1.55/1.26 ((~hskp30) | c1_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[684, 681])).
% 1.55/1.26 tff(686,plain,
% 1.55/1.26 ((~hskp30) | c1_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[685, 681])).
% 1.55/1.26 tff(687,plain,
% 1.55/1.26 ((~hskp30) | c1_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[686, 681])).
% 1.55/1.26 tff(688,plain,
% 1.55/1.26 ((~hskp30) | c1_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[687, 681])).
% 1.55/1.26 tff(689,plain,
% 1.55/1.26 ((~hskp30) | c1_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[688, 681])).
% 1.55/1.26 tff(690,plain,
% 1.55/1.26 ((~hskp30) | c1_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[689, 681])).
% 1.55/1.26 tff(691,plain,
% 1.55/1.26 (c1_1(a1136)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[690, 680])).
% 1.55/1.26 tff(692,assumption,(~hskp14), introduced(assumption)).
% 1.55/1.26 tff(693,plain,
% 1.55/1.26 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(694,plain,
% 1.55/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[693])).
% 1.55/1.26 tff(695,plain,
% 1.55/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(696,plain,
% 1.55/1.26 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(697,plain,
% 1.55/1.26 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[696])).
% 1.55/1.26 tff(698,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 1.55/1.26 tff(699,plain,
% 1.55/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[698, 697])).
% 1.55/1.26 tff(700,plain,
% 1.55/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[699, 695])).
% 1.55/1.26 tff(701,plain,(
% 1.55/1.26 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.26 inference(skolemize,[status(sab)],[700])).
% 1.55/1.26 tff(702,plain,
% 1.55/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[701, 694])).
% 1.55/1.26 tff(703,assumption,(~hskp20), introduced(assumption)).
% 1.55/1.26 tff(704,assumption,(~hskp19), introduced(assumption)).
% 1.55/1.26 tff(705,plain,
% 1.55/1.26 (^[U: $i] : refl((hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(706,plain,
% 1.55/1.26 (![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[705])).
% 1.55/1.26 tff(707,plain,
% 1.55/1.26 (![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(708,plain,
% 1.55/1.26 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp14) <=> ((hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp14))), rewrite(((hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp14) <=> (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp14) <=> (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(709,plain,
% 1.55/1.26 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp14) <=> ![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[708])).
% 1.55/1.26 tff(710,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 1.55/1.26 tff(711,plain,
% 1.55/1.26 (![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[710, 709])).
% 1.55/1.26 tff(712,plain,
% 1.55/1.26 (![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[711, 707])).
% 1.55/1.26 tff(713,plain,(
% 1.55/1.26 ![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.55/1.26 inference(skolemize,[status(sab)],[712])).
% 1.55/1.26 tff(714,plain,
% 1.55/1.26 (![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[713, 706])).
% 1.55/1.26 tff(715,plain,
% 1.55/1.26 (c3_1(a1105)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[657, 628])).
% 1.55/1.26 tff(716,plain,
% 1.55/1.26 (c0_1(a1105)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[646, 628])).
% 1.55/1.26 tff(717,plain,
% 1.55/1.26 (((~hskp30) | c3_1(a1136)) <=> ((~hskp30) | c3_1(a1136))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(718,axiom,((~hskp30) | c3_1(a1136)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.55/1.26 tff(719,plain,
% 1.55/1.26 ((~hskp30) | c3_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[718, 717])).
% 1.55/1.26 tff(720,plain,
% 1.55/1.26 ((~hskp30) | c3_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[719, 717])).
% 1.55/1.26 tff(721,plain,
% 1.55/1.26 ((~hskp30) | c3_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[720, 717])).
% 1.55/1.26 tff(722,plain,
% 1.55/1.26 ((~hskp30) | c3_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[721, 717])).
% 1.55/1.26 tff(723,plain,
% 1.55/1.26 ((~hskp30) | c3_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[722, 717])).
% 1.55/1.26 tff(724,plain,
% 1.55/1.26 ((~hskp30) | c3_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[723, 717])).
% 1.55/1.26 tff(725,plain,
% 1.55/1.26 ((~hskp30) | c3_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[724, 717])).
% 1.55/1.26 tff(726,plain,
% 1.55/1.26 ((~hskp30) | c3_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[725, 717])).
% 1.55/1.26 tff(727,plain,
% 1.55/1.26 (c3_1(a1136)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[726, 680])).
% 1.55/1.26 tff(728,plain,
% 1.55/1.26 (((~hskp30) | c2_1(a1136)) <=> ((~hskp30) | c2_1(a1136))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(729,axiom,((~hskp30) | c2_1(a1136)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.55/1.26 tff(730,plain,
% 1.55/1.26 ((~hskp30) | c2_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[729, 728])).
% 1.55/1.26 tff(731,plain,
% 1.55/1.26 ((~hskp30) | c2_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[730, 728])).
% 1.55/1.26 tff(732,plain,
% 1.55/1.26 ((~hskp30) | c2_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[731, 728])).
% 1.55/1.26 tff(733,plain,
% 1.55/1.26 ((~hskp30) | c2_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[732, 728])).
% 1.55/1.26 tff(734,plain,
% 1.55/1.26 ((~hskp30) | c2_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[733, 728])).
% 1.55/1.26 tff(735,plain,
% 1.55/1.26 ((~hskp30) | c2_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[734, 728])).
% 1.55/1.26 tff(736,plain,
% 1.55/1.26 ((~hskp30) | c2_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[735, 728])).
% 1.55/1.26 tff(737,plain,
% 1.55/1.26 ((~hskp30) | c2_1(a1136)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[736, 728])).
% 1.55/1.26 tff(738,plain,
% 1.55/1.26 (c2_1(a1136)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[737, 680])).
% 1.55/1.26 tff(739,assumption,(c3_1(a1136)), introduced(assumption)).
% 1.55/1.26 tff(740,plain,
% 1.55/1.26 ((hskp23 | hskp14) <=> (hskp23 | hskp14)),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(741,axiom,(hskp23 | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 1.55/1.26 tff(742,plain,
% 1.55/1.26 (hskp23 | hskp14),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[741, 740])).
% 1.55/1.26 tff(743,plain,
% 1.55/1.26 (hskp23 | hskp14),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[742, 740])).
% 1.55/1.26 tff(744,plain,
% 1.55/1.26 (hskp23 | hskp14),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[743, 740])).
% 1.55/1.26 tff(745,plain,
% 1.55/1.26 (hskp23 | hskp14),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[744, 740])).
% 1.55/1.26 tff(746,plain,
% 1.55/1.26 (hskp23 | hskp14),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[745, 740])).
% 1.55/1.26 tff(747,plain,
% 1.55/1.26 (hskp23 | hskp14),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[746, 740])).
% 1.55/1.26 tff(748,plain,
% 1.55/1.26 (hskp23 | hskp14),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[747, 740])).
% 1.55/1.26 tff(749,plain,
% 1.55/1.26 (hskp23 | hskp14),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[748, 740])).
% 1.55/1.26 tff(750,plain,
% 1.55/1.26 (hskp23),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[749, 692])).
% 1.55/1.26 tff(751,plain,
% 1.55/1.26 (((~hskp23) | (~c3_1(a1147))) <=> ((~hskp23) | (~c3_1(a1147)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(752,plain,
% 1.55/1.26 (((~c3_1(a1147)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1147)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(753,axiom,((~c3_1(a1147)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.55/1.26 tff(754,plain,
% 1.55/1.26 ((~hskp23) | (~c3_1(a1147))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[753, 752])).
% 1.55/1.26 tff(755,plain,
% 1.55/1.26 ((~hskp23) | (~c3_1(a1147))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[754, 751])).
% 1.55/1.26 tff(756,plain,
% 1.55/1.26 (~c3_1(a1147)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[755, 750])).
% 1.55/1.26 tff(757,plain,
% 1.55/1.26 (((~hskp23) | c0_1(a1147)) <=> ((~hskp23) | c0_1(a1147))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(758,axiom,((~hskp23) | c0_1(a1147)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.55/1.26 tff(759,plain,
% 1.55/1.26 ((~hskp23) | c0_1(a1147)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[758, 757])).
% 1.55/1.26 tff(760,plain,
% 1.55/1.26 ((~hskp23) | c0_1(a1147)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[759, 757])).
% 1.55/1.26 tff(761,plain,
% 1.55/1.26 ((~hskp23) | c0_1(a1147)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[760, 757])).
% 1.55/1.26 tff(762,plain,
% 1.55/1.26 ((~hskp23) | c0_1(a1147)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[761, 757])).
% 1.55/1.26 tff(763,plain,
% 1.55/1.26 ((~hskp23) | c0_1(a1147)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[762, 757])).
% 1.55/1.26 tff(764,plain,
% 1.55/1.26 ((~hskp23) | c0_1(a1147)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[763, 757])).
% 1.55/1.26 tff(765,plain,
% 1.55/1.26 ((~hskp23) | c0_1(a1147)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[764, 757])).
% 1.55/1.26 tff(766,plain,
% 1.55/1.26 ((~hskp23) | c0_1(a1147)),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[765, 757])).
% 1.55/1.26 tff(767,plain,
% 1.55/1.26 (c0_1(a1147)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[766, 750])).
% 1.55/1.26 tff(768,assumption,(c2_1(a1136)), introduced(assumption)).
% 1.55/1.26 tff(769,assumption,(c1_1(a1136)), introduced(assumption)).
% 1.55/1.26 tff(770,assumption,(~hskp29), introduced(assumption)).
% 1.55/1.26 tff(771,assumption,(~c3_1(a1147)), introduced(assumption)).
% 1.55/1.26 tff(772,assumption,(c0_1(a1147)), introduced(assumption)).
% 1.55/1.26 tff(773,plain,
% 1.55/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(774,plain,
% 1.55/1.26 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136))) <=> (c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(775,plain,
% 1.55/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.55/1.26 inference(monotonicity,[status(thm)],[774])).
% 1.55/1.26 tff(776,plain,
% 1.55/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.55/1.26 inference(transitivity,[status(thm)],[775, 773])).
% 1.55/1.26 tff(777,plain,
% 1.55/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136)))),
% 1.55/1.26 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(778,plain,
% 1.55/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[777, 776])).
% 1.55/1.27 tff(779,plain,
% 1.55/1.27 (~c1_1(a1147)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[778, 113, 769, 768, 739, 772, 771, 45, 46])).
% 1.55/1.27 tff(780,plain,
% 1.55/1.27 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.55/1.27 inference(bind,[status(th)],[])).
% 1.55/1.27 tff(781,plain,
% 1.55/1.27 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(quant_intro,[status(thm)],[780])).
% 1.55/1.27 tff(782,plain,
% 1.55/1.27 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(783,plain,
% 1.55/1.27 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.55/1.27 inference(bind,[status(th)],[])).
% 1.55/1.27 tff(784,plain,
% 1.55/1.27 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(quant_intro,[status(thm)],[783])).
% 1.55/1.27 tff(785,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.55/1.27 tff(786,plain,
% 1.55/1.27 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[785, 784])).
% 1.55/1.27 tff(787,plain,
% 1.55/1.27 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[786, 782])).
% 1.55/1.27 tff(788,plain,(
% 1.55/1.27 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(skolemize,[status(sab)],[787])).
% 1.55/1.27 tff(789,plain,
% 1.55/1.27 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[788, 781])).
% 1.55/1.27 tff(790,plain,
% 1.55/1.27 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(791,plain,
% 1.55/1.27 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136))) <=> (hskp29 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(792,plain,
% 1.55/1.27 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[791])).
% 1.55/1.27 tff(793,plain,
% 1.55/1.27 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.55/1.27 inference(transitivity,[status(thm)],[792, 790])).
% 1.55/1.27 tff(794,plain,
% 1.55/1.27 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(795,plain,
% 1.55/1.27 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[794, 793])).
% 1.55/1.27 tff(796,plain,
% 1.55/1.27 ($false),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[795, 113, 770, 769, 768, 772, 771, 789, 46, 779])).
% 1.55/1.27 tff(797,plain,(c0_1(a1136) | hskp29 | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1147)) | c3_1(a1147) | (~c3_1(a1136))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.27 tff(798,plain,
% 1.55/1.27 (c0_1(a1136)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[797, 770, 769, 768, 767, 756, 739])).
% 1.55/1.27 tff(799,plain,
% 1.55/1.27 (((~hskp23) | (~c2_1(a1147))) <=> ((~hskp23) | (~c2_1(a1147)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(800,plain,
% 1.55/1.27 (((~c2_1(a1147)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a1147)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(801,axiom,((~c2_1(a1147)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 1.55/1.27 tff(802,plain,
% 1.55/1.27 ((~hskp23) | (~c2_1(a1147))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[801, 800])).
% 1.55/1.27 tff(803,plain,
% 1.55/1.27 ((~hskp23) | (~c2_1(a1147))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[802, 799])).
% 1.55/1.27 tff(804,plain,
% 1.55/1.27 (~c2_1(a1147)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[803, 750])).
% 1.55/1.27 tff(805,assumption,(c0_1(a1136)), introduced(assumption)).
% 1.55/1.27 tff(806,assumption,(hskp21), introduced(assumption)).
% 1.55/1.27 tff(807,plain,
% 1.55/1.27 (((~hskp21) | (~c3_1(a1131))) <=> ((~hskp21) | (~c3_1(a1131)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(808,plain,
% 1.55/1.27 (((~c3_1(a1131)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a1131)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(809,axiom,((~c3_1(a1131)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.55/1.27 tff(810,plain,
% 1.55/1.27 ((~hskp21) | (~c3_1(a1131))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[809, 808])).
% 1.55/1.27 tff(811,plain,
% 1.55/1.27 ((~hskp21) | (~c3_1(a1131))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[810, 807])).
% 1.55/1.27 tff(812,plain,
% 1.55/1.27 (~c3_1(a1131)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[811, 806])).
% 1.55/1.27 tff(813,plain,
% 1.55/1.27 (((~hskp21) | (~c0_1(a1131))) <=> ((~hskp21) | (~c0_1(a1131)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(814,plain,
% 1.55/1.27 (((~c0_1(a1131)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a1131)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(815,axiom,((~c0_1(a1131)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.55/1.27 tff(816,plain,
% 1.55/1.27 ((~hskp21) | (~c0_1(a1131))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[815, 814])).
% 1.55/1.27 tff(817,plain,
% 1.55/1.27 ((~hskp21) | (~c0_1(a1131))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[816, 813])).
% 1.55/1.27 tff(818,plain,
% 1.55/1.27 (~c0_1(a1131)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[817, 806])).
% 1.55/1.27 tff(819,assumption,(~c2_1(a1147)), introduced(assumption)).
% 1.55/1.27 tff(820,plain,
% 1.55/1.27 (((~hskp21) | c1_1(a1131)) <=> ((~hskp21) | c1_1(a1131))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(821,axiom,((~hskp21) | c1_1(a1131)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.55/1.27 tff(822,plain,
% 1.55/1.27 ((~hskp21) | c1_1(a1131)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[821, 820])).
% 1.55/1.27 tff(823,plain,
% 1.55/1.27 ((~hskp21) | c1_1(a1131)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[822, 820])).
% 1.55/1.27 tff(824,plain,
% 1.55/1.27 ((~hskp21) | c1_1(a1131)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[823, 820])).
% 1.55/1.27 tff(825,plain,
% 1.55/1.27 ((~hskp21) | c1_1(a1131)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[824, 820])).
% 1.55/1.27 tff(826,plain,
% 1.55/1.27 ((~hskp21) | c1_1(a1131)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[825, 820])).
% 1.55/1.27 tff(827,plain,
% 1.55/1.27 ((~hskp21) | c1_1(a1131)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[826, 820])).
% 1.55/1.27 tff(828,plain,
% 1.55/1.27 ((~hskp21) | c1_1(a1131)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[827, 820])).
% 1.55/1.27 tff(829,plain,
% 1.55/1.27 ((~hskp21) | c1_1(a1131)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[828, 820])).
% 1.55/1.27 tff(830,plain,
% 1.55/1.27 (c1_1(a1131)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[829, 806])).
% 1.55/1.27 tff(831,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1131)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1131)) | (~c0_1(a1147)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(832,plain,
% 1.55/1.27 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131))) <=> (c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1131)) | (~c0_1(a1147)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(833,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1131)) | (~c0_1(a1147))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[832])).
% 1.55/1.27 tff(834,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1131)) | (~c0_1(a1147)))),
% 1.55/1.27 inference(transitivity,[status(thm)],[833, 831])).
% 1.55/1.27 tff(835,plain,
% 1.55/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131)))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(836,plain,
% 1.55/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1131)) | (~c0_1(a1147))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[835, 834])).
% 1.55/1.27 tff(837,plain,
% 1.55/1.27 ($false),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[836, 113, 768, 739, 772, 830, 819, 771, 818, 812, 344, 805])).
% 1.55/1.27 tff(838,plain,((~hskp21) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1136))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.27 tff(839,plain,
% 1.55/1.27 (~hskp21),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[838, 798, 739, 767, 804, 756, 768])).
% 1.55/1.27 tff(840,assumption,(~hskp6), introduced(assumption)).
% 1.55/1.27 tff(841,assumption,(~hskp21), introduced(assumption)).
% 1.55/1.27 tff(842,plain,
% 1.55/1.27 ((hskp24 | hskp21 | hskp6) <=> (hskp24 | hskp21 | hskp6)),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(843,plain,
% 1.55/1.27 (((hskp21 | hskp6) | hskp24) <=> (hskp24 | hskp21 | hskp6)),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(844,plain,
% 1.55/1.27 ((hskp6 | hskp21) <=> (hskp21 | hskp6)),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(845,plain,
% 1.55/1.27 (((hskp6 | hskp21) | hskp24) <=> ((hskp21 | hskp6) | hskp24)),
% 1.55/1.27 inference(monotonicity,[status(thm)],[844])).
% 1.55/1.27 tff(846,plain,
% 1.55/1.27 (((hskp6 | hskp21) | hskp24) <=> (hskp24 | hskp21 | hskp6)),
% 1.55/1.27 inference(transitivity,[status(thm)],[845, 843])).
% 1.55/1.27 tff(847,axiom,((hskp6 | hskp21) | hskp24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 1.55/1.27 tff(848,plain,
% 1.55/1.27 (hskp24 | hskp21 | hskp6),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[847, 846])).
% 1.55/1.27 tff(849,plain,
% 1.55/1.27 (hskp24 | hskp21 | hskp6),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[848, 842])).
% 1.55/1.27 tff(850,plain,
% 1.55/1.27 (hskp24 | hskp21 | hskp6),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[849, 842])).
% 1.55/1.27 tff(851,plain,
% 1.55/1.27 (hskp24 | hskp21 | hskp6),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[850, 842])).
% 1.55/1.27 tff(852,plain,
% 1.55/1.27 (hskp24 | hskp21 | hskp6),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[851, 842])).
% 1.55/1.27 tff(853,plain,
% 1.55/1.27 (hskp24 | hskp21 | hskp6),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[852, 842])).
% 1.55/1.27 tff(854,plain,
% 1.55/1.27 (hskp24 | hskp21 | hskp6),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[853, 842])).
% 1.55/1.27 tff(855,plain,
% 1.55/1.27 (hskp24 | hskp21 | hskp6),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[854, 842])).
% 1.55/1.27 tff(856,plain,
% 1.55/1.27 (hskp24),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[855, 841, 840])).
% 1.55/1.27 tff(857,plain,
% 1.55/1.27 (((~hskp24) | (~c0_1(a1149))) <=> ((~hskp24) | (~c0_1(a1149)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(858,plain,
% 1.55/1.27 (((~c0_1(a1149)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a1149)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(859,axiom,((~c0_1(a1149)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.55/1.27 tff(860,plain,
% 1.55/1.27 ((~hskp24) | (~c0_1(a1149))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[859, 858])).
% 1.55/1.27 tff(861,plain,
% 1.55/1.27 ((~hskp24) | (~c0_1(a1149))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[860, 857])).
% 1.55/1.27 tff(862,plain,
% 1.55/1.27 (~c0_1(a1149)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[861, 856])).
% 1.55/1.27 tff(863,plain,
% 1.55/1.27 (((~hskp24) | c3_1(a1149)) <=> ((~hskp24) | c3_1(a1149))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(864,axiom,((~hskp24) | c3_1(a1149)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.55/1.27 tff(865,plain,
% 1.55/1.27 ((~hskp24) | c3_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[864, 863])).
% 1.55/1.27 tff(866,plain,
% 1.55/1.27 ((~hskp24) | c3_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[865, 863])).
% 1.55/1.27 tff(867,plain,
% 1.55/1.27 ((~hskp24) | c3_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[866, 863])).
% 1.55/1.27 tff(868,plain,
% 1.55/1.27 ((~hskp24) | c3_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[867, 863])).
% 1.55/1.27 tff(869,plain,
% 1.55/1.27 ((~hskp24) | c3_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[868, 863])).
% 1.55/1.27 tff(870,plain,
% 1.55/1.27 ((~hskp24) | c3_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[869, 863])).
% 1.55/1.27 tff(871,plain,
% 1.55/1.27 ((~hskp24) | c3_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[870, 863])).
% 1.55/1.27 tff(872,plain,
% 1.55/1.27 ((~hskp24) | c3_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[871, 863])).
% 1.55/1.27 tff(873,plain,
% 1.55/1.27 (c3_1(a1149)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[872, 856])).
% 1.55/1.27 tff(874,plain,
% 1.55/1.27 (((~hskp24) | c2_1(a1149)) <=> ((~hskp24) | c2_1(a1149))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(875,axiom,((~hskp24) | c2_1(a1149)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.55/1.27 tff(876,plain,
% 1.55/1.27 ((~hskp24) | c2_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[875, 874])).
% 1.55/1.27 tff(877,plain,
% 1.55/1.27 ((~hskp24) | c2_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[876, 874])).
% 1.55/1.27 tff(878,plain,
% 1.55/1.27 ((~hskp24) | c2_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[877, 874])).
% 1.55/1.27 tff(879,plain,
% 1.55/1.27 ((~hskp24) | c2_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[878, 874])).
% 1.55/1.27 tff(880,plain,
% 1.55/1.27 ((~hskp24) | c2_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[879, 874])).
% 1.55/1.27 tff(881,plain,
% 1.55/1.27 ((~hskp24) | c2_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[880, 874])).
% 1.55/1.27 tff(882,plain,
% 1.55/1.27 ((~hskp24) | c2_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[881, 874])).
% 1.55/1.27 tff(883,plain,
% 1.55/1.27 ((~hskp24) | c2_1(a1149)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[882, 874])).
% 1.55/1.27 tff(884,plain,
% 1.55/1.27 (c2_1(a1149)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[883, 856])).
% 1.55/1.27 tff(885,plain,
% 1.55/1.27 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.55/1.27 inference(bind,[status(th)],[])).
% 1.55/1.27 tff(886,plain,
% 1.55/1.27 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(quant_intro,[status(thm)],[885])).
% 1.55/1.27 tff(887,plain,
% 1.55/1.27 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(888,plain,
% 1.55/1.27 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.55/1.27 inference(bind,[status(th)],[])).
% 1.55/1.27 tff(889,plain,
% 1.55/1.27 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(quant_intro,[status(thm)],[888])).
% 1.55/1.27 tff(890,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.55/1.27 tff(891,plain,
% 1.55/1.27 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[890, 889])).
% 1.55/1.27 tff(892,plain,
% 1.55/1.27 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[891, 887])).
% 1.55/1.27 tff(893,plain,(
% 1.55/1.27 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(skolemize,[status(sab)],[892])).
% 1.55/1.27 tff(894,plain,
% 1.55/1.27 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[893, 886])).
% 1.55/1.27 tff(895,assumption,(hskp19), introduced(assumption)).
% 1.55/1.27 tff(896,plain,
% 1.55/1.27 (((~hskp19) | (~c2_1(a1127))) <=> ((~hskp19) | (~c2_1(a1127)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(897,plain,
% 1.55/1.27 (((~c2_1(a1127)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a1127)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(898,axiom,((~c2_1(a1127)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 1.55/1.27 tff(899,plain,
% 1.55/1.27 ((~hskp19) | (~c2_1(a1127))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[898, 897])).
% 1.55/1.27 tff(900,plain,
% 1.55/1.27 ((~hskp19) | (~c2_1(a1127))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[899, 896])).
% 1.55/1.27 tff(901,plain,
% 1.55/1.27 (~c2_1(a1127)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[900, 895])).
% 1.55/1.27 tff(902,assumption,(~c0_1(a1149)), introduced(assumption)).
% 1.55/1.27 tff(903,plain,
% 1.55/1.27 (((~hskp19) | c3_1(a1127)) <=> ((~hskp19) | c3_1(a1127))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(904,axiom,((~hskp19) | c3_1(a1127)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 1.55/1.27 tff(905,plain,
% 1.55/1.27 ((~hskp19) | c3_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[904, 903])).
% 1.55/1.27 tff(906,plain,
% 1.55/1.27 ((~hskp19) | c3_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[905, 903])).
% 1.55/1.27 tff(907,plain,
% 1.55/1.27 ((~hskp19) | c3_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[906, 903])).
% 1.55/1.27 tff(908,plain,
% 1.55/1.27 ((~hskp19) | c3_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[907, 903])).
% 1.55/1.27 tff(909,plain,
% 1.55/1.27 ((~hskp19) | c3_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[908, 903])).
% 1.55/1.27 tff(910,plain,
% 1.55/1.27 ((~hskp19) | c3_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[909, 903])).
% 1.55/1.27 tff(911,plain,
% 1.55/1.27 ((~hskp19) | c3_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[910, 903])).
% 1.55/1.27 tff(912,plain,
% 1.55/1.27 ((~hskp19) | c3_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[911, 903])).
% 1.55/1.27 tff(913,plain,
% 1.55/1.27 (c3_1(a1127)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[912, 895])).
% 1.55/1.27 tff(914,plain,
% 1.55/1.27 (((~hskp19) | c1_1(a1127)) <=> ((~hskp19) | c1_1(a1127))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(915,axiom,((~hskp19) | c1_1(a1127)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.55/1.27 tff(916,plain,
% 1.55/1.27 ((~hskp19) | c1_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[915, 914])).
% 1.55/1.27 tff(917,plain,
% 1.55/1.27 ((~hskp19) | c1_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[916, 914])).
% 1.55/1.27 tff(918,plain,
% 1.55/1.27 ((~hskp19) | c1_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[917, 914])).
% 1.55/1.27 tff(919,plain,
% 1.55/1.27 ((~hskp19) | c1_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[918, 914])).
% 1.55/1.27 tff(920,plain,
% 1.55/1.27 ((~hskp19) | c1_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[919, 914])).
% 1.55/1.27 tff(921,plain,
% 1.55/1.27 ((~hskp19) | c1_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[920, 914])).
% 1.55/1.27 tff(922,plain,
% 1.55/1.27 ((~hskp19) | c1_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[921, 914])).
% 1.55/1.27 tff(923,plain,
% 1.55/1.27 ((~hskp19) | c1_1(a1127)),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[922, 914])).
% 1.55/1.27 tff(924,plain,
% 1.55/1.27 (c1_1(a1127)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[923, 895])).
% 1.55/1.27 tff(925,assumption,(c3_1(a1149)), introduced(assumption)).
% 1.55/1.27 tff(926,assumption,(c2_1(a1149)), introduced(assumption)).
% 1.55/1.27 tff(927,plain,
% 1.55/1.27 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp21 | c0_1(a1149) | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c2_1(a1149)) | (~c3_1(a1149)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp21 | c0_1(a1149) | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c2_1(a1149)) | (~c3_1(a1149)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(928,plain,
% 1.55/1.27 ((hskp21 | (~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)) | c0_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149))) <=> (hskp21 | c0_1(a1149) | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c2_1(a1149)) | (~c3_1(a1149)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(929,plain,
% 1.55/1.27 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)) | c0_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp21 | c0_1(a1149) | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c2_1(a1149)) | (~c3_1(a1149))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[928])).
% 1.55/1.27 tff(930,plain,
% 1.55/1.27 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)) | c0_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp21 | c0_1(a1149) | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c2_1(a1149)) | (~c3_1(a1149)))),
% 1.55/1.27 inference(transitivity,[status(thm)],[929, 927])).
% 1.55/1.27 tff(931,plain,
% 1.55/1.27 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)) | c0_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149)))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(932,plain,
% 1.55/1.27 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp21 | c0_1(a1149) | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c2_1(a1149)) | (~c3_1(a1149))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[931, 930])).
% 1.55/1.27 tff(933,plain,
% 1.55/1.27 ($false),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[932, 113, 841, 926, 925, 924, 913, 902, 901, 894])).
% 1.55/1.27 tff(934,plain,((~hskp19) | hskp21 | (~c2_1(a1149)) | (~c3_1(a1149)) | c0_1(a1149)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.27 tff(935,plain,
% 1.55/1.27 (~hskp19),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[934, 841, 884, 873, 862])).
% 1.55/1.27 tff(936,plain,
% 1.55/1.27 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | (~c2_1(a1149)) | c1_1(a1149) | (~c3_1(a1149)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | (~ndr1_0) | (~c2_1(a1149)) | c1_1(a1149) | (~c3_1(a1149)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(937,plain,
% 1.55/1.27 ((hskp14 | hskp19 | (~ndr1_0) | c1_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149))) <=> (hskp14 | hskp19 | (~ndr1_0) | (~c2_1(a1149)) | c1_1(a1149) | (~c3_1(a1149)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(938,plain,
% 1.55/1.27 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | (~c2_1(a1149)) | c1_1(a1149) | (~c3_1(a1149))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[937])).
% 1.55/1.27 tff(939,plain,
% 1.55/1.27 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | (~ndr1_0) | (~c2_1(a1149)) | c1_1(a1149) | (~c3_1(a1149)))),
% 1.55/1.27 inference(transitivity,[status(thm)],[938, 936])).
% 1.55/1.27 tff(940,plain,
% 1.55/1.27 ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1149) | (~c3_1(a1149)) | (~c2_1(a1149)))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(941,plain,
% 1.55/1.27 ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | (~ndr1_0) | (~c2_1(a1149)) | c1_1(a1149) | (~c3_1(a1149))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[940, 939])).
% 1.55/1.27 tff(942,plain,
% 1.55/1.27 (hskp19 | c1_1(a1149)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[941, 692, 113, 884, 873, 714])).
% 1.55/1.28 tff(943,plain,
% 1.55/1.28 (c1_1(a1149)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[942, 935])).
% 1.55/1.28 tff(944,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c1_1(a1149)) | (~c3_1(a1149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(945,plain,
% 1.55/1.28 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149))) <=> (c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(946,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c1_1(a1149)) | (~c3_1(a1149))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[945])).
% 1.55/1.28 tff(947,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[946, 944])).
% 1.55/1.28 tff(948,plain,
% 1.55/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(949,plain,
% 1.55/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c1_1(a1149)) | (~c3_1(a1149))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[948, 947])).
% 1.55/1.28 tff(950,plain,
% 1.55/1.28 ((~c1_1(a1147)) | (~c1_1(a1149))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[949, 113, 769, 768, 739, 873, 767, 862, 756, 45])).
% 1.55/1.28 tff(951,plain,
% 1.55/1.28 (~c1_1(a1147)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[950, 943])).
% 1.55/1.28 tff(952,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)) | (~c2_1(a1149)) | (~c1_1(a1149)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)) | (~c2_1(a1149)) | (~c1_1(a1149)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(953,plain,
% 1.55/1.28 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c2_1(a1149))) <=> (hskp29 | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)) | (~c2_1(a1149)) | (~c1_1(a1149)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(954,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c2_1(a1149)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)) | (~c2_1(a1149)) | (~c1_1(a1149))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[953])).
% 1.55/1.28 tff(955,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c2_1(a1149)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)) | (~c2_1(a1149)) | (~c1_1(a1149)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[954, 952])).
% 1.55/1.28 tff(956,plain,
% 1.55/1.28 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c0_1(a1149) | (~c1_1(a1149)) | (~c2_1(a1149)))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(957,plain,
% 1.55/1.28 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c0_1(a1149) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)) | (~c2_1(a1149)) | (~c1_1(a1149))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[956, 955])).
% 1.55/1.28 tff(958,plain,
% 1.55/1.28 (c1_1(a1147) | (~c1_1(a1149))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[957, 113, 770, 884, 767, 862, 756, 789])).
% 1.55/1.28 tff(959,plain,
% 1.55/1.28 ($false),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[958, 951, 943])).
% 1.55/1.28 tff(960,plain,(hskp21 | hskp29 | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c3_1(a1136)) | hskp14 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.55/1.28 tff(961,plain,
% 1.55/1.28 (hskp6),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[960, 839, 769, 768, 739, 692, 770])).
% 1.55/1.28 tff(962,plain,
% 1.55/1.28 (~c2_1(a1104)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[538, 961])).
% 1.55/1.28 tff(963,plain,
% 1.55/1.28 (c1_1(a1104)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[577, 961])).
% 1.55/1.28 tff(964,plain,
% 1.55/1.28 (c0_1(a1104)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[549, 961])).
% 1.55/1.28 tff(965,assumption,(c3_1(a1105)), introduced(assumption)).
% 1.55/1.28 tff(966,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(967,plain,
% 1.55/1.28 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105))) <=> (c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(968,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c2_1(a1105) | (~c3_1(a1105))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[967])).
% 1.55/1.28 tff(969,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[968, 966])).
% 1.55/1.28 tff(970,plain,
% 1.55/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(971,plain,
% 1.55/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c2_1(a1105) | (~c3_1(a1105))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[970, 969])).
% 1.55/1.28 tff(972,plain,
% 1.55/1.28 (c2_1(a1105)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[971, 113, 768, 739, 965, 964, 963, 669, 962, 246, 798])).
% 1.55/1.28 tff(973,plain,
% 1.55/1.28 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.55/1.28 inference(bind,[status(th)],[])).
% 1.55/1.28 tff(974,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(quant_intro,[status(thm)],[973])).
% 1.55/1.28 tff(975,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(976,plain,
% 1.55/1.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp24) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp24))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.55/1.28 inference(bind,[status(th)],[])).
% 1.55/1.28 tff(977,plain,
% 1.55/1.28 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(quant_intro,[status(thm)],[976])).
% 1.55/1.28 tff(978,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 1.55/1.28 tff(979,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[978, 977])).
% 1.55/1.28 tff(980,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[979, 975])).
% 1.55/1.28 tff(981,plain,(
% 1.55/1.28 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(skolemize,[status(sab)],[980])).
% 1.55/1.28 tff(982,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[981, 974])).
% 1.55/1.28 tff(983,plain,
% 1.55/1.28 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(984,plain,
% 1.55/1.28 ((hskp14 | hskp19 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))) <=> (hskp14 | hskp19 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(985,plain,
% 1.55/1.28 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[984])).
% 1.55/1.28 tff(986,plain,
% 1.55/1.28 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[985, 983])).
% 1.55/1.28 tff(987,plain,
% 1.55/1.28 ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(988,plain,
% 1.55/1.28 ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[987, 986])).
% 1.55/1.28 tff(989,plain,
% 1.55/1.28 (hskp14 | hskp19 | (~c2_1(a1105))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[988, 113, 965, 669, 714])).
% 1.55/1.28 tff(990,plain,
% 1.55/1.28 (hskp19),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[989, 972, 692])).
% 1.55/1.28 tff(991,plain,
% 1.55/1.28 (~c2_1(a1127)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[900, 990])).
% 1.55/1.28 tff(992,assumption,(c0_1(a1105)), introduced(assumption)).
% 1.55/1.28 tff(993,plain,
% 1.55/1.28 (c3_1(a1127)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[912, 990])).
% 1.55/1.28 tff(994,plain,
% 1.55/1.28 (c1_1(a1127)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[923, 990])).
% 1.55/1.28 tff(995,assumption,(c2_1(a1105)), introduced(assumption)).
% 1.55/1.28 tff(996,plain,
% 1.55/1.28 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.55/1.28 inference(bind,[status(th)],[])).
% 1.55/1.28 tff(997,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(quant_intro,[status(thm)],[996])).
% 1.55/1.28 tff(998,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(999,plain,
% 1.55/1.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.55/1.28 inference(bind,[status(th)],[])).
% 1.55/1.28 tff(1000,plain,
% 1.55/1.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(quant_intro,[status(thm)],[999])).
% 1.55/1.28 tff(1001,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 1.55/1.28 tff(1002,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 1.55/1.28 tff(1003,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1002, 998])).
% 1.55/1.28 tff(1004,plain,(
% 1.55/1.28 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(skolemize,[status(sab)],[1003])).
% 1.55/1.28 tff(1005,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1004, 997])).
% 1.55/1.28 tff(1006,assumption,(~c2_1(a1127)), introduced(assumption)).
% 1.55/1.28 tff(1007,assumption,(c3_1(a1127)), introduced(assumption)).
% 1.55/1.28 tff(1008,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1009,plain,
% 1.55/1.28 ((hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105))) <=> (hskp20 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1010,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[1009])).
% 1.55/1.28 tff(1011,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[1010, 1008])).
% 1.55/1.28 tff(1012,plain,
% 1.55/1.28 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(1013,plain,
% 1.55/1.28 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 1.55/1.28 tff(1014,plain,
% 1.55/1.28 (hskp20 | (~c0_1(a1127))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1013, 113, 1007, 992, 1006, 669, 1005, 995])).
% 1.55/1.28 tff(1015,plain,
% 1.55/1.28 (~c0_1(a1127)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1014, 703])).
% 1.55/1.28 tff(1016,assumption,(~c2_1(a1104)), introduced(assumption)).
% 1.55/1.28 tff(1017,assumption,(c0_1(a1104)), introduced(assumption)).
% 1.55/1.28 tff(1018,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c0_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c0_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1105)) | (~c2_1(a1105)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1019,plain,
% 1.55/1.28 ((hskp20 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105))) <=> (hskp20 | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c0_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1105)) | (~c2_1(a1105)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1020,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c0_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1105)) | (~c2_1(a1105))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[1019])).
% 1.55/1.28 tff(1021,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c0_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1105)) | (~c2_1(a1105)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[1020, 1018])).
% 1.55/1.28 tff(1022,plain,
% 1.55/1.28 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(1023,plain,
% 1.55/1.28 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1105) | c2_1(a1104) | (~ndr1_0) | (~c0_1(a1104)) | (~c3_1(a1104)) | (~c0_1(a1105)) | (~c2_1(a1105))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 1.55/1.28 tff(1024,plain,
% 1.55/1.28 (hskp20 | (~c3_1(a1104))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1023, 113, 992, 1017, 669, 1016, 1005, 995])).
% 1.55/1.28 tff(1025,plain,
% 1.55/1.28 (~c3_1(a1104)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1024, 703])).
% 1.55/1.28 tff(1026,assumption,(c1_1(a1104)), introduced(assumption)).
% 1.55/1.28 tff(1027,assumption,(c1_1(a1127)), introduced(assumption)).
% 1.55/1.28 tff(1028,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1029,plain,
% 1.55/1.29 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c0_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127))) <=> ((~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1030,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c0_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127))))),
% 1.55/1.29 inference(monotonicity,[status(thm)],[1029])).
% 1.55/1.29 tff(1031,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c0_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.55/1.29 inference(transitivity,[status(thm)],[1030, 1028])).
% 1.55/1.29 tff(1032,plain,
% 1.55/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c0_1(a1127) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(1033,plain,
% 1.55/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c3_1(a1104) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1032, 1031])).
% 1.55/1.29 tff(1034,plain,
% 1.55/1.29 ($false),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1033, 113, 769, 768, 739, 1027, 1007, 1017, 1026, 45, 1025, 1015])).
% 1.55/1.29 tff(1035,plain,(hskp20 | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c0_1(a1104)) | (~c1_1(a1104)) | (~c0_1(a1105)) | c2_1(a1127) | c1_1(a1105) | (~c2_1(a1105)) | c2_1(a1104)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.29 tff(1036,plain,
% 1.55/1.29 (hskp20),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1035, 994, 768, 739, 769, 993, 964, 963, 992, 991, 669, 972, 962])).
% 1.55/1.29 tff(1037,plain,
% 1.55/1.29 (~c3_1(a1130)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[332, 1036])).
% 1.55/1.29 tff(1038,plain,
% 1.55/1.29 (~c0_1(a1130)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[326, 1036])).
% 1.55/1.29 tff(1039,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1130)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1130)) | (~c0_1(a1147)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1040,plain,
% 1.55/1.29 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130))) <=> (c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1130)) | (~c0_1(a1147)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1041,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1130)) | (~c0_1(a1147))))),
% 1.55/1.29 inference(monotonicity,[status(thm)],[1040])).
% 1.55/1.29 tff(1042,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1130)) | (~c0_1(a1147)))),
% 1.55/1.29 inference(transitivity,[status(thm)],[1041, 1039])).
% 1.55/1.29 tff(1043,plain,
% 1.55/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(1044,plain,
% 1.55/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1130)) | (~c0_1(a1147))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 1.55/1.29 tff(1045,plain,
% 1.55/1.29 (~c1_1(a1130)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1044, 113, 768, 739, 767, 804, 756, 1038, 1037, 344, 798])).
% 1.55/1.29 tff(1046,plain,
% 1.55/1.29 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.55/1.29 inference(bind,[status(th)],[])).
% 1.55/1.29 tff(1047,plain,
% 1.55/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.29 inference(quant_intro,[status(thm)],[1046])).
% 1.55/1.29 tff(1048,plain,
% 1.55/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1049,plain,
% 1.55/1.29 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.55/1.29 inference(bind,[status(th)],[])).
% 1.55/1.29 tff(1050,plain,
% 1.55/1.29 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.29 inference(quant_intro,[status(thm)],[1049])).
% 1.55/1.29 tff(1051,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 1.55/1.29 tff(1052,plain,
% 1.55/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 1.55/1.29 tff(1053,plain,
% 1.55/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1052, 1048])).
% 1.55/1.29 tff(1054,plain,(
% 1.55/1.29 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.29 inference(skolemize,[status(sab)],[1053])).
% 1.55/1.29 tff(1055,plain,
% 1.55/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1054, 1047])).
% 1.55/1.29 tff(1056,plain,
% 1.55/1.29 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.55/1.29 inference(bind,[status(th)],[])).
% 1.55/1.29 tff(1057,plain,
% 1.55/1.29 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.29 inference(quant_intro,[status(thm)],[1056])).
% 1.55/1.29 tff(1058,plain,
% 1.55/1.29 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1059,plain,
% 1.55/1.29 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp2) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp2))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.55/1.29 inference(bind,[status(th)],[])).
% 1.55/1.29 tff(1060,plain,
% 1.55/1.29 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.29 inference(quant_intro,[status(thm)],[1059])).
% 1.55/1.29 tff(1061,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 1.55/1.29 tff(1062,plain,
% 1.55/1.29 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 1.55/1.29 tff(1063,plain,
% 1.55/1.29 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1062, 1058])).
% 1.55/1.29 tff(1064,plain,(
% 1.55/1.29 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.29 inference(skolemize,[status(sab)],[1063])).
% 1.55/1.29 tff(1065,plain,
% 1.55/1.29 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1064, 1057])).
% 1.55/1.29 tff(1066,plain,
% 1.55/1.29 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1067,plain,
% 1.55/1.29 ((hskp2 | (~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))) <=> (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1068,plain,
% 1.55/1.29 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105))))),
% 1.55/1.29 inference(monotonicity,[status(thm)],[1067])).
% 1.55/1.29 tff(1069,plain,
% 1.55/1.29 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.55/1.29 inference(transitivity,[status(thm)],[1068, 1066])).
% 1.55/1.29 tff(1070,plain,
% 1.55/1.29 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(1071,plain,
% 1.55/1.29 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 1.55/1.29 tff(1072,plain,
% 1.55/1.29 (hskp2 | (~c2_1(a1105))),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1071, 113, 992, 965, 669, 1065])).
% 1.55/1.29 tff(1073,plain,
% 1.55/1.29 (hskp2),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1072, 972])).
% 1.55/1.29 tff(1074,plain,
% 1.55/1.29 (~c3_1(a1100)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[291, 1073])).
% 1.55/1.29 tff(1075,plain,
% 1.55/1.29 (c2_1(a1100)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[302, 1073])).
% 1.55/1.29 tff(1076,plain,
% 1.55/1.29 (c0_1(a1100)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[313, 1073])).
% 1.55/1.29 tff(1077,plain,
% 1.55/1.29 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1130))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1078,plain,
% 1.55/1.29 ((hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130)) <=> (hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1130))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1079,plain,
% 1.55/1.29 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1130)))),
% 1.55/1.29 inference(monotonicity,[status(thm)],[1078])).
% 1.55/1.29 tff(1080,plain,
% 1.55/1.29 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1130))),
% 1.55/1.29 inference(transitivity,[status(thm)],[1079, 1077])).
% 1.55/1.29 tff(1081,plain,
% 1.55/1.29 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(1082,plain,
% 1.55/1.29 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1130)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 1.55/1.29 tff(1083,plain,
% 1.55/1.29 (hskp3),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1082, 113, 1076, 1075, 1038, 1037, 1074, 1055, 1045])).
% 1.55/1.29 tff(1084,plain,
% 1.55/1.29 (((~hskp3) | (~c3_1(a1101))) <=> ((~hskp3) | (~c3_1(a1101)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1085,plain,
% 1.55/1.29 (((~c3_1(a1101)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a1101)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1086,axiom,((~c3_1(a1101)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.55/1.29 tff(1087,plain,
% 1.55/1.29 ((~hskp3) | (~c3_1(a1101))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 1.55/1.29 tff(1088,plain,
% 1.55/1.29 ((~hskp3) | (~c3_1(a1101))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1087, 1084])).
% 1.55/1.29 tff(1089,plain,
% 1.55/1.29 (~c3_1(a1101)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1088, 1083])).
% 1.55/1.29 tff(1090,plain,
% 1.55/1.29 (((~hskp3) | c2_1(a1101)) <=> ((~hskp3) | c2_1(a1101))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1091,axiom,((~hskp3) | c2_1(a1101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.55/1.29 tff(1092,plain,
% 1.55/1.29 ((~hskp3) | c2_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 1.55/1.29 tff(1093,plain,
% 1.55/1.29 ((~hskp3) | c2_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1092, 1090])).
% 1.55/1.29 tff(1094,plain,
% 1.55/1.29 ((~hskp3) | c2_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1093, 1090])).
% 1.55/1.29 tff(1095,plain,
% 1.55/1.29 ((~hskp3) | c2_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1094, 1090])).
% 1.55/1.29 tff(1096,plain,
% 1.55/1.29 ((~hskp3) | c2_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1095, 1090])).
% 1.55/1.29 tff(1097,plain,
% 1.55/1.29 ((~hskp3) | c2_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1096, 1090])).
% 1.55/1.29 tff(1098,plain,
% 1.55/1.29 ((~hskp3) | c2_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1097, 1090])).
% 1.55/1.29 tff(1099,plain,
% 1.55/1.29 ((~hskp3) | c2_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1098, 1090])).
% 1.55/1.29 tff(1100,plain,
% 1.55/1.29 (c2_1(a1101)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1099, 1083])).
% 1.55/1.29 tff(1101,plain,
% 1.55/1.29 (((~hskp3) | c1_1(a1101)) <=> ((~hskp3) | c1_1(a1101))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1102,axiom,((~hskp3) | c1_1(a1101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.55/1.29 tff(1103,plain,
% 1.55/1.29 ((~hskp3) | c1_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 1.55/1.29 tff(1104,plain,
% 1.55/1.29 ((~hskp3) | c1_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1103, 1101])).
% 1.55/1.29 tff(1105,plain,
% 1.55/1.29 ((~hskp3) | c1_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1104, 1101])).
% 1.55/1.29 tff(1106,plain,
% 1.55/1.29 ((~hskp3) | c1_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1105, 1101])).
% 1.55/1.29 tff(1107,plain,
% 1.55/1.29 ((~hskp3) | c1_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1106, 1101])).
% 1.55/1.29 tff(1108,plain,
% 1.55/1.29 ((~hskp3) | c1_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1107, 1101])).
% 1.55/1.29 tff(1109,plain,
% 1.55/1.29 ((~hskp3) | c1_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1108, 1101])).
% 1.55/1.29 tff(1110,plain,
% 1.55/1.29 ((~hskp3) | c1_1(a1101)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1109, 1101])).
% 1.55/1.29 tff(1111,plain,
% 1.55/1.29 (c1_1(a1101)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1110, 1083])).
% 1.55/1.29 tff(1112,plain,
% 1.55/1.29 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | c1_1(a1105) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c1_1(a1105) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1105)) | (~c2_1(a1105)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1113,plain,
% 1.55/1.29 ((hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105))) <=> (hskp24 | c1_1(a1105) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1105)) | (~c2_1(a1105)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1114,plain,
% 1.55/1.29 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | c1_1(a1105) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1105)) | (~c2_1(a1105))))),
% 1.55/1.29 inference(monotonicity,[status(thm)],[1113])).
% 1.55/1.29 tff(1115,plain,
% 1.55/1.29 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c1_1(a1105) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1105)) | (~c2_1(a1105)))),
% 1.55/1.29 inference(transitivity,[status(thm)],[1114, 1112])).
% 1.55/1.29 tff(1116,plain,
% 1.55/1.29 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(1117,plain,
% 1.55/1.29 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c1_1(a1105) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1105)) | (~c2_1(a1105))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 1.55/1.29 tff(1118,plain,
% 1.55/1.29 (hskp24),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1117, 113, 992, 1111, 1100, 669, 1089, 982, 972])).
% 1.55/1.29 tff(1119,plain,
% 1.55/1.29 (~c0_1(a1149)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[861, 1118])).
% 1.55/1.29 tff(1120,plain,
% 1.55/1.29 (c2_1(a1149)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[883, 1118])).
% 1.55/1.29 tff(1121,plain,
% 1.55/1.29 (c3_1(a1149)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[872, 1118])).
% 1.55/1.29 tff(1122,plain,
% 1.55/1.29 ($false),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[934, 1121, 1120, 839, 990, 1119])).
% 1.55/1.29 tff(1123,plain,(hskp29 | (~c0_1(a1105)) | c1_1(a1105) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | hskp14 | (~c3_1(a1105))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.29 tff(1124,plain,
% 1.55/1.29 (hskp29),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1123, 692, 634, 738, 727, 691, 716, 715])).
% 1.55/1.29 tff(1125,plain,
% 1.55/1.29 (c3_1(a1116)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[201, 1124])).
% 1.55/1.29 tff(1126,plain,
% 1.55/1.29 (c2_1(a1116)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[212, 1124])).
% 1.55/1.29 tff(1127,plain,
% 1.55/1.29 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | c1_1(a1116))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | c1_1(a1116))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1128,plain,
% 1.55/1.30 ((hskp14 | hskp19 | (~ndr1_0) | c1_1(a1116) | (~c3_1(a1116)) | (~c2_1(a1116))) <=> (hskp14 | hskp19 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | c1_1(a1116))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1129,plain,
% 1.55/1.30 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1116) | (~c3_1(a1116)) | (~c2_1(a1116)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | c1_1(a1116)))),
% 1.55/1.30 inference(monotonicity,[status(thm)],[1128])).
% 1.55/1.30 tff(1130,plain,
% 1.55/1.30 (((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1116) | (~c3_1(a1116)) | (~c2_1(a1116)))) <=> ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | c1_1(a1116))),
% 1.55/1.30 inference(transitivity,[status(thm)],[1129, 1127])).
% 1.55/1.30 tff(1131,plain,
% 1.55/1.30 ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp19 | (~ndr1_0) | c1_1(a1116) | (~c3_1(a1116)) | (~c2_1(a1116)))),
% 1.55/1.30 inference(quant_inst,[status(thm)],[])).
% 1.55/1.30 tff(1132,plain,
% 1.55/1.30 ((~![U: $i] : (hskp14 | hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp19 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | c1_1(a1116)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 1.55/1.30 tff(1133,plain,
% 1.55/1.30 (hskp19 | c1_1(a1116)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1132, 692, 113, 1126, 1125, 714])).
% 1.55/1.30 tff(1134,plain,
% 1.55/1.30 (c1_1(a1116)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1133, 704])).
% 1.55/1.30 tff(1135,plain,
% 1.55/1.30 (hskp14 | hskp19 | (~c2_1(a1105))),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[988, 113, 715, 634, 714])).
% 1.55/1.30 tff(1136,plain,
% 1.55/1.30 (~c2_1(a1105)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1135, 704, 692])).
% 1.55/1.30 tff(1137,plain,
% 1.55/1.30 (c0_1(a1116)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[223, 1124])).
% 1.55/1.30 tff(1138,plain,
% 1.55/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1139,plain,
% 1.55/1.30 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105))) <=> (c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1140,plain,
% 1.55/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.55/1.30 inference(monotonicity,[status(thm)],[1139])).
% 1.55/1.30 tff(1141,plain,
% 1.55/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.55/1.30 inference(transitivity,[status(thm)],[1140, 1138])).
% 1.55/1.30 tff(1142,plain,
% 1.55/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.55/1.30 inference(quant_inst,[status(thm)],[])).
% 1.55/1.30 tff(1143,plain,
% 1.55/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 1.55/1.30 tff(1144,plain,
% 1.55/1.30 (c2_1(a1105) | (~c1_1(a1147))),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1143, 113, 1137, 1126, 1125, 767, 715, 804, 634, 246])).
% 1.55/1.30 tff(1145,plain,
% 1.55/1.30 (~c1_1(a1147)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1144, 1136])).
% 1.55/1.30 tff(1146,plain,
% 1.55/1.30 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.55/1.30 inference(bind,[status(th)],[])).
% 1.55/1.30 tff(1147,plain,
% 1.55/1.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.30 inference(quant_intro,[status(thm)],[1146])).
% 1.55/1.30 tff(1148,plain,
% 1.55/1.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1149,plain,
% 1.55/1.30 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_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)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.55/1.30 inference(bind,[status(th)],[])).
% 1.55/1.30 tff(1150,plain,
% 1.55/1.30 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.30 inference(quant_intro,[status(thm)],[1149])).
% 1.55/1.30 tff(1151,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 1.55/1.30 tff(1152,plain,
% 1.55/1.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 1.55/1.30 tff(1153,plain,
% 1.55/1.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1152, 1148])).
% 1.55/1.30 tff(1154,plain,(
% 1.55/1.30 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.30 inference(skolemize,[status(sab)],[1153])).
% 1.55/1.30 tff(1155,plain,
% 1.55/1.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1154, 1147])).
% 1.55/1.30 tff(1156,plain,
% 1.55/1.30 (^[U: $i] : refl((hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 1.55/1.30 inference(bind,[status(th)],[])).
% 1.55/1.30 tff(1157,plain,
% 1.55/1.30 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(quant_intro,[status(thm)],[1156])).
% 1.55/1.30 tff(1158,plain,
% 1.55/1.30 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1159,plain,
% 1.55/1.30 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp8))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp8) <=> (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8) <=> (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 1.55/1.30 inference(bind,[status(th)],[])).
% 1.55/1.30 tff(1160,plain,
% 1.55/1.30 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8) <=> ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(quant_intro,[status(thm)],[1159])).
% 1.55/1.30 tff(1161,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.55/1.30 tff(1162,plain,
% 1.55/1.30 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 1.55/1.30 tff(1163,plain,
% 1.55/1.30 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1162, 1158])).
% 1.55/1.30 tff(1164,plain,(
% 1.55/1.30 ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(skolemize,[status(sab)],[1163])).
% 1.55/1.30 tff(1165,plain,
% 1.55/1.30 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1164, 1157])).
% 1.55/1.30 tff(1166,plain,
% 1.55/1.30 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp8 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1167,plain,
% 1.55/1.30 ((hskp19 | hskp8 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098)) <=> (hskp19 | hskp8 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1168,plain,
% 1.55/1.30 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0)))),
% 1.55/1.30 inference(monotonicity,[status(thm)],[1167])).
% 1.55/1.30 tff(1169,plain,
% 1.55/1.30 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp8 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0))),
% 1.55/1.30 inference(transitivity,[status(thm)],[1168, 1166])).
% 1.55/1.30 tff(1170,plain,
% 1.55/1.30 ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | (~ndr1_0) | c3_1(a1098) | c2_1(a1098) | c1_1(a1098))),
% 1.55/1.30 inference(quant_inst,[status(thm)],[])).
% 1.55/1.30 tff(1171,plain,
% 1.55/1.30 ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp8 | c1_1(a1098) | c2_1(a1098) | c3_1(a1098) | (~ndr1_0)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 1.55/1.30 tff(1172,plain,
% 1.55/1.30 (hskp19 | hskp8 | c2_1(a1098) | c3_1(a1098)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1171, 113, 34, 1165])).
% 1.55/1.30 tff(1173,plain,
% 1.55/1.30 (hskp8),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1172, 704, 35, 47])).
% 1.55/1.30 tff(1174,assumption,(hskp8), introduced(assumption)).
% 1.55/1.30 tff(1175,plain,
% 1.55/1.30 (((~hskp8) | (~c1_1(a1107))) <=> ((~hskp8) | (~c1_1(a1107)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1176,plain,
% 1.55/1.30 (((~c1_1(a1107)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a1107)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1177,axiom,((~c1_1(a1107)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.55/1.30 tff(1178,plain,
% 1.55/1.30 ((~hskp8) | (~c1_1(a1107))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 1.55/1.30 tff(1179,plain,
% 1.55/1.30 ((~hskp8) | (~c1_1(a1107))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1178, 1175])).
% 1.55/1.30 tff(1180,plain,
% 1.55/1.30 (~c1_1(a1107)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1179, 1174])).
% 1.55/1.30 tff(1181,plain,
% 1.55/1.30 (((~hskp8) | (~c0_1(a1107))) <=> ((~hskp8) | (~c0_1(a1107)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1182,plain,
% 1.55/1.30 (((~c0_1(a1107)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a1107)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1183,axiom,((~c0_1(a1107)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.55/1.30 tff(1184,plain,
% 1.55/1.30 ((~hskp8) | (~c0_1(a1107))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 1.55/1.30 tff(1185,plain,
% 1.55/1.30 ((~hskp8) | (~c0_1(a1107))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1184, 1181])).
% 1.55/1.30 tff(1186,plain,
% 1.55/1.30 (~c0_1(a1107)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1185, 1174])).
% 1.55/1.30 tff(1187,plain,
% 1.55/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1188,plain,
% 1.55/1.30 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107))) <=> (c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1189,plain,
% 1.55/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107))))),
% 1.55/1.30 inference(monotonicity,[status(thm)],[1188])).
% 1.55/1.30 tff(1190,plain,
% 1.55/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))),
% 1.55/1.30 inference(transitivity,[status(thm)],[1189, 1187])).
% 1.55/1.30 tff(1191,plain,
% 1.55/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107)))),
% 1.55/1.30 inference(quant_inst,[status(thm)],[])).
% 1.55/1.30 tff(1192,plain,
% 1.55/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 1.55/1.30 tff(1193,plain,
% 1.55/1.30 (~c2_1(a1107)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1192, 113, 249, 248, 247, 992, 965, 1186, 1180, 669, 702])).
% 1.55/1.30 tff(1194,plain,
% 1.55/1.30 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.55/1.30 inference(bind,[status(th)],[])).
% 1.55/1.30 tff(1195,plain,
% 1.55/1.30 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.30 inference(quant_intro,[status(thm)],[1194])).
% 1.55/1.30 tff(1196,plain,
% 1.55/1.30 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1197,plain,
% 1.55/1.30 (^[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(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.55/1.30 inference(bind,[status(th)],[])).
% 1.55/1.30 tff(1198,plain,
% 1.55/1.30 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.30 inference(quant_intro,[status(thm)],[1197])).
% 1.55/1.30 tff(1199,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.55/1.30 tff(1200,plain,
% 1.55/1.30 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1199, 1198])).
% 1.55/1.30 tff(1201,plain,
% 1.55/1.30 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1200, 1196])).
% 1.55/1.30 tff(1202,plain,(
% 1.55/1.30 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.30 inference(skolemize,[status(sab)],[1201])).
% 1.55/1.30 tff(1203,plain,
% 1.55/1.30 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1202, 1195])).
% 1.55/1.30 tff(1204,plain,
% 1.55/1.30 (((~hskp8) | c3_1(a1107)) <=> ((~hskp8) | c3_1(a1107))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1205,axiom,((~hskp8) | c3_1(a1107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.55/1.30 tff(1206,plain,
% 1.55/1.30 ((~hskp8) | c3_1(a1107)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 1.55/1.30 tff(1207,plain,
% 1.55/1.30 ((~hskp8) | c3_1(a1107)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1206, 1204])).
% 1.55/1.30 tff(1208,plain,
% 1.55/1.30 ((~hskp8) | c3_1(a1107)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1207, 1204])).
% 1.55/1.30 tff(1209,plain,
% 1.55/1.30 ((~hskp8) | c3_1(a1107)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1208, 1204])).
% 1.55/1.30 tff(1210,plain,
% 1.55/1.30 ((~hskp8) | c3_1(a1107)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1209, 1204])).
% 1.55/1.30 tff(1211,plain,
% 1.55/1.30 ((~hskp8) | c3_1(a1107)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1210, 1204])).
% 1.55/1.30 tff(1212,plain,
% 1.55/1.30 ((~hskp8) | c3_1(a1107)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1211, 1204])).
% 1.55/1.30 tff(1213,plain,
% 1.55/1.30 ((~hskp8) | c3_1(a1107)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1212, 1204])).
% 1.55/1.30 tff(1214,plain,
% 1.55/1.30 (c3_1(a1107)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1213, 1174])).
% 1.55/1.30 tff(1215,assumption,(~hskp13), introduced(assumption)).
% 1.55/1.30 tff(1216,plain,
% 1.55/1.30 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1217,plain,
% 1.55/1.30 ((hskp13 | (~ndr1_0) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c0_1(a1107) | (~c3_1(a1107))) <=> (hskp13 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1218,plain,
% 1.55/1.30 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c0_1(a1107) | (~c3_1(a1107)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107))))),
% 1.55/1.30 inference(monotonicity,[status(thm)],[1217])).
% 1.55/1.30 tff(1219,plain,
% 1.55/1.30 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c0_1(a1107) | (~c3_1(a1107)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.55/1.30 inference(transitivity,[status(thm)],[1218, 1216])).
% 1.55/1.30 tff(1220,plain,
% 1.55/1.30 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c0_1(a1107) | (~c3_1(a1107)))),
% 1.55/1.30 inference(quant_inst,[status(thm)],[])).
% 1.55/1.30 tff(1221,plain,
% 1.55/1.30 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 1.55/1.30 tff(1222,plain,
% 1.55/1.30 ($false),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1221, 113, 1215, 1214, 1186, 1180, 1203, 1193])).
% 1.55/1.30 tff(1223,plain,((~hskp8) | hskp13 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.30 tff(1224,plain,
% 1.55/1.30 (hskp13),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1223, 1173, 1137, 1126, 1125, 716, 715, 634])).
% 1.55/1.30 tff(1225,plain,
% 1.55/1.30 (((~hskp13) | (~c1_1(a1115))) <=> ((~hskp13) | (~c1_1(a1115)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1226,plain,
% 1.55/1.30 (((~c1_1(a1115)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1115)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1227,axiom,((~c1_1(a1115)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.55/1.30 tff(1228,plain,
% 1.55/1.30 ((~hskp13) | (~c1_1(a1115))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 1.55/1.30 tff(1229,plain,
% 1.55/1.30 ((~hskp13) | (~c1_1(a1115))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1228, 1225])).
% 1.55/1.30 tff(1230,plain,
% 1.55/1.30 (~c1_1(a1115)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1229, 1224])).
% 1.55/1.30 tff(1231,plain,
% 1.55/1.30 (((~hskp13) | c2_1(a1115)) <=> ((~hskp13) | c2_1(a1115))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1232,axiom,((~hskp13) | c2_1(a1115)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.55/1.30 tff(1233,plain,
% 1.55/1.30 ((~hskp13) | c2_1(a1115)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 1.55/1.30 tff(1234,plain,
% 1.55/1.30 ((~hskp13) | c2_1(a1115)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1233, 1231])).
% 1.55/1.30 tff(1235,plain,
% 1.55/1.30 ((~hskp13) | c2_1(a1115)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1234, 1231])).
% 1.55/1.30 tff(1236,plain,
% 1.55/1.30 ((~hskp13) | c2_1(a1115)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1235, 1231])).
% 1.55/1.30 tff(1237,plain,
% 1.55/1.30 ((~hskp13) | c2_1(a1115)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1236, 1231])).
% 1.55/1.30 tff(1238,plain,
% 1.55/1.30 ((~hskp13) | c2_1(a1115)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1237, 1231])).
% 1.55/1.30 tff(1239,plain,
% 1.55/1.30 ((~hskp13) | c2_1(a1115)),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1238, 1231])).
% 1.55/1.31 tff(1240,plain,
% 1.55/1.31 ((~hskp13) | c2_1(a1115)),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1239, 1231])).
% 1.55/1.31 tff(1241,plain,
% 1.55/1.31 (c2_1(a1115)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1240, 1224])).
% 1.55/1.31 tff(1242,plain,
% 1.55/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c1_1(a1116)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c1_1(a1116)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1243,plain,
% 1.55/1.31 (((~ndr1_0) | (~c1_1(a1116)) | (~c3_1(a1116)) | (~c2_1(a1116)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115))) <=> (c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c1_1(a1116)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1244,plain,
% 1.55/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1116)) | (~c3_1(a1116)) | (~c2_1(a1116)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c1_1(a1116)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.55/1.31 inference(monotonicity,[status(thm)],[1243])).
% 1.55/1.31 tff(1245,plain,
% 1.55/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1116)) | (~c3_1(a1116)) | (~c2_1(a1116)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c1_1(a1116)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.55/1.31 inference(transitivity,[status(thm)],[1244, 1242])).
% 1.55/1.31 tff(1246,plain,
% 1.55/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1116)) | (~c3_1(a1116)) | (~c2_1(a1116)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.55/1.31 inference(quant_inst,[status(thm)],[])).
% 1.55/1.31 tff(1247,plain,
% 1.55/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c1_1(a1116)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 1.55/1.31 tff(1248,plain,
% 1.55/1.31 (c0_1(a1115)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1247, 113, 1126, 1125, 767, 1241, 804, 1230, 1155, 1145, 1134])).
% 1.55/1.31 tff(1249,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1115)) | (~c2_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1250,plain,
% 1.55/1.31 ((hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115))) <=> (hskp20 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1251,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1115)) | (~c2_1(a1115))))),
% 1.55/1.31 inference(monotonicity,[status(thm)],[1250])).
% 1.55/1.31 tff(1252,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.55/1.31 inference(transitivity,[status(thm)],[1251, 1249])).
% 1.55/1.31 tff(1253,plain,
% 1.55/1.31 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))),
% 1.55/1.31 inference(quant_inst,[status(thm)],[])).
% 1.55/1.31 tff(1254,plain,
% 1.55/1.31 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1115)) | (~c2_1(a1115))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 1.55/1.31 tff(1255,plain,
% 1.55/1.31 ($false),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1254, 113, 703, 1241, 716, 715, 1230, 1005, 1136, 1248])).
% 1.55/1.31 tff(1256,plain,(hskp19 | hskp20 | hskp14 | c2_1(a1098) | c3_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.31 tff(1257,plain,
% 1.55/1.31 (hskp19),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1256, 703, 692, 35, 47, 34])).
% 1.55/1.31 tff(1258,plain,
% 1.55/1.31 (~c2_1(a1127)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[900, 1257])).
% 1.55/1.31 tff(1259,plain,
% 1.55/1.31 (c3_1(a1127)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[912, 1257])).
% 1.55/1.31 tff(1260,plain,
% 1.55/1.31 (c1_1(a1127)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[923, 1257])).
% 1.55/1.31 tff(1261,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1262,plain,
% 1.55/1.31 ((hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127))) <=> (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1263,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1127)) | (~c3_1(a1127))))),
% 1.55/1.31 inference(monotonicity,[status(thm)],[1262])).
% 1.55/1.31 tff(1264,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.55/1.31 inference(transitivity,[status(thm)],[1263, 1261])).
% 1.55/1.31 tff(1265,plain,
% 1.55/1.31 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))),
% 1.55/1.31 inference(quant_inst,[status(thm)],[])).
% 1.55/1.31 tff(1266,plain,
% 1.55/1.31 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1127)) | (~c3_1(a1127))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 1.55/1.31 tff(1267,plain,
% 1.55/1.31 (hskp2),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1266, 113, 1137, 1126, 1125, 1260, 1259, 1258, 278])).
% 1.55/1.31 tff(1268,plain,
% 1.55/1.31 (~c3_1(a1100)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[291, 1267])).
% 1.55/1.31 tff(1269,assumption,(~hskp5), introduced(assumption)).
% 1.55/1.31 tff(1270,plain,
% 1.55/1.31 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.55/1.31 inference(bind,[status(th)],[])).
% 1.55/1.31 tff(1271,plain,
% 1.55/1.31 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.55/1.31 inference(quant_intro,[status(thm)],[1270])).
% 1.55/1.31 tff(1272,plain,
% 1.55/1.31 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1273,plain,
% 1.55/1.31 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.55/1.31 inference(bind,[status(th)],[])).
% 1.55/1.31 tff(1274,plain,
% 1.55/1.31 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.55/1.31 inference(quant_intro,[status(thm)],[1273])).
% 1.55/1.31 tff(1275,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 1.55/1.31 tff(1276,plain,
% 1.55/1.31 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1275, 1274])).
% 1.55/1.31 tff(1277,plain,
% 1.55/1.31 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1276, 1272])).
% 1.55/1.31 tff(1278,plain,(
% 1.55/1.31 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.55/1.31 inference(skolemize,[status(sab)],[1277])).
% 1.55/1.31 tff(1279,plain,
% 1.55/1.31 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1278, 1271])).
% 1.55/1.31 tff(1280,plain,
% 1.55/1.31 (hskp2),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1266, 113, 249, 248, 247, 924, 913, 901, 278])).
% 1.55/1.31 tff(1281,plain,
% 1.55/1.31 (~c3_1(a1100)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[291, 1280])).
% 1.55/1.31 tff(1282,plain,
% 1.55/1.31 (c2_1(a1100)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[302, 1280])).
% 1.55/1.31 tff(1283,plain,
% 1.55/1.31 (c0_1(a1100)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[313, 1280])).
% 1.55/1.31 tff(1284,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c2_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1285,plain,
% 1.55/1.31 ((hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100))) <=> (hskp5 | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1286,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c2_1(a1100))))),
% 1.55/1.31 inference(monotonicity,[status(thm)],[1285])).
% 1.55/1.31 tff(1287,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.55/1.31 inference(transitivity,[status(thm)],[1286, 1284])).
% 1.55/1.31 tff(1288,plain,
% 1.55/1.31 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)))),
% 1.55/1.31 inference(quant_inst,[status(thm)],[])).
% 1.55/1.31 tff(1289,plain,
% 1.55/1.31 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c2_1(a1100))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 1.55/1.31 tff(1290,plain,
% 1.55/1.31 (~c1_1(a1100)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1289, 113, 1269, 1283, 1282, 1281, 1279])).
% 1.55/1.31 tff(1291,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1127) | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c0_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1292,plain,
% 1.55/1.31 ((hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100))) <=> (hskp20 | c2_1(a1127) | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1293,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1127) | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c0_1(a1127)) | (~c3_1(a1127))))),
% 1.55/1.31 inference(monotonicity,[status(thm)],[1292])).
% 1.55/1.31 tff(1294,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.55/1.31 inference(transitivity,[status(thm)],[1293, 1291])).
% 1.55/1.31 tff(1295,plain,
% 1.55/1.31 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))),
% 1.55/1.31 inference(quant_inst,[status(thm)],[])).
% 1.55/1.31 tff(1296,plain,
% 1.55/1.31 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c0_1(a1127)) | (~c3_1(a1127))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 1.55/1.31 tff(1297,plain,
% 1.55/1.31 (~c0_1(a1127)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1296, 113, 703, 913, 1283, 1282, 901, 1005, 1290])).
% 1.55/1.31 tff(1298,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1299,plain,
% 1.55/1.31 ((hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127))) <=> (hskp20 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1300,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127))))),
% 1.55/1.31 inference(monotonicity,[status(thm)],[1299])).
% 1.55/1.31 tff(1301,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.55/1.31 inference(transitivity,[status(thm)],[1300, 1298])).
% 1.55/1.31 tff(1302,plain,
% 1.55/1.31 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))),
% 1.55/1.31 inference(quant_inst,[status(thm)],[])).
% 1.55/1.31 tff(1303,plain,
% 1.55/1.31 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 1.55/1.31 tff(1304,plain,
% 1.55/1.31 ($false),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1303, 113, 703, 924, 913, 1283, 1282, 1281, 268, 1297])).
% 1.55/1.31 tff(1305,plain,((~hskp19) | hskp20 | hskp5 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.31 tff(1306,plain,
% 1.55/1.31 (~hskp19),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1305, 703, 1269, 1137, 1126, 1125])).
% 1.55/1.31 tff(1307,plain,
% 1.55/1.31 (c1_1(a1116)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1133, 1306])).
% 1.55/1.31 tff(1308,plain,
% 1.55/1.31 (~c2_1(a1105)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1135, 1306, 692])).
% 1.55/1.31 tff(1309,plain,
% 1.55/1.31 (~c1_1(a1147)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1144, 1308])).
% 1.55/1.31 tff(1310,plain,
% 1.55/1.31 (hskp8),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1172, 1306, 35, 47])).
% 1.55/1.31 tff(1311,plain,
% 1.55/1.31 (hskp13),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1223, 1310, 1137, 1126, 1125, 716, 715, 634])).
% 1.55/1.31 tff(1312,plain,
% 1.55/1.31 (~c1_1(a1115)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1229, 1311])).
% 1.55/1.31 tff(1313,plain,
% 1.55/1.31 (c2_1(a1115)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1240, 1311])).
% 1.55/1.31 tff(1314,plain,
% 1.55/1.31 (c0_1(a1115)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1247, 113, 1126, 1125, 767, 1313, 804, 1312, 1155, 1309, 1307])).
% 1.55/1.31 tff(1315,plain,
% 1.55/1.31 ($false),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1254, 113, 703, 1313, 716, 715, 1312, 1005, 1308, 1314])).
% 1.55/1.31 tff(1316,plain,(hskp20 | hskp14 | c2_1(a1098) | c3_1(a1098) | c1_1(a1098) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.55/1.31 tff(1317,plain,
% 1.55/1.31 (hskp20),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1316, 1269, 35, 47, 34, 692])).
% 1.55/1.31 tff(1318,plain,
% 1.55/1.31 (~c0_1(a1130)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[326, 1317])).
% 1.55/1.31 tff(1319,plain,
% 1.55/1.31 (~c3_1(a1130)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[332, 1317])).
% 1.55/1.31 tff(1320,plain,
% 1.55/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1130)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1130)) | (~c0_1(a1147)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1321,plain,
% 1.55/1.31 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130))) <=> (c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1130)) | (~c0_1(a1147)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1322,plain,
% 1.55/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1130)) | (~c0_1(a1147))))),
% 1.55/1.31 inference(monotonicity,[status(thm)],[1321])).
% 1.55/1.31 tff(1323,plain,
% 1.55/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1130)) | (~c0_1(a1147)))),
% 1.55/1.31 inference(transitivity,[status(thm)],[1322, 1320])).
% 1.55/1.31 tff(1324,plain,
% 1.55/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))),
% 1.55/1.31 inference(quant_inst,[status(thm)],[])).
% 1.55/1.31 tff(1325,plain,
% 1.55/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1130) | c3_1(a1130) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1130)) | (~c0_1(a1147))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 1.55/1.31 tff(1326,plain,
% 1.55/1.31 (c0_1(a1130) | (~c1_1(a1130))),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1325, 113, 249, 248, 247, 772, 819, 771, 345, 344])).
% 1.55/1.31 tff(1327,plain,
% 1.55/1.31 (~c1_1(a1130)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1326, 334])).
% 1.55/1.31 tff(1328,assumption,(hskp3), introduced(assumption)).
% 1.55/1.31 tff(1329,plain,
% 1.55/1.31 (~c3_1(a1101)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1088, 1328])).
% 1.55/1.31 tff(1330,plain,
% 1.55/1.31 (c1_1(a1101)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1110, 1328])).
% 1.55/1.31 tff(1331,plain,
% 1.55/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1101)) | c0_1(a1101) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1101)) | c0_1(a1101) | (~c0_1(a1147)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1332,plain,
% 1.55/1.32 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1101) | c0_1(a1101) | (~c1_1(a1101))) <=> (c2_1(a1147) | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1101)) | c0_1(a1101) | (~c0_1(a1147)))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1333,plain,
% 1.55/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1101) | c0_1(a1101) | (~c1_1(a1101)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1101)) | c0_1(a1101) | (~c0_1(a1147))))),
% 1.55/1.32 inference(monotonicity,[status(thm)],[1332])).
% 1.55/1.32 tff(1334,plain,
% 1.55/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1101) | c0_1(a1101) | (~c1_1(a1101)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1101)) | c0_1(a1101) | (~c0_1(a1147)))),
% 1.55/1.32 inference(transitivity,[status(thm)],[1333, 1331])).
% 1.55/1.32 tff(1335,plain,
% 1.55/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1101) | c0_1(a1101) | (~c1_1(a1101)))),
% 1.55/1.32 inference(quant_inst,[status(thm)],[])).
% 1.55/1.32 tff(1336,plain,
% 1.55/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1101)) | c0_1(a1101) | (~c0_1(a1147))),
% 1.55/1.32 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 1.55/1.32 tff(1337,plain,
% 1.55/1.32 (c0_1(a1101)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1336, 113, 249, 248, 247, 772, 1330, 819, 771, 1329, 344])).
% 1.55/1.32 tff(1338,plain,
% 1.55/1.32 (c2_1(a1101)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1099, 1328])).
% 1.55/1.32 tff(1339,plain,
% 1.55/1.32 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1340,plain,
% 1.55/1.32 ((hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101))) <=> (hskp5 | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1341,plain,
% 1.55/1.32 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101))))),
% 1.55/1.32 inference(monotonicity,[status(thm)],[1340])).
% 1.55/1.32 tff(1342,plain,
% 1.55/1.32 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)))),
% 1.55/1.32 inference(transitivity,[status(thm)],[1341, 1339])).
% 1.55/1.32 tff(1343,plain,
% 1.55/1.32 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)))),
% 1.55/1.32 inference(quant_inst,[status(thm)],[])).
% 1.55/1.32 tff(1344,plain,
% 1.55/1.32 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101))),
% 1.55/1.32 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 1.55/1.32 tff(1345,plain,
% 1.55/1.32 ($false),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1344, 113, 1269, 1330, 1338, 1329, 1279, 1337])).
% 1.55/1.32 tff(1346,plain,((~hskp3) | hskp5 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.32 tff(1347,plain,
% 1.55/1.32 (~hskp3),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1346, 1269, 249, 248, 247, 772, 819, 771])).
% 1.55/1.32 tff(1348,assumption,(~c1_1(a1130)), introduced(assumption)).
% 1.55/1.32 tff(1349,assumption,(hskp13), introduced(assumption)).
% 1.55/1.32 tff(1350,plain,
% 1.55/1.32 (((~hskp13) | (~c3_1(a1115))) <=> ((~hskp13) | (~c3_1(a1115)))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1351,plain,
% 1.55/1.32 (((~c3_1(a1115)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a1115)))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1352,axiom,((~c3_1(a1115)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.55/1.32 tff(1353,plain,
% 1.55/1.32 ((~hskp13) | (~c3_1(a1115))),
% 1.55/1.32 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 1.55/1.32 tff(1354,plain,
% 1.55/1.32 ((~hskp13) | (~c3_1(a1115))),
% 1.55/1.32 inference(modus_ponens,[status(thm)],[1353, 1350])).
% 1.55/1.32 tff(1355,plain,
% 1.55/1.32 (~c3_1(a1115)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1354, 1349])).
% 1.55/1.32 tff(1356,plain,
% 1.55/1.32 (c2_1(a1115)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1240, 1349])).
% 1.55/1.32 tff(1357,assumption,(~hskp3), introduced(assumption)).
% 1.55/1.32 tff(1358,plain,
% 1.55/1.32 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | c1_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | c1_1(a1130))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1359,plain,
% 1.55/1.32 ((hskp3 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130)) <=> (hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | c1_1(a1130))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1360,plain,
% 1.55/1.32 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | c1_1(a1130)))),
% 1.55/1.32 inference(monotonicity,[status(thm)],[1359])).
% 1.55/1.32 tff(1361,plain,
% 1.55/1.32 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | c1_1(a1130))),
% 1.55/1.32 inference(transitivity,[status(thm)],[1360, 1358])).
% 1.55/1.32 tff(1362,plain,
% 1.55/1.32 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c1_1(a1130) | c0_1(a1130) | c3_1(a1130))),
% 1.55/1.32 inference(quant_inst,[status(thm)],[])).
% 1.55/1.32 tff(1363,plain,
% 1.55/1.32 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1130) | c3_1(a1130) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | c1_1(a1130)),
% 1.55/1.32 inference(modus_ponens,[status(thm)],[1362, 1361])).
% 1.55/1.32 tff(1364,plain,
% 1.55/1.32 (~c0_1(a1115)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1363, 113, 1357, 1356, 334, 345, 1355, 1055, 1348])).
% 1.55/1.32 tff(1365,plain,
% 1.55/1.32 (~c1_1(a1115)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1229, 1349])).
% 1.55/1.32 tff(1366,plain,
% 1.55/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1367,plain,
% 1.55/1.32 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115))) <=> (c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1368,plain,
% 1.55/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115))))),
% 1.55/1.32 inference(monotonicity,[status(thm)],[1367])).
% 1.55/1.32 tff(1369,plain,
% 1.55/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.55/1.32 inference(transitivity,[status(thm)],[1368, 1366])).
% 1.55/1.32 tff(1370,plain,
% 1.55/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.55/1.32 inference(quant_inst,[status(thm)],[])).
% 1.55/1.32 tff(1371,plain,
% 1.55/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115))),
% 1.55/1.32 inference(modus_ponens,[status(thm)],[1370, 1369])).
% 1.55/1.32 tff(1372,plain,
% 1.55/1.32 ($false),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1371, 113, 249, 248, 247, 1356, 992, 965, 1365, 669, 702, 1364])).
% 1.55/1.32 tff(1373,plain,((~hskp13) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105) | hskp3 | c0_1(a1130) | c3_1(a1130) | c1_1(a1130)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.32 tff(1374,plain,
% 1.55/1.32 (~hskp13),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1373, 334, 248, 247, 716, 715, 634, 1347, 249, 345, 1327])).
% 1.55/1.32 tff(1375,plain,
% 1.55/1.32 (~hskp8),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1223, 1374, 249, 248, 247, 716, 715, 634])).
% 1.55/1.32 tff(1376,plain,
% 1.55/1.32 (hskp19),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1172, 1375, 35, 47])).
% 1.55/1.32 tff(1377,plain,
% 1.55/1.32 (~c2_1(a1127)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[900, 1376])).
% 1.55/1.32 tff(1378,plain,
% 1.55/1.32 (c3_1(a1127)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[912, 1376])).
% 1.55/1.32 tff(1379,plain,
% 1.55/1.32 (c1_1(a1127)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[923, 1376])).
% 1.55/1.32 tff(1380,plain,
% 1.55/1.32 (hskp2),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1266, 113, 249, 248, 247, 1379, 1378, 1377, 278])).
% 1.55/1.32 tff(1381,plain,
% 1.55/1.32 (~c3_1(a1100)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[291, 1380])).
% 1.55/1.32 tff(1382,plain,
% 1.55/1.32 (c2_1(a1100)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[302, 1380])).
% 1.55/1.32 tff(1383,plain,
% 1.55/1.32 (c0_1(a1100)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[313, 1380])).
% 1.55/1.32 tff(1384,plain,
% 1.55/1.32 (c0_1(a1130) | (~c1_1(a1130))),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1044, 113, 768, 739, 772, 819, 771, 345, 344, 805])).
% 1.55/1.32 tff(1385,plain,
% 1.55/1.32 (~c1_1(a1130)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1384, 334])).
% 1.55/1.32 tff(1386,assumption,(~c3_1(a1100)), introduced(assumption)).
% 1.55/1.32 tff(1387,assumption,(c2_1(a1100)), introduced(assumption)).
% 1.55/1.32 tff(1388,assumption,(c0_1(a1100)), introduced(assumption)).
% 1.55/1.32 tff(1389,plain,
% 1.55/1.32 (hskp3),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1082, 113, 1388, 1387, 334, 345, 1386, 1055, 1385])).
% 1.55/1.32 tff(1390,plain,
% 1.55/1.32 (~c3_1(a1101)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1088, 1389])).
% 1.55/1.32 tff(1391,plain,
% 1.55/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1392,plain,
% 1.55/1.32 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130))) <=> (c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1393,plain,
% 1.55/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130)))),
% 1.55/1.32 inference(monotonicity,[status(thm)],[1392])).
% 1.55/1.32 tff(1394,plain,
% 1.55/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.55/1.32 inference(transitivity,[status(thm)],[1393, 1391])).
% 1.55/1.32 tff(1395,plain,
% 1.55/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130)))),
% 1.55/1.32 inference(quant_inst,[status(thm)],[])).
% 1.55/1.32 tff(1396,plain,
% 1.55/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130)),
% 1.55/1.32 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 1.55/1.32 tff(1397,plain,
% 1.55/1.32 (~c2_1(a1130)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1396, 113, 768, 739, 992, 965, 334, 669, 702, 805, 1385])).
% 1.55/1.32 tff(1398,plain,
% 1.55/1.32 (c2_1(a1101)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1099, 1389])).
% 1.55/1.32 tff(1399,plain,
% 1.55/1.32 (c1_1(a1101)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1110, 1389])).
% 1.55/1.32 tff(1400,plain,
% 1.55/1.32 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1401,plain,
% 1.55/1.32 ((hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130)) <=> (hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1402,plain,
% 1.55/1.32 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101))))),
% 1.55/1.32 inference(monotonicity,[status(thm)],[1401])).
% 1.55/1.32 tff(1403,plain,
% 1.55/1.32 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)))),
% 1.55/1.32 inference(transitivity,[status(thm)],[1402, 1400])).
% 1.55/1.32 tff(1404,plain,
% 1.55/1.32 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))),
% 1.55/1.32 inference(quant_inst,[status(thm)],[])).
% 1.55/1.32 tff(1405,plain,
% 1.55/1.32 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101))),
% 1.55/1.32 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 1.55/1.32 tff(1406,plain,
% 1.55/1.32 ($false),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1405, 113, 1269, 1399, 1398, 334, 1397, 345, 1390, 10])).
% 1.55/1.32 tff(1407,plain,(c0_1(a1130) | hskp5 | c3_1(a1130) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105) | (~c0_1(a1136)) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.32 tff(1408,plain,
% 1.55/1.32 (~c0_1(a1136)),
% 1.55/1.32 inference(unit_resolution,[status(thm)],[1407, 1383, 1269, 345, 1382, 1381, 738, 727, 716, 715, 634, 334, 772, 819, 771])).
% 1.55/1.32 tff(1409,plain,
% 1.55/1.32 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 1.55/1.32 inference(bind,[status(th)],[])).
% 1.55/1.32 tff(1410,plain,
% 1.55/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.55/1.32 inference(quant_intro,[status(thm)],[1409])).
% 1.55/1.32 tff(1411,plain,
% 1.55/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1412,plain,
% 1.55/1.32 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 1.55/1.32 inference(bind,[status(th)],[])).
% 1.55/1.32 tff(1413,plain,
% 1.55/1.32 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.55/1.32 inference(quant_intro,[status(thm)],[1412])).
% 1.55/1.32 tff(1414,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 1.55/1.32 tff(1415,plain,
% 1.55/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.55/1.32 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 1.55/1.32 tff(1416,plain,
% 1.55/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.55/1.32 inference(modus_ponens,[status(thm)],[1415, 1411])).
% 1.55/1.32 tff(1417,plain,(
% 1.55/1.32 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.55/1.32 inference(skolemize,[status(sab)],[1416])).
% 1.55/1.32 tff(1418,plain,
% 1.55/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.55/1.32 inference(modus_ponens,[status(thm)],[1417, 1410])).
% 1.55/1.32 tff(1419,plain,
% 1.55/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.55/1.32 inference(rewrite,[status(thm)],[])).
% 1.55/1.32 tff(1420,plain,
% 1.55/1.32 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130))) <=> (c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.55/1.33 inference(rewrite,[status(thm)],[])).
% 1.55/1.33 tff(1421,plain,
% 1.55/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130)))),
% 1.55/1.33 inference(monotonicity,[status(thm)],[1420])).
% 1.55/1.33 tff(1422,plain,
% 1.55/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.55/1.33 inference(transitivity,[status(thm)],[1421, 1419])).
% 1.55/1.33 tff(1423,plain,
% 1.55/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1130) | c0_1(a1130) | (~c2_1(a1130)))),
% 1.55/1.33 inference(quant_inst,[status(thm)],[])).
% 1.55/1.33 tff(1424,plain,
% 1.55/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1130) | (~c2_1(a1130)) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130)),
% 1.55/1.33 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 1.55/1.33 tff(1425,plain,
% 1.55/1.33 (~c2_1(a1130)),
% 1.55/1.33 inference(unit_resolution,[status(thm)],[1424, 113, 249, 248, 247, 716, 715, 334, 634, 702, 1327])).
% 1.55/1.33 tff(1426,plain,
% 1.55/1.33 (^[U: $i] : refl((hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))),
% 1.55/1.33 inference(bind,[status(th)],[])).
% 1.55/1.33 tff(1427,plain,
% 1.55/1.33 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.33 inference(quant_intro,[status(thm)],[1426])).
% 1.55/1.33 tff(1428,plain,
% 1.55/1.33 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.33 inference(rewrite,[status(thm)],[])).
% 1.55/1.33 tff(1429,plain,
% 1.55/1.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp8) <=> ((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp8))), rewrite(((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp8) <=> (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp8) <=> (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))))),
% 1.55/1.33 inference(bind,[status(th)],[])).
% 1.55/1.33 tff(1430,plain,
% 1.55/1.33 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp8) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.33 inference(quant_intro,[status(thm)],[1429])).
% 1.55/1.33 tff(1431,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 1.55/1.33 tff(1432,plain,
% 1.55/1.33 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.33 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 1.55/1.33 tff(1433,plain,
% 1.55/1.33 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.33 inference(modus_ponens,[status(thm)],[1432, 1428])).
% 1.55/1.33 tff(1434,plain,(
% 1.55/1.33 ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.33 inference(skolemize,[status(sab)],[1433])).
% 1.55/1.33 tff(1435,plain,
% 1.55/1.33 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.55/1.33 inference(modus_ponens,[status(thm)],[1434, 1427])).
% 1.55/1.33 tff(1436,plain,
% 1.55/1.33 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0))),
% 1.55/1.33 inference(rewrite,[status(thm)],[])).
% 1.55/1.33 tff(1437,plain,
% 1.55/1.33 ((hskp8 | hskp6 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c0_1(a1130)) <=> (hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0))),
% 1.55/1.33 inference(rewrite,[status(thm)],[])).
% 1.55/1.33 tff(1438,plain,
% 1.55/1.33 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c0_1(a1130))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0)))),
% 1.55/1.33 inference(monotonicity,[status(thm)],[1437])).
% 1.55/1.33 tff(1439,plain,
% 1.55/1.33 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c0_1(a1130))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0))),
% 1.55/1.33 inference(transitivity,[status(thm)],[1438, 1436])).
% 1.55/1.33 tff(1440,plain,
% 1.55/1.33 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c0_1(a1130))),
% 1.55/1.33 inference(quant_inst,[status(thm)],[])).
% 1.55/1.33 tff(1441,plain,
% 1.55/1.33 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0)),
% 1.55/1.33 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 1.55/1.33 tff(1442,plain,
% 1.55/1.33 (hskp8 | hskp6 | c0_1(a1130) | c2_1(a1130)),
% 1.55/1.33 inference(unit_resolution,[status(thm)],[1441, 113, 345, 1435])).
% 1.55/1.33 tff(1443,plain,
% 1.55/1.33 (hskp6),
% 1.55/1.33 inference(unit_resolution,[status(thm)],[1442, 1375, 334, 1425])).
% 1.55/1.33 tff(1444,plain,
% 1.55/1.33 (~c2_1(a1104)),
% 1.55/1.33 inference(unit_resolution,[status(thm)],[538, 1443])).
% 1.55/1.33 tff(1445,plain,
% 1.55/1.33 (c1_1(a1104)),
% 1.55/1.33 inference(unit_resolution,[status(thm)],[577, 1443])).
% 1.55/1.33 tff(1446,plain,
% 1.55/1.33 (c0_1(a1104)),
% 1.55/1.33 inference(unit_resolution,[status(thm)],[549, 1443])).
% 1.55/1.33 tff(1447,plain,
% 1.55/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a1104) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1104) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(1448,plain,
% 1.64/1.33 (((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136))) <=> (c2_1(a1104) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(1449,plain,
% 1.64/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a1104) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104))))),
% 1.64/1.33 inference(monotonicity,[status(thm)],[1448])).
% 1.64/1.33 tff(1450,plain,
% 1.64/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1104) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104)))),
% 1.64/1.33 inference(transitivity,[status(thm)],[1449, 1447])).
% 1.64/1.33 tff(1451,plain,
% 1.64/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1098) | c3_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))),
% 1.64/1.33 inference(quant_inst,[status(thm)],[])).
% 1.64/1.33 tff(1452,plain,
% 1.64/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1104) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1104)) | (~c0_1(a1104))),
% 1.64/1.33 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 1.64/1.33 tff(1453,plain,
% 1.64/1.33 (~c0_1(a1098)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1452, 113, 691, 738, 1446, 1445, 1444, 34, 47, 1418, 1408])).
% 1.64/1.33 tff(1454,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c3_1(a1100) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c0_1(a1100)) | (~c2_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a1100) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(1455,plain,
% 1.64/1.33 ((hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098)) <=> (hskp3 | c3_1(a1100) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(1456,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c3_1(a1100) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c0_1(a1100)) | (~c2_1(a1100))))),
% 1.64/1.33 inference(monotonicity,[status(thm)],[1455])).
% 1.64/1.33 tff(1457,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a1100) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.64/1.33 inference(transitivity,[status(thm)],[1456, 1454])).
% 1.64/1.33 tff(1458,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1098) | c0_1(a1098) | c3_1(a1098))),
% 1.64/1.33 inference(quant_inst,[status(thm)],[])).
% 1.64/1.33 tff(1459,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a1100) | c1_1(a1098) | c3_1(a1098) | (~ndr1_0) | c0_1(a1098) | (~c0_1(a1100)) | (~c2_1(a1100))),
% 1.64/1.33 inference(modus_ponens,[status(thm)],[1458, 1457])).
% 1.64/1.33 tff(1460,plain,
% 1.64/1.33 ($false),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1459, 113, 1347, 1383, 1382, 1381, 34, 47, 1055, 1453])).
% 1.64/1.33 tff(1461,plain,(c0_1(a1130) | c1_1(a1098) | c3_1(a1098) | hskp5 | c3_1(a1130) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.33 tff(1462,plain,
% 1.64/1.33 ($false),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1461, 1319, 1318, 47, 1269, 34, 767, 804, 756, 1137, 1126, 1125, 35])).
% 1.64/1.33 tff(1463,plain,(hskp5 | c3_1(a1098) | c1_1(a1098) | c2_1(a1098) | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.64/1.33 tff(1464,plain,
% 1.64/1.33 (hskp5),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1463, 692, 34, 35, 47])).
% 1.64/1.33 tff(1465,plain,
% 1.64/1.33 (~c0_1(a1103)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[132, 1464])).
% 1.64/1.33 tff(1466,plain,
% 1.64/1.33 (c2_1(a1100)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[302, 1267])).
% 1.64/1.33 tff(1467,plain,
% 1.64/1.33 (c0_1(a1100)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[313, 1267])).
% 1.64/1.33 tff(1468,plain,
% 1.64/1.33 (c3_1(a1103)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[153, 1464])).
% 1.64/1.33 tff(1469,plain,
% 1.64/1.33 (~c1_1(a1103)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[320, 113, 703, 1468, 1467, 1466, 1465, 1268, 268])).
% 1.64/1.33 tff(1470,plain,
% 1.64/1.33 (~c2_1(a1103)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[126, 1464])).
% 1.64/1.33 tff(1471,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(1472,plain,
% 1.64/1.33 ((hskp13 | (~ndr1_0) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103))) <=> (hskp13 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(1473,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103))))),
% 1.64/1.33 inference(monotonicity,[status(thm)],[1472])).
% 1.64/1.33 tff(1474,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))),
% 1.64/1.33 inference(transitivity,[status(thm)],[1473, 1471])).
% 1.64/1.33 tff(1475,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a1103) | c1_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))),
% 1.64/1.33 inference(quant_inst,[status(thm)],[])).
% 1.64/1.33 tff(1476,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103))),
% 1.64/1.33 inference(modus_ponens,[status(thm)],[1475, 1474])).
% 1.64/1.33 tff(1477,plain,
% 1.64/1.33 (hskp13 | c1_1(a1103)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1476, 113, 1468, 1465, 1470, 1203])).
% 1.64/1.33 tff(1478,plain,
% 1.64/1.33 (hskp13),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1477, 1469])).
% 1.64/1.33 tff(1479,plain,
% 1.64/1.33 (~c1_1(a1115)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1229, 1478])).
% 1.64/1.33 tff(1480,plain,
% 1.64/1.33 (c2_1(a1115)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1240, 1478])).
% 1.64/1.33 tff(1481,plain,
% 1.64/1.33 (c0_1(a1115)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1371, 113, 1137, 1126, 1125, 1480, 716, 715, 1479, 634, 702])).
% 1.64/1.33 tff(1482,plain,
% 1.64/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1127) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1127)) | (~c0_1(a1127)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1127) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1127)) | (~c0_1(a1127)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(1483,plain,
% 1.64/1.33 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103))) <=> (c2_1(a1127) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1127)) | (~c0_1(a1127)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(1484,plain,
% 1.64/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1127) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1127)) | (~c0_1(a1127))))),
% 1.64/1.33 inference(monotonicity,[status(thm)],[1483])).
% 1.64/1.33 tff(1485,plain,
% 1.64/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1127) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1127)) | (~c0_1(a1127)))),
% 1.64/1.33 inference(transitivity,[status(thm)],[1484, 1482])).
% 1.64/1.33 tff(1486,plain,
% 1.64/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))),
% 1.64/1.33 inference(quant_inst,[status(thm)],[])).
% 1.64/1.33 tff(1487,plain,
% 1.64/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1127) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1127)) | (~c0_1(a1127))),
% 1.64/1.33 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 1.64/1.33 tff(1488,plain,
% 1.64/1.33 (~c0_1(a1127)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1487, 113, 1137, 1126, 1125, 1260, 1468, 1258, 1470, 246, 1469])).
% 1.64/1.33 tff(1489,plain,
% 1.64/1.33 (~c3_1(a1115)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1354, 1478])).
% 1.64/1.33 tff(1490,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(1491,plain,
% 1.64/1.33 ((hskp20 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127))) <=> (hskp20 | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(1492,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127))))),
% 1.64/1.33 inference(monotonicity,[status(thm)],[1491])).
% 1.64/1.33 tff(1493,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.64/1.33 inference(transitivity,[status(thm)],[1492, 1490])).
% 1.64/1.33 tff(1494,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))),
% 1.64/1.33 inference(quant_inst,[status(thm)],[])).
% 1.64/1.33 tff(1495,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)) | (~c1_1(a1127)) | c0_1(a1127) | (~c3_1(a1127))),
% 1.64/1.33 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 1.64/1.33 tff(1496,plain,
% 1.64/1.33 ($false),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1495, 113, 703, 1260, 1259, 1480, 1489, 268, 1488, 1481])).
% 1.64/1.33 tff(1497,plain,(hskp20 | hskp14 | c2_1(a1098) | c3_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.33 tff(1498,plain,
% 1.64/1.33 (hskp20),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1497, 692, 35, 47, 34])).
% 1.64/1.33 tff(1499,plain,
% 1.64/1.33 (~c0_1(a1130)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[326, 1498])).
% 1.64/1.33 tff(1500,plain,
% 1.64/1.33 (~c3_1(a1130)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[332, 1498])).
% 1.64/1.33 tff(1501,plain,
% 1.64/1.33 (c0_1(a1130) | (~c1_1(a1130))),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1325, 113, 1137, 1126, 1125, 767, 804, 756, 345, 344])).
% 1.64/1.33 tff(1502,plain,
% 1.64/1.33 (~c1_1(a1130)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1501, 334])).
% 1.64/1.33 tff(1503,plain,
% 1.64/1.33 (hskp3),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1373, 1224, 1126, 1125, 716, 715, 634, 1502, 334, 345, 1137])).
% 1.64/1.33 tff(1504,plain,
% 1.64/1.33 (~c3_1(a1101)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1088, 1503])).
% 1.64/1.33 tff(1505,plain,
% 1.64/1.33 (c1_1(a1101)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1110, 1503])).
% 1.64/1.33 tff(1506,plain,
% 1.64/1.33 (c0_1(a1101)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1336, 113, 1137, 1126, 1125, 767, 1505, 804, 756, 1504, 344])).
% 1.64/1.33 tff(1507,plain,
% 1.64/1.33 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.64/1.33 inference(bind,[status(th)],[])).
% 1.64/1.33 tff(1508,plain,
% 1.64/1.33 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.64/1.33 inference(quant_intro,[status(thm)],[1507])).
% 1.64/1.33 tff(1509,plain,
% 1.64/1.33 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(1510,plain,
% 1.64/1.33 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.64/1.33 inference(bind,[status(th)],[])).
% 1.64/1.33 tff(1511,plain,
% 1.64/1.33 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.64/1.33 inference(quant_intro,[status(thm)],[1510])).
% 1.64/1.33 tff(1512,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 1.64/1.34 tff(1513,plain,
% 1.64/1.34 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 1.64/1.34 tff(1514,plain,
% 1.64/1.34 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1513, 1509])).
% 1.64/1.34 tff(1515,plain,(
% 1.64/1.34 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.64/1.34 inference(skolemize,[status(sab)],[1514])).
% 1.64/1.34 tff(1516,plain,
% 1.64/1.34 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1515, 1508])).
% 1.64/1.34 tff(1517,plain,
% 1.64/1.34 (~c2_1(a1130)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1424, 113, 1137, 1126, 1125, 716, 715, 334, 634, 702, 1502])).
% 1.64/1.34 tff(1518,plain,
% 1.64/1.34 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1519,plain,
% 1.64/1.34 ((hskp4 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130)) <=> (hskp4 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1520,plain,
% 1.64/1.34 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101))))),
% 1.64/1.34 inference(monotonicity,[status(thm)],[1519])).
% 1.64/1.34 tff(1521,plain,
% 1.64/1.34 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)))),
% 1.64/1.34 inference(transitivity,[status(thm)],[1520, 1518])).
% 1.64/1.34 tff(1522,plain,
% 1.64/1.34 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))),
% 1.64/1.34 inference(quant_inst,[status(thm)],[])).
% 1.64/1.34 tff(1523,plain,
% 1.64/1.34 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp4 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 1.64/1.34 tff(1524,plain,
% 1.64/1.34 (hskp4),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1523, 113, 1505, 334, 1517, 345, 1504, 1516, 1506])).
% 1.64/1.34 tff(1525,plain,
% 1.64/1.34 (((~hskp4) | (~c3_1(a1102))) <=> ((~hskp4) | (~c3_1(a1102)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1526,plain,
% 1.64/1.34 (((~c3_1(a1102)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a1102)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1527,axiom,((~c3_1(a1102)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.64/1.34 tff(1528,plain,
% 1.64/1.34 ((~hskp4) | (~c3_1(a1102))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 1.64/1.34 tff(1529,plain,
% 1.64/1.34 ((~hskp4) | (~c3_1(a1102))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1528, 1525])).
% 1.64/1.34 tff(1530,plain,
% 1.64/1.34 (~c3_1(a1102)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1529, 1524])).
% 1.64/1.34 tff(1531,plain,
% 1.64/1.34 (c2_1(a1101)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1099, 1503])).
% 1.64/1.34 tff(1532,plain,
% 1.64/1.34 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | c1_1(a1115) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1115)) | (~c2_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c1_1(a1115) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1533,plain,
% 1.64/1.34 ((hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115))) <=> (hskp24 | c1_1(a1115) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1534,plain,
% 1.64/1.34 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | c1_1(a1115) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1115)) | (~c2_1(a1115))))),
% 1.64/1.34 inference(monotonicity,[status(thm)],[1533])).
% 1.64/1.34 tff(1535,plain,
% 1.64/1.34 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c1_1(a1115) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.64/1.34 inference(transitivity,[status(thm)],[1534, 1532])).
% 1.64/1.34 tff(1536,plain,
% 1.64/1.34 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))),
% 1.64/1.34 inference(quant_inst,[status(thm)],[])).
% 1.64/1.34 tff(1537,plain,
% 1.64/1.34 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c1_1(a1115) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1115)) | (~c2_1(a1115))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1536, 1535])).
% 1.64/1.34 tff(1538,plain,
% 1.64/1.34 (hskp24),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1537, 113, 1241, 1505, 1531, 1230, 1504, 982, 1248])).
% 1.64/1.34 tff(1539,plain,
% 1.64/1.34 (~c0_1(a1149)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[861, 1538])).
% 1.64/1.34 tff(1540,plain,
% 1.64/1.34 (((~hskp4) | c1_1(a1102)) <=> ((~hskp4) | c1_1(a1102))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1541,axiom,((~hskp4) | c1_1(a1102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.64/1.34 tff(1542,plain,
% 1.64/1.34 ((~hskp4) | c1_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 1.64/1.34 tff(1543,plain,
% 1.64/1.34 ((~hskp4) | c1_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1542, 1540])).
% 1.64/1.34 tff(1544,plain,
% 1.64/1.34 ((~hskp4) | c1_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1543, 1540])).
% 1.64/1.34 tff(1545,plain,
% 1.64/1.34 ((~hskp4) | c1_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1544, 1540])).
% 1.64/1.34 tff(1546,plain,
% 1.64/1.34 ((~hskp4) | c1_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1545, 1540])).
% 1.64/1.34 tff(1547,plain,
% 1.64/1.34 ((~hskp4) | c1_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1546, 1540])).
% 1.64/1.34 tff(1548,plain,
% 1.64/1.34 ((~hskp4) | c1_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1547, 1540])).
% 1.64/1.34 tff(1549,plain,
% 1.64/1.34 ((~hskp4) | c1_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1548, 1540])).
% 1.64/1.34 tff(1550,plain,
% 1.64/1.34 (c1_1(a1102)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1549, 1524])).
% 1.64/1.34 tff(1551,plain,
% 1.64/1.34 (((~hskp4) | c0_1(a1102)) <=> ((~hskp4) | c0_1(a1102))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1552,axiom,((~hskp4) | c0_1(a1102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.64/1.34 tff(1553,plain,
% 1.64/1.34 ((~hskp4) | c0_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1552, 1551])).
% 1.64/1.34 tff(1554,plain,
% 1.64/1.34 ((~hskp4) | c0_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1553, 1551])).
% 1.64/1.34 tff(1555,plain,
% 1.64/1.34 ((~hskp4) | c0_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1554, 1551])).
% 1.64/1.34 tff(1556,plain,
% 1.64/1.34 ((~hskp4) | c0_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1555, 1551])).
% 1.64/1.34 tff(1557,plain,
% 1.64/1.34 ((~hskp4) | c0_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1556, 1551])).
% 1.64/1.34 tff(1558,plain,
% 1.64/1.34 ((~hskp4) | c0_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1557, 1551])).
% 1.64/1.34 tff(1559,plain,
% 1.64/1.34 ((~hskp4) | c0_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1558, 1551])).
% 1.64/1.34 tff(1560,plain,
% 1.64/1.34 ((~hskp4) | c0_1(a1102)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1559, 1551])).
% 1.64/1.34 tff(1561,plain,
% 1.64/1.34 (c0_1(a1102)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1560, 1524])).
% 1.64/1.34 tff(1562,plain,
% 1.64/1.34 (c3_1(a1149)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[872, 1538])).
% 1.64/1.34 tff(1563,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1149) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1149)) | (~c3_1(a1149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1149) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1564,plain,
% 1.64/1.34 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149))) <=> (c0_1(a1149) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1565,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1149) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1149)) | (~c3_1(a1149))))),
% 1.64/1.34 inference(monotonicity,[status(thm)],[1564])).
% 1.64/1.34 tff(1566,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1149) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 1.64/1.34 inference(transitivity,[status(thm)],[1565, 1563])).
% 1.64/1.34 tff(1567,plain,
% 1.64/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1149) | (~c1_1(a1149)) | (~c3_1(a1149)))),
% 1.64/1.34 inference(quant_inst,[status(thm)],[])).
% 1.64/1.34 tff(1568,plain,
% 1.64/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1149) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1149)) | (~c3_1(a1149))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1567, 1566])).
% 1.64/1.34 tff(1569,plain,
% 1.64/1.34 (~c1_1(a1149)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1568, 113, 691, 738, 727, 1562, 1561, 1550, 1539, 1530, 45])).
% 1.64/1.34 tff(1570,plain,
% 1.64/1.34 (c2_1(a1149)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[883, 1538])).
% 1.64/1.34 tff(1571,plain,
% 1.64/1.34 ($false),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[941, 692, 113, 704, 1570, 1562, 714, 1569])).
% 1.64/1.34 tff(1572,plain,(hskp19 | hskp14 | c0_1(a1130) | c3_1(a1130) | c2_1(a1098) | c3_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.34 tff(1573,plain,
% 1.64/1.34 (hskp19),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1572, 334, 692, 345, 35, 47, 34])).
% 1.64/1.34 tff(1574,plain,
% 1.64/1.34 (~c2_1(a1127)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[900, 1573])).
% 1.64/1.34 tff(1575,plain,
% 1.64/1.34 (c3_1(a1127)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[912, 1573])).
% 1.64/1.34 tff(1576,plain,
% 1.64/1.34 (c1_1(a1127)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[923, 1573])).
% 1.64/1.34 tff(1577,plain,
% 1.64/1.34 (hskp2),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1266, 113, 1137, 1126, 1125, 1576, 1575, 1574, 278])).
% 1.64/1.34 tff(1578,plain,
% 1.64/1.34 (~c3_1(a1100)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[291, 1577])).
% 1.64/1.34 tff(1579,plain,
% 1.64/1.34 (c2_1(a1100)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[302, 1577])).
% 1.64/1.34 tff(1580,plain,
% 1.64/1.34 (c0_1(a1100)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[313, 1577])).
% 1.64/1.34 tff(1581,plain,
% 1.64/1.34 (hskp3),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1082, 113, 1580, 1579, 334, 345, 1578, 1055, 1502])).
% 1.64/1.34 tff(1582,plain,
% 1.64/1.34 (~c3_1(a1101)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1088, 1581])).
% 1.64/1.34 tff(1583,plain,
% 1.64/1.34 (c1_1(a1101)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1110, 1581])).
% 1.64/1.34 tff(1584,plain,
% 1.64/1.34 (c0_1(a1101)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1336, 113, 1137, 1126, 1125, 767, 1583, 804, 756, 1582, 344])).
% 1.64/1.34 tff(1585,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1130) | c3_1(a1130) | c0_1(a1103) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c1_1(a1103)) | (~c3_1(a1103)) | c1_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1130) | c3_1(a1130) | c0_1(a1103) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c1_1(a1103)) | (~c3_1(a1103)) | c1_1(a1130))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1586,plain,
% 1.64/1.34 (((~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130)) <=> (c0_1(a1130) | c3_1(a1130) | c0_1(a1103) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c1_1(a1103)) | (~c3_1(a1103)) | c1_1(a1130))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1587,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1130) | c3_1(a1130) | c0_1(a1103) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c1_1(a1103)) | (~c3_1(a1103)) | c1_1(a1130)))),
% 1.64/1.34 inference(monotonicity,[status(thm)],[1586])).
% 1.64/1.34 tff(1588,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1130) | c3_1(a1130) | c0_1(a1103) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c1_1(a1103)) | (~c3_1(a1103)) | c1_1(a1130))),
% 1.64/1.34 inference(transitivity,[status(thm)],[1587, 1585])).
% 1.64/1.34 tff(1589,plain,
% 1.64/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c0_1(a1101)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)) | c3_1(a1130) | c1_1(a1130) | c0_1(a1130))),
% 1.64/1.34 inference(quant_inst,[status(thm)],[])).
% 1.64/1.34 tff(1590,plain,
% 1.64/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1130) | c3_1(a1130) | c0_1(a1103) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c1_1(a1103)) | (~c3_1(a1103)) | c1_1(a1130)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 1.64/1.34 tff(1591,plain,
% 1.64/1.34 (~c1_1(a1103)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1590, 113, 1468, 1583, 334, 345, 1465, 1582, 363, 1502, 1584])).
% 1.64/1.34 tff(1592,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1593,plain,
% 1.64/1.34 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103))) <=> (c2_1(a1147) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1594,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.64/1.34 inference(monotonicity,[status(thm)],[1593])).
% 1.64/1.34 tff(1595,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.64/1.34 inference(transitivity,[status(thm)],[1594, 1592])).
% 1.64/1.34 tff(1596,plain,
% 1.64/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))),
% 1.64/1.34 inference(quant_inst,[status(thm)],[])).
% 1.64/1.34 tff(1597,plain,
% 1.64/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1596, 1595])).
% 1.64/1.34 tff(1598,plain,
% 1.64/1.34 (~c1_1(a1147)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1597, 113, 1137, 1126, 1125, 767, 1468, 804, 1470, 246, 1591])).
% 1.64/1.34 tff(1599,plain,
% 1.64/1.34 (hskp13),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1477, 1591])).
% 1.64/1.34 tff(1600,plain,
% 1.64/1.34 (~c1_1(a1115)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1229, 1599])).
% 1.64/1.34 tff(1601,plain,
% 1.64/1.34 (c2_1(a1115)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1240, 1599])).
% 1.64/1.34 tff(1602,plain,
% 1.64/1.34 (c0_1(a1115)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1371, 113, 1137, 1126, 1125, 1601, 716, 715, 1600, 634, 702])).
% 1.64/1.34 tff(1603,plain,
% 1.64/1.34 (c2_1(a1101)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1099, 1581])).
% 1.64/1.34 tff(1604,plain,
% 1.64/1.34 (hskp24),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1537, 113, 1601, 1583, 1603, 1600, 1582, 982, 1602])).
% 1.64/1.34 tff(1605,plain,
% 1.64/1.34 (~c0_1(a1149)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[861, 1604])).
% 1.64/1.34 tff(1606,plain,
% 1.64/1.34 (c3_1(a1149)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[872, 1604])).
% 1.64/1.34 tff(1607,plain,
% 1.64/1.34 (c2_1(a1149)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[883, 1604])).
% 1.64/1.34 tff(1608,plain,
% 1.64/1.34 (hskp21),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[934, 1607, 1573, 1606, 1605])).
% 1.64/1.34 tff(1609,plain,
% 1.64/1.34 (~c0_1(a1136)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[838, 1608, 727, 767, 804, 756, 738])).
% 1.64/1.34 tff(1610,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1611,plain,
% 1.64/1.34 (((~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1101)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136))) <=> (c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1612,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1101)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.64/1.34 inference(monotonicity,[status(thm)],[1611])).
% 1.64/1.34 tff(1613,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1101)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.64/1.34 inference(transitivity,[status(thm)],[1612, 1610])).
% 1.64/1.34 tff(1614,plain,
% 1.64/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c0_1(a1101)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))),
% 1.64/1.34 inference(quant_inst,[status(thm)],[])).
% 1.64/1.34 tff(1615,plain,
% 1.64/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1101)) | (~c0_1(a1101)) | (~c2_1(a1101)) | c1_1(a1147) | (~c0_1(a1147))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 1.64/1.34 tff(1616,plain,
% 1.64/1.34 ($false),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1615, 113, 691, 738, 767, 1583, 1603, 756, 57, 1609, 1598, 1584])).
% 1.64/1.34 tff(1617,plain,(c0_1(a1130) | c3_1(a1130) | hskp14 | c2_1(a1098) | c3_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.34 tff(1618,plain,
% 1.64/1.34 ($false),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1617, 1500, 1499, 692, 35, 47, 34])).
% 1.64/1.34 tff(1619,plain,(hskp14 | c2_1(a1098) | c3_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.34 tff(1620,plain,
% 1.64/1.34 (hskp14),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1619, 47, 35, 34])).
% 1.64/1.34 tff(1621,plain,
% 1.64/1.34 (~c3_1(a1118)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[166, 1620])).
% 1.64/1.34 tff(1622,plain,
% 1.64/1.34 (c1_1(a1118)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[183, 1620])).
% 1.64/1.34 tff(1623,plain,
% 1.64/1.34 (~c2_1(a1118)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[172, 1620])).
% 1.64/1.34 tff(1624,plain,
% 1.64/1.34 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.64/1.34 inference(bind,[status(th)],[])).
% 1.64/1.34 tff(1625,plain,
% 1.64/1.34 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.64/1.34 inference(quant_intro,[status(thm)],[1624])).
% 1.64/1.34 tff(1626,plain,
% 1.64/1.34 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(1627,plain,
% 1.64/1.34 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp23) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp23))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.64/1.35 inference(bind,[status(th)],[])).
% 1.64/1.35 tff(1628,plain,
% 1.64/1.35 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.64/1.35 inference(quant_intro,[status(thm)],[1627])).
% 1.64/1.35 tff(1629,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.64/1.35 tff(1630,plain,
% 1.64/1.35 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1629, 1628])).
% 1.64/1.35 tff(1631,plain,
% 1.64/1.35 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1630, 1626])).
% 1.64/1.35 tff(1632,plain,(
% 1.64/1.35 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.64/1.35 inference(skolemize,[status(sab)],[1631])).
% 1.64/1.35 tff(1633,plain,
% 1.64/1.35 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1632, 1625])).
% 1.64/1.35 tff(1634,assumption,(~hskp23), introduced(assumption)).
% 1.64/1.35 tff(1635,assumption,(hskp9), introduced(assumption)).
% 1.64/1.35 tff(1636,plain,
% 1.64/1.35 (~c3_1(a1108)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[497, 1635])).
% 1.64/1.35 tff(1637,plain,
% 1.64/1.35 (~c1_1(a1108)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[503, 1635])).
% 1.64/1.35 tff(1638,plain,
% 1.64/1.35 (c0_1(a1108)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[514, 1635])).
% 1.64/1.35 tff(1639,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1108)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1108)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1640,plain,
% 1.64/1.35 ((hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108))) <=> (hskp23 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1108)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1641,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1108))))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[1640])).
% 1.64/1.35 tff(1642,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1108)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[1641, 1639])).
% 1.64/1.35 tff(1643,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(1644,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1108))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1643, 1642])).
% 1.64/1.35 tff(1645,plain,
% 1.64/1.35 (~c0_1(a1136)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1644, 1634, 113, 769, 768, 1638, 1637, 1636, 1633])).
% 1.64/1.35 tff(1646,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1647,plain,
% 1.64/1.35 ((hskp29 | (~ndr1_0) | c3_1(a1108) | c1_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136))) <=> (hskp29 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1648,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1108) | c1_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108))))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[1647])).
% 1.64/1.35 tff(1649,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1108) | c1_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[1648, 1646])).
% 1.64/1.35 tff(1650,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1108) | c1_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(1651,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp29 | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 1.64/1.35 tff(1652,plain,
% 1.64/1.35 ($false),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1651, 113, 770, 769, 768, 1638, 1637, 1636, 789, 1645])).
% 1.64/1.35 tff(1653,plain,((~hskp9) | hskp29 | (~c1_1(a1136)) | (~c2_1(a1136)) | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.64/1.35 tff(1654,plain,
% 1.64/1.35 (~hskp9),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1653, 1634, 769, 768, 770])).
% 1.64/1.35 tff(1655,plain,
% 1.64/1.35 (^[U: $i] : refl((hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))),
% 1.64/1.35 inference(bind,[status(th)],[])).
% 1.64/1.35 tff(1656,plain,
% 1.64/1.35 (![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.64/1.35 inference(quant_intro,[status(thm)],[1655])).
% 1.64/1.35 tff(1657,plain,
% 1.64/1.35 (![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1658,plain,
% 1.64/1.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_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)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp9))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp19) <=> ((hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp19))), rewrite(((hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp19) <=> (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp19) <=> (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.64/1.35 inference(bind,[status(th)],[])).
% 1.64/1.35 tff(1659,plain,
% 1.64/1.35 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp19) <=> ![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.64/1.35 inference(quant_intro,[status(thm)],[1658])).
% 1.64/1.35 tff(1660,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 1.64/1.35 tff(1661,plain,
% 1.64/1.35 (![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1660, 1659])).
% 1.64/1.35 tff(1662,plain,
% 1.64/1.35 (![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1661, 1657])).
% 1.64/1.35 tff(1663,plain,(
% 1.64/1.35 ![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.64/1.35 inference(skolemize,[status(sab)],[1662])).
% 1.64/1.35 tff(1664,plain,
% 1.64/1.35 (![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1663, 1656])).
% 1.64/1.35 tff(1665,plain,
% 1.64/1.35 (((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp9 | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)))) <=> ((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp19 | hskp9 | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1666,plain,
% 1.64/1.35 ((hskp19 | hskp9 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136))) <=> (hskp19 | hskp9 | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1667,plain,
% 1.64/1.35 (((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)))) <=> ((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp9 | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136))))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[1666])).
% 1.64/1.35 tff(1668,plain,
% 1.64/1.35 (((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)))) <=> ((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp19 | hskp9 | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[1667, 1665])).
% 1.64/1.35 tff(1669,plain,
% 1.64/1.35 ((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(1670,plain,
% 1.64/1.35 ((~![U: $i] : (hskp19 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp19 | hskp9 | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1669, 1668])).
% 1.64/1.35 tff(1671,plain,
% 1.64/1.35 (hskp19 | hskp9),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1670, 113, 769, 768, 739, 1664])).
% 1.64/1.35 tff(1672,plain,
% 1.64/1.35 (hskp19),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1671, 1654])).
% 1.64/1.35 tff(1673,plain,
% 1.64/1.35 (~c2_1(a1127)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[900, 1672])).
% 1.64/1.35 tff(1674,plain,
% 1.64/1.35 (c3_1(a1127)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[912, 1672])).
% 1.64/1.35 tff(1675,plain,
% 1.64/1.35 (c1_1(a1127)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[923, 1672])).
% 1.64/1.35 tff(1676,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1127) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1127) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1677,plain,
% 1.64/1.35 ((hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127))) <=> (hskp29 | c2_1(a1127) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1678,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1127) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1127) | (~c3_1(a1127))))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[1677])).
% 1.64/1.35 tff(1679,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1127) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[1678, 1676])).
% 1.64/1.35 tff(1680,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(1681,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1127) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1127) | (~c3_1(a1127))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 1.64/1.35 tff(1682,plain,
% 1.64/1.35 (c0_1(a1127)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1681, 113, 770, 1674, 228, 1673, 230, 226, 67])).
% 1.64/1.35 tff(1683,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c0_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1684,plain,
% 1.64/1.35 ((hskp28 | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c0_1(a1127)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127))) <=> (hskp28 | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1685,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c0_1(a1127)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c0_1(a1127)) | (~c3_1(a1127))))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[1684])).
% 1.64/1.35 tff(1686,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c0_1(a1127)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[1685, 1683])).
% 1.64/1.35 tff(1687,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a1127)) | (~c3_1(a1127)) | (~c0_1(a1127)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(1688,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | c2_1(a1127) | (~ndr1_0) | (~c1_1(a1127)) | (~c0_1(a1127)) | (~c3_1(a1127))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1687, 1686])).
% 1.64/1.35 tff(1689,plain,
% 1.64/1.35 (hskp28 | (~c0_1(a1127))),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1688, 113, 1675, 1674, 1673, 567])).
% 1.64/1.35 tff(1690,plain,
% 1.64/1.35 (hskp28),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1689, 1682])).
% 1.64/1.35 tff(1691,plain,
% 1.64/1.35 (c2_1(a1111)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[596, 1690])).
% 1.64/1.35 tff(1692,plain,
% 1.64/1.35 (c0_1(a1111)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[618, 1690])).
% 1.64/1.35 tff(1693,plain,
% 1.64/1.35 (^[U: $i] : refl((hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.64/1.35 inference(bind,[status(th)],[])).
% 1.64/1.35 tff(1694,plain,
% 1.64/1.35 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.64/1.35 inference(quant_intro,[status(thm)],[1693])).
% 1.64/1.35 tff(1695,plain,
% 1.64/1.35 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1696,plain,
% 1.64/1.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp13) <=> ((hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp13))), rewrite(((hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp13) <=> (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.64/1.35 inference(bind,[status(th)],[])).
% 1.64/1.35 tff(1697,plain,
% 1.64/1.35 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp13) <=> ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.64/1.35 inference(quant_intro,[status(thm)],[1696])).
% 1.64/1.35 tff(1698,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp9) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 1.64/1.35 tff(1699,plain,
% 1.64/1.35 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 1.64/1.35 tff(1700,plain,
% 1.64/1.35 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1699, 1695])).
% 1.64/1.35 tff(1701,plain,(
% 1.64/1.35 ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.64/1.35 inference(skolemize,[status(sab)],[1700])).
% 1.64/1.35 tff(1702,plain,
% 1.64/1.35 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1701, 1694])).
% 1.64/1.35 tff(1703,assumption,(c2_1(a1111)), introduced(assumption)).
% 1.64/1.35 tff(1704,assumption,(c0_1(a1111)), introduced(assumption)).
% 1.64/1.35 tff(1705,assumption,(~hskp9), introduced(assumption)).
% 1.64/1.35 tff(1706,plain,
% 1.64/1.35 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c3_1(a1111) | (~c2_1(a1111)) | (~c0_1(a1111)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | hskp9 | (~ndr1_0) | c3_1(a1111) | (~c2_1(a1111)) | (~c0_1(a1111)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1707,plain,
% 1.64/1.35 ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c3_1(a1111) | (~c2_1(a1111)) | (~c0_1(a1111)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(1708,plain,
% 1.64/1.35 ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | hskp9 | (~ndr1_0) | c3_1(a1111) | (~c2_1(a1111)) | (~c0_1(a1111))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 1.64/1.35 tff(1709,plain,
% 1.64/1.35 (hskp13 | c3_1(a1111)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1708, 113, 1705, 1704, 1703, 1702])).
% 1.64/1.35 tff(1710,plain,
% 1.64/1.35 (c3_1(a1111)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1709, 1215])).
% 1.64/1.35 tff(1711,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1712,plain,
% 1.64/1.35 ((hskp2 | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127))) <=> (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1713,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127))))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[1712])).
% 1.64/1.35 tff(1714,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[1713, 1711])).
% 1.64/1.35 tff(1715,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(1716,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c3_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1715, 1714])).
% 1.64/1.35 tff(1717,plain,
% 1.64/1.35 (hskp2),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1716, 113, 1704, 1703, 1027, 1007, 1006, 278, 1710])).
% 1.64/1.35 tff(1718,plain,
% 1.64/1.35 (~c3_1(a1100)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[291, 1717])).
% 1.64/1.35 tff(1719,plain,
% 1.64/1.35 (c2_1(a1100)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[302, 1717])).
% 1.64/1.35 tff(1720,plain,
% 1.64/1.35 (c0_1(a1100)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[313, 1717])).
% 1.64/1.35 tff(1721,plain,
% 1.64/1.35 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | hskp9 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1722,plain,
% 1.64/1.35 ((hskp13 | hskp9 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100))) <=> (hskp13 | hskp9 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(1723,plain,
% 1.64/1.35 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100))))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[1722])).
% 1.64/1.35 tff(1724,plain,
% 1.64/1.35 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | hskp9 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[1723, 1721])).
% 1.64/1.35 tff(1725,plain,
% 1.64/1.35 ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(1726,plain,
% 1.64/1.35 ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp13 | hskp9 | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[1725, 1724])).
% 1.64/1.35 tff(1727,plain,
% 1.64/1.36 ($false),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1726, 113, 1215, 1705, 1720, 1719, 1718, 1702])).
% 1.64/1.36 tff(1728,plain,(hskp13 | hskp9 | (~c0_1(a1111)) | (~c2_1(a1111)) | (~c1_1(a1127)) | (~c3_1(a1127)) | c2_1(a1127)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.36 tff(1729,plain,
% 1.64/1.36 (hskp13),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1728, 1654, 1692, 1691, 1675, 1674, 1673])).
% 1.64/1.36 tff(1730,plain,
% 1.64/1.36 (~c3_1(a1115)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1354, 1729])).
% 1.64/1.36 tff(1731,plain,
% 1.64/1.36 (~c1_1(a1115)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1229, 1729])).
% 1.64/1.36 tff(1732,plain,
% 1.64/1.36 (c1_1(a1111)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[607, 1690])).
% 1.64/1.36 tff(1733,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1734,plain,
% 1.64/1.36 ((hskp23 | (~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115))) <=> (hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1735,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111))))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[1734])).
% 1.64/1.36 tff(1736,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.64/1.36 inference(transitivity,[status(thm)],[1735, 1733])).
% 1.64/1.36 tff(1737,plain,
% 1.64/1.36 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(1738,plain,
% 1.64/1.36 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 1.64/1.36 tff(1739,plain,
% 1.64/1.36 (~c0_1(a1115)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1738, 1634, 113, 1692, 1732, 1691, 1731, 1730, 1633])).
% 1.64/1.36 tff(1740,plain,
% 1.64/1.36 (c2_1(a1115)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1240, 1729])).
% 1.64/1.36 tff(1741,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1742,plain,
% 1.64/1.36 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115))) <=> (c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1743,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115))))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[1742])).
% 1.64/1.36 tff(1744,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.64/1.36 inference(transitivity,[status(thm)],[1743, 1741])).
% 1.64/1.36 tff(1745,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(1746,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c0_1(a1115) | (~c2_1(a1115))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 1.64/1.36 tff(1747,plain,
% 1.64/1.36 ((~c0_1(a1136)) | c0_1(a1115)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1746, 113, 768, 739, 1740, 992, 965, 1731, 669, 702])).
% 1.64/1.36 tff(1748,plain,
% 1.64/1.36 (~c0_1(a1136)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1747, 1739])).
% 1.64/1.36 tff(1749,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1750,plain,
% 1.64/1.36 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136))) <=> (c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1751,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[1750])).
% 1.64/1.36 tff(1752,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.64/1.36 inference(transitivity,[status(thm)],[1751, 1749])).
% 1.64/1.36 tff(1753,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1136) | (~c1_1(a1136)) | (~c3_1(a1136)))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(1754,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 1.64/1.36 tff(1755,plain,
% 1.64/1.36 (~c0_1(a1118)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1754, 113, 769, 768, 739, 228, 226, 45, 1748])).
% 1.64/1.36 tff(1756,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1757,plain,
% 1.64/1.36 ((hskp9 | (~ndr1_0) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118))) <=> (hskp9 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1758,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118)))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[1757])).
% 1.64/1.36 tff(1759,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.64/1.36 inference(transitivity,[status(thm)],[1758, 1756])).
% 1.64/1.36 tff(1760,plain,
% 1.64/1.36 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(1761,plain,
% 1.64/1.36 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118)),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 1.64/1.36 tff(1762,plain,
% 1.64/1.36 ($false),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1761, 113, 1654, 769, 768, 228, 230, 422, 1755, 1748])).
% 1.64/1.36 tff(1763,plain,(hskp23 | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c1_1(a1118)) | c2_1(a1118) | (~c3_1(a1136)) | c3_1(a1118) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105) | hskp29), inference(lemma,lemma(discharge,[]))).
% 1.64/1.36 tff(1764,plain,
% 1.64/1.36 (hskp23),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1763, 770, 738, 1622, 1623, 727, 1621, 716, 715, 634, 691])).
% 1.64/1.36 tff(1765,plain,
% 1.64/1.36 (~c3_1(a1147)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[755, 1764])).
% 1.64/1.36 tff(1766,plain,
% 1.64/1.36 (c0_1(a1147)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[766, 1764])).
% 1.64/1.36 tff(1767,plain,
% 1.64/1.36 (c0_1(a1136)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[797, 1766, 691, 738, 770, 1765, 727])).
% 1.64/1.36 tff(1768,plain,
% 1.64/1.36 (~c2_1(a1147)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[803, 1764])).
% 1.64/1.36 tff(1769,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118) | (~c0_1(a1147)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1770,plain,
% 1.64/1.36 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118))) <=> (c2_1(a1147) | c3_1(a1147) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118) | (~c0_1(a1147)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1771,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118) | (~c0_1(a1147))))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[1770])).
% 1.64/1.36 tff(1772,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118) | (~c0_1(a1147)))),
% 1.64/1.36 inference(transitivity,[status(thm)],[1771, 1769])).
% 1.64/1.36 tff(1773,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(1774,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118) | (~c0_1(a1147))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[1773, 1772])).
% 1.64/1.36 tff(1775,plain,
% 1.64/1.36 (c0_1(a1118)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1774, 113, 738, 727, 1766, 1622, 1768, 1765, 1621, 344, 1767])).
% 1.64/1.36 tff(1776,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1777,plain,
% 1.64/1.36 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107))) <=> (c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1778,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[1777])).
% 1.64/1.36 tff(1779,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.64/1.36 inference(transitivity,[status(thm)],[1778, 1776])).
% 1.64/1.36 tff(1780,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(1781,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 1.64/1.36 tff(1782,plain,
% 1.64/1.36 (c2_1(a1107)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1781, 113, 768, 739, 228, 1214, 230, 1180, 246, 227, 805])).
% 1.64/1.36 tff(1783,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1784,plain,
% 1.64/1.36 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107))) <=> (c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1785,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107))))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[1784])).
% 1.64/1.36 tff(1786,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107)))),
% 1.64/1.36 inference(transitivity,[status(thm)],[1785, 1783])).
% 1.64/1.36 tff(1787,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1107) | c0_1(a1107) | (~c2_1(a1107)))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(1788,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1107) | c1_1(a1107) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | (~c2_1(a1107))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[1787, 1786])).
% 1.64/1.36 tff(1789,plain,
% 1.64/1.36 ($false),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1788, 113, 768, 739, 992, 965, 1186, 1180, 669, 702, 805, 1782])).
% 1.64/1.36 tff(1790,plain,((~hskp8) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105) | (~c0_1(a1136)) | (~c1_1(a1118)) | c2_1(a1118) | (~c0_1(a1118))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.36 tff(1791,plain,
% 1.64/1.36 (~hskp8),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1790, 1767, 727, 716, 715, 634, 738, 1622, 1623, 1775])).
% 1.64/1.36 tff(1792,plain,
% 1.64/1.36 (hskp19),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1172, 1791, 35, 47])).
% 1.64/1.36 tff(1793,plain,
% 1.64/1.36 (~c2_1(a1127)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[900, 1792])).
% 1.64/1.36 tff(1794,plain,
% 1.64/1.36 (c3_1(a1127)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[912, 1792])).
% 1.64/1.36 tff(1795,plain,
% 1.64/1.36 (c0_1(a1127)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1681, 113, 770, 1794, 1622, 1793, 1623, 1621, 67])).
% 1.64/1.36 tff(1796,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1797,plain,
% 1.64/1.36 (((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105))) <=> (c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(1798,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[1797])).
% 1.64/1.37 tff(1799,plain,
% 1.64/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.64/1.37 inference(transitivity,[status(thm)],[1798, 1796])).
% 1.64/1.37 tff(1800,plain,
% 1.64/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.64/1.37 inference(quant_inst,[status(thm)],[])).
% 1.64/1.37 tff(1801,plain,
% 1.64/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.64/1.37 tff(1802,plain,
% 1.64/1.37 ((~c0_1(a1136)) | c2_1(a1105) | (~c0_1(a1118))),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1801, 113, 738, 727, 1622, 715, 1623, 634, 246])).
% 1.64/1.37 tff(1803,plain,
% 1.64/1.37 (c2_1(a1105)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1802, 1775, 1767])).
% 1.64/1.37 tff(1804,plain,
% 1.64/1.37 (hskp20 | (~c0_1(a1127))),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1013, 113, 1794, 716, 1793, 634, 1005, 1803])).
% 1.64/1.37 tff(1805,plain,
% 1.64/1.37 (hskp20),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1804, 1795])).
% 1.64/1.37 tff(1806,plain,
% 1.64/1.37 (~c3_1(a1130)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[332, 1805])).
% 1.64/1.37 tff(1807,plain,
% 1.64/1.37 (~c0_1(a1130)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[326, 1805])).
% 1.64/1.37 tff(1808,plain,
% 1.64/1.37 (hskp2 | (~c2_1(a1105))),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1071, 113, 716, 715, 634, 1065])).
% 1.64/1.37 tff(1809,plain,
% 1.64/1.37 (hskp2),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1808, 1803])).
% 1.64/1.37 tff(1810,plain,
% 1.64/1.37 (c0_1(a1100)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[313, 1809])).
% 1.64/1.37 tff(1811,plain,
% 1.64/1.37 (~c3_1(a1100)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[291, 1809])).
% 1.64/1.37 tff(1812,plain,
% 1.64/1.37 (c2_1(a1100)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[302, 1809])).
% 1.64/1.37 tff(1813,plain,
% 1.64/1.37 (hskp5),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1407, 1807, 1767, 1806, 1812, 1811, 738, 727, 716, 715, 634, 1810, 1766, 1768, 1765])).
% 1.64/1.37 tff(1814,plain,
% 1.64/1.37 (~c2_1(a1103)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[126, 1813])).
% 1.64/1.37 tff(1815,plain,
% 1.64/1.37 (c3_1(a1103)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[153, 1813])).
% 1.64/1.37 tff(1816,plain,
% 1.64/1.37 (~c0_1(a1103)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[132, 1813])).
% 1.64/1.37 tff(1817,plain,
% 1.64/1.37 ($false),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[373, 1816, 1815, 1623, 1775, 1814, 1807, 1806, 1621, 1622])).
% 1.64/1.37 tff(1818,plain,(hskp29 | c2_1(a1098) | c3_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.37 tff(1819,plain,
% 1.64/1.37 (hskp29),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1818, 47, 35, 34])).
% 1.64/1.37 tff(1820,plain,
% 1.64/1.37 (c3_1(a1116)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[201, 1819])).
% 1.64/1.37 tff(1821,plain,
% 1.64/1.37 (c2_1(a1116)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[212, 1819])).
% 1.64/1.37 tff(1822,plain,
% 1.64/1.37 (c0_1(a1116)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[223, 1819])).
% 1.64/1.37 tff(1823,plain,
% 1.64/1.37 (hskp13),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1223, 1174, 1822, 1821, 1820, 716, 715, 634])).
% 1.64/1.37 tff(1824,plain,
% 1.64/1.37 (~c1_1(a1115)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1229, 1823])).
% 1.64/1.37 tff(1825,plain,
% 1.64/1.37 (c2_1(a1115)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1240, 1823])).
% 1.64/1.37 tff(1826,plain,
% 1.64/1.37 (c0_1(a1115)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1371, 113, 1822, 1821, 1820, 1825, 716, 715, 1824, 634, 702])).
% 1.64/1.37 tff(1827,plain,
% 1.64/1.37 (~c2_1(a1107)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1192, 113, 1822, 1821, 1820, 716, 715, 1186, 1180, 634, 702])).
% 1.64/1.37 tff(1828,plain,
% 1.64/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1829,plain,
% 1.64/1.37 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107))) <=> (c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1830,plain,
% 1.64/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[1829])).
% 1.64/1.37 tff(1831,plain,
% 1.64/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.64/1.37 inference(transitivity,[status(thm)],[1830, 1828])).
% 1.64/1.37 tff(1832,plain,
% 1.64/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1107) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.64/1.37 inference(quant_inst,[status(thm)],[])).
% 1.64/1.37 tff(1833,plain,
% 1.64/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1107) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1832, 1831])).
% 1.64/1.37 tff(1834,plain,
% 1.64/1.37 (c2_1(a1107) | (~c0_1(a1118))),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1833, 113, 1822, 1821, 1820, 1622, 1214, 1623, 1180, 246])).
% 1.64/1.37 tff(1835,plain,
% 1.64/1.37 (~c0_1(a1118)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1834, 1827])).
% 1.64/1.37 tff(1836,plain,
% 1.64/1.37 (hskp1),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[405, 1835, 1622, 1621, 34, 47, 1822, 1821, 1820, 35])).
% 1.64/1.37 tff(1837,plain,
% 1.64/1.37 (~c0_1(a1099)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[411, 1836])).
% 1.64/1.37 tff(1838,plain,
% 1.64/1.37 (~c3_1(a1115)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1354, 1823])).
% 1.64/1.37 tff(1839,plain,
% 1.64/1.37 (c2_1(a1099)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[462, 1836])).
% 1.64/1.37 tff(1840,plain,
% 1.64/1.37 (c1_1(a1099)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[473, 1836])).
% 1.64/1.37 tff(1841,plain,
% 1.64/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1115) | c3_1(a1115) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1115) | c3_1(a1115) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1842,plain,
% 1.64/1.37 (((~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099))) <=> (c1_1(a1115) | c3_1(a1115) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1843,plain,
% 1.64/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1115) | c3_1(a1115) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115))))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[1842])).
% 1.64/1.37 tff(1844,plain,
% 1.64/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1115) | c3_1(a1115) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))),
% 1.64/1.37 inference(transitivity,[status(thm)],[1843, 1841])).
% 1.64/1.37 tff(1845,plain,
% 1.64/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))),
% 1.64/1.37 inference(quant_inst,[status(thm)],[])).
% 1.64/1.37 tff(1846,plain,
% 1.64/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1115) | c3_1(a1115) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 1.64/1.37 tff(1847,plain,
% 1.64/1.37 (~c0_1(a1136)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1846, 113, 691, 738, 1840, 1839, 1824, 1838, 1837, 57, 1826])).
% 1.64/1.37 tff(1848,plain,
% 1.64/1.37 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.64/1.37 inference(bind,[status(th)],[])).
% 1.64/1.37 tff(1849,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.64/1.37 inference(quant_intro,[status(thm)],[1848])).
% 1.64/1.37 tff(1850,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1851,plain,
% 1.64/1.37 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.64/1.37 inference(bind,[status(th)],[])).
% 1.64/1.37 tff(1852,plain,
% 1.64/1.37 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.64/1.37 inference(quant_intro,[status(thm)],[1851])).
% 1.64/1.37 tff(1853,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 1.64/1.37 tff(1854,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 1.64/1.37 tff(1855,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1854, 1850])).
% 1.64/1.37 tff(1856,plain,(
% 1.64/1.37 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.64/1.37 inference(skolemize,[status(sab)],[1855])).
% 1.64/1.37 tff(1857,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1856, 1849])).
% 1.64/1.37 tff(1858,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1859,plain,
% 1.64/1.37 ((hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107))) <=> (hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1860,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118))))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[1859])).
% 1.64/1.37 tff(1861,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118)))),
% 1.64/1.37 inference(transitivity,[status(thm)],[1860, 1858])).
% 1.64/1.37 tff(1862,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1107) | c1_1(a1107) | (~c3_1(a1107)))),
% 1.64/1.37 inference(quant_inst,[status(thm)],[])).
% 1.64/1.37 tff(1863,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)) | (~c1_1(a1118))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 1.64/1.37 tff(1864,plain,
% 1.64/1.37 (hskp11),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1863, 113, 1622, 1214, 1623, 1621, 1180, 1857, 1827])).
% 1.64/1.37 tff(1865,plain,
% 1.64/1.37 (((~hskp11) | (~c2_1(a1113))) <=> ((~hskp11) | (~c2_1(a1113)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1866,plain,
% 1.64/1.37 (((~c2_1(a1113)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a1113)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1867,axiom,((~c2_1(a1113)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.64/1.37 tff(1868,plain,
% 1.64/1.37 ((~hskp11) | (~c2_1(a1113))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1867, 1866])).
% 1.64/1.37 tff(1869,plain,
% 1.64/1.37 ((~hskp11) | (~c2_1(a1113))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1868, 1865])).
% 1.64/1.37 tff(1870,plain,
% 1.64/1.37 (~c2_1(a1113)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1869, 1864])).
% 1.64/1.37 tff(1871,plain,
% 1.64/1.37 (((~hskp11) | c0_1(a1113)) <=> ((~hskp11) | c0_1(a1113))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1872,axiom,((~hskp11) | c0_1(a1113)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.64/1.37 tff(1873,plain,
% 1.64/1.37 ((~hskp11) | c0_1(a1113)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1872, 1871])).
% 1.64/1.37 tff(1874,plain,
% 1.64/1.37 ((~hskp11) | c0_1(a1113)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1873, 1871])).
% 1.64/1.37 tff(1875,plain,
% 1.64/1.37 ((~hskp11) | c0_1(a1113)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1874, 1871])).
% 1.64/1.37 tff(1876,plain,
% 1.64/1.37 ((~hskp11) | c0_1(a1113)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1875, 1871])).
% 1.64/1.37 tff(1877,plain,
% 1.64/1.37 ((~hskp11) | c0_1(a1113)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1876, 1871])).
% 1.64/1.37 tff(1878,plain,
% 1.64/1.37 ((~hskp11) | c0_1(a1113)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1877, 1871])).
% 1.64/1.37 tff(1879,plain,
% 1.64/1.37 ((~hskp11) | c0_1(a1113)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1878, 1871])).
% 1.64/1.37 tff(1880,plain,
% 1.64/1.37 ((~hskp11) | c0_1(a1113)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1879, 1871])).
% 1.64/1.37 tff(1881,plain,
% 1.64/1.37 (c0_1(a1113)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1880, 1864])).
% 1.64/1.37 tff(1882,plain,
% 1.64/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1115) | c3_1(a1115) | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1113)) | (~c0_1(a1113)) | (~c0_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1115) | c3_1(a1115) | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1113)) | (~c0_1(a1113)) | (~c0_1(a1115)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1883,plain,
% 1.64/1.37 (((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136))) <=> (c1_1(a1115) | c3_1(a1115) | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1113)) | (~c0_1(a1113)) | (~c0_1(a1115)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1884,plain,
% 1.64/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1115) | c3_1(a1115) | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1113)) | (~c0_1(a1113)) | (~c0_1(a1115))))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[1883])).
% 1.64/1.37 tff(1885,plain,
% 1.64/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1115) | c3_1(a1115) | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1113)) | (~c0_1(a1113)) | (~c0_1(a1115)))),
% 1.64/1.37 inference(transitivity,[status(thm)],[1884, 1882])).
% 1.64/1.37 tff(1886,plain,
% 1.64/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1113) | (~c1_1(a1113)) | (~c0_1(a1113)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))),
% 1.64/1.37 inference(quant_inst,[status(thm)],[])).
% 1.64/1.37 tff(1887,plain,
% 1.64/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1115) | c3_1(a1115) | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c1_1(a1113)) | (~c0_1(a1113)) | (~c0_1(a1115))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 1.64/1.37 tff(1888,plain,
% 1.64/1.37 (~c1_1(a1113)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[1887, 113, 691, 738, 1881, 1824, 1838, 1870, 1418, 1847, 1826])).
% 1.64/1.37 tff(1889,plain,
% 1.64/1.37 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.64/1.37 inference(bind,[status(th)],[])).
% 1.64/1.37 tff(1890,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.64/1.37 inference(quant_intro,[status(thm)],[1889])).
% 1.64/1.37 tff(1891,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1892,plain,
% 1.64/1.37 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~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)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.64/1.37 inference(bind,[status(th)],[])).
% 1.64/1.37 tff(1893,plain,
% 1.64/1.37 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.64/1.37 inference(quant_intro,[status(thm)],[1892])).
% 1.64/1.37 tff(1894,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.64/1.37 tff(1895,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1894, 1893])).
% 1.64/1.37 tff(1896,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1895, 1891])).
% 1.64/1.37 tff(1897,plain,(
% 1.64/1.37 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.64/1.37 inference(skolemize,[status(sab)],[1896])).
% 1.64/1.37 tff(1898,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[1897, 1890])).
% 1.64/1.37 tff(1899,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | c1_1(a1113) | (~c0_1(a1113)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | c1_1(a1113) | (~c0_1(a1113)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1900,plain,
% 1.64/1.37 ((hskp4 | (~ndr1_0) | c2_1(a1113) | c1_1(a1113) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136))) <=> (hskp4 | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | c1_1(a1113) | (~c0_1(a1113)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(1901,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1113) | c1_1(a1113) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | c1_1(a1113) | (~c0_1(a1113))))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[1900])).
% 1.64/1.37 tff(1902,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1113) | c1_1(a1113) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | c1_1(a1113) | (~c0_1(a1113)))),
% 1.64/1.37 inference(transitivity,[status(thm)],[1901, 1899])).
% 1.64/1.37 tff(1903,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1113) | c1_1(a1113) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)))),
% 1.64/1.38 inference(quant_inst,[status(thm)],[])).
% 1.64/1.38 tff(1904,plain,
% 1.64/1.38 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c2_1(a1113) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | c1_1(a1113) | (~c0_1(a1113))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 1.64/1.38 tff(1905,plain,
% 1.64/1.38 (hskp4),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1904, 113, 738, 727, 1881, 1870, 1898, 1847, 1888])).
% 1.64/1.38 tff(1906,plain,
% 1.64/1.38 (~c3_1(a1102)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1529, 1905])).
% 1.64/1.38 tff(1907,plain,
% 1.64/1.38 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.64/1.38 inference(bind,[status(th)],[])).
% 1.64/1.38 tff(1908,plain,
% 1.64/1.38 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.64/1.38 inference(quant_intro,[status(thm)],[1907])).
% 1.64/1.38 tff(1909,plain,
% 1.64/1.38 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1910,plain,
% 1.64/1.38 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.64/1.38 inference(bind,[status(th)],[])).
% 1.64/1.38 tff(1911,plain,
% 1.64/1.38 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.64/1.38 inference(quant_intro,[status(thm)],[1910])).
% 1.64/1.38 tff(1912,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.64/1.38 tff(1913,plain,
% 1.64/1.38 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1912, 1911])).
% 1.64/1.38 tff(1914,plain,
% 1.64/1.38 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1913, 1909])).
% 1.64/1.38 tff(1915,plain,(
% 1.64/1.38 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.64/1.38 inference(skolemize,[status(sab)],[1914])).
% 1.64/1.38 tff(1916,plain,
% 1.64/1.38 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1915, 1908])).
% 1.64/1.38 tff(1917,plain,
% 1.64/1.38 (((~hskp11) | c3_1(a1113)) <=> ((~hskp11) | c3_1(a1113))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1918,axiom,((~hskp11) | c3_1(a1113)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.64/1.38 tff(1919,plain,
% 1.64/1.38 ((~hskp11) | c3_1(a1113)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.64/1.38 tff(1920,plain,
% 1.64/1.38 ((~hskp11) | c3_1(a1113)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1919, 1917])).
% 1.64/1.38 tff(1921,plain,
% 1.64/1.38 ((~hskp11) | c3_1(a1113)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1920, 1917])).
% 1.64/1.38 tff(1922,plain,
% 1.64/1.38 ((~hskp11) | c3_1(a1113)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1921, 1917])).
% 1.64/1.38 tff(1923,plain,
% 1.64/1.38 ((~hskp11) | c3_1(a1113)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1922, 1917])).
% 1.64/1.38 tff(1924,plain,
% 1.64/1.38 ((~hskp11) | c3_1(a1113)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1923, 1917])).
% 1.64/1.38 tff(1925,plain,
% 1.64/1.38 ((~hskp11) | c3_1(a1113)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1924, 1917])).
% 1.64/1.38 tff(1926,plain,
% 1.64/1.38 ((~hskp11) | c3_1(a1113)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1925, 1917])).
% 1.64/1.38 tff(1927,plain,
% 1.64/1.38 (c3_1(a1113)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1926, 1864])).
% 1.64/1.38 tff(1928,plain,
% 1.64/1.38 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1113) | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1113)) | (~c3_1(a1113)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1113) | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1113)) | (~c3_1(a1113)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1929,plain,
% 1.64/1.38 ((hskp16 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136))) <=> (hskp16 | c2_1(a1113) | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1113)) | (~c3_1(a1113)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1930,plain,
% 1.64/1.38 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1113) | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1113)) | (~c3_1(a1113))))),
% 1.64/1.38 inference(monotonicity,[status(thm)],[1929])).
% 1.64/1.38 tff(1931,plain,
% 1.64/1.38 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1113) | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1113)) | (~c3_1(a1113)))),
% 1.64/1.38 inference(transitivity,[status(thm)],[1930, 1928])).
% 1.64/1.38 tff(1932,plain,
% 1.64/1.38 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.64/1.38 inference(quant_inst,[status(thm)],[])).
% 1.64/1.38 tff(1933,plain,
% 1.64/1.38 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1113) | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1113)) | (~c3_1(a1113))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 1.64/1.38 tff(1934,plain,
% 1.64/1.38 (hskp16),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1933, 113, 691, 727, 1881, 1927, 1870, 1916, 1847])).
% 1.64/1.38 tff(1935,plain,
% 1.64/1.38 (((~hskp16) | (~c0_1(a1121))) <=> ((~hskp16) | (~c0_1(a1121)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1936,plain,
% 1.64/1.38 (((~c0_1(a1121)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a1121)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1937,axiom,((~c0_1(a1121)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.64/1.38 tff(1938,plain,
% 1.64/1.38 ((~hskp16) | (~c0_1(a1121))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 1.64/1.38 tff(1939,plain,
% 1.64/1.38 ((~hskp16) | (~c0_1(a1121))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1938, 1935])).
% 1.64/1.38 tff(1940,plain,
% 1.64/1.38 (~c0_1(a1121)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1939, 1934])).
% 1.64/1.38 tff(1941,plain,
% 1.64/1.38 (c1_1(a1102)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1549, 1905])).
% 1.64/1.38 tff(1942,plain,
% 1.64/1.38 (c0_1(a1102)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1560, 1905])).
% 1.64/1.38 tff(1943,plain,
% 1.64/1.38 (((~hskp16) | c3_1(a1121)) <=> ((~hskp16) | c3_1(a1121))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1944,axiom,((~hskp16) | c3_1(a1121)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.64/1.38 tff(1945,plain,
% 1.64/1.38 ((~hskp16) | c3_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1944, 1943])).
% 1.64/1.38 tff(1946,plain,
% 1.64/1.38 ((~hskp16) | c3_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1945, 1943])).
% 1.64/1.38 tff(1947,plain,
% 1.64/1.38 ((~hskp16) | c3_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1946, 1943])).
% 1.64/1.38 tff(1948,plain,
% 1.64/1.38 ((~hskp16) | c3_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1947, 1943])).
% 1.64/1.38 tff(1949,plain,
% 1.64/1.38 ((~hskp16) | c3_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1948, 1943])).
% 1.64/1.38 tff(1950,plain,
% 1.64/1.38 ((~hskp16) | c3_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1949, 1943])).
% 1.64/1.38 tff(1951,plain,
% 1.64/1.38 ((~hskp16) | c3_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1950, 1943])).
% 1.64/1.38 tff(1952,plain,
% 1.64/1.38 ((~hskp16) | c3_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1951, 1943])).
% 1.64/1.38 tff(1953,plain,
% 1.64/1.38 (c3_1(a1121)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1952, 1934])).
% 1.64/1.38 tff(1954,plain,
% 1.64/1.38 (((~hskp16) | c1_1(a1121)) <=> ((~hskp16) | c1_1(a1121))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1955,axiom,((~hskp16) | c1_1(a1121)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.64/1.38 tff(1956,plain,
% 1.64/1.38 ((~hskp16) | c1_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1955, 1954])).
% 1.64/1.38 tff(1957,plain,
% 1.64/1.38 ((~hskp16) | c1_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1956, 1954])).
% 1.64/1.38 tff(1958,plain,
% 1.64/1.38 ((~hskp16) | c1_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1957, 1954])).
% 1.64/1.38 tff(1959,plain,
% 1.64/1.38 ((~hskp16) | c1_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1958, 1954])).
% 1.64/1.38 tff(1960,plain,
% 1.64/1.38 ((~hskp16) | c1_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1959, 1954])).
% 1.64/1.38 tff(1961,plain,
% 1.64/1.38 ((~hskp16) | c1_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1960, 1954])).
% 1.64/1.38 tff(1962,plain,
% 1.64/1.38 ((~hskp16) | c1_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1961, 1954])).
% 1.64/1.38 tff(1963,plain,
% 1.64/1.38 ((~hskp16) | c1_1(a1121)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1962, 1954])).
% 1.64/1.38 tff(1964,plain,
% 1.64/1.38 (c1_1(a1121)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1963, 1934])).
% 1.64/1.38 tff(1965,plain,
% 1.64/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1121) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1121) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1966,plain,
% 1.64/1.38 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121))) <=> (c0_1(a1121) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1967,plain,
% 1.64/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1121) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1121)) | (~c3_1(a1121))))),
% 1.64/1.38 inference(monotonicity,[status(thm)],[1966])).
% 1.64/1.38 tff(1968,plain,
% 1.64/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1121) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.64/1.38 inference(transitivity,[status(thm)],[1967, 1965])).
% 1.64/1.38 tff(1969,plain,
% 1.64/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.64/1.38 inference(quant_inst,[status(thm)],[])).
% 1.64/1.38 tff(1970,plain,
% 1.64/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1121) | c3_1(a1102) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c1_1(a1121)) | (~c3_1(a1121))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1969, 1968])).
% 1.64/1.38 tff(1971,plain,
% 1.64/1.38 ($false),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1970, 113, 691, 738, 727, 1964, 1953, 1942, 1941, 1940, 1906, 45])).
% 1.64/1.38 tff(1972,plain,((~hskp8) | c1_1(a1098) | c3_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.38 tff(1973,plain,
% 1.64/1.38 (~hskp8),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1972, 47, 34, 35])).
% 1.64/1.38 tff(1974,assumption,(~hskp8), introduced(assumption)).
% 1.64/1.38 tff(1975,plain,
% 1.64/1.38 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp8 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1976,plain,
% 1.64/1.38 ((hskp8 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118)) <=> (hskp8 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1977,plain,
% 1.64/1.38 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118)))),
% 1.64/1.38 inference(monotonicity,[status(thm)],[1976])).
% 1.64/1.38 tff(1978,plain,
% 1.64/1.38 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp8 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118))),
% 1.64/1.38 inference(transitivity,[status(thm)],[1977, 1975])).
% 1.64/1.38 tff(1979,plain,
% 1.64/1.38 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp8 | hskp6 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | c0_1(a1118))),
% 1.64/1.38 inference(quant_inst,[status(thm)],[])).
% 1.64/1.38 tff(1980,plain,
% 1.64/1.38 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp8 | hskp6 | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | c0_1(a1118)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 1.64/1.38 tff(1981,plain,
% 1.64/1.38 (hskp8 | hskp6 | c0_1(a1118)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1980, 113, 230, 226, 1435])).
% 1.64/1.38 tff(1982,plain,
% 1.64/1.38 (hskp6),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1981, 378, 1974])).
% 1.64/1.38 tff(1983,plain,
% 1.64/1.38 (~c2_1(a1104)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[538, 1982])).
% 1.64/1.38 tff(1984,plain,
% 1.64/1.38 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.64/1.38 inference(bind,[status(th)],[])).
% 1.64/1.38 tff(1985,plain,
% 1.64/1.38 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.64/1.38 inference(quant_intro,[status(thm)],[1984])).
% 1.64/1.38 tff(1986,plain,
% 1.64/1.38 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1987,plain,
% 1.64/1.38 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_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)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_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)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.64/1.38 inference(bind,[status(th)],[])).
% 1.64/1.38 tff(1988,plain,
% 1.64/1.38 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.64/1.38 inference(quant_intro,[status(thm)],[1987])).
% 1.64/1.38 tff(1989,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 1.64/1.38 tff(1990,plain,
% 1.64/1.38 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 1.64/1.38 tff(1991,plain,
% 1.64/1.38 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1990, 1986])).
% 1.64/1.38 tff(1992,plain,(
% 1.64/1.38 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.64/1.38 inference(skolemize,[status(sab)],[1991])).
% 1.64/1.38 tff(1993,plain,
% 1.64/1.38 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1992, 1985])).
% 1.64/1.38 tff(1994,plain,
% 1.64/1.38 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1995,plain,
% 1.64/1.38 ((hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118))) <=> (hskp10 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(1996,plain,
% 1.64/1.38 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118)))),
% 1.64/1.38 inference(monotonicity,[status(thm)],[1995])).
% 1.64/1.38 tff(1997,plain,
% 1.64/1.38 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.64/1.38 inference(transitivity,[status(thm)],[1996, 1994])).
% 1.64/1.38 tff(1998,plain,
% 1.64/1.38 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))),
% 1.64/1.38 inference(quant_inst,[status(thm)],[])).
% 1.64/1.38 tff(1999,plain,
% 1.64/1.38 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | c0_1(a1118)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 1.64/1.38 tff(2000,plain,
% 1.64/1.38 (hskp10 | c0_1(a1118)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1999, 113, 769, 768, 739, 228, 230, 1993])).
% 1.64/1.38 tff(2001,plain,
% 1.64/1.38 (hskp10),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[2000, 378])).
% 1.64/1.38 tff(2002,plain,
% 1.64/1.38 (((~hskp10) | (~c2_1(a1110))) <=> ((~hskp10) | (~c2_1(a1110)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(2003,plain,
% 1.64/1.38 (((~c2_1(a1110)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a1110)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(2004,axiom,((~c2_1(a1110)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.64/1.38 tff(2005,plain,
% 1.64/1.38 ((~hskp10) | (~c2_1(a1110))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 1.64/1.38 tff(2006,plain,
% 1.64/1.38 ((~hskp10) | (~c2_1(a1110))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2005, 2002])).
% 1.64/1.38 tff(2007,plain,
% 1.64/1.38 (~c2_1(a1110)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[2006, 2001])).
% 1.64/1.38 tff(2008,plain,
% 1.64/1.38 (((~hskp10) | (~c1_1(a1110))) <=> ((~hskp10) | (~c1_1(a1110)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(2009,plain,
% 1.64/1.38 (((~c1_1(a1110)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1110)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(2010,axiom,((~c1_1(a1110)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.64/1.38 tff(2011,plain,
% 1.64/1.38 ((~hskp10) | (~c1_1(a1110))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2010, 2009])).
% 1.64/1.38 tff(2012,plain,
% 1.64/1.38 ((~hskp10) | (~c1_1(a1110))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2011, 2008])).
% 1.64/1.38 tff(2013,plain,
% 1.64/1.38 (~c1_1(a1110)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[2012, 2001])).
% 1.64/1.38 tff(2014,plain,
% 1.64/1.38 (c1_1(a1104)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[577, 1982])).
% 1.64/1.38 tff(2015,plain,
% 1.64/1.38 (c0_1(a1104)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[549, 1982])).
% 1.64/1.38 tff(2016,plain,
% 1.64/1.38 (((~hskp10) | c3_1(a1110)) <=> ((~hskp10) | c3_1(a1110))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(2017,axiom,((~hskp10) | c3_1(a1110)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.64/1.38 tff(2018,plain,
% 1.64/1.38 ((~hskp10) | c3_1(a1110)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 1.64/1.38 tff(2019,plain,
% 1.64/1.38 ((~hskp10) | c3_1(a1110)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2018, 2016])).
% 1.64/1.38 tff(2020,plain,
% 1.64/1.38 ((~hskp10) | c3_1(a1110)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2019, 2016])).
% 1.64/1.38 tff(2021,plain,
% 1.64/1.38 ((~hskp10) | c3_1(a1110)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2020, 2016])).
% 1.64/1.38 tff(2022,plain,
% 1.64/1.38 ((~hskp10) | c3_1(a1110)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2021, 2016])).
% 1.64/1.38 tff(2023,plain,
% 1.64/1.38 ((~hskp10) | c3_1(a1110)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2022, 2016])).
% 1.64/1.38 tff(2024,plain,
% 1.64/1.38 ((~hskp10) | c3_1(a1110)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2023, 2016])).
% 1.64/1.38 tff(2025,plain,
% 1.64/1.38 ((~hskp10) | c3_1(a1110)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2024, 2016])).
% 1.64/1.38 tff(2026,plain,
% 1.64/1.38 (c3_1(a1110)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[2025, 2001])).
% 1.64/1.38 tff(2027,plain,
% 1.64/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1110) | c2_1(a1110) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1110) | c2_1(a1110) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1110)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(2028,plain,
% 1.64/1.38 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110))) <=> (c1_1(a1110) | c2_1(a1110) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1110)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(2029,plain,
% 1.64/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1110) | c2_1(a1110) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1110))))),
% 1.64/1.38 inference(monotonicity,[status(thm)],[2028])).
% 1.64/1.38 tff(2030,plain,
% 1.64/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1110) | c2_1(a1110) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1110)))),
% 1.64/1.38 inference(transitivity,[status(thm)],[2029, 2027])).
% 1.64/1.38 tff(2031,plain,
% 1.64/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110)))),
% 1.64/1.38 inference(quant_inst,[status(thm)],[])).
% 1.64/1.38 tff(2032,plain,
% 1.64/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1110) | c2_1(a1110) | c2_1(a1104) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c3_1(a1110))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 1.64/1.38 tff(2033,plain,
% 1.64/1.38 ($false),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[2032, 113, 249, 248, 247, 2026, 2015, 2014, 2013, 2007, 1983, 246])).
% 1.64/1.38 tff(2034,plain,(c0_1(a1118) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | hskp8 | c2_1(a1118) | c3_1(a1118) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.38 tff(2035,plain,
% 1.64/1.38 (c0_1(a1118)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[2034, 1822, 1821, 1820, 1973, 1623, 1621, 691, 738, 727, 1622])).
% 1.64/1.38 tff(2036,plain,
% 1.64/1.38 ($false),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[1754, 113, 769, 768, 739, 228, 226, 45, 227, 46])).
% 1.64/1.38 tff(2037,plain,(c0_1(a1136) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1118)) | c3_1(a1118) | (~c0_1(a1118))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.38 tff(2038,plain,
% 1.64/1.38 (c0_1(a1136)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[2037, 2035, 738, 727, 1622, 1621, 691])).
% 1.64/1.38 tff(2039,plain,
% 1.64/1.38 (hskp1),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[405, 378, 1622, 1621, 34, 47, 1822, 1821, 1820, 35])).
% 1.64/1.39 tff(2040,plain,
% 1.64/1.39 (~c0_1(a1099)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[411, 2039])).
% 1.64/1.39 tff(2041,plain,
% 1.64/1.39 (hskp8 | hskp6 | c0_1(a1118)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[1980, 113, 1623, 1621, 1435])).
% 1.64/1.39 tff(2042,plain,
% 1.64/1.39 (hskp6),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2041, 378, 1973])).
% 1.64/1.39 tff(2043,plain,
% 1.64/1.39 (~c2_1(a1104)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[538, 2042])).
% 1.64/1.39 tff(2044,assumption,(~c3_1(a1108)), introduced(assumption)).
% 1.64/1.39 tff(2045,assumption,(~c1_1(a1108)), introduced(assumption)).
% 1.64/1.39 tff(2046,plain,
% 1.64/1.39 (c2_1(a1099)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[462, 2039])).
% 1.64/1.39 tff(2047,plain,
% 1.64/1.39 (c1_1(a1099)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[473, 2039])).
% 1.64/1.39 tff(2048,plain,
% 1.64/1.39 (c1_1(a1104)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[577, 2042])).
% 1.64/1.39 tff(2049,plain,
% 1.64/1.39 (c0_1(a1104)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[549, 2042])).
% 1.64/1.39 tff(2050,assumption,(c0_1(a1108)), introduced(assumption)).
% 1.64/1.39 tff(2051,plain,
% 1.64/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1108) | c3_1(a1108) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c0_1(a1108)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c0_1(a1108)))),
% 1.64/1.39 inference(rewrite,[status(thm)],[])).
% 1.64/1.39 tff(2052,plain,
% 1.64/1.39 (((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099))) <=> (c1_1(a1108) | c3_1(a1108) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c0_1(a1108)))),
% 1.64/1.39 inference(rewrite,[status(thm)],[])).
% 1.64/1.39 tff(2053,plain,
% 1.64/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1108) | c3_1(a1108) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c0_1(a1108))))),
% 1.64/1.39 inference(monotonicity,[status(thm)],[2052])).
% 1.64/1.39 tff(2054,plain,
% 1.64/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c0_1(a1108)))),
% 1.64/1.39 inference(transitivity,[status(thm)],[2053, 2051])).
% 1.64/1.39 tff(2055,plain,
% 1.64/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))),
% 1.64/1.39 inference(quant_inst,[status(thm)],[])).
% 1.64/1.39 tff(2056,plain,
% 1.64/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | (~c0_1(a1108))),
% 1.64/1.39 inference(modus_ponens,[status(thm)],[2055, 2054])).
% 1.64/1.39 tff(2057,plain,
% 1.64/1.39 ($false),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2056, 113, 2050, 2049, 2048, 2047, 2046, 2045, 2044, 2043, 2040, 1418])).
% 1.64/1.39 tff(2058,plain,(c0_1(a1118) | (~c0_1(a1108)) | c1_1(a1108) | c3_1(a1108) | c1_1(a1098) | c3_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.39 tff(2059,plain,
% 1.64/1.39 (c0_1(a1118)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2058, 1638, 1637, 1636, 34, 47, 35])).
% 1.64/1.39 tff(2060,plain,
% 1.64/1.39 (c0_1(a1136)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2037, 2059, 738, 727, 1622, 1621, 691])).
% 1.64/1.39 tff(2061,plain,
% 1.64/1.39 (hskp23 | (~c0_1(a1136))),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[1644, 113, 691, 738, 1638, 1637, 1636, 1633])).
% 1.64/1.39 tff(2062,plain,
% 1.64/1.39 (hskp23),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2061, 2060])).
% 1.64/1.39 tff(2063,plain,
% 1.64/1.39 (~c3_1(a1147)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[755, 2062])).
% 1.64/1.39 tff(2064,plain,
% 1.64/1.39 (~c2_1(a1147)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[803, 2062])).
% 1.64/1.39 tff(2065,plain,
% 1.64/1.39 (c0_1(a1147)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[766, 2062])).
% 1.64/1.39 tff(2066,plain,
% 1.64/1.39 (hskp19),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[1172, 1973, 35, 47])).
% 1.64/1.39 tff(2067,plain,
% 1.64/1.39 (~c2_1(a1127)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[900, 2066])).
% 1.64/1.39 tff(2068,plain,
% 1.64/1.39 (c3_1(a1127)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[912, 2066])).
% 1.64/1.39 tff(2069,plain,
% 1.64/1.39 (c1_1(a1127)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[923, 2066])).
% 1.64/1.39 tff(2070,plain,
% 1.64/1.39 (hskp2),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[1266, 113, 1822, 1821, 1820, 2069, 2068, 2067, 278])).
% 1.64/1.39 tff(2071,plain,
% 1.64/1.39 (c0_1(a1100)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[313, 2070])).
% 1.64/1.39 tff(2072,plain,
% 1.64/1.39 (~c3_1(a1100)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[291, 2070])).
% 1.64/1.39 tff(2073,plain,
% 1.64/1.39 (c2_1(a1100)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[302, 2070])).
% 1.64/1.39 tff(2074,assumption,(hskp5), introduced(assumption)).
% 1.64/1.39 tff(2075,plain,
% 1.64/1.39 (c3_1(a1103)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[153, 2074])).
% 1.64/1.39 tff(2076,plain,
% 1.64/1.39 (~c0_1(a1103)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[132, 2074])).
% 1.64/1.39 tff(2077,plain,
% 1.64/1.39 (~c2_1(a1103)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[126, 2074])).
% 1.64/1.39 tff(2078,plain,
% 1.64/1.39 ($false),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[375, 2077, 2076, 230, 228, 227, 226, 2075])).
% 1.64/1.39 tff(2079,plain,((~hskp5) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c3_1(a1118)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.39 tff(2080,plain,
% 1.64/1.39 (~hskp5),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2079, 2059, 1622, 1623, 1621])).
% 1.64/1.39 tff(2081,plain,
% 1.64/1.39 (hskp20),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[1305, 2080, 2066, 1822, 1821, 1820])).
% 1.64/1.39 tff(2082,plain,
% 1.64/1.39 (~c0_1(a1130)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[326, 2081])).
% 1.64/1.39 tff(2083,plain,
% 1.64/1.39 (~c3_1(a1130)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[332, 2081])).
% 1.64/1.39 tff(2084,plain,
% 1.64/1.39 ($false),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[1407, 2083, 2082, 2060, 2080, 2073, 2072, 738, 727, 716, 715, 634, 2071, 2065, 2064, 2063])).
% 1.64/1.39 tff(2085,plain,((~hskp9) | c1_1(a1098) | c3_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.39 tff(2086,plain,
% 1.64/1.39 (~hskp9),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2085, 47, 34, 35])).
% 1.64/1.39 tff(2087,plain,
% 1.64/1.39 (hskp13 | hskp9),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[1726, 113, 2071, 2073, 2072, 1702])).
% 1.64/1.39 tff(2088,plain,
% 1.64/1.39 (hskp13),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2087, 2086])).
% 1.64/1.39 tff(2089,plain,
% 1.64/1.39 (~c1_1(a1115)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[1229, 2088])).
% 1.64/1.39 tff(2090,plain,
% 1.64/1.39 (c2_1(a1115)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[1240, 2088])).
% 1.64/1.39 tff(2091,plain,
% 1.64/1.39 (c0_1(a1115)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[1371, 113, 1822, 1821, 1820, 2090, 716, 715, 2089, 634, 702])).
% 1.64/1.39 tff(2092,plain,
% 1.64/1.39 (~c3_1(a1115)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[1354, 2088])).
% 1.64/1.39 tff(2093,plain,
% 1.64/1.39 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))),
% 1.64/1.39 inference(rewrite,[status(thm)],[])).
% 1.64/1.39 tff(2094,plain,
% 1.64/1.39 ((hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115))) <=> (hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))),
% 1.64/1.39 inference(rewrite,[status(thm)],[])).
% 1.64/1.39 tff(2095,plain,
% 1.64/1.39 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115))))),
% 1.64/1.39 inference(monotonicity,[status(thm)],[2094])).
% 1.64/1.39 tff(2096,plain,
% 1.64/1.39 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115)))),
% 1.64/1.39 inference(transitivity,[status(thm)],[2095, 2093])).
% 1.64/1.39 tff(2097,plain,
% 1.64/1.39 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1115) | c3_1(a1115) | (~c0_1(a1115)))),
% 1.64/1.39 inference(quant_inst,[status(thm)],[])).
% 1.64/1.39 tff(2098,plain,
% 1.64/1.39 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1115))),
% 1.64/1.39 inference(modus_ponens,[status(thm)],[2097, 2096])).
% 1.64/1.39 tff(2099,plain,
% 1.64/1.39 (hskp23 | (~c0_1(a1136))),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2098, 113, 691, 738, 2089, 2092, 1633, 2091])).
% 1.64/1.39 tff(2100,plain,
% 1.64/1.39 (hskp23),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2099, 2038])).
% 1.64/1.39 tff(2101,plain,
% 1.64/1.39 (~c3_1(a1147)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[755, 2100])).
% 1.64/1.39 tff(2102,plain,
% 1.64/1.39 (~c2_1(a1147)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[803, 2100])).
% 1.64/1.39 tff(2103,plain,
% 1.64/1.39 (c0_1(a1147)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[766, 2100])).
% 1.64/1.39 tff(2104,plain,
% 1.64/1.39 (~hskp5),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2079, 2035, 1622, 1623, 1621])).
% 1.64/1.39 tff(2105,plain,
% 1.64/1.39 (hskp20),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[1305, 2104, 2066, 1822, 1821, 1820])).
% 1.64/1.39 tff(2106,plain,
% 1.64/1.39 (~c0_1(a1130)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[326, 2105])).
% 1.64/1.39 tff(2107,plain,
% 1.64/1.39 (~c3_1(a1130)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[332, 2105])).
% 1.64/1.39 tff(2108,plain,
% 1.64/1.39 ($false),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[1407, 2107, 2106, 2038, 2104, 2073, 2072, 738, 727, 716, 715, 634, 2071, 2103, 2102, 2101])).
% 1.64/1.39 tff(2109,plain,(c3_1(a1098) | c1_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.39 tff(2110,plain,
% 1.64/1.39 (c3_1(a1098)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2109, 35, 34])).
% 1.64/1.39 tff(2111,plain,
% 1.64/1.39 (((~hskp0) | (~c3_1(a1098))) <=> ((~hskp0) | (~c3_1(a1098)))),
% 1.64/1.39 inference(rewrite,[status(thm)],[])).
% 1.64/1.39 tff(2112,plain,
% 1.64/1.39 (((~c3_1(a1098)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a1098)))),
% 1.64/1.39 inference(rewrite,[status(thm)],[])).
% 1.64/1.39 tff(2113,axiom,((~c3_1(a1098)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 1.71/1.39 tff(2114,plain,
% 1.71/1.39 ((~hskp0) | (~c3_1(a1098))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2113, 2112])).
% 1.71/1.39 tff(2115,plain,
% 1.71/1.39 ((~hskp0) | (~c3_1(a1098))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2114, 2111])).
% 1.71/1.39 tff(2116,plain,
% 1.71/1.39 (~hskp0),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[2115, 2110])).
% 1.71/1.39 tff(2117,plain,
% 1.71/1.39 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.71/1.39 inference(bind,[status(th)],[])).
% 1.71/1.39 tff(2118,plain,
% 1.71/1.39 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.39 inference(quant_intro,[status(thm)],[2117])).
% 1.71/1.39 tff(2119,plain,
% 1.71/1.39 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2120,plain,
% 1.71/1.39 (^[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) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.71/1.39 inference(bind,[status(th)],[])).
% 1.71/1.39 tff(2121,plain,
% 1.71/1.39 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.39 inference(quant_intro,[status(thm)],[2120])).
% 1.71/1.39 tff(2122,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 1.71/1.39 tff(2123,plain,
% 1.71/1.39 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 1.71/1.39 tff(2124,plain,
% 1.71/1.39 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2123, 2119])).
% 1.71/1.39 tff(2125,plain,(
% 1.71/1.39 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.39 inference(skolemize,[status(sab)],[2124])).
% 1.71/1.39 tff(2126,plain,
% 1.71/1.39 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2125, 2118])).
% 1.71/1.39 tff(2127,plain,
% 1.71/1.39 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | c0_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | c0_1(a1098))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2128,plain,
% 1.71/1.39 ((hskp0 | (~ndr1_0) | c2_1(a1098) | c0_1(a1098) | (~c3_1(a1098)) | c2_1(a1098) | c1_1(a1098) | c0_1(a1098)) <=> (hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | c0_1(a1098))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2129,plain,
% 1.71/1.39 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1098) | c0_1(a1098) | (~c3_1(a1098)) | c2_1(a1098) | c1_1(a1098) | c0_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | c0_1(a1098)))),
% 1.71/1.39 inference(monotonicity,[status(thm)],[2128])).
% 1.71/1.39 tff(2130,plain,
% 1.71/1.39 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1098) | c0_1(a1098) | (~c3_1(a1098)) | c2_1(a1098) | c1_1(a1098) | c0_1(a1098))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | c0_1(a1098))),
% 1.71/1.39 inference(transitivity,[status(thm)],[2129, 2127])).
% 1.71/1.39 tff(2131,plain,
% 1.71/1.39 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1098) | c0_1(a1098) | (~c3_1(a1098)) | c2_1(a1098) | c1_1(a1098) | c0_1(a1098))),
% 1.71/1.39 inference(quant_inst,[status(thm)],[])).
% 1.71/1.39 tff(2132,plain,
% 1.71/1.39 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | c0_1(a1098)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2131, 2130])).
% 1.71/1.39 tff(2133,plain,
% 1.71/1.39 (hskp0 | (~c3_1(a1098)) | c0_1(a1098)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[2132, 113, 34, 35, 2126])).
% 1.71/1.39 tff(2134,plain,
% 1.71/1.39 (c0_1(a1098)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[2133, 2116, 2110])).
% 1.71/1.39 tff(2135,plain,
% 1.71/1.39 (^[U: $i] : refl((hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 1.71/1.39 inference(bind,[status(th)],[])).
% 1.71/1.39 tff(2136,plain,
% 1.71/1.39 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.71/1.39 inference(quant_intro,[status(thm)],[2135])).
% 1.71/1.39 tff(2137,plain,
% 1.71/1.39 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2138,plain,
% 1.71/1.39 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | 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)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp0) <=> ((hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp0))), rewrite(((hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp0) <=> (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp0) <=> (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 1.71/1.39 inference(bind,[status(th)],[])).
% 1.71/1.39 tff(2139,plain,
% 1.71/1.39 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp0) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.71/1.39 inference(quant_intro,[status(thm)],[2138])).
% 1.71/1.39 tff(2140,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 1.71/1.39 tff(2141,plain,
% 1.71/1.39 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 1.71/1.39 tff(2142,plain,
% 1.71/1.39 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2141, 2137])).
% 1.71/1.39 tff(2143,plain,(
% 1.71/1.39 ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.71/1.39 inference(skolemize,[status(sab)],[2142])).
% 1.71/1.39 tff(2144,plain,
% 1.71/1.39 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2143, 2136])).
% 1.71/1.39 tff(2145,plain,
% 1.71/1.39 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2146,plain,
% 1.71/1.39 ((hskp22 | hskp0 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098))) <=> (hskp22 | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2147,plain,
% 1.71/1.39 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0)))),
% 1.71/1.39 inference(monotonicity,[status(thm)],[2146])).
% 1.71/1.39 tff(2148,plain,
% 1.71/1.39 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0))),
% 1.71/1.39 inference(transitivity,[status(thm)],[2147, 2145])).
% 1.71/1.39 tff(2149,plain,
% 1.71/1.39 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098)))),
% 1.71/1.39 inference(quant_inst,[status(thm)],[])).
% 1.71/1.39 tff(2150,plain,
% 1.71/1.39 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2149, 2148])).
% 1.71/1.39 tff(2151,plain,
% 1.71/1.39 (hskp22 | hskp0 | c2_1(a1098) | (~c3_1(a1098))),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[2150, 113, 34, 2144])).
% 1.71/1.39 tff(2152,plain,
% 1.71/1.39 (hskp22),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[2151, 2116, 35, 2110])).
% 1.71/1.39 tff(2153,plain,
% 1.71/1.39 (((~hskp22) | (~c1_1(a1145))) <=> ((~hskp22) | (~c1_1(a1145)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2154,plain,
% 1.71/1.39 (((~c1_1(a1145)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a1145)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2155,axiom,((~c1_1(a1145)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.71/1.39 tff(2156,plain,
% 1.71/1.39 ((~hskp22) | (~c1_1(a1145))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2155, 2154])).
% 1.71/1.39 tff(2157,plain,
% 1.71/1.39 ((~hskp22) | (~c1_1(a1145))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2156, 2153])).
% 1.71/1.39 tff(2158,plain,
% 1.71/1.39 (~c1_1(a1145)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[2157, 2152])).
% 1.71/1.39 tff(2159,plain,
% 1.71/1.39 (((~hskp22) | c2_1(a1145)) <=> ((~hskp22) | c2_1(a1145))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2160,axiom,((~hskp22) | c2_1(a1145)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 1.71/1.39 tff(2161,plain,
% 1.71/1.39 ((~hskp22) | c2_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2160, 2159])).
% 1.71/1.39 tff(2162,plain,
% 1.71/1.39 ((~hskp22) | c2_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2161, 2159])).
% 1.71/1.39 tff(2163,plain,
% 1.71/1.39 ((~hskp22) | c2_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2162, 2159])).
% 1.71/1.39 tff(2164,plain,
% 1.71/1.39 ((~hskp22) | c2_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2163, 2159])).
% 1.71/1.39 tff(2165,plain,
% 1.71/1.39 ((~hskp22) | c2_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2164, 2159])).
% 1.71/1.39 tff(2166,plain,
% 1.71/1.39 ((~hskp22) | c2_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2165, 2159])).
% 1.71/1.39 tff(2167,plain,
% 1.71/1.39 ((~hskp22) | c2_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2166, 2159])).
% 1.71/1.39 tff(2168,plain,
% 1.71/1.39 ((~hskp22) | c2_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2167, 2159])).
% 1.71/1.39 tff(2169,plain,
% 1.71/1.39 (c2_1(a1145)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[2168, 2152])).
% 1.71/1.39 tff(2170,plain,
% 1.71/1.39 ((hskp23 | hskp30 | hskp0) <=> (hskp23 | hskp30 | hskp0)),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2171,plain,
% 1.71/1.39 (((hskp23 | hskp30) | hskp0) <=> (hskp23 | hskp30 | hskp0)),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2172,axiom,((hskp23 | hskp30) | hskp0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.71/1.39 tff(2173,plain,
% 1.71/1.39 (hskp23 | hskp30 | hskp0),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 1.71/1.39 tff(2174,plain,
% 1.71/1.39 (hskp23 | hskp30 | hskp0),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2173, 2170])).
% 1.71/1.39 tff(2175,plain,
% 1.71/1.39 (hskp23 | hskp30 | hskp0),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2174, 2170])).
% 1.71/1.39 tff(2176,plain,
% 1.71/1.39 (hskp23 | hskp30 | hskp0),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2175, 2170])).
% 1.71/1.39 tff(2177,plain,
% 1.71/1.39 (hskp23 | hskp30 | hskp0),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2176, 2170])).
% 1.71/1.39 tff(2178,plain,
% 1.71/1.39 (hskp23 | hskp30 | hskp0),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2177, 2170])).
% 1.71/1.39 tff(2179,plain,
% 1.71/1.39 (hskp23 | hskp30 | hskp0),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2178, 2170])).
% 1.71/1.39 tff(2180,plain,
% 1.71/1.39 (hskp23 | hskp30 | hskp0),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2179, 2170])).
% 1.71/1.39 tff(2181,plain,
% 1.71/1.39 (hskp23),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[2180, 670, 2116])).
% 1.71/1.39 tff(2182,plain,
% 1.71/1.39 (~c3_1(a1147)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[755, 2181])).
% 1.71/1.39 tff(2183,plain,
% 1.71/1.39 (~c2_1(a1147)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[803, 2181])).
% 1.71/1.39 tff(2184,plain,
% 1.71/1.39 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c1_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c1_1(a1147))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2185,plain,
% 1.71/1.39 ((hskp30 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147)) <=> (hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c1_1(a1147))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2186,plain,
% 1.71/1.39 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c1_1(a1147)))),
% 1.71/1.39 inference(monotonicity,[status(thm)],[2185])).
% 1.71/1.39 tff(2187,plain,
% 1.71/1.39 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c1_1(a1147))),
% 1.71/1.39 inference(transitivity,[status(thm)],[2186, 2184])).
% 1.71/1.39 tff(2188,plain,
% 1.71/1.39 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147))),
% 1.71/1.39 inference(quant_inst,[status(thm)],[])).
% 1.71/1.39 tff(2189,plain,
% 1.71/1.39 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c1_1(a1147)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 1.71/1.39 tff(2190,plain,
% 1.71/1.39 (c1_1(a1147)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[2189, 113, 670, 2183, 2182, 34, 2110, 668, 2134])).
% 1.71/1.39 tff(2191,plain,
% 1.71/1.39 (((~hskp22) | c3_1(a1145)) <=> ((~hskp22) | c3_1(a1145))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(2192,axiom,((~hskp22) | c3_1(a1145)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.71/1.39 tff(2193,plain,
% 1.71/1.39 ((~hskp22) | c3_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 1.71/1.39 tff(2194,plain,
% 1.71/1.39 ((~hskp22) | c3_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2193, 2191])).
% 1.71/1.39 tff(2195,plain,
% 1.71/1.39 ((~hskp22) | c3_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2194, 2191])).
% 1.71/1.39 tff(2196,plain,
% 1.71/1.39 ((~hskp22) | c3_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2195, 2191])).
% 1.71/1.39 tff(2197,plain,
% 1.71/1.39 ((~hskp22) | c3_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2196, 2191])).
% 1.71/1.39 tff(2198,plain,
% 1.71/1.39 ((~hskp22) | c3_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2197, 2191])).
% 1.71/1.39 tff(2199,plain,
% 1.71/1.39 ((~hskp22) | c3_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2198, 2191])).
% 1.71/1.39 tff(2200,plain,
% 1.71/1.39 ((~hskp22) | c3_1(a1145)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[2199, 2191])).
% 1.71/1.39 tff(2201,plain,
% 1.71/1.39 (c3_1(a1145)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[2200, 2152])).
% 1.71/1.39 tff(2202,plain,
% 1.71/1.39 (c0_1(a1147)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[766, 2181])).
% 1.71/1.39 tff(2203,plain,
% 1.71/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2204,plain,
% 1.71/1.40 (((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098))) <=> (c2_1(a1147) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2205,plain,
% 1.71/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.71/1.40 inference(monotonicity,[status(thm)],[2204])).
% 1.71/1.40 tff(2206,plain,
% 1.71/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.40 inference(transitivity,[status(thm)],[2205, 2203])).
% 1.71/1.40 tff(2207,plain,
% 1.71/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)))),
% 1.71/1.40 inference(quant_inst,[status(thm)],[])).
% 1.71/1.40 tff(2208,plain,
% 1.71/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 1.71/1.40 tff(2209,plain,
% 1.71/1.40 ((~c0_1(a1145)) | (~c1_1(a1147))),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[2208, 113, 2202, 2169, 2201, 2183, 34, 35, 2110, 246])).
% 1.71/1.40 tff(2210,plain,
% 1.71/1.40 (~c0_1(a1145)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[2209, 2190])).
% 1.71/1.40 tff(2211,plain,
% 1.71/1.40 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.71/1.40 inference(bind,[status(th)],[])).
% 1.71/1.40 tff(2212,plain,
% 1.71/1.40 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.71/1.40 inference(quant_intro,[status(thm)],[2211])).
% 1.71/1.40 tff(2213,plain,
% 1.71/1.40 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2214,plain,
% 1.71/1.40 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.71/1.40 inference(bind,[status(th)],[])).
% 1.71/1.40 tff(2215,plain,
% 1.71/1.40 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.71/1.40 inference(quant_intro,[status(thm)],[2214])).
% 1.71/1.40 tff(2216,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 1.71/1.40 tff(2217,plain,
% 1.71/1.40 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2216, 2215])).
% 1.71/1.40 tff(2218,plain,
% 1.71/1.40 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2217, 2213])).
% 1.71/1.40 tff(2219,plain,(
% 1.71/1.40 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.71/1.40 inference(skolemize,[status(sab)],[2218])).
% 1.71/1.40 tff(2220,plain,
% 1.71/1.40 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2219, 2212])).
% 1.71/1.40 tff(2221,plain,
% 1.71/1.40 (^[U: $i] : refl((hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.71/1.40 inference(bind,[status(th)],[])).
% 1.71/1.40 tff(2222,plain,
% 1.71/1.40 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.71/1.40 inference(quant_intro,[status(thm)],[2221])).
% 1.71/1.40 tff(2223,plain,
% 1.71/1.40 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2224,plain,
% 1.71/1.40 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp18))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp30) <=> ((hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp30))), rewrite(((hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp30) <=> (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp30) <=> (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.71/1.40 inference(bind,[status(th)],[])).
% 1.71/1.40 tff(2225,plain,
% 1.71/1.40 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp30) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.71/1.40 inference(quant_intro,[status(thm)],[2224])).
% 1.71/1.40 tff(2226,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 1.71/1.40 tff(2227,plain,
% 1.71/1.40 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2226, 2225])).
% 1.71/1.40 tff(2228,plain,
% 1.71/1.40 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2227, 2223])).
% 1.71/1.40 tff(2229,plain,(
% 1.71/1.40 ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.71/1.40 inference(skolemize,[status(sab)],[2228])).
% 1.71/1.40 tff(2230,plain,
% 1.71/1.40 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2229, 2222])).
% 1.71/1.40 tff(2231,plain,
% 1.71/1.40 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp18 | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2232,plain,
% 1.71/1.40 ((hskp30 | hskp18 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098))) <=> (hskp30 | hskp18 | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2233,plain,
% 1.71/1.40 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098))))),
% 1.71/1.40 inference(monotonicity,[status(thm)],[2232])).
% 1.71/1.40 tff(2234,plain,
% 1.71/1.40 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp18 | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)))),
% 1.71/1.40 inference(transitivity,[status(thm)],[2233, 2231])).
% 1.71/1.40 tff(2235,plain,
% 1.71/1.40 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)))),
% 1.71/1.40 inference(quant_inst,[status(thm)],[])).
% 1.71/1.40 tff(2236,plain,
% 1.71/1.40 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp18 | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2235, 2234])).
% 1.71/1.40 tff(2237,plain,
% 1.71/1.40 (hskp30 | hskp18 | (~c3_1(a1098)) | (~c0_1(a1098))),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[2236, 113, 34, 2230])).
% 1.71/1.40 tff(2238,plain,
% 1.71/1.40 (hskp18),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[2237, 670, 2110, 2134])).
% 1.71/1.40 tff(2239,plain,
% 1.71/1.40 (((~hskp18) | (~c1_1(a1125))) <=> ((~hskp18) | (~c1_1(a1125)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2240,plain,
% 1.71/1.40 (((~c1_1(a1125)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a1125)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2241,axiom,((~c1_1(a1125)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.71/1.40 tff(2242,plain,
% 1.71/1.40 ((~hskp18) | (~c1_1(a1125))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 1.71/1.40 tff(2243,plain,
% 1.71/1.40 ((~hskp18) | (~c1_1(a1125))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2242, 2239])).
% 1.71/1.40 tff(2244,plain,
% 1.71/1.40 (~c1_1(a1125)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[2243, 2238])).
% 1.71/1.40 tff(2245,plain,
% 1.71/1.40 (((~hskp18) | c2_1(a1125)) <=> ((~hskp18) | c2_1(a1125))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2246,axiom,((~hskp18) | c2_1(a1125)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.71/1.40 tff(2247,plain,
% 1.71/1.40 ((~hskp18) | c2_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2246, 2245])).
% 1.71/1.40 tff(2248,plain,
% 1.71/1.40 ((~hskp18) | c2_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2247, 2245])).
% 1.71/1.40 tff(2249,plain,
% 1.71/1.40 ((~hskp18) | c2_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2248, 2245])).
% 1.71/1.40 tff(2250,plain,
% 1.71/1.40 ((~hskp18) | c2_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2249, 2245])).
% 1.71/1.40 tff(2251,plain,
% 1.71/1.40 ((~hskp18) | c2_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2250, 2245])).
% 1.71/1.40 tff(2252,plain,
% 1.71/1.40 ((~hskp18) | c2_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2251, 2245])).
% 1.71/1.40 tff(2253,plain,
% 1.71/1.40 ((~hskp18) | c2_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2252, 2245])).
% 1.71/1.40 tff(2254,plain,
% 1.71/1.40 ((~hskp18) | c2_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2253, 2245])).
% 1.71/1.40 tff(2255,plain,
% 1.71/1.40 (c2_1(a1125)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[2254, 2238])).
% 1.71/1.40 tff(2256,plain,
% 1.71/1.40 (((~hskp18) | c0_1(a1125)) <=> ((~hskp18) | c0_1(a1125))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2257,axiom,((~hskp18) | c0_1(a1125)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.71/1.40 tff(2258,plain,
% 1.71/1.40 ((~hskp18) | c0_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 1.71/1.40 tff(2259,plain,
% 1.71/1.40 ((~hskp18) | c0_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2258, 2256])).
% 1.71/1.40 tff(2260,plain,
% 1.71/1.40 ((~hskp18) | c0_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2259, 2256])).
% 1.71/1.40 tff(2261,plain,
% 1.71/1.40 ((~hskp18) | c0_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2260, 2256])).
% 1.71/1.40 tff(2262,plain,
% 1.71/1.40 ((~hskp18) | c0_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2261, 2256])).
% 1.71/1.40 tff(2263,plain,
% 1.71/1.40 ((~hskp18) | c0_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2262, 2256])).
% 1.71/1.40 tff(2264,plain,
% 1.71/1.40 ((~hskp18) | c0_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2263, 2256])).
% 1.71/1.40 tff(2265,plain,
% 1.71/1.40 ((~hskp18) | c0_1(a1125)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2264, 2256])).
% 1.71/1.40 tff(2266,plain,
% 1.71/1.40 (c0_1(a1125)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[2265, 2238])).
% 1.71/1.40 tff(2267,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2268,plain,
% 1.71/1.40 ((hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125))) <=> (hskp7 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2269,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125))))),
% 1.71/1.40 inference(monotonicity,[status(thm)],[2268])).
% 1.71/1.40 tff(2270,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.71/1.40 inference(transitivity,[status(thm)],[2269, 2267])).
% 1.71/1.40 tff(2271,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))),
% 1.71/1.40 inference(quant_inst,[status(thm)],[])).
% 1.71/1.40 tff(2272,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2271, 2270])).
% 1.71/1.40 tff(2273,plain,
% 1.71/1.40 (hskp7),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[2272, 113, 2266, 2255, 2244, 35, 2110, 2220, 2134])).
% 1.71/1.40 tff(2274,plain,
% 1.71/1.40 (~c1_1(a1105)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[633, 2273])).
% 1.71/1.40 tff(2275,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2276,plain,
% 1.71/1.40 ((hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125))) <=> (hskp20 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2277,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125))))),
% 1.71/1.40 inference(monotonicity,[status(thm)],[2276])).
% 1.71/1.40 tff(2278,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.71/1.40 inference(transitivity,[status(thm)],[2277, 2275])).
% 1.71/1.40 tff(2279,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))),
% 1.71/1.40 inference(quant_inst,[status(thm)],[])).
% 1.71/1.40 tff(2280,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1125) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1125)) | (~c2_1(a1125))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2279, 2278])).
% 1.71/1.40 tff(2281,plain,
% 1.71/1.40 (hskp20),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[2280, 113, 2266, 2255, 2244, 35, 2110, 1005, 2134])).
% 1.71/1.40 tff(2282,plain,
% 1.71/1.40 (~c3_1(a1130)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[332, 2281])).
% 1.71/1.40 tff(2283,plain,
% 1.71/1.40 (((~hskp20) | (~c2_1(a1130))) <=> ((~hskp20) | (~c2_1(a1130)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2284,plain,
% 1.71/1.40 (((~c2_1(a1130)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a1130)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2285,axiom,((~c2_1(a1130)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.71/1.40 tff(2286,plain,
% 1.71/1.40 ((~hskp20) | (~c2_1(a1130))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2285, 2284])).
% 1.71/1.40 tff(2287,plain,
% 1.71/1.40 ((~hskp20) | (~c2_1(a1130))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2286, 2283])).
% 1.71/1.40 tff(2288,plain,
% 1.71/1.40 (~c2_1(a1130)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[2287, 2281])).
% 1.71/1.40 tff(2289,plain,
% 1.71/1.40 (c3_1(a1105)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[657, 2273])).
% 1.71/1.40 tff(2290,plain,
% 1.71/1.40 (c0_1(a1105)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[646, 2273])).
% 1.71/1.40 tff(2291,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c2_1(a1130) | c3_1(a1130) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1130) | c3_1(a1130) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2292,plain,
% 1.71/1.40 ((hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130)) <=> (hskp30 | c2_1(a1130) | c3_1(a1130) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2293,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c2_1(a1130) | c3_1(a1130) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130)))),
% 1.71/1.40 inference(monotonicity,[status(thm)],[2292])).
% 1.71/1.40 tff(2294,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1130) | c3_1(a1130) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130))),
% 1.71/1.40 inference(transitivity,[status(thm)],[2293, 2291])).
% 1.71/1.40 tff(2295,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130))),
% 1.71/1.40 inference(quant_inst,[status(thm)],[])).
% 1.71/1.40 tff(2296,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1130) | c3_1(a1130) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1130)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[2295, 2294])).
% 1.71/1.40 tff(2297,plain,
% 1.71/1.40 (c1_1(a1130)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[2296, 113, 670, 2290, 2289, 2288, 2282, 2274, 668])).
% 1.71/1.40 tff(2298,plain,
% 1.71/1.40 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.71/1.40 inference(bind,[status(th)],[])).
% 1.71/1.40 tff(2299,plain,
% 1.71/1.40 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.71/1.40 inference(quant_intro,[status(thm)],[2298])).
% 1.71/1.40 tff(2300,plain,
% 1.71/1.40 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(2301,plain,
% 1.71/1.40 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.71/1.40 inference(bind,[status(th)],[])).
% 1.71/1.40 tff(2302,plain,
% 1.71/1.40 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.71/1.40 inference(quant_intro,[status(thm)],[2301])).
% 1.71/1.41 tff(2303,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.71/1.41 tff(2304,plain,
% 1.71/1.41 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[2303, 2302])).
% 1.71/1.41 tff(2305,plain,
% 1.71/1.41 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[2304, 2300])).
% 1.71/1.41 tff(2306,plain,(
% 1.71/1.41 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.71/1.41 inference(skolemize,[status(sab)],[2305])).
% 1.71/1.41 tff(2307,plain,
% 1.71/1.41 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[2306, 2299])).
% 1.71/1.41 tff(2308,plain,
% 1.71/1.41 (~c0_1(a1130)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[326, 2281])).
% 1.71/1.41 tff(2309,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c1_1(a1130)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c1_1(a1130)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2310,plain,
% 1.71/1.41 ((hskp3 | (~ndr1_0) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130))) <=> (hskp3 | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c1_1(a1130)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2311,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c1_1(a1130)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145))))),
% 1.71/1.41 inference(monotonicity,[status(thm)],[2310])).
% 1.71/1.41 tff(2312,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c1_1(a1130)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.41 inference(transitivity,[status(thm)],[2311, 2309])).
% 1.71/1.41 tff(2313,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))),
% 1.71/1.41 inference(quant_inst,[status(thm)],[])).
% 1.71/1.41 tff(2314,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c1_1(a1130)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[2313, 2312])).
% 1.71/1.41 tff(2315,plain,
% 1.71/1.41 (hskp3),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[2314, 113, 2169, 2201, 2308, 2288, 2307, 2297, 2210])).
% 1.71/1.41 tff(2316,plain,
% 1.71/1.41 (~c3_1(a1101)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1088, 2315])).
% 1.71/1.41 tff(2317,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2318,plain,
% 1.71/1.41 ((hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145))) <=> (hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2319,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145))))),
% 1.71/1.41 inference(monotonicity,[status(thm)],[2318])).
% 1.71/1.41 tff(2320,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.41 inference(transitivity,[status(thm)],[2319, 2317])).
% 1.71/1.41 tff(2321,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))),
% 1.71/1.41 inference(quant_inst,[status(thm)],[])).
% 1.71/1.41 tff(2322,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1145) | (~c2_1(a1145)) | (~c3_1(a1145))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[2321, 2320])).
% 1.71/1.41 tff(2323,plain,
% 1.71/1.41 (hskp4),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[2322, 113, 2169, 2201, 34, 35, 1898, 2134, 2210])).
% 1.71/1.41 tff(2324,plain,
% 1.71/1.41 (~c3_1(a1102)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1529, 2323])).
% 1.71/1.41 tff(2325,plain,
% 1.71/1.41 (c2_1(a1101)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1099, 2315])).
% 1.71/1.41 tff(2326,plain,
% 1.71/1.41 (c1_1(a1101)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1110, 2315])).
% 1.71/1.41 tff(2327,plain,
% 1.71/1.41 (c1_1(a1102)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1549, 2323])).
% 1.71/1.41 tff(2328,plain,
% 1.71/1.41 (c0_1(a1102)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1560, 2323])).
% 1.71/1.41 tff(2329,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1102) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1102)) | (~c0_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1102) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1102)) | (~c0_1(a1102)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2330,plain,
% 1.71/1.41 ((hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102))) <=> (hskp5 | c3_1(a1102) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1102)) | (~c0_1(a1102)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2331,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1102) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1102)) | (~c0_1(a1102))))),
% 1.71/1.41 inference(monotonicity,[status(thm)],[2330])).
% 1.71/1.41 tff(2332,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1102) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1102)) | (~c0_1(a1102)))),
% 1.71/1.41 inference(transitivity,[status(thm)],[2331, 2329])).
% 1.71/1.41 tff(2333,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)))),
% 1.71/1.41 inference(quant_inst,[status(thm)],[])).
% 1.71/1.41 tff(2334,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1102) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1102)) | (~c0_1(a1102))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[2333, 2332])).
% 1.71/1.41 tff(2335,plain,
% 1.71/1.41 (hskp5),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[2334, 113, 2328, 2327, 2326, 2325, 2324, 2316, 1279])).
% 1.71/1.41 tff(2336,plain,
% 1.71/1.41 (~c2_1(a1103)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[126, 2335])).
% 1.71/1.41 tff(2337,plain,
% 1.71/1.41 (~c0_1(a1103)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[132, 2335])).
% 1.71/1.41 tff(2338,plain,
% 1.71/1.41 (c3_1(a1103)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[153, 2335])).
% 1.71/1.41 tff(2339,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1147)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2340,plain,
% 1.71/1.41 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103))) <=> (hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1147)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2341,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1147))))),
% 1.71/1.41 inference(monotonicity,[status(thm)],[2340])).
% 1.71/1.41 tff(2342,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1147)))),
% 1.71/1.41 inference(transitivity,[status(thm)],[2341, 2339])).
% 1.71/1.41 tff(2343,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)))),
% 1.71/1.41 inference(quant_inst,[status(thm)],[])).
% 1.71/1.41 tff(2344,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | (~c1_1(a1147))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 1.71/1.41 tff(2345,plain,
% 1.71/1.41 ($false),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[2344, 113, 770, 2338, 2183, 2182, 2337, 2336, 67, 2190])).
% 1.71/1.41 tff(2346,plain,(hskp30 | hskp29 | c1_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.41 tff(2347,plain,
% 1.71/1.41 (hskp30),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[2346, 770, 34, 35])).
% 1.71/1.41 tff(2348,plain,
% 1.71/1.41 (c1_1(a1136)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[690, 2347])).
% 1.71/1.41 tff(2349,plain,
% 1.71/1.41 (c2_1(a1136)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[737, 2347])).
% 1.71/1.41 tff(2350,plain,
% 1.71/1.41 (c3_1(a1136)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[726, 2347])).
% 1.71/1.41 tff(2351,plain,
% 1.71/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2352,plain,
% 1.71/1.41 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145))) <=> (c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2353,plain,
% 1.71/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1145) | (~c2_1(a1145))))),
% 1.71/1.41 inference(monotonicity,[status(thm)],[2352])).
% 1.71/1.41 tff(2354,plain,
% 1.71/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.71/1.41 inference(transitivity,[status(thm)],[2353, 2351])).
% 1.71/1.41 tff(2355,plain,
% 1.71/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.71/1.41 inference(quant_inst,[status(thm)],[])).
% 1.71/1.41 tff(2356,plain,
% 1.71/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1145) | (~c2_1(a1145))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[2355, 2354])).
% 1.71/1.41 tff(2357,plain,
% 1.71/1.41 (c0_1(a1145)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[2356, 113, 2348, 2349, 2350, 2169, 2158, 34, 35, 1155, 2134])).
% 1.71/1.41 tff(2358,plain,
% 1.71/1.41 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.71/1.41 inference(bind,[status(th)],[])).
% 1.71/1.41 tff(2359,plain,
% 1.71/1.41 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.71/1.41 inference(quant_intro,[status(thm)],[2358])).
% 1.71/1.41 tff(2360,plain,
% 1.71/1.41 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2361,plain,
% 1.71/1.41 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.71/1.41 inference(bind,[status(th)],[])).
% 1.71/1.41 tff(2362,plain,
% 1.71/1.41 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.71/1.41 inference(quant_intro,[status(thm)],[2361])).
% 1.71/1.41 tff(2363,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 1.71/1.41 tff(2364,plain,
% 1.71/1.41 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[2363, 2362])).
% 1.71/1.41 tff(2365,plain,
% 1.71/1.41 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[2364, 2360])).
% 1.71/1.41 tff(2366,plain,(
% 1.71/1.41 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.71/1.41 inference(skolemize,[status(sab)],[2365])).
% 1.71/1.41 tff(2367,plain,
% 1.71/1.41 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[2366, 2359])).
% 1.71/1.41 tff(2368,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2369,plain,
% 1.71/1.41 ((hskp9 | (~ndr1_0) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098))) <=> (hskp9 | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2370,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145))))),
% 1.71/1.41 inference(monotonicity,[status(thm)],[2369])).
% 1.71/1.41 tff(2371,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.71/1.41 inference(transitivity,[status(thm)],[2370, 2368])).
% 1.71/1.41 tff(2372,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1098) | c1_1(a1098) | (~c3_1(a1098)))),
% 1.71/1.41 inference(quant_inst,[status(thm)],[])).
% 1.71/1.41 tff(2373,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a1145) | c1_1(a1098) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[2372, 2371])).
% 1.71/1.41 tff(2374,plain,
% 1.71/1.41 (hskp9 | (~c0_1(a1145))),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[2373, 113, 2169, 2158, 34, 35, 2110, 2367])).
% 1.71/1.41 tff(2375,plain,
% 1.71/1.41 (hskp9),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[2374, 2357])).
% 1.71/1.41 tff(2376,plain,
% 1.71/1.41 (hskp23),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1653, 2375, 770, 2349, 2348])).
% 1.71/1.41 tff(2377,plain,
% 1.71/1.41 (~c3_1(a1147)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[755, 2376])).
% 1.71/1.41 tff(2378,plain,
% 1.71/1.41 (~c2_1(a1147)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[803, 2376])).
% 1.71/1.41 tff(2379,plain,
% 1.71/1.41 (c0_1(a1147)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[766, 2376])).
% 1.71/1.41 tff(2380,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2381,plain,
% 1.71/1.41 ((hskp2 | (~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145))) <=> (hskp2 | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2382,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145))))),
% 1.71/1.41 inference(monotonicity,[status(thm)],[2381])).
% 1.71/1.41 tff(2383,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.41 inference(transitivity,[status(thm)],[2382, 2380])).
% 1.71/1.41 tff(2384,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))),
% 1.71/1.41 inference(quant_inst,[status(thm)],[])).
% 1.71/1.41 tff(2385,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 1.71/1.41 tff(2386,plain,
% 1.71/1.41 (hskp2 | (~c0_1(a1145))),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[2385, 113, 2169, 2201, 2158, 1065])).
% 1.71/1.41 tff(2387,plain,
% 1.71/1.41 (hskp2),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[2386, 2357])).
% 1.71/1.41 tff(2388,plain,
% 1.71/1.41 (c2_1(a1100)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[302, 2387])).
% 1.71/1.41 tff(2389,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2390,plain,
% 1.71/1.41 ((hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145))) <=> (hskp7 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(2391,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145))))),
% 1.71/1.41 inference(monotonicity,[status(thm)],[2390])).
% 1.71/1.41 tff(2392,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.71/1.41 inference(transitivity,[status(thm)],[2391, 2389])).
% 1.71/1.41 tff(2393,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(2394,plain,
% 1.71/1.42 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145))),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[2393, 2392])).
% 1.71/1.42 tff(2395,plain,
% 1.71/1.42 (hskp7 | (~c0_1(a1145))),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2394, 113, 2169, 2158, 35, 2110, 2220, 2134])).
% 1.71/1.42 tff(2396,plain,
% 1.71/1.42 (hskp7),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2395, 2357])).
% 1.71/1.42 tff(2397,plain,
% 1.71/1.42 (~c1_1(a1105)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[633, 2396])).
% 1.71/1.42 tff(2398,plain,
% 1.71/1.42 (c3_1(a1105)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[657, 2396])).
% 1.71/1.42 tff(2399,plain,
% 1.71/1.42 (c0_1(a1105)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[646, 2396])).
% 1.71/1.42 tff(2400,plain,
% 1.71/1.42 (~c3_1(a1100)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[291, 2387])).
% 1.71/1.42 tff(2401,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2402,plain,
% 1.71/1.42 ((hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145))) <=> (hskp20 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2403,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145))))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[2402])).
% 1.71/1.42 tff(2404,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.71/1.42 inference(transitivity,[status(thm)],[2403, 2401])).
% 1.71/1.42 tff(2405,plain,
% 1.71/1.42 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(2406,plain,
% 1.71/1.42 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1145) | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c0_1(a1145)) | (~c2_1(a1145))),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[2405, 2404])).
% 1.71/1.42 tff(2407,plain,
% 1.71/1.42 (hskp20 | (~c0_1(a1145))),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2406, 113, 2169, 2158, 35, 2110, 1005, 2134])).
% 1.71/1.42 tff(2408,plain,
% 1.71/1.42 (hskp20),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2407, 2357])).
% 1.71/1.42 tff(2409,plain,
% 1.71/1.42 (~c3_1(a1130)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[332, 2408])).
% 1.71/1.42 tff(2410,plain,
% 1.71/1.42 (~c0_1(a1130)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[326, 2408])).
% 1.71/1.42 tff(2411,plain,
% 1.71/1.42 (c0_1(a1100)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[313, 2387])).
% 1.71/1.42 tff(2412,plain,
% 1.71/1.42 (c0_1(a1136)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[797, 2379, 2348, 2349, 2350, 2377, 770])).
% 1.71/1.42 tff(2413,plain,
% 1.71/1.42 (hskp5),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1407, 2412, 2411, 2410, 2409, 2400, 2349, 2350, 2399, 2398, 2397, 2388, 2379, 2378, 2377])).
% 1.71/1.42 tff(2414,plain,
% 1.71/1.42 (~c2_1(a1103)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[126, 2413])).
% 1.71/1.42 tff(2415,plain,
% 1.71/1.42 (~c0_1(a1103)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[132, 2413])).
% 1.71/1.42 tff(2416,plain,
% 1.71/1.42 (~c2_1(a1130)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2287, 2408])).
% 1.71/1.42 tff(2417,plain,
% 1.71/1.42 (c3_1(a1103)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[153, 2413])).
% 1.71/1.42 tff(2418,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1130) | c2_1(a1130) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1130) | c2_1(a1130) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1130))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2419,plain,
% 1.71/1.42 ((hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130)) <=> (hskp0 | c0_1(a1130) | c2_1(a1130) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1130))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2420,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1130) | c2_1(a1130) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1130)))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[2419])).
% 1.71/1.42 tff(2421,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1130) | c2_1(a1130) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1130))),
% 1.71/1.42 inference(transitivity,[status(thm)],[2420, 2418])).
% 1.71/1.42 tff(2422,plain,
% 1.71/1.42 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(2423,plain,
% 1.71/1.42 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1130) | c2_1(a1130) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1130)),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 1.71/1.42 tff(2424,plain,
% 1.71/1.42 (c1_1(a1130)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2423, 113, 2116, 2417, 2410, 2416, 2415, 2414, 2126])).
% 1.71/1.42 tff(2425,plain,
% 1.71/1.42 ($false),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1044, 113, 2349, 2350, 2379, 2378, 2377, 2410, 2409, 344, 2412, 2424])).
% 1.71/1.42 tff(2426,plain,(hskp29 | c1_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.42 tff(2427,plain,
% 1.71/1.42 (hskp29),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2426, 35, 34])).
% 1.71/1.42 tff(2428,plain,
% 1.71/1.42 (c3_1(a1116)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[201, 2427])).
% 1.71/1.42 tff(2429,plain,
% 1.71/1.42 (c2_1(a1116)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[212, 2427])).
% 1.71/1.42 tff(2430,plain,
% 1.71/1.42 (c0_1(a1116)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[223, 2427])).
% 1.71/1.42 tff(2431,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2432,plain,
% 1.71/1.42 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145))) <=> (c1_1(a1145) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2433,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1145) | (~c2_1(a1145))))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[2432])).
% 1.71/1.42 tff(2434,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.71/1.42 inference(transitivity,[status(thm)],[2433, 2431])).
% 1.71/1.42 tff(2435,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(2436,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1145) | (~c2_1(a1145))),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[2435, 2434])).
% 1.71/1.42 tff(2437,plain,
% 1.71/1.42 (c0_1(a1145)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2436, 113, 2430, 2429, 2428, 2169, 2158, 34, 2110, 702, 2134])).
% 1.71/1.42 tff(2438,plain,
% 1.71/1.42 (hskp20),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2407, 2437])).
% 1.71/1.42 tff(2439,plain,
% 1.71/1.42 (~c2_1(a1130)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2287, 2438])).
% 1.71/1.42 tff(2440,plain,
% 1.71/1.42 (~c3_1(a1130)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[332, 2438])).
% 1.71/1.42 tff(2441,plain,
% 1.71/1.42 (~c0_1(a1130)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[326, 2438])).
% 1.71/1.42 tff(2442,assumption,(c0_1(a1145)), introduced(assumption)).
% 1.71/1.42 tff(2443,assumption,(~c2_1(a1130)), introduced(assumption)).
% 1.71/1.42 tff(2444,assumption,(~c1_1(a1145)), introduced(assumption)).
% 1.71/1.42 tff(2445,assumption,(c3_1(a1145)), introduced(assumption)).
% 1.71/1.42 tff(2446,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c1_1(a1145) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130) | (~c0_1(a1145)) | (~c3_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c1_1(a1145) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130) | (~c0_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2447,plain,
% 1.71/1.42 ((hskp30 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c0_1(a1145)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130)) <=> (hskp30 | c1_1(a1145) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130) | (~c0_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2448,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c0_1(a1145)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c1_1(a1145) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130) | (~c0_1(a1145)) | (~c3_1(a1145))))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[2447])).
% 1.71/1.42 tff(2449,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c0_1(a1145)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c1_1(a1145) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130) | (~c0_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.42 inference(transitivity,[status(thm)],[2448, 2446])).
% 1.71/1.42 tff(2450,plain,
% 1.71/1.42 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c0_1(a1145)) | c2_1(a1130) | c1_1(a1130) | c3_1(a1130))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(2451,plain,
% 1.71/1.42 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c1_1(a1145) | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130) | (~c0_1(a1145)) | (~c3_1(a1145))),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 1.71/1.42 tff(2452,plain,
% 1.71/1.42 (hskp30 | c1_1(a1130)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2451, 113, 2445, 2444, 2443, 345, 668, 2442])).
% 1.71/1.42 tff(2453,plain,
% 1.71/1.42 (c1_1(a1130)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2452, 670])).
% 1.71/1.42 tff(2454,assumption,(~hskp0), introduced(assumption)).
% 1.71/1.42 tff(2455,plain,
% 1.71/1.42 (hskp23),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2180, 670, 2454])).
% 1.71/1.42 tff(2456,plain,
% 1.71/1.42 (~c3_1(a1147)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[755, 2455])).
% 1.71/1.42 tff(2457,plain,
% 1.71/1.42 (~c2_1(a1147)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[803, 2455])).
% 1.71/1.42 tff(2458,plain,
% 1.71/1.42 (c0_1(a1147)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[766, 2455])).
% 1.71/1.42 tff(2459,plain,
% 1.71/1.42 ($false),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1325, 113, 249, 248, 247, 2458, 2457, 2456, 334, 345, 344, 2453])).
% 1.71/1.42 tff(2460,plain,(hskp30 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | c0_1(a1130) | c3_1(a1130) | (~c3_1(a1145)) | c1_1(a1145) | c2_1(a1130) | (~c0_1(a1145)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.71/1.42 tff(2461,plain,
% 1.71/1.42 (hskp30),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2460, 2430, 2429, 2428, 2441, 2440, 2201, 2158, 2439, 2437, 2116])).
% 1.71/1.42 tff(2462,plain,
% 1.71/1.42 (c3_1(a1136)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[726, 2461])).
% 1.71/1.42 tff(2463,plain,
% 1.71/1.42 (c2_1(a1136)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[737, 2461])).
% 1.71/1.42 tff(2464,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2465,plain,
% 1.71/1.42 ((hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136))) <=> (hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2466,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136))))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[2465])).
% 1.71/1.42 tff(2467,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)))),
% 1.71/1.42 inference(transitivity,[status(thm)],[2466, 2464])).
% 1.71/1.42 tff(2468,plain,
% 1.71/1.42 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a1098) | c1_1(a1098) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(2469,plain,
% 1.71/1.42 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp4 | c1_1(a1098) | c2_1(a1098) | (~ndr1_0) | (~c0_1(a1098)) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136))),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[2468, 2467])).
% 1.71/1.42 tff(2470,plain,
% 1.71/1.42 (hskp4),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2469, 113, 2463, 2462, 34, 35, 1898, 2134, 46])).
% 1.71/1.42 tff(2471,plain,
% 1.71/1.42 (~c3_1(a1102)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1529, 2470])).
% 1.71/1.42 tff(2472,plain,
% 1.71/1.42 (c1_1(a1136)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[690, 2461])).
% 1.71/1.42 tff(2473,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2474,plain,
% 1.71/1.42 ((hskp16 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136))) <=> (hskp16 | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2475,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136))))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[2474])).
% 1.71/1.42 tff(2476,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.71/1.42 inference(transitivity,[status(thm)],[2475, 2473])).
% 1.71/1.42 tff(2477,plain,
% 1.71/1.42 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1098) | (~c3_1(a1098)) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136)))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(2478,plain,
% 1.71/1.42 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1098) | (~c3_1(a1098)) | (~ndr1_0) | (~c0_1(a1098)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1136))),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[2477, 2476])).
% 1.71/1.42 tff(2479,plain,
% 1.71/1.42 (hskp16),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2478, 113, 2472, 2462, 35, 2110, 1916, 2134, 46])).
% 1.71/1.42 tff(2480,plain,
% 1.71/1.42 (~c0_1(a1121)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1939, 2479])).
% 1.71/1.42 tff(2481,plain,
% 1.71/1.42 (c1_1(a1102)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1549, 2470])).
% 1.71/1.42 tff(2482,plain,
% 1.71/1.42 (c0_1(a1102)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1560, 2470])).
% 1.71/1.42 tff(2483,plain,
% 1.71/1.42 (c3_1(a1121)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1952, 2479])).
% 1.71/1.42 tff(2484,plain,
% 1.71/1.42 (c1_1(a1121)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1963, 2479])).
% 1.71/1.42 tff(2485,plain,
% 1.71/1.42 ($false),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1970, 113, 2472, 2463, 2462, 2484, 2483, 2482, 2481, 2480, 2471, 45])).
% 1.71/1.42 tff(2486,plain,(c0_1(a1136) | c1_1(a1098) | c2_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.42 tff(2487,plain,
% 1.71/1.42 (c0_1(a1136)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2486, 35, 34])).
% 1.71/1.42 tff(2488,plain,
% 1.71/1.42 (hskp9),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2374, 2437])).
% 1.71/1.42 tff(2489,plain,
% 1.71/1.42 (~c3_1(a1108)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[497, 2488])).
% 1.71/1.42 tff(2490,plain,
% 1.71/1.42 (~c1_1(a1108)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[503, 2488])).
% 1.71/1.42 tff(2491,plain,
% 1.71/1.42 (c0_1(a1108)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[514, 2488])).
% 1.71/1.42 tff(2492,plain,
% 1.71/1.42 (hskp23 | (~c0_1(a1136))),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1644, 113, 2472, 2463, 2491, 2490, 2489, 1633])).
% 1.71/1.42 tff(2493,plain,
% 1.71/1.42 (hskp23),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2492, 2487])).
% 1.71/1.42 tff(2494,plain,
% 1.71/1.42 (~c3_1(a1147)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[755, 2493])).
% 1.71/1.42 tff(2495,plain,
% 1.71/1.42 (~c2_1(a1147)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[803, 2493])).
% 1.71/1.42 tff(2496,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1145) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1145)) | (~c3_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1145) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2497,plain,
% 1.71/1.42 ((hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145))) <=> (hskp2 | c1_1(a1145) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2498,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1145) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1145)) | (~c3_1(a1145))))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[2497])).
% 1.71/1.42 tff(2499,plain,
% 1.71/1.42 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1145) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.71/1.42 inference(transitivity,[status(thm)],[2498, 2496])).
% 1.71/1.42 tff(2500,plain,
% 1.71/1.42 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(2501,plain,
% 1.71/1.42 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1145) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1145)) | (~c3_1(a1145))),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[2500, 2499])).
% 1.71/1.42 tff(2502,plain,
% 1.71/1.42 (hskp2),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2501, 113, 2430, 2429, 2428, 2169, 2201, 2158, 1065])).
% 1.71/1.42 tff(2503,plain,
% 1.71/1.42 (c2_1(a1100)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[302, 2502])).
% 1.71/1.42 tff(2504,plain,
% 1.71/1.42 (hskp7),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[2395, 2437])).
% 1.71/1.42 tff(2505,plain,
% 1.71/1.42 (~c1_1(a1105)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[633, 2504])).
% 1.71/1.42 tff(2506,plain,
% 1.71/1.42 (c3_1(a1105)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[657, 2504])).
% 1.71/1.42 tff(2507,plain,
% 1.71/1.42 (c0_1(a1105)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[646, 2504])).
% 1.71/1.42 tff(2508,plain,
% 1.71/1.42 (~c3_1(a1100)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[291, 2502])).
% 1.71/1.42 tff(2509,plain,
% 1.71/1.42 (c0_1(a1100)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[313, 2502])).
% 1.71/1.42 tff(2510,plain,
% 1.71/1.42 (c0_1(a1147)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[766, 2493])).
% 1.71/1.42 tff(2511,plain,
% 1.71/1.42 (hskp5),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1407, 2510, 2509, 2441, 2440, 2508, 2463, 2462, 2507, 2506, 2505, 2503, 2487, 2495, 2494])).
% 1.71/1.42 tff(2512,plain,
% 1.71/1.42 (~c0_1(a1103)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[132, 2511])).
% 1.71/1.42 tff(2513,plain,
% 1.71/1.42 (c3_1(a1103)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[153, 2511])).
% 1.71/1.42 tff(2514,plain,
% 1.71/1.42 (~hskp21),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[838, 2510, 2462, 2487, 2495, 2494, 2463])).
% 1.71/1.42 tff(2515,plain,
% 1.71/1.42 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp21 | hskp0 | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp21 | hskp0 | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2516,plain,
% 1.71/1.42 ((hskp21 | hskp0 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c3_1(a1103))) <=> (hskp21 | hskp0 | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(2517,plain,
% 1.71/1.42 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c3_1(a1103)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp21 | hskp0 | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103))))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[2516])).
% 1.71/1.42 tff(2518,plain,
% 1.71/1.42 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c3_1(a1103)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp21 | hskp0 | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.71/1.42 inference(transitivity,[status(thm)],[2517, 2515])).
% 1.71/1.42 tff(2519,plain,
% 1.71/1.42 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c3_1(a1103)))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(2520,plain,
% 1.71/1.42 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp21 | hskp0 | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103))),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[2519, 2518])).
% 1.71/1.43 tff(2521,plain,
% 1.71/1.43 (~c1_1(a1103)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2520, 113, 2514, 2116, 2513, 2512, 33])).
% 1.71/1.43 tff(2522,plain,
% 1.71/1.43 (~c2_1(a1103)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[126, 2511])).
% 1.71/1.43 tff(2523,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2524,plain,
% 1.71/1.43 ((hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c1_1(a1103) | c0_1(a1103)) <=> (hskp0 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2525,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c1_1(a1103) | c0_1(a1103))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103))))),
% 1.71/1.43 inference(monotonicity,[status(thm)],[2524])).
% 1.71/1.43 tff(2526,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c1_1(a1103) | c0_1(a1103))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103)))),
% 1.71/1.43 inference(transitivity,[status(thm)],[2525, 2523])).
% 1.71/1.43 tff(2527,plain,
% 1.71/1.43 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1103) | c1_1(a1103) | c0_1(a1103))),
% 1.71/1.43 inference(quant_inst,[status(thm)],[])).
% 1.71/1.43 tff(2528,plain,
% 1.71/1.43 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | c1_1(a1103) | (~c3_1(a1103))),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2527, 2526])).
% 1.71/1.43 tff(2529,plain,
% 1.71/1.43 ($false),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2528, 113, 2116, 2513, 2512, 2522, 2126, 2521])).
% 1.71/1.43 tff(2530,plain,(c2_1(a1098) | c1_1(a1098)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.43 tff(2531,plain,
% 1.71/1.43 ($false),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2530, 23, 17])).
% 1.71/1.43 tff(2532,plain,(~hskp0), inference(lemma,lemma(discharge,[]))).
% 1.71/1.43 tff(2533,assumption,(~c0_1(a1147)), introduced(assumption)).
% 1.71/1.43 tff(2534,plain,
% 1.71/1.43 (~hskp23),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[766, 2533])).
% 1.71/1.43 tff(2535,plain,
% 1.71/1.43 (hskp30),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2180, 2534, 2532])).
% 1.71/1.43 tff(2536,plain,
% 1.71/1.43 (c1_1(a1136)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[690, 2535])).
% 1.71/1.43 tff(2537,plain,
% 1.71/1.43 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp6 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2538,plain,
% 1.71/1.43 ((hskp7 | hskp6 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c0_1(a1147)) <=> (hskp7 | hskp6 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2539,plain,
% 1.71/1.43 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c0_1(a1147))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0)))),
% 1.71/1.43 inference(monotonicity,[status(thm)],[2538])).
% 1.71/1.43 tff(2540,plain,
% 1.71/1.43 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c0_1(a1147))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp6 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0))),
% 1.71/1.43 inference(transitivity,[status(thm)],[2539, 2537])).
% 1.71/1.43 tff(2541,plain,
% 1.71/1.43 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c0_1(a1147))),
% 1.71/1.43 inference(quant_inst,[status(thm)],[])).
% 1.71/1.43 tff(2542,plain,
% 1.71/1.43 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp6 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0)),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2541, 2540])).
% 1.71/1.43 tff(2543,plain,
% 1.71/1.43 (hskp7 | hskp6 | c0_1(a1147) | c3_1(a1147)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2542, 113, 819, 525])).
% 1.71/1.43 tff(2544,plain,
% 1.71/1.43 (hskp6),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2543, 68, 2533, 771])).
% 1.71/1.43 tff(2545,plain,
% 1.71/1.43 (c0_1(a1104)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[549, 2544])).
% 1.71/1.43 tff(2546,plain,
% 1.71/1.43 ((hskp23 | hskp13 | hskp7) <=> (hskp23 | hskp13 | hskp7)),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2547,plain,
% 1.71/1.43 (((hskp23 | hskp7) | hskp13) <=> (hskp23 | hskp13 | hskp7)),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2548,plain,
% 1.71/1.43 ((hskp7 | hskp23) <=> (hskp23 | hskp7)),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2549,plain,
% 1.71/1.43 (((hskp7 | hskp23) | hskp13) <=> ((hskp23 | hskp7) | hskp13)),
% 1.71/1.43 inference(monotonicity,[status(thm)],[2548])).
% 1.71/1.43 tff(2550,plain,
% 1.71/1.43 (((hskp7 | hskp23) | hskp13) <=> (hskp23 | hskp13 | hskp7)),
% 1.71/1.43 inference(transitivity,[status(thm)],[2549, 2547])).
% 1.71/1.43 tff(2551,axiom,((hskp7 | hskp23) | hskp13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.71/1.43 tff(2552,plain,
% 1.71/1.43 (hskp23 | hskp13 | hskp7),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2551, 2550])).
% 1.71/1.43 tff(2553,plain,
% 1.71/1.43 (hskp23 | hskp13 | hskp7),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2552, 2546])).
% 1.71/1.43 tff(2554,plain,
% 1.71/1.43 (hskp23 | hskp13 | hskp7),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2553, 2546])).
% 1.71/1.43 tff(2555,plain,
% 1.71/1.43 (hskp23 | hskp13 | hskp7),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2554, 2546])).
% 1.71/1.43 tff(2556,plain,
% 1.71/1.43 (hskp23 | hskp13 | hskp7),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2555, 2546])).
% 1.71/1.43 tff(2557,plain,
% 1.71/1.43 (hskp23 | hskp13 | hskp7),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2556, 2546])).
% 1.71/1.43 tff(2558,plain,
% 1.71/1.43 (hskp23 | hskp13 | hskp7),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2557, 2546])).
% 1.71/1.43 tff(2559,plain,
% 1.71/1.43 (hskp23 | hskp13 | hskp7),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2558, 2546])).
% 1.71/1.43 tff(2560,plain,
% 1.71/1.43 (hskp13),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2559, 68, 2534])).
% 1.71/1.43 tff(2561,plain,
% 1.71/1.43 (~c1_1(a1115)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[1229, 2560])).
% 1.71/1.43 tff(2562,plain,
% 1.71/1.43 (~c3_1(a1115)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[1354, 2560])).
% 1.71/1.43 tff(2563,plain,
% 1.71/1.43 (~c2_1(a1104)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[538, 2544])).
% 1.71/1.43 tff(2564,plain,
% 1.71/1.43 (c1_1(a1104)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[577, 2544])).
% 1.71/1.43 tff(2565,plain,
% 1.71/1.43 (^[U: $i] : refl((hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.71/1.43 inference(bind,[status(th)],[])).
% 1.71/1.43 tff(2566,plain,
% 1.71/1.43 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.43 inference(quant_intro,[status(thm)],[2565])).
% 1.71/1.43 tff(2567,plain,
% 1.71/1.43 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2568,plain,
% 1.71/1.43 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp23) <=> ((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp23) <=> (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.71/1.43 inference(bind,[status(th)],[])).
% 1.71/1.43 tff(2569,plain,
% 1.71/1.43 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp23) <=> ![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.43 inference(quant_intro,[status(thm)],[2568])).
% 1.71/1.43 tff(2570,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 1.71/1.43 tff(2571,plain,
% 1.71/1.43 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2570, 2569])).
% 1.71/1.43 tff(2572,plain,
% 1.71/1.43 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2571, 2567])).
% 1.71/1.43 tff(2573,plain,(
% 1.71/1.43 ![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.43 inference(skolemize,[status(sab)],[2572])).
% 1.71/1.43 tff(2574,plain,
% 1.71/1.43 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2573, 2566])).
% 1.71/1.43 tff(2575,plain,
% 1.71/1.43 (c2_1(a1115)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[1240, 2560])).
% 1.71/1.43 tff(2576,plain,
% 1.71/1.43 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2577,plain,
% 1.71/1.43 ((hskp23 | hskp7 | (~ndr1_0) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115))) <=> (hskp23 | hskp7 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2578,plain,
% 1.71/1.43 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115))))),
% 1.71/1.43 inference(monotonicity,[status(thm)],[2577])).
% 1.71/1.43 tff(2579,plain,
% 1.71/1.43 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115)))),
% 1.71/1.43 inference(transitivity,[status(thm)],[2578, 2576])).
% 1.71/1.43 tff(2580,plain,
% 1.71/1.43 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1115) | (~c2_1(a1115)) | (~c0_1(a1115)))),
% 1.71/1.43 inference(quant_inst,[status(thm)],[])).
% 1.71/1.43 tff(2581,plain,
% 1.71/1.43 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | c1_1(a1115) | (~ndr1_0) | (~c0_1(a1115)) | (~c2_1(a1115))),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 1.71/1.43 tff(2582,plain,
% 1.71/1.43 (~c0_1(a1115)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2581, 2534, 113, 68, 2575, 2561, 2574])).
% 1.71/1.43 tff(2583,assumption,(~c0_1(a1115)), introduced(assumption)).
% 1.71/1.43 tff(2584,assumption,(c1_1(a1147)), introduced(assumption)).
% 1.71/1.43 tff(2585,assumption,(~c3_1(a1115)), introduced(assumption)).
% 1.71/1.43 tff(2586,assumption,(~c1_1(a1115)), introduced(assumption)).
% 1.71/1.43 tff(2587,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a1147) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | c0_1(a1115) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a1147) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | c0_1(a1115) | (~c1_1(a1147)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2588,plain,
% 1.71/1.43 ((hskp1 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c1_1(a1147)) | c1_1(a1115) | c0_1(a1115) | c3_1(a1115)) <=> (hskp1 | c0_1(a1147) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | c0_1(a1115) | (~c1_1(a1147)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2589,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c1_1(a1147)) | c1_1(a1115) | c0_1(a1115) | c3_1(a1115))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a1147) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | c0_1(a1115) | (~c1_1(a1147))))),
% 1.71/1.43 inference(monotonicity,[status(thm)],[2588])).
% 1.71/1.43 tff(2590,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c1_1(a1147)) | c1_1(a1115) | c0_1(a1115) | c3_1(a1115))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a1147) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | c0_1(a1115) | (~c1_1(a1147)))),
% 1.71/1.43 inference(transitivity,[status(thm)],[2589, 2587])).
% 1.71/1.43 tff(2591,plain,
% 1.71/1.43 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c1_1(a1147)) | c1_1(a1115) | c0_1(a1115) | c3_1(a1115))),
% 1.71/1.43 inference(quant_inst,[status(thm)],[])).
% 1.71/1.43 tff(2592,plain,
% 1.71/1.43 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a1147) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115) | (~ndr1_0) | c0_1(a1115) | (~c1_1(a1147))),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2591, 2590])).
% 1.71/1.43 tff(2593,plain,
% 1.71/1.43 (hskp1 | c0_1(a1115) | (~c1_1(a1147))),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2592, 113, 2533, 771, 2586, 2585, 396])).
% 1.71/1.43 tff(2594,plain,
% 1.71/1.43 (hskp1),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2593, 2584, 2583])).
% 1.71/1.43 tff(2595,plain,
% 1.71/1.43 (~c0_1(a1099)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[411, 2594])).
% 1.71/1.43 tff(2596,plain,
% 1.71/1.43 (c2_1(a1099)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[462, 2594])).
% 1.71/1.43 tff(2597,plain,
% 1.71/1.43 (c1_1(a1099)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[473, 2594])).
% 1.71/1.43 tff(2598,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1147) | c2_1(a1147) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1147) | c2_1(a1147) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1147)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2599,plain,
% 1.71/1.43 ((hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147))) <=> (hskp9 | c0_1(a1147) | c2_1(a1147) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1147)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2600,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1147) | c2_1(a1147) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1147))))),
% 1.71/1.43 inference(monotonicity,[status(thm)],[2599])).
% 1.71/1.43 tff(2601,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1147) | c2_1(a1147) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1147)))),
% 1.71/1.43 inference(transitivity,[status(thm)],[2600, 2598])).
% 1.71/1.43 tff(2602,plain,
% 1.71/1.43 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a1099) | (~c1_1(a1099)) | (~c2_1(a1099)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147)))),
% 1.71/1.43 inference(quant_inst,[status(thm)],[])).
% 1.71/1.43 tff(2603,plain,
% 1.71/1.43 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1147) | c2_1(a1147) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1147))),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2602, 2601])).
% 1.71/1.43 tff(2604,plain,
% 1.71/1.43 (hskp9),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2603, 113, 2533, 2597, 2596, 819, 2595, 422, 2584])).
% 1.71/1.43 tff(2605,plain,
% 1.71/1.43 (~c3_1(a1108)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[497, 2604])).
% 1.71/1.43 tff(2606,plain,
% 1.71/1.43 (~c1_1(a1108)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[503, 2604])).
% 1.71/1.43 tff(2607,plain,
% 1.71/1.43 (c0_1(a1108)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[514, 2604])).
% 1.71/1.43 tff(2608,plain,
% 1.71/1.43 ($false),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2056, 113, 2607, 1017, 1026, 2597, 2596, 2606, 2605, 1016, 2595, 1418])).
% 1.71/1.43 tff(2609,plain,((~c1_1(a1147)) | (~c0_1(a1104)) | (~c1_1(a1104)) | c2_1(a1104) | c0_1(a1147) | c2_1(a1147) | c0_1(a1115) | c3_1(a1147) | c1_1(a1115) | c3_1(a1115)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.43 tff(2610,plain,
% 1.71/1.43 (~c1_1(a1147)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2609, 2582, 2564, 2563, 2533, 819, 2562, 771, 2561, 2545])).
% 1.71/1.43 tff(2611,plain,
% 1.71/1.43 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2612,plain,
% 1.71/1.43 ((hskp7 | hskp5 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c1_1(a1147)) <=> (hskp7 | hskp5 | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2613,plain,
% 1.71/1.43 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c1_1(a1147))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147)))),
% 1.71/1.43 inference(monotonicity,[status(thm)],[2612])).
% 1.71/1.43 tff(2614,plain,
% 1.71/1.43 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c1_1(a1147))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147))),
% 1.71/1.43 inference(transitivity,[status(thm)],[2613, 2611])).
% 1.71/1.43 tff(2615,plain,
% 1.71/1.43 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | c1_1(a1147))),
% 1.71/1.43 inference(quant_inst,[status(thm)],[])).
% 1.71/1.43 tff(2616,plain,
% 1.71/1.43 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c1_1(a1147)),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2615, 2614])).
% 1.71/1.43 tff(2617,plain,
% 1.71/1.43 (hskp7 | hskp5 | c3_1(a1147) | c1_1(a1147)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2616, 113, 819, 78])).
% 1.71/1.43 tff(2618,plain,
% 1.71/1.43 (hskp5),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2617, 2610, 771, 68])).
% 1.71/1.43 tff(2619,plain,
% 1.71/1.43 (~c2_1(a1103)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[126, 2618])).
% 1.71/1.43 tff(2620,plain,
% 1.71/1.43 (~c0_1(a1103)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[132, 2618])).
% 1.71/1.43 tff(2621,plain,
% 1.71/1.43 (c3_1(a1103)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[153, 2618])).
% 1.71/1.43 tff(2622,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1147) | c2_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1147) | c2_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1147))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2623,plain,
% 1.71/1.43 ((hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147)) <=> (hskp0 | c0_1(a1147) | c2_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1147))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2624,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1147) | c2_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1147)))),
% 1.71/1.43 inference(monotonicity,[status(thm)],[2623])).
% 1.71/1.43 tff(2625,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1147) | c2_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1147))),
% 1.71/1.43 inference(transitivity,[status(thm)],[2624, 2622])).
% 1.71/1.43 tff(2626,plain,
% 1.71/1.43 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147))),
% 1.71/1.43 inference(quant_inst,[status(thm)],[])).
% 1.71/1.43 tff(2627,plain,
% 1.71/1.43 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1147) | c2_1(a1147) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c1_1(a1147)),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2626, 2625])).
% 1.71/1.43 tff(2628,plain,
% 1.71/1.43 ($false),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2627, 113, 2532, 2533, 2621, 819, 2620, 2619, 2126, 2610])).
% 1.71/1.43 tff(2629,plain,(hskp7 | c0_1(a1147) | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.43 tff(2630,plain,
% 1.71/1.43 (hskp7),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2629, 2533, 819, 771])).
% 1.71/1.43 tff(2631,plain,
% 1.71/1.43 (~c1_1(a1105)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[633, 2630])).
% 1.71/1.43 tff(2632,plain,
% 1.71/1.43 (c3_1(a1105)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[657, 2630])).
% 1.71/1.43 tff(2633,plain,
% 1.71/1.43 (c3_1(a1136)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[726, 2535])).
% 1.71/1.43 tff(2634,plain,
% 1.71/1.43 (hskp14),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[749, 2534])).
% 1.71/1.43 tff(2635,plain,
% 1.71/1.43 (~c3_1(a1118)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[166, 2634])).
% 1.71/1.43 tff(2636,plain,
% 1.71/1.43 (c2_1(a1136)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[737, 2535])).
% 1.71/1.43 tff(2637,plain,
% 1.71/1.43 (~c2_1(a1118)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[172, 2634])).
% 1.71/1.43 tff(2638,plain,
% 1.71/1.43 (c1_1(a1118)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[183, 2634])).
% 1.71/1.43 tff(2639,plain,
% 1.71/1.43 (c0_1(a1105)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[646, 2630])).
% 1.71/1.43 tff(2640,plain,
% 1.71/1.43 (hskp29),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[1763, 2639, 2534, 2638, 2637, 2636, 2635, 2633, 2632, 2631, 2536])).
% 1.71/1.43 tff(2641,plain,
% 1.71/1.43 (c0_1(a1116)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[223, 2640])).
% 1.71/1.43 tff(2642,plain,
% 1.71/1.43 (c3_1(a1116)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[201, 2640])).
% 1.71/1.43 tff(2643,plain,
% 1.71/1.43 (c2_1(a1116)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[212, 2640])).
% 1.71/1.43 tff(2644,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2645,plain,
% 1.71/1.43 ((hskp0 | (~ndr1_0) | c2_1(a1107) | c0_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c1_1(a1107) | c0_1(a1107)) <=> (hskp0 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2646,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1107) | c0_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c1_1(a1107) | c0_1(a1107))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107))))),
% 1.71/1.43 inference(monotonicity,[status(thm)],[2645])).
% 1.71/1.43 tff(2647,plain,
% 1.71/1.43 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1107) | c0_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c1_1(a1107) | c0_1(a1107))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107)))),
% 1.71/1.43 inference(transitivity,[status(thm)],[2646, 2644])).
% 1.71/1.43 tff(2648,plain,
% 1.71/1.43 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1107) | c0_1(a1107) | (~c3_1(a1107)) | c2_1(a1107) | c1_1(a1107) | c0_1(a1107))),
% 1.71/1.43 inference(quant_inst,[status(thm)],[])).
% 1.71/1.43 tff(2649,plain,
% 1.71/1.43 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1107) | c1_1(a1107) | (~ndr1_0) | c2_1(a1107) | (~c3_1(a1107))),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[2648, 2647])).
% 1.71/1.43 tff(2650,plain,
% 1.71/1.43 ($false),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2649, 113, 2532, 1214, 1186, 1180, 2126, 1193])).
% 1.71/1.43 tff(2651,plain,((~hskp8) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.43 tff(2652,plain,
% 1.71/1.43 (~hskp8),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2651, 2641, 2643, 2642, 2639, 2632, 2631])).
% 1.71/1.43 tff(2653,plain,
% 1.71/1.43 (c0_1(a1118)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[2034, 2652, 2638, 2536, 2643, 2637, 2635, 2642, 2636, 2633, 2641])).
% 1.71/1.43 tff(2654,plain,
% 1.71/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(2655,plain,
% 1.71/1.43 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105))) <=> (c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2656,plain,
% 1.71/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 1.71/1.44 inference(monotonicity,[status(thm)],[2655])).
% 1.71/1.44 tff(2657,plain,
% 1.71/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.71/1.44 inference(transitivity,[status(thm)],[2656, 2654])).
% 1.71/1.44 tff(2658,plain,
% 1.71/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.71/1.44 inference(quant_inst,[status(thm)],[])).
% 1.71/1.44 tff(2659,plain,
% 1.71/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 1.71/1.44 inference(modus_ponens,[status(thm)],[2658, 2657])).
% 1.71/1.44 tff(2660,plain,
% 1.71/1.44 (c2_1(a1105) | (~c0_1(a1118))),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2659, 113, 2641, 2643, 2642, 2638, 2632, 2637, 2631, 246])).
% 1.71/1.44 tff(2661,plain,
% 1.71/1.44 (c2_1(a1105)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2660, 2653])).
% 1.71/1.44 tff(2662,plain,
% 1.71/1.44 (hskp2 | (~c2_1(a1105))),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[1071, 113, 2639, 2632, 2631, 1065])).
% 1.71/1.44 tff(2663,plain,
% 1.71/1.44 (hskp2),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2662, 2661])).
% 1.71/1.44 tff(2664,plain,
% 1.71/1.44 (~c3_1(a1100)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[291, 2663])).
% 1.71/1.44 tff(2665,plain,
% 1.71/1.44 (~hskp5),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2079, 2653, 2638, 2635, 2637])).
% 1.71/1.44 tff(2666,plain,
% 1.71/1.44 (^[U: $i] : refl((hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.71/1.44 inference(bind,[status(th)],[])).
% 1.71/1.44 tff(2667,plain,
% 1.71/1.44 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.71/1.44 inference(quant_intro,[status(thm)],[2666])).
% 1.71/1.44 tff(2668,plain,
% 1.71/1.44 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2669,plain,
% 1.71/1.44 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp8) <=> ((hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp8))), rewrite(((hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp8) <=> (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp8) <=> (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.71/1.44 inference(bind,[status(th)],[])).
% 1.71/1.44 tff(2670,plain,
% 1.71/1.44 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp8) <=> ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.71/1.44 inference(quant_intro,[status(thm)],[2669])).
% 1.71/1.44 tff(2671,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 1.71/1.44 tff(2672,plain,
% 1.71/1.44 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.71/1.44 inference(modus_ponens,[status(thm)],[2671, 2670])).
% 1.71/1.44 tff(2673,plain,
% 1.71/1.44 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.71/1.44 inference(modus_ponens,[status(thm)],[2672, 2668])).
% 1.71/1.44 tff(2674,plain,(
% 1.71/1.44 ![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.71/1.44 inference(skolemize,[status(sab)],[2673])).
% 1.71/1.44 tff(2675,plain,
% 1.71/1.44 (![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.71/1.44 inference(modus_ponens,[status(thm)],[2674, 2667])).
% 1.71/1.44 tff(2676,plain,
% 1.71/1.44 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp8 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp19 | hskp8 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2677,plain,
% 1.71/1.44 ((hskp19 | hskp8 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))) <=> (hskp19 | hskp8 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2678,plain,
% 1.71/1.44 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp8 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp8 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105))))),
% 1.71/1.44 inference(monotonicity,[status(thm)],[2677])).
% 1.71/1.44 tff(2679,plain,
% 1.71/1.44 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp8 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp19 | hskp8 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.71/1.44 inference(transitivity,[status(thm)],[2678, 2676])).
% 1.71/1.44 tff(2680,plain,
% 1.71/1.44 ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp19 | hskp8 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))),
% 1.71/1.44 inference(quant_inst,[status(thm)],[])).
% 1.71/1.44 tff(2681,plain,
% 1.71/1.44 ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp19 | hskp8 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105))),
% 1.71/1.44 inference(modus_ponens,[status(thm)],[2680, 2679])).
% 1.71/1.44 tff(2682,plain,
% 1.71/1.44 (hskp19 | hskp8 | (~c2_1(a1105))),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2681, 113, 2632, 2631, 2675])).
% 1.71/1.44 tff(2683,plain,
% 1.71/1.44 (hskp19),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2682, 2661, 2652])).
% 1.71/1.44 tff(2684,plain,
% 1.71/1.44 (hskp20),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[1305, 2683, 2641, 2665, 2643, 2642])).
% 1.71/1.44 tff(2685,plain,
% 1.71/1.44 (~c3_1(a1130)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[332, 2684])).
% 1.71/1.44 tff(2686,plain,
% 1.71/1.44 (~c2_1(a1130)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2287, 2684])).
% 1.71/1.44 tff(2687,plain,
% 1.71/1.44 (~c0_1(a1130)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[326, 2684])).
% 1.71/1.44 tff(2688,plain,
% 1.71/1.44 (c2_1(a1100)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[302, 2663])).
% 1.71/1.44 tff(2689,plain,
% 1.71/1.44 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c2_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c2_1(a1100)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2690,plain,
% 1.71/1.44 ((hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130)) <=> (hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c2_1(a1100)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2691,plain,
% 1.71/1.44 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c2_1(a1100))))),
% 1.71/1.44 inference(monotonicity,[status(thm)],[2690])).
% 1.71/1.44 tff(2692,plain,
% 1.71/1.44 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c2_1(a1100)))),
% 1.71/1.44 inference(transitivity,[status(thm)],[2691, 2689])).
% 1.71/1.44 tff(2693,plain,
% 1.71/1.44 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1100) | (~c1_1(a1100)) | (~c2_1(a1100)) | c2_1(a1130) | c0_1(a1130) | c3_1(a1130))),
% 1.71/1.44 inference(quant_inst,[status(thm)],[])).
% 1.71/1.44 tff(2694,plain,
% 1.71/1.44 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a1130) | c2_1(a1130) | c3_1(a1130) | c3_1(a1100) | (~ndr1_0) | (~c1_1(a1100)) | (~c2_1(a1100))),
% 1.71/1.44 inference(modus_ponens,[status(thm)],[2693, 2692])).
% 1.71/1.44 tff(2695,plain,
% 1.71/1.44 (~c1_1(a1100)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2694, 113, 2665, 2688, 2687, 2686, 2685, 2664, 10])).
% 1.71/1.44 tff(2696,plain,
% 1.71/1.44 (c0_1(a1136)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2037, 2653, 2636, 2633, 2638, 2635, 2536])).
% 1.71/1.44 tff(2697,plain,
% 1.71/1.44 (c0_1(a1100)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[313, 2663])).
% 1.71/1.44 tff(2698,plain,
% 1.71/1.44 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2699,plain,
% 1.71/1.44 ((hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100))) <=> (hskp23 | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2700,plain,
% 1.71/1.44 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100))))),
% 1.71/1.44 inference(monotonicity,[status(thm)],[2699])).
% 1.71/1.44 tff(2701,plain,
% 1.71/1.44 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)))),
% 1.71/1.44 inference(transitivity,[status(thm)],[2700, 2698])).
% 1.71/1.44 tff(2702,plain,
% 1.71/1.44 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)))),
% 1.71/1.44 inference(quant_inst,[status(thm)],[])).
% 1.71/1.44 tff(2703,plain,
% 1.71/1.44 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100))),
% 1.71/1.44 inference(modus_ponens,[status(thm)],[2702, 2701])).
% 1.71/1.44 tff(2704,plain,
% 1.71/1.44 ($false),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2703, 2534, 113, 2536, 2636, 2697, 2664, 1633, 2696, 2695])).
% 1.71/1.44 tff(2705,plain,(c0_1(a1147) | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.44 tff(2706,plain,
% 1.71/1.44 (c0_1(a1147)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2705, 771, 819])).
% 1.71/1.44 tff(2707,plain,
% 1.71/1.44 (c1_1(a1103)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2528, 113, 2454, 2075, 2076, 2077, 2126])).
% 1.71/1.44 tff(2708,plain,
% 1.71/1.44 (hskp21 | (~c1_1(a1103))),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2520, 113, 2454, 2075, 2076, 33])).
% 1.71/1.44 tff(2709,plain,
% 1.71/1.44 (hskp21),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2708, 2707])).
% 1.71/1.44 tff(2710,plain,
% 1.71/1.44 (~c3_1(a1131)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[811, 2709])).
% 1.71/1.44 tff(2711,plain,
% 1.71/1.44 (~c0_1(a1131)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[817, 2709])).
% 1.71/1.44 tff(2712,plain,
% 1.71/1.44 (c1_1(a1131)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[829, 2709])).
% 1.71/1.44 tff(2713,plain,
% 1.71/1.44 (hskp14),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[160, 113, 68, 2075, 2076, 2077, 143])).
% 1.71/1.44 tff(2714,plain,
% 1.71/1.44 (~c3_1(a1118)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[166, 2713])).
% 1.71/1.44 tff(2715,plain,
% 1.71/1.44 (~c2_1(a1118)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[172, 2713])).
% 1.71/1.44 tff(2716,plain,
% 1.71/1.44 (c1_1(a1118)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[183, 2713])).
% 1.71/1.44 tff(2717,plain,
% 1.71/1.44 (hskp29),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[190, 113, 2716, 2075, 2715, 2714, 2076, 2077, 67])).
% 1.71/1.44 tff(2718,plain,
% 1.71/1.44 (c3_1(a1116)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[201, 2717])).
% 1.71/1.44 tff(2719,plain,
% 1.71/1.44 (c2_1(a1116)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[212, 2717])).
% 1.71/1.44 tff(2720,plain,
% 1.71/1.44 (c0_1(a1116)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[223, 2717])).
% 1.71/1.44 tff(2721,plain,
% 1.71/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1131)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1131)) | (~c0_1(a1147)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2722,plain,
% 1.71/1.44 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131))) <=> (c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1131)) | (~c0_1(a1147)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2723,plain,
% 1.71/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1131)) | (~c0_1(a1147))))),
% 1.71/1.44 inference(monotonicity,[status(thm)],[2722])).
% 1.71/1.44 tff(2724,plain,
% 1.71/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1131)) | (~c0_1(a1147)))),
% 1.71/1.44 inference(transitivity,[status(thm)],[2723, 2721])).
% 1.71/1.44 tff(2725,plain,
% 1.71/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1131) | c0_1(a1131) | (~c1_1(a1131)))),
% 1.71/1.44 inference(quant_inst,[status(thm)],[])).
% 1.71/1.44 tff(2726,plain,
% 1.71/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1131) | c3_1(a1131) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1131)) | (~c0_1(a1147))),
% 1.71/1.44 inference(modus_ponens,[status(thm)],[2725, 2724])).
% 1.71/1.44 tff(2727,plain,
% 1.71/1.44 ($false),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2726, 113, 2720, 2719, 2718, 772, 2712, 819, 771, 2711, 2710, 344])).
% 1.71/1.44 tff(2728,plain,((~hskp5) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | hskp0 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.71/1.44 tff(2729,plain,
% 1.71/1.44 (~hskp5),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2728, 68, 819, 771, 2532, 2706])).
% 1.71/1.44 tff(2730,plain,
% 1.71/1.44 (c1_1(a1147)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2617, 2729, 771, 68])).
% 1.71/1.44 tff(2731,assumption,(hskp16), introduced(assumption)).
% 1.71/1.44 tff(2732,plain,
% 1.71/1.44 (~c0_1(a1121)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[1939, 2731])).
% 1.71/1.44 tff(2733,plain,
% 1.71/1.44 (c3_1(a1121)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[1952, 2731])).
% 1.71/1.44 tff(2734,plain,
% 1.71/1.44 (c1_1(a1121)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[1963, 2731])).
% 1.71/1.44 tff(2735,plain,
% 1.71/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1121)) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1121)) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2736,plain,
% 1.71/1.44 (((~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1121)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121))) <=> (c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1121)) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2737,plain,
% 1.71/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1121)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1121)) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.71/1.44 inference(monotonicity,[status(thm)],[2736])).
% 1.71/1.44 tff(2738,plain,
% 1.71/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1121)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1121)) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.44 inference(transitivity,[status(thm)],[2737, 2735])).
% 1.71/1.44 tff(2739,plain,
% 1.71/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1121)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.71/1.44 inference(quant_inst,[status(thm)],[])).
% 1.71/1.44 tff(2740,plain,
% 1.71/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1121)) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.71/1.44 inference(modus_ponens,[status(thm)],[2739, 2738])).
% 1.71/1.44 tff(2741,plain,
% 1.71/1.44 (~c2_1(a1121)),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2740, 113, 772, 2734, 2733, 771, 2732, 45, 2584])).
% 1.71/1.44 tff(2742,plain,
% 1.71/1.44 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1147)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2743,plain,
% 1.71/1.44 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121))) <=> (hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1147)))),
% 1.71/1.44 inference(rewrite,[status(thm)],[])).
% 1.71/1.44 tff(2744,plain,
% 1.71/1.44 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1147))))),
% 1.71/1.44 inference(monotonicity,[status(thm)],[2743])).
% 1.71/1.44 tff(2745,plain,
% 1.71/1.44 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1147)))),
% 1.71/1.44 inference(transitivity,[status(thm)],[2744, 2742])).
% 1.71/1.44 tff(2746,plain,
% 1.71/1.44 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121)))),
% 1.71/1.44 inference(quant_inst,[status(thm)],[])).
% 1.71/1.44 tff(2747,plain,
% 1.71/1.44 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1147))),
% 1.71/1.44 inference(modus_ponens,[status(thm)],[2746, 2745])).
% 1.71/1.44 tff(2748,plain,
% 1.71/1.44 ($false),
% 1.71/1.44 inference(unit_resolution,[status(thm)],[2747, 113, 770, 2733, 819, 771, 2732, 67, 2584, 2741])).
% 1.71/1.45 tff(2749,plain,((~hskp16) | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.71/1.45 tff(2750,plain,
% 1.71/1.45 (~hskp16),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2749, 770, 819, 771, 2706, 2730])).
% 1.71/1.45 tff(2751,assumption,(hskp26), introduced(assumption)).
% 1.71/1.45 tff(2752,plain,
% 1.71/1.45 (((~hskp26) | (~c2_1(a1180))) <=> ((~hskp26) | (~c2_1(a1180)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2753,plain,
% 1.71/1.45 (((~c2_1(a1180)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a1180)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2754,axiom,((~c2_1(a1180)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.71/1.45 tff(2755,plain,
% 1.71/1.45 ((~hskp26) | (~c2_1(a1180))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2754, 2753])).
% 1.71/1.45 tff(2756,plain,
% 1.71/1.45 ((~hskp26) | (~c2_1(a1180))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2755, 2752])).
% 1.71/1.45 tff(2757,plain,
% 1.71/1.45 (~c2_1(a1180)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2756, 2751])).
% 1.71/1.45 tff(2758,plain,
% 1.71/1.45 (((~hskp26) | (~c1_1(a1180))) <=> ((~hskp26) | (~c1_1(a1180)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2759,plain,
% 1.71/1.45 (((~c1_1(a1180)) | (~hskp26)) <=> ((~hskp26) | (~c1_1(a1180)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2760,axiom,((~c1_1(a1180)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.71/1.45 tff(2761,plain,
% 1.71/1.45 ((~hskp26) | (~c1_1(a1180))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2760, 2759])).
% 1.71/1.45 tff(2762,plain,
% 1.71/1.45 ((~hskp26) | (~c1_1(a1180))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2761, 2758])).
% 1.71/1.45 tff(2763,plain,
% 1.71/1.45 (~c1_1(a1180)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2762, 2751])).
% 1.71/1.45 tff(2764,plain,
% 1.71/1.45 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2765,plain,
% 1.71/1.45 ((hskp7 | hskp5 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180)) <=> (hskp7 | hskp5 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2766,plain,
% 1.71/1.45 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180)))),
% 1.71/1.45 inference(monotonicity,[status(thm)],[2765])).
% 1.71/1.45 tff(2767,plain,
% 1.71/1.45 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))),
% 1.71/1.45 inference(transitivity,[status(thm)],[2766, 2764])).
% 1.71/1.45 tff(2768,plain,
% 1.71/1.45 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180))),
% 1.71/1.45 inference(quant_inst,[status(thm)],[])).
% 1.71/1.45 tff(2769,plain,
% 1.71/1.45 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180)),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2768, 2767])).
% 1.71/1.45 tff(2770,plain,
% 1.71/1.45 (c3_1(a1180)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2769, 113, 68, 2729, 2763, 2757, 78])).
% 1.71/1.45 tff(2771,plain,
% 1.71/1.45 (((~hskp26) | (~c0_1(a1180))) <=> ((~hskp26) | (~c0_1(a1180)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2772,plain,
% 1.71/1.45 (((~c0_1(a1180)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a1180)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2773,axiom,((~c0_1(a1180)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.71/1.45 tff(2774,plain,
% 1.71/1.45 ((~hskp26) | (~c0_1(a1180))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2773, 2772])).
% 1.71/1.45 tff(2775,plain,
% 1.71/1.45 ((~hskp26) | (~c0_1(a1180))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2774, 2771])).
% 1.71/1.45 tff(2776,plain,
% 1.71/1.45 (~c0_1(a1180)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2775, 2751])).
% 1.71/1.45 tff(2777,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1180) | c2_1(a1180) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c3_1(a1180)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1180) | c2_1(a1180) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c3_1(a1180)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2778,plain,
% 1.71/1.45 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1180) | c0_1(a1180) | (~c3_1(a1180))) <=> (hskp29 | c0_1(a1180) | c2_1(a1180) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c3_1(a1180)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2779,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1180) | c0_1(a1180) | (~c3_1(a1180)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1180) | c2_1(a1180) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c3_1(a1180))))),
% 1.71/1.45 inference(monotonicity,[status(thm)],[2778])).
% 1.71/1.45 tff(2780,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1180) | c0_1(a1180) | (~c3_1(a1180)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1180) | c2_1(a1180) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c3_1(a1180)))),
% 1.71/1.45 inference(transitivity,[status(thm)],[2779, 2777])).
% 1.71/1.45 tff(2781,plain,
% 1.71/1.45 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1180) | c0_1(a1180) | (~c3_1(a1180)))),
% 1.71/1.45 inference(quant_inst,[status(thm)],[])).
% 1.71/1.45 tff(2782,plain,
% 1.71/1.45 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1180) | c2_1(a1180) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c3_1(a1180))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2781, 2780])).
% 1.71/1.45 tff(2783,plain,
% 1.71/1.45 ($false),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2782, 113, 770, 2776, 2757, 819, 771, 67, 2770, 2730])).
% 1.71/1.45 tff(2784,plain,((~hskp26) | hskp29 | c2_1(a1147) | c3_1(a1147) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.71/1.45 tff(2785,plain,
% 1.71/1.45 (~hskp26),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2784, 770, 819, 771, 68])).
% 1.71/1.45 tff(2786,plain,
% 1.71/1.45 ((hskp26 | hskp18 | hskp16) <=> (hskp26 | hskp18 | hskp16)),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2787,plain,
% 1.71/1.45 (((hskp18 | hskp16) | hskp26) <=> (hskp26 | hskp18 | hskp16)),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2788,plain,
% 1.71/1.45 ((hskp18 | hskp16) <=> (hskp18 | hskp16)),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2789,plain,
% 1.71/1.45 (((hskp18 | hskp16) | hskp26) <=> ((hskp18 | hskp16) | hskp26)),
% 1.71/1.45 inference(monotonicity,[status(thm)],[2788])).
% 1.71/1.45 tff(2790,plain,
% 1.71/1.45 (((hskp18 | hskp16) | hskp26) <=> (hskp26 | hskp18 | hskp16)),
% 1.71/1.45 inference(transitivity,[status(thm)],[2789, 2787])).
% 1.71/1.45 tff(2791,axiom,((hskp18 | hskp16) | hskp26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 1.71/1.45 tff(2792,plain,
% 1.71/1.45 (hskp26 | hskp18 | hskp16),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2791, 2790])).
% 1.71/1.45 tff(2793,plain,
% 1.71/1.45 (hskp26 | hskp18 | hskp16),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2792, 2786])).
% 1.71/1.45 tff(2794,plain,
% 1.71/1.45 (hskp26 | hskp18 | hskp16),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2793, 2786])).
% 1.71/1.45 tff(2795,plain,
% 1.71/1.45 (hskp26 | hskp18 | hskp16),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2794, 2786])).
% 1.71/1.45 tff(2796,plain,
% 1.71/1.45 (hskp26 | hskp18 | hskp16),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2795, 2786])).
% 1.71/1.45 tff(2797,plain,
% 1.71/1.45 (hskp26 | hskp18 | hskp16),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2796, 2786])).
% 1.71/1.45 tff(2798,plain,
% 1.71/1.45 (hskp26 | hskp18 | hskp16),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2797, 2786])).
% 1.71/1.45 tff(2799,plain,
% 1.71/1.45 (hskp26 | hskp18 | hskp16),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2798, 2786])).
% 1.71/1.45 tff(2800,plain,
% 1.71/1.45 (hskp18),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2799, 2785, 2750])).
% 1.71/1.45 tff(2801,plain,
% 1.71/1.45 (~c1_1(a1125)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2243, 2800])).
% 1.71/1.45 tff(2802,assumption,(~hskp26), introduced(assumption)).
% 1.71/1.45 tff(2803,assumption,(~hskp16), introduced(assumption)).
% 1.71/1.45 tff(2804,plain,
% 1.71/1.45 (hskp18),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2799, 2803, 2802])).
% 1.71/1.45 tff(2805,plain,
% 1.71/1.45 (~c1_1(a1125)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2243, 2804])).
% 1.71/1.45 tff(2806,assumption,(~hskp2), introduced(assumption)).
% 1.71/1.45 tff(2807,plain,
% 1.71/1.45 (^[U: $i] : refl((hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.71/1.45 inference(bind,[status(th)],[])).
% 1.71/1.45 tff(2808,plain,
% 1.71/1.45 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.71/1.45 inference(quant_intro,[status(thm)],[2807])).
% 1.71/1.45 tff(2809,plain,
% 1.71/1.45 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2810,plain,
% 1.71/1.45 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp16) <=> ((hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp16))), rewrite(((hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp16) <=> (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp16) <=> (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.71/1.45 inference(bind,[status(th)],[])).
% 1.71/1.45 tff(2811,plain,
% 1.71/1.45 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp16) <=> ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.71/1.45 inference(quant_intro,[status(thm)],[2810])).
% 1.71/1.45 tff(2812,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 1.71/1.45 tff(2813,plain,
% 1.71/1.45 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2812, 2811])).
% 1.71/1.45 tff(2814,plain,
% 1.71/1.45 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2813, 2809])).
% 1.71/1.45 tff(2815,plain,(
% 1.71/1.45 ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.71/1.45 inference(skolemize,[status(sab)],[2814])).
% 1.71/1.45 tff(2816,plain,
% 1.71/1.45 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2815, 2808])).
% 1.71/1.45 tff(2817,assumption,(hskp12), introduced(assumption)).
% 1.71/1.45 tff(2818,plain,
% 1.71/1.45 (((~hskp12) | (~c3_1(a1114))) <=> ((~hskp12) | (~c3_1(a1114)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2819,plain,
% 1.71/1.45 (((~c3_1(a1114)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a1114)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2820,axiom,((~c3_1(a1114)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.71/1.45 tff(2821,plain,
% 1.71/1.45 ((~hskp12) | (~c3_1(a1114))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2820, 2819])).
% 1.71/1.45 tff(2822,plain,
% 1.71/1.45 ((~hskp12) | (~c3_1(a1114))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2821, 2818])).
% 1.71/1.45 tff(2823,plain,
% 1.71/1.45 (~c3_1(a1114)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2822, 2817])).
% 1.71/1.45 tff(2824,plain,
% 1.71/1.45 (((~hskp12) | (~c0_1(a1114))) <=> ((~hskp12) | (~c0_1(a1114)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2825,plain,
% 1.71/1.45 (((~c0_1(a1114)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a1114)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2826,axiom,((~c0_1(a1114)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.71/1.45 tff(2827,plain,
% 1.71/1.45 ((~hskp12) | (~c0_1(a1114))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2826, 2825])).
% 1.71/1.45 tff(2828,plain,
% 1.71/1.45 ((~hskp12) | (~c0_1(a1114))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2827, 2824])).
% 1.71/1.45 tff(2829,plain,
% 1.71/1.45 (~c0_1(a1114)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2828, 2817])).
% 1.71/1.45 tff(2830,plain,
% 1.71/1.45 (((~hskp12) | c2_1(a1114)) <=> ((~hskp12) | c2_1(a1114))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2831,axiom,((~hskp12) | c2_1(a1114)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.71/1.45 tff(2832,plain,
% 1.71/1.45 ((~hskp12) | c2_1(a1114)),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2831, 2830])).
% 1.71/1.45 tff(2833,plain,
% 1.71/1.45 ((~hskp12) | c2_1(a1114)),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2832, 2830])).
% 1.71/1.45 tff(2834,plain,
% 1.71/1.45 ((~hskp12) | c2_1(a1114)),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2833, 2830])).
% 1.71/1.45 tff(2835,plain,
% 1.71/1.45 ((~hskp12) | c2_1(a1114)),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2834, 2830])).
% 1.71/1.45 tff(2836,plain,
% 1.71/1.45 ((~hskp12) | c2_1(a1114)),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2835, 2830])).
% 1.71/1.45 tff(2837,plain,
% 1.71/1.45 ((~hskp12) | c2_1(a1114)),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2836, 2830])).
% 1.71/1.45 tff(2838,plain,
% 1.71/1.45 ((~hskp12) | c2_1(a1114)),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2837, 2830])).
% 1.71/1.45 tff(2839,plain,
% 1.71/1.45 ((~hskp12) | c2_1(a1114)),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2838, 2830])).
% 1.71/1.45 tff(2840,plain,
% 1.71/1.45 (c2_1(a1114)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2839, 2817])).
% 1.71/1.45 tff(2841,plain,
% 1.71/1.45 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c2_1(a1114)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c2_1(a1114)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2842,plain,
% 1.71/1.45 ((hskp16 | hskp2 | (~ndr1_0) | c3_1(a1114) | c0_1(a1114) | (~c2_1(a1114))) <=> (hskp16 | hskp2 | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c2_1(a1114)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2843,plain,
% 1.71/1.45 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1114) | c0_1(a1114) | (~c2_1(a1114)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c2_1(a1114))))),
% 1.71/1.45 inference(monotonicity,[status(thm)],[2842])).
% 1.71/1.45 tff(2844,plain,
% 1.71/1.45 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1114) | c0_1(a1114) | (~c2_1(a1114)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c2_1(a1114)))),
% 1.71/1.45 inference(transitivity,[status(thm)],[2843, 2841])).
% 1.71/1.45 tff(2845,plain,
% 1.71/1.45 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1114) | c0_1(a1114) | (~c2_1(a1114)))),
% 1.71/1.45 inference(quant_inst,[status(thm)],[])).
% 1.71/1.45 tff(2846,plain,
% 1.71/1.45 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c2_1(a1114))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2845, 2844])).
% 1.71/1.45 tff(2847,plain,
% 1.71/1.45 ($false),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2846, 113, 2803, 2806, 2840, 2829, 2823, 2816])).
% 1.71/1.45 tff(2848,plain,((~hskp12) | hskp16 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.71/1.45 tff(2849,plain,
% 1.71/1.45 (~hskp12),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2848, 2803, 2806])).
% 1.71/1.45 tff(2850,plain,
% 1.71/1.45 ((hskp26 | hskp19 | hskp12) <=> (hskp26 | hskp19 | hskp12)),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2851,plain,
% 1.71/1.45 (((hskp19 | hskp12) | hskp26) <=> (hskp26 | hskp19 | hskp12)),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2852,plain,
% 1.71/1.45 ((hskp19 | hskp12) <=> (hskp19 | hskp12)),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2853,plain,
% 1.71/1.45 (((hskp19 | hskp12) | hskp26) <=> ((hskp19 | hskp12) | hskp26)),
% 1.71/1.45 inference(monotonicity,[status(thm)],[2852])).
% 1.71/1.45 tff(2854,plain,
% 1.71/1.45 (((hskp19 | hskp12) | hskp26) <=> (hskp26 | hskp19 | hskp12)),
% 1.71/1.45 inference(transitivity,[status(thm)],[2853, 2851])).
% 1.71/1.45 tff(2855,axiom,((hskp19 | hskp12) | hskp26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.71/1.45 tff(2856,plain,
% 1.71/1.45 (hskp26 | hskp19 | hskp12),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2855, 2854])).
% 1.71/1.45 tff(2857,plain,
% 1.71/1.45 (hskp26 | hskp19 | hskp12),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2856, 2850])).
% 1.71/1.45 tff(2858,plain,
% 1.71/1.45 (hskp26 | hskp19 | hskp12),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2857, 2850])).
% 1.71/1.45 tff(2859,plain,
% 1.71/1.45 (hskp26 | hskp19 | hskp12),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2858, 2850])).
% 1.71/1.45 tff(2860,plain,
% 1.71/1.45 (hskp26 | hskp19 | hskp12),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2859, 2850])).
% 1.71/1.45 tff(2861,plain,
% 1.71/1.45 (hskp26 | hskp19 | hskp12),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2860, 2850])).
% 1.71/1.45 tff(2862,plain,
% 1.71/1.45 (hskp26 | hskp19 | hskp12),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2861, 2850])).
% 1.71/1.45 tff(2863,plain,
% 1.71/1.45 (hskp26 | hskp19 | hskp12),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2862, 2850])).
% 1.71/1.45 tff(2864,plain,
% 1.71/1.45 (hskp19),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2863, 2849, 2802])).
% 1.71/1.45 tff(2865,plain,
% 1.71/1.45 (~c2_1(a1127)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[900, 2864])).
% 1.71/1.45 tff(2866,plain,
% 1.71/1.45 (c2_1(a1125)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2254, 2804])).
% 1.71/1.45 tff(2867,plain,
% 1.71/1.45 (c0_1(a1125)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2265, 2804])).
% 1.71/1.45 tff(2868,plain,
% 1.71/1.45 (c3_1(a1127)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[912, 2864])).
% 1.71/1.45 tff(2869,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2870,plain,
% 1.71/1.45 ((hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125))) <=> (hskp7 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2871,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127))))),
% 1.71/1.45 inference(monotonicity,[status(thm)],[2870])).
% 1.71/1.45 tff(2872,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.71/1.45 inference(transitivity,[status(thm)],[2871, 2869])).
% 1.71/1.45 tff(2873,plain,
% 1.71/1.45 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))),
% 1.71/1.45 inference(quant_inst,[status(thm)],[])).
% 1.71/1.45 tff(2874,plain,
% 1.71/1.45 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2873, 2872])).
% 1.71/1.45 tff(2875,plain,
% 1.71/1.45 (~c0_1(a1127)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2874, 113, 68, 2868, 2867, 2866, 2865, 2805, 2220])).
% 1.71/1.45 tff(2876,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1147) | c3_1(a1147) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1147)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2877,plain,
% 1.71/1.45 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127))) <=> (hskp29 | c2_1(a1147) | c3_1(a1147) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1147)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2878,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1147) | c3_1(a1147) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1147))))),
% 1.71/1.45 inference(monotonicity,[status(thm)],[2877])).
% 1.71/1.45 tff(2879,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1147)))),
% 1.71/1.45 inference(transitivity,[status(thm)],[2878, 2876])).
% 1.71/1.45 tff(2880,plain,
% 1.71/1.45 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)))),
% 1.71/1.45 inference(quant_inst,[status(thm)],[])).
% 1.71/1.45 tff(2881,plain,
% 1.71/1.45 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1147) | c3_1(a1147) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1147))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2880, 2879])).
% 1.71/1.45 tff(2882,plain,
% 1.71/1.45 ($false),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2881, 113, 770, 2868, 819, 771, 2865, 67, 2584, 2875])).
% 1.71/1.45 tff(2883,plain,(hskp16 | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147)) | hskp7 | hskp26 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.71/1.45 tff(2884,plain,
% 1.71/1.45 (hskp2),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2883, 2785, 819, 771, 2730, 68, 2750, 770])).
% 1.71/1.45 tff(2885,plain,
% 1.71/1.45 (c0_1(a1100)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[313, 2884])).
% 1.71/1.45 tff(2886,plain,
% 1.71/1.45 (~c3_1(a1100)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[291, 2884])).
% 1.71/1.45 tff(2887,plain,
% 1.71/1.45 (c2_1(a1100)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[302, 2884])).
% 1.71/1.45 tff(2888,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1147) | c3_1(a1114) | (~ndr1_0) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1147) | c3_1(a1114) | (~ndr1_0) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2889,plain,
% 1.71/1.45 ((hskp5 | (~ndr1_0) | c3_1(a1114) | (~c1_1(a1114)) | (~c2_1(a1114)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147))) <=> (hskp5 | c3_1(a1147) | c3_1(a1114) | (~ndr1_0) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2890,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1114) | (~c1_1(a1114)) | (~c2_1(a1114)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1147) | c3_1(a1114) | (~ndr1_0) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.71/1.45 inference(monotonicity,[status(thm)],[2889])).
% 1.71/1.45 tff(2891,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1114) | (~c1_1(a1114)) | (~c2_1(a1114)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1147) | c3_1(a1114) | (~ndr1_0) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.45 inference(transitivity,[status(thm)],[2890, 2888])).
% 1.71/1.45 tff(2892,plain,
% 1.71/1.45 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1114) | (~c1_1(a1114)) | (~c2_1(a1114)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.45 inference(quant_inst,[status(thm)],[])).
% 1.71/1.45 tff(2893,plain,
% 1.71/1.45 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1147) | c3_1(a1114) | (~ndr1_0) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2892, 2891])).
% 1.71/1.45 tff(2894,plain,
% 1.71/1.45 (~c1_1(a1114)),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2893, 113, 1269, 772, 2840, 771, 2823, 1279, 2584])).
% 1.71/1.45 tff(2895,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2896,plain,
% 1.71/1.45 ((hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147))) <=> (hskp5 | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2897,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.71/1.45 inference(monotonicity,[status(thm)],[2896])).
% 1.71/1.45 tff(2898,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.45 inference(transitivity,[status(thm)],[2897, 2895])).
% 1.71/1.45 tff(2899,plain,
% 1.71/1.45 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1101) | (~c1_1(a1101)) | (~c2_1(a1101)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.71/1.45 inference(quant_inst,[status(thm)],[])).
% 1.71/1.45 tff(2900,plain,
% 1.71/1.45 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1147) | c3_1(a1101) | (~ndr1_0) | (~c1_1(a1101)) | (~c2_1(a1101)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.71/1.45 inference(modus_ponens,[status(thm)],[2899, 2898])).
% 1.71/1.45 tff(2901,plain,
% 1.71/1.45 ($false),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2900, 113, 1269, 772, 1330, 1338, 771, 1329, 1279, 2584])).
% 1.71/1.45 tff(2902,plain,((~hskp3) | hskp5 | (~c0_1(a1147)) | c3_1(a1147) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.71/1.45 tff(2903,plain,
% 1.71/1.45 (~hskp3),
% 1.71/1.45 inference(unit_resolution,[status(thm)],[2902, 1269, 772, 771, 2584])).
% 1.71/1.45 tff(2904,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1114) | c3_1(a1114) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1114))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1114) | c3_1(a1114) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1114))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2905,plain,
% 1.71/1.45 ((hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1114) | c0_1(a1114) | c3_1(a1114)) <=> (hskp3 | c0_1(a1114) | c3_1(a1114) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1114))),
% 1.71/1.45 inference(rewrite,[status(thm)],[])).
% 1.71/1.45 tff(2906,plain,
% 1.71/1.45 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1114) | c0_1(a1114) | c3_1(a1114))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1114) | c3_1(a1114) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1114)))),
% 1.71/1.46 inference(monotonicity,[status(thm)],[2905])).
% 1.71/1.46 tff(2907,plain,
% 1.71/1.46 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1114) | c0_1(a1114) | c3_1(a1114))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1114) | c3_1(a1114) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1114))),
% 1.71/1.46 inference(transitivity,[status(thm)],[2906, 2904])).
% 1.71/1.46 tff(2908,plain,
% 1.71/1.46 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1114) | c0_1(a1114) | c3_1(a1114))),
% 1.71/1.46 inference(quant_inst,[status(thm)],[])).
% 1.71/1.46 tff(2909,plain,
% 1.71/1.46 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1114) | c3_1(a1114) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c1_1(a1114)),
% 1.71/1.46 inference(modus_ponens,[status(thm)],[2908, 2907])).
% 1.71/1.46 tff(2910,plain,
% 1.71/1.46 ($false),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[2909, 113, 2903, 1388, 1387, 2829, 2823, 1386, 1055, 2894])).
% 1.71/1.46 tff(2911,plain,((~hskp12) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | hskp5 | (~c0_1(a1147)) | c3_1(a1147) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.71/1.46 tff(2912,plain,
% 1.71/1.46 (~hskp12),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[2911, 2887, 2730, 2886, 2729, 2706, 771, 2885])).
% 1.71/1.46 tff(2913,plain,
% 1.71/1.46 (hskp19),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[2863, 2912, 2785])).
% 1.71/1.46 tff(2914,plain,
% 1.71/1.46 (~c2_1(a1127)),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[900, 2913])).
% 1.71/1.46 tff(2915,plain,
% 1.71/1.46 (c2_1(a1125)),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[2254, 2800])).
% 1.71/1.46 tff(2916,plain,
% 1.71/1.46 (c0_1(a1125)),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[2265, 2800])).
% 1.71/1.46 tff(2917,plain,
% 1.71/1.46 (c3_1(a1127)),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[912, 2913])).
% 1.71/1.46 tff(2918,plain,
% 1.71/1.46 (~c0_1(a1127)),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[2874, 113, 68, 2917, 2916, 2915, 2914, 2801, 2220])).
% 1.71/1.46 tff(2919,plain,
% 1.71/1.46 ($false),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[2881, 113, 770, 2917, 819, 771, 2914, 67, 2730, 2918])).
% 1.71/1.46 tff(2920,plain,(hskp29 | c2_1(a1147) | c3_1(a1147) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.71/1.46 tff(2921,plain,
% 1.71/1.46 (hskp29),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[2920, 68, 771, 819])).
% 1.71/1.46 tff(2922,plain,
% 1.71/1.46 (c3_1(a1116)),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[201, 2921])).
% 1.71/1.46 tff(2923,plain,
% 1.71/1.46 (c2_1(a1116)),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[212, 2921])).
% 1.71/1.46 tff(2924,plain,
% 1.71/1.46 (c0_1(a1116)),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[223, 2921])).
% 1.71/1.46 tff(2925,assumption,(hskp20), introduced(assumption)).
% 1.71/1.46 tff(2926,plain,
% 1.71/1.46 (~c3_1(a1130)),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[332, 2925])).
% 1.71/1.46 tff(2927,plain,
% 1.71/1.46 (~c2_1(a1130)),
% 1.71/1.46 inference(unit_resolution,[status(thm)],[2287, 2925])).
% 1.71/1.46 tff(2928,plain,
% 1.71/1.46 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130))),
% 1.71/1.46 inference(rewrite,[status(thm)],[])).
% 1.71/1.46 tff(2929,plain,
% 1.71/1.46 ((hskp7 | hskp5 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c1_1(a1130)) <=> (hskp7 | hskp5 | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130))),
% 1.71/1.46 inference(rewrite,[status(thm)],[])).
% 1.71/1.46 tff(2930,plain,
% 1.71/1.46 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c1_1(a1130))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130)))),
% 1.71/1.46 inference(monotonicity,[status(thm)],[2929])).
% 1.71/1.46 tff(2931,plain,
% 1.71/1.46 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c1_1(a1130))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130))),
% 1.77/1.46 inference(transitivity,[status(thm)],[2930, 2928])).
% 1.77/1.46 tff(2932,plain,
% 1.77/1.46 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1130) | c2_1(a1130) | c1_1(a1130))),
% 1.77/1.46 inference(quant_inst,[status(thm)],[])).
% 1.77/1.46 tff(2933,plain,
% 1.77/1.46 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c2_1(a1130) | c3_1(a1130) | (~ndr1_0) | c1_1(a1130)),
% 1.77/1.46 inference(modus_ponens,[status(thm)],[2932, 2931])).
% 1.77/1.46 tff(2934,plain,
% 1.77/1.46 (c1_1(a1130)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2933, 113, 68, 2729, 2927, 2926, 78])).
% 1.77/1.46 tff(2935,plain,
% 1.77/1.46 (~c0_1(a1130)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[326, 2925])).
% 1.77/1.46 tff(2936,plain,
% 1.77/1.46 ($false),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[1325, 113, 2924, 2923, 2922, 2706, 819, 771, 2935, 2926, 344, 2934])).
% 1.77/1.46 tff(2937,plain,((~hskp20) | c2_1(a1147) | c3_1(a1147) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.77/1.46 tff(2938,plain,
% 1.77/1.46 (~hskp20),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2937, 68, 771, 819])).
% 1.77/1.46 tff(2939,plain,
% 1.77/1.46 (~hskp19),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[1305, 2938, 2924, 2729, 2923, 2922])).
% 1.77/1.46 tff(2940,plain,
% 1.77/1.46 ($false),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[1266, 113, 2806, 249, 248, 247, 924, 913, 901, 278])).
% 1.77/1.46 tff(2941,plain,((~hskp19) | hskp2 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.46 tff(2942,plain,
% 1.77/1.46 (~hskp19),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2941, 2806, 249, 248, 247])).
% 1.77/1.46 tff(2943,plain,
% 1.77/1.46 (hskp12),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2863, 2942, 2802])).
% 1.77/1.46 tff(2944,plain,
% 1.77/1.46 (~c3_1(a1114)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2822, 2943])).
% 1.77/1.46 tff(2945,plain,
% 1.77/1.46 (~c0_1(a1114)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2828, 2943])).
% 1.77/1.46 tff(2946,plain,
% 1.77/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1114)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1114)) | (~c0_1(a1147)))),
% 1.77/1.46 inference(rewrite,[status(thm)],[])).
% 1.77/1.46 tff(2947,plain,
% 1.77/1.46 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1114) | c0_1(a1114) | (~c1_1(a1114))) <=> (c2_1(a1147) | c3_1(a1147) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1114)) | (~c0_1(a1147)))),
% 1.77/1.46 inference(rewrite,[status(thm)],[])).
% 1.77/1.46 tff(2948,plain,
% 1.77/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1114) | c0_1(a1114) | (~c1_1(a1114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a1147) | c3_1(a1147) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1114)) | (~c0_1(a1147))))),
% 1.77/1.46 inference(monotonicity,[status(thm)],[2947])).
% 1.77/1.46 tff(2949,plain,
% 1.77/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1114) | c0_1(a1114) | (~c1_1(a1114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1114)) | (~c0_1(a1147)))),
% 1.77/1.46 inference(transitivity,[status(thm)],[2948, 2946])).
% 1.77/1.46 tff(2950,plain,
% 1.77/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c3_1(a1114) | c0_1(a1114) | (~c1_1(a1114)))),
% 1.77/1.46 inference(quant_inst,[status(thm)],[])).
% 1.77/1.46 tff(2951,plain,
% 1.77/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a1147) | c3_1(a1147) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1114)) | (~c0_1(a1147))),
% 1.77/1.46 inference(modus_ponens,[status(thm)],[2950, 2949])).
% 1.77/1.46 tff(2952,plain,
% 1.77/1.46 (~c1_1(a1114)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2951, 113, 249, 248, 247, 2706, 819, 771, 2945, 2944, 344])).
% 1.77/1.46 tff(2953,plain,
% 1.77/1.46 (hskp16),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2848, 2943, 2806])).
% 1.77/1.46 tff(2954,plain,
% 1.77/1.46 (~c0_1(a1121)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[1939, 2953])).
% 1.77/1.46 tff(2955,plain,
% 1.77/1.46 (c3_1(a1121)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[1952, 2953])).
% 1.77/1.46 tff(2956,plain,
% 1.77/1.46 (c1_1(a1121)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[1963, 2953])).
% 1.77/1.46 tff(2957,plain,
% 1.77/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1147) | c0_1(a1121) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | c1_1(a1114) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1147) | c0_1(a1121) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | c1_1(a1114) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.77/1.46 inference(rewrite,[status(thm)],[])).
% 1.77/1.46 tff(2958,plain,
% 1.77/1.46 (((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1114) | c1_1(a1114) | c0_1(a1114)) <=> (c3_1(a1147) | c0_1(a1121) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | c1_1(a1114) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.77/1.46 inference(rewrite,[status(thm)],[])).
% 1.77/1.46 tff(2959,plain,
% 1.77/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1114) | c1_1(a1114) | c0_1(a1114))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1147) | c0_1(a1121) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | c1_1(a1114) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.77/1.46 inference(monotonicity,[status(thm)],[2958])).
% 1.77/1.46 tff(2960,plain,
% 1.77/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1114) | c1_1(a1114) | c0_1(a1114))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1147) | c0_1(a1121) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | c1_1(a1114) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.77/1.46 inference(transitivity,[status(thm)],[2959, 2957])).
% 1.77/1.46 tff(2961,plain,
% 1.77/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1114) | c1_1(a1114) | c0_1(a1114))),
% 1.77/1.46 inference(quant_inst,[status(thm)],[])).
% 1.77/1.46 tff(2962,plain,
% 1.77/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1147) | c0_1(a1121) | c0_1(a1114) | c3_1(a1114) | (~ndr1_0) | c1_1(a1114) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.77/1.46 inference(modus_ponens,[status(thm)],[2961, 2960])).
% 1.77/1.46 tff(2963,plain,
% 1.77/1.46 ($false),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2962, 113, 2706, 2956, 2955, 771, 2954, 2945, 2944, 363, 2584, 2952])).
% 1.77/1.46 tff(2964,plain,(hskp2 | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | c2_1(a1147) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.77/1.46 tff(2965,plain,
% 1.77/1.46 (hskp2),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2964, 2802, 2584, 249, 248, 247, 819, 771])).
% 1.77/1.46 tff(2966,plain,
% 1.77/1.46 (c0_1(a1100)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[313, 2965])).
% 1.77/1.46 tff(2967,plain,
% 1.77/1.46 (c2_1(a1100)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[302, 2965])).
% 1.77/1.46 tff(2968,plain,
% 1.77/1.46 (hskp12),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2863, 2802, 704])).
% 1.77/1.46 tff(2969,plain,
% 1.77/1.46 (~c3_1(a1100)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[291, 2965])).
% 1.77/1.46 tff(2970,plain,
% 1.77/1.46 ($false),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2911, 2969, 2968, 2584, 2967, 1269, 2706, 771, 2966])).
% 1.77/1.46 tff(2971,plain,(hskp26 | (~c1_1(a1147)) | hskp5 | c3_1(a1147) | hskp19 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.46 tff(2972,plain,
% 1.77/1.46 (hskp26),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2971, 2730, 2729, 771, 2939, 2924, 2923, 2922, 819])).
% 1.77/1.46 tff(2973,plain,
% 1.77/1.46 (~c2_1(a1180)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2756, 2972])).
% 1.77/1.46 tff(2974,plain,
% 1.77/1.46 (~c1_1(a1180)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2762, 2972])).
% 1.77/1.46 tff(2975,plain,
% 1.77/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1180) | c2_1(a1180) | c2_1(a1147) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c3_1(a1180)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1180) | c2_1(a1180) | c2_1(a1147) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c3_1(a1180)))),
% 1.77/1.46 inference(rewrite,[status(thm)],[])).
% 1.77/1.46 tff(2976,plain,
% 1.77/1.46 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1180) | c2_1(a1180) | (~c3_1(a1180))) <=> (c1_1(a1180) | c2_1(a1180) | c2_1(a1147) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c3_1(a1180)))),
% 1.77/1.46 inference(rewrite,[status(thm)],[])).
% 1.77/1.46 tff(2977,plain,
% 1.77/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1180) | c2_1(a1180) | (~c3_1(a1180)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1180) | c2_1(a1180) | c2_1(a1147) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c3_1(a1180))))),
% 1.77/1.46 inference(monotonicity,[status(thm)],[2976])).
% 1.77/1.46 tff(2978,plain,
% 1.77/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1180) | c2_1(a1180) | (~c3_1(a1180)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1180) | c2_1(a1180) | c2_1(a1147) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c3_1(a1180)))),
% 1.77/1.46 inference(transitivity,[status(thm)],[2977, 2975])).
% 1.77/1.46 tff(2979,plain,
% 1.77/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1180) | c2_1(a1180) | (~c3_1(a1180)))),
% 1.77/1.46 inference(quant_inst,[status(thm)],[])).
% 1.77/1.46 tff(2980,plain,
% 1.77/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1180) | c2_1(a1180) | c2_1(a1147) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)) | (~c0_1(a1147)) | (~c3_1(a1180))),
% 1.77/1.46 inference(modus_ponens,[status(thm)],[2979, 2978])).
% 1.77/1.46 tff(2981,plain,
% 1.77/1.46 (~c3_1(a1180)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2980, 113, 2924, 2923, 2922, 2706, 2974, 2973, 819, 246, 2730])).
% 1.77/1.46 tff(2982,plain,
% 1.77/1.46 ($false),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2769, 113, 68, 2729, 2974, 2973, 78, 2981])).
% 1.77/1.46 tff(2983,plain,(hskp7 | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.46 tff(2984,plain,
% 1.77/1.46 (hskp7),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2983, 771, 819])).
% 1.77/1.46 tff(2985,plain,
% 1.77/1.46 (c3_1(a1105)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[657, 2984])).
% 1.77/1.46 tff(2986,plain,
% 1.77/1.46 (c0_1(a1105)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[646, 2984])).
% 1.77/1.46 tff(2987,plain,
% 1.77/1.46 (~c1_1(a1105)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[633, 2984])).
% 1.77/1.46 tff(2988,assumption,(~c0_1(a1105)), introduced(assumption)).
% 1.77/1.46 tff(2989,plain,
% 1.77/1.46 (~hskp7),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[646, 2988])).
% 1.77/1.46 tff(2990,plain,
% 1.77/1.46 (hskp7 | hskp5 | c1_1(a1147)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2616, 113, 819, 771, 78])).
% 1.77/1.46 tff(2991,plain,
% 1.77/1.46 (c1_1(a1147)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2990, 1269, 2989])).
% 1.77/1.46 tff(2992,assumption,(~c3_1(a1105)), introduced(assumption)).
% 1.77/1.46 tff(2993,plain,
% 1.77/1.46 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c3_1(a1105) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c3_1(a1105) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105))),
% 1.77/1.46 inference(rewrite,[status(thm)],[])).
% 1.77/1.46 tff(2994,plain,
% 1.77/1.46 ((hskp7 | hskp5 | (~ndr1_0) | c3_1(a1105) | c2_1(a1105) | c1_1(a1105)) <=> (hskp7 | hskp5 | c3_1(a1105) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105))),
% 1.77/1.46 inference(rewrite,[status(thm)],[])).
% 1.77/1.46 tff(2995,plain,
% 1.77/1.46 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1105) | c2_1(a1105) | c1_1(a1105))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | c3_1(a1105) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105)))),
% 1.77/1.46 inference(monotonicity,[status(thm)],[2994])).
% 1.77/1.46 tff(2996,plain,
% 1.77/1.46 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1105) | c2_1(a1105) | c1_1(a1105))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c3_1(a1105) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105))),
% 1.77/1.46 inference(transitivity,[status(thm)],[2995, 2993])).
% 1.77/1.46 tff(2997,plain,
% 1.77/1.46 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a1105) | c2_1(a1105) | c1_1(a1105))),
% 1.77/1.46 inference(quant_inst,[status(thm)],[])).
% 1.77/1.46 tff(2998,plain,
% 1.77/1.46 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp7 | hskp5 | c3_1(a1105) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105)),
% 1.77/1.46 inference(modus_ponens,[status(thm)],[2997, 2996])).
% 1.77/1.46 tff(2999,plain,
% 1.77/1.46 (hskp7 | hskp5 | c3_1(a1105) | c2_1(a1105)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2998, 113, 669, 78])).
% 1.77/1.46 tff(3000,plain,
% 1.77/1.46 (c2_1(a1105)),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[2999, 1269, 2989, 2992])).
% 1.77/1.46 tff(3001,plain,
% 1.77/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c0_1(a1121) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c0_1(a1121) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.77/1.46 inference(rewrite,[status(thm)],[])).
% 1.77/1.46 tff(3002,plain,
% 1.77/1.46 (((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1105) | c1_1(a1105) | c0_1(a1105)) <=> (c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c0_1(a1121) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.77/1.46 inference(rewrite,[status(thm)],[])).
% 1.77/1.46 tff(3003,plain,
% 1.77/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1105) | c1_1(a1105) | c0_1(a1105))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c0_1(a1121) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.77/1.46 inference(monotonicity,[status(thm)],[3002])).
% 1.77/1.46 tff(3004,plain,
% 1.77/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1105) | c1_1(a1105) | c0_1(a1105))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c0_1(a1121) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.77/1.46 inference(transitivity,[status(thm)],[3003, 3001])).
% 1.77/1.46 tff(3005,plain,
% 1.77/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)) | c3_1(a1105) | c1_1(a1105) | c0_1(a1105))),
% 1.77/1.46 inference(quant_inst,[status(thm)],[])).
% 1.77/1.46 tff(3006,plain,
% 1.77/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c0_1(a1121) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.77/1.46 inference(modus_ponens,[status(thm)],[3005, 3004])).
% 1.77/1.46 tff(3007,plain,
% 1.77/1.46 ($false),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[3006, 113, 772, 2734, 2733, 2988, 2992, 771, 2732, 669, 363, 2584])).
% 1.77/1.46 tff(3008,plain,((~hskp16) | (~c0_1(a1147)) | c0_1(a1105) | c3_1(a1105) | c3_1(a1147) | c1_1(a1105) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.46 tff(3009,plain,
% 1.77/1.46 (~hskp16),
% 1.77/1.46 inference(unit_resolution,[status(thm)],[3008, 2991, 2988, 2992, 771, 669, 772])).
% 1.77/1.46 tff(3010,plain,
% 1.77/1.46 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | c0_1(a1105) | c3_1(a1105) | (~ndr1_0) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1105) | c3_1(a1105) | (~ndr1_0) | (~c2_1(a1105)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3011,plain,
% 1.78/1.47 ((hskp16 | hskp2 | (~ndr1_0) | c3_1(a1105) | c0_1(a1105) | (~c2_1(a1105))) <=> (hskp16 | hskp2 | c0_1(a1105) | c3_1(a1105) | (~ndr1_0) | (~c2_1(a1105)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3012,plain,
% 1.78/1.47 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1105) | c0_1(a1105) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | c0_1(a1105) | c3_1(a1105) | (~ndr1_0) | (~c2_1(a1105))))),
% 1.78/1.47 inference(monotonicity,[status(thm)],[3011])).
% 1.78/1.47 tff(3013,plain,
% 1.78/1.47 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1105) | c0_1(a1105) | (~c2_1(a1105)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1105) | c3_1(a1105) | (~ndr1_0) | (~c2_1(a1105)))),
% 1.78/1.47 inference(transitivity,[status(thm)],[3012, 3010])).
% 1.78/1.47 tff(3014,plain,
% 1.78/1.47 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1105) | c0_1(a1105) | (~c2_1(a1105)))),
% 1.78/1.47 inference(quant_inst,[status(thm)],[])).
% 1.78/1.47 tff(3015,plain,
% 1.78/1.47 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1105) | c3_1(a1105) | (~ndr1_0) | (~c2_1(a1105))),
% 1.78/1.47 inference(modus_ponens,[status(thm)],[3014, 3013])).
% 1.78/1.47 tff(3016,plain,
% 1.78/1.47 (hskp16 | hskp2 | c3_1(a1105) | (~c2_1(a1105))),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3015, 113, 2988, 2816])).
% 1.78/1.47 tff(3017,plain,
% 1.78/1.47 (hskp2),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3016, 3009, 2992, 3000])).
% 1.78/1.47 tff(3018,plain,
% 1.78/1.47 (~c3_1(a1100)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[291, 3017])).
% 1.78/1.47 tff(3019,plain,
% 1.78/1.47 (c2_1(a1100)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[302, 3017])).
% 1.78/1.47 tff(3020,plain,
% 1.78/1.47 (c0_1(a1100)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[313, 3017])).
% 1.78/1.47 tff(3021,plain,
% 1.78/1.47 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3022,plain,
% 1.78/1.47 ((hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105)) <=> (hskp3 | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3023,plain,
% 1.78/1.47 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100))))),
% 1.78/1.47 inference(monotonicity,[status(thm)],[3022])).
% 1.78/1.47 tff(3024,plain,
% 1.78/1.47 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.78/1.47 inference(transitivity,[status(thm)],[3023, 3021])).
% 1.78/1.47 tff(3025,plain,
% 1.78/1.47 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105))),
% 1.78/1.47 inference(quant_inst,[status(thm)],[])).
% 1.78/1.47 tff(3026,plain,
% 1.78/1.47 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100))),
% 1.78/1.47 inference(modus_ponens,[status(thm)],[3025, 3024])).
% 1.78/1.47 tff(3027,plain,
% 1.78/1.47 (hskp3),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3026, 113, 2988, 2992, 3020, 3019, 669, 3018, 1055])).
% 1.78/1.47 tff(3028,plain,
% 1.78/1.47 (~c3_1(a1101)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[1088, 3027])).
% 1.78/1.47 tff(3029,plain,
% 1.78/1.47 (c2_1(a1101)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[1099, 3027])).
% 1.78/1.47 tff(3030,plain,
% 1.78/1.47 (c1_1(a1101)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[1110, 3027])).
% 1.78/1.47 tff(3031,plain,
% 1.78/1.47 ($false),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[2900, 113, 1269, 772, 3030, 3029, 771, 3028, 1279, 2991])).
% 1.78/1.47 tff(3032,plain,(hskp5 | (~c0_1(a1147)) | c3_1(a1147) | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.47 tff(3033,plain,
% 1.78/1.47 (hskp5),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3032, 2992, 771, 2988, 772, 669, 819])).
% 1.78/1.47 tff(3034,plain,
% 1.78/1.47 (c3_1(a1103)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[153, 3033])).
% 1.78/1.47 tff(3035,plain,
% 1.78/1.47 (~c0_1(a1103)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[132, 3033])).
% 1.78/1.47 tff(3036,plain,
% 1.78/1.47 (~c2_1(a1103)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[126, 3033])).
% 1.78/1.47 tff(3037,plain,
% 1.78/1.47 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3038,plain,
% 1.78/1.47 ((hskp14 | hskp7 | (~ndr1_0) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121))) <=> (hskp14 | hskp7 | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3039,plain,
% 1.78/1.47 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121))))),
% 1.78/1.47 inference(monotonicity,[status(thm)],[3038])).
% 1.78/1.47 tff(3040,plain,
% 1.78/1.47 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121)))),
% 1.78/1.47 inference(transitivity,[status(thm)],[3039, 3037])).
% 1.78/1.47 tff(3041,plain,
% 1.78/1.47 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a1121) | c0_1(a1121) | (~c3_1(a1121)))),
% 1.78/1.47 inference(quant_inst,[status(thm)],[])).
% 1.78/1.47 tff(3042,plain,
% 1.78/1.47 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a1121) | (~ndr1_0) | c2_1(a1121) | (~c3_1(a1121))),
% 1.78/1.47 inference(modus_ponens,[status(thm)],[3041, 3040])).
% 1.78/1.47 tff(3043,plain,
% 1.78/1.47 ($false),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3042, 692, 113, 68, 2733, 2732, 143, 2741])).
% 1.78/1.47 tff(3044,plain,((~hskp16) | hskp14 | hskp7 | (~c0_1(a1147)) | c3_1(a1147) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.47 tff(3045,plain,
% 1.78/1.47 (~hskp16),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3044, 2991, 2989, 772, 771, 692])).
% 1.78/1.47 tff(3046,plain,
% 1.78/1.47 (hskp2),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3016, 3045, 2992, 3000])).
% 1.78/1.47 tff(3047,plain,
% 1.78/1.47 (~c3_1(a1100)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[291, 3046])).
% 1.78/1.47 tff(3048,plain,
% 1.78/1.47 (c2_1(a1100)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[302, 3046])).
% 1.78/1.47 tff(3049,plain,
% 1.78/1.47 (c0_1(a1100)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[313, 3046])).
% 1.78/1.47 tff(3050,plain,
% 1.78/1.47 (hskp3),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3026, 113, 2988, 2992, 3049, 3048, 669, 3047, 1055])).
% 1.78/1.47 tff(3051,plain,
% 1.78/1.47 (~c3_1(a1101)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[1088, 3050])).
% 1.78/1.47 tff(3052,plain,
% 1.78/1.47 (c2_1(a1101)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[1099, 3050])).
% 1.78/1.47 tff(3053,plain,
% 1.78/1.47 (c1_1(a1101)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[1110, 3050])).
% 1.78/1.47 tff(3054,plain,
% 1.78/1.47 ($false),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[2900, 113, 1269, 772, 3053, 3052, 771, 3051, 1279, 2991])).
% 1.78/1.47 tff(3055,plain,(hskp5 | (~c0_1(a1147)) | c3_1(a1147) | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | hskp14 | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.47 tff(3056,plain,
% 1.78/1.47 (hskp5),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3055, 692, 771, 2988, 2992, 669, 772, 819])).
% 1.78/1.47 tff(3057,plain,
% 1.78/1.47 (~c2_1(a1103)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[126, 3056])).
% 1.78/1.47 tff(3058,plain,
% 1.78/1.47 (~c0_1(a1103)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[132, 3056])).
% 1.78/1.47 tff(3059,plain,
% 1.78/1.47 (c3_1(a1103)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[153, 3056])).
% 1.78/1.47 tff(3060,plain,
% 1.78/1.47 ($false),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[160, 692, 113, 2989, 3059, 3058, 3057, 143])).
% 1.78/1.47 tff(3061,plain,(hskp14 | c3_1(a1147) | c0_1(a1105) | c3_1(a1105) | c1_1(a1105) | (~c0_1(a1147)) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.47 tff(3062,plain,
% 1.78/1.47 (hskp14),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3061, 2992, 2988, 771, 669, 772, 819])).
% 1.78/1.47 tff(3063,plain,
% 1.78/1.47 (~c2_1(a1118)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[172, 3062])).
% 1.78/1.47 tff(3064,plain,
% 1.78/1.47 (~c3_1(a1118)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[166, 3062])).
% 1.78/1.47 tff(3065,plain,
% 1.78/1.47 (c1_1(a1118)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[183, 3062])).
% 1.78/1.47 tff(3066,plain,
% 1.78/1.47 (~c0_1(a1118)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[2079, 3033, 3065, 3064, 3063])).
% 1.78/1.47 tff(3067,plain,
% 1.78/1.47 (hskp14),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[160, 113, 68, 231, 225, 229, 143])).
% 1.78/1.47 tff(3068,plain,
% 1.78/1.47 (~c3_1(a1118)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[166, 3067])).
% 1.78/1.47 tff(3069,plain,
% 1.78/1.47 (~c2_1(a1118)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[172, 3067])).
% 1.78/1.47 tff(3070,plain,
% 1.78/1.47 (hskp6 | c0_1(a1118)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[531, 113, 68, 3069, 3068, 525])).
% 1.78/1.47 tff(3071,plain,
% 1.78/1.47 (hskp6),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3070, 378])).
% 1.78/1.47 tff(3072,plain,
% 1.78/1.47 (~c2_1(a1104)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[538, 3071])).
% 1.78/1.47 tff(3073,plain,
% 1.78/1.47 (c0_1(a1104)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[549, 3071])).
% 1.78/1.47 tff(3074,plain,
% 1.78/1.47 (c1_1(a1118)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[183, 3067])).
% 1.78/1.47 tff(3075,plain,
% 1.78/1.47 (hskp29),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[190, 113, 3074, 231, 3069, 3068, 225, 229, 67])).
% 1.78/1.47 tff(3076,plain,
% 1.78/1.47 (c3_1(a1116)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[201, 3075])).
% 1.78/1.47 tff(3077,plain,
% 1.78/1.47 (c2_1(a1116)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[212, 3075])).
% 1.78/1.47 tff(3078,plain,
% 1.78/1.47 (c0_1(a1116)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[223, 3075])).
% 1.78/1.47 tff(3079,plain,
% 1.78/1.47 (c3_1(a1104)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[556, 113, 3078, 3077, 3076, 3074, 3073, 3068, 3072, 344, 378])).
% 1.78/1.47 tff(3080,plain,
% 1.78/1.47 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1104) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1104)) | (~c3_1(a1104)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1104) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1104)) | (~c3_1(a1104)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3081,plain,
% 1.78/1.47 ((hskp16 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103))) <=> (hskp16 | c2_1(a1104) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1104)) | (~c3_1(a1104)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3082,plain,
% 1.78/1.47 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1104) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1104)) | (~c3_1(a1104))))),
% 1.78/1.47 inference(monotonicity,[status(thm)],[3081])).
% 1.78/1.47 tff(3083,plain,
% 1.78/1.47 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1104) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1104)) | (~c3_1(a1104)))),
% 1.78/1.47 inference(transitivity,[status(thm)],[3082, 3080])).
% 1.78/1.47 tff(3084,plain,
% 1.78/1.47 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1104) | (~c3_1(a1104)) | (~c0_1(a1104)) | c0_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1103)))),
% 1.78/1.47 inference(quant_inst,[status(thm)],[])).
% 1.78/1.47 tff(3085,plain,
% 1.78/1.47 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1104) | c0_1(a1103) | (~ndr1_0) | (~c1_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1104)) | (~c3_1(a1104))),
% 1.78/1.47 inference(modus_ponens,[status(thm)],[3084, 3083])).
% 1.78/1.47 tff(3086,plain,
% 1.78/1.47 (~c1_1(a1103)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3085, 113, 2803, 3073, 231, 3072, 225, 1916, 3079])).
% 1.78/1.47 tff(3087,plain,
% 1.78/1.47 (c1_1(a1104)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[577, 3071])).
% 1.78/1.47 tff(3088,plain,
% 1.78/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1104) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1104)) | (~c0_1(a1104)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1104) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1104)) | (~c0_1(a1104)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3089,plain,
% 1.78/1.47 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103))) <=> (c2_1(a1104) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1104)) | (~c0_1(a1104)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3090,plain,
% 1.78/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1104) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1104)) | (~c0_1(a1104))))),
% 1.78/1.47 inference(monotonicity,[status(thm)],[3089])).
% 1.78/1.47 tff(3091,plain,
% 1.78/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1104) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1104)) | (~c0_1(a1104)))),
% 1.78/1.47 inference(transitivity,[status(thm)],[3090, 3088])).
% 1.78/1.47 tff(3092,plain,
% 1.78/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1103) | c2_1(a1103) | (~c3_1(a1103)))),
% 1.78/1.47 inference(quant_inst,[status(thm)],[])).
% 1.78/1.47 tff(3093,plain,
% 1.78/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1104) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1103) | (~c3_1(a1103)) | (~c1_1(a1104)) | (~c0_1(a1104))),
% 1.78/1.47 inference(modus_ponens,[status(thm)],[3092, 3091])).
% 1.78/1.47 tff(3094,plain,
% 1.78/1.47 ($false),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3093, 113, 3078, 3077, 3076, 3073, 3087, 231, 3072, 229, 246, 3086])).
% 1.78/1.47 tff(3095,plain,(c0_1(a1118) | (~c3_1(a1103)) | c2_1(a1103) | hskp16 | c0_1(a1103) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.78/1.47 tff(3096,plain,
% 1.78/1.47 (hskp16),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3095, 3066, 2989, 3036, 3035, 3034])).
% 1.78/1.47 tff(3097,plain,
% 1.78/1.47 (~c1_1(a1147)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3008, 3096, 2988, 2992, 771, 669, 772])).
% 1.78/1.47 tff(3098,plain,
% 1.78/1.47 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a1105) | c3_1(a1105) | c3_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a1105) | c3_1(a1105) | c3_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3099,plain,
% 1.78/1.47 ((hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105)) <=> (hskp1 | c0_1(a1105) | c3_1(a1105) | c3_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3100,plain,
% 1.78/1.47 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a1105) | c3_1(a1105) | c3_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118)))),
% 1.78/1.47 inference(monotonicity,[status(thm)],[3099])).
% 1.78/1.47 tff(3101,plain,
% 1.78/1.47 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a1105) | c3_1(a1105) | c3_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.78/1.47 inference(transitivity,[status(thm)],[3100, 3098])).
% 1.78/1.47 tff(3102,plain,
% 1.78/1.47 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a1118) | c0_1(a1118) | (~c1_1(a1118)) | c1_1(a1105) | c0_1(a1105) | c3_1(a1105))),
% 1.78/1.47 inference(quant_inst,[status(thm)],[])).
% 1.78/1.47 tff(3103,plain,
% 1.78/1.47 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a1105) | c3_1(a1105) | c3_1(a1118) | c1_1(a1105) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118)),
% 1.78/1.47 inference(modus_ponens,[status(thm)],[3102, 3101])).
% 1.78/1.47 tff(3104,plain,
% 1.78/1.47 (hskp1 | c0_1(a1118)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3103, 113, 3065, 2988, 2992, 3064, 669, 396])).
% 1.78/1.47 tff(3105,plain,
% 1.78/1.47 (hskp1),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3104, 3066])).
% 1.78/1.47 tff(3106,plain,
% 1.78/1.47 (~c0_1(a1099)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[411, 3105])).
% 1.78/1.47 tff(3107,plain,
% 1.78/1.47 (hskp6 | c0_1(a1118)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[531, 113, 2989, 3063, 3064, 525])).
% 1.78/1.47 tff(3108,plain,
% 1.78/1.47 (hskp6),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3107, 3066])).
% 1.78/1.47 tff(3109,plain,
% 1.78/1.47 (~c2_1(a1104)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[538, 3108])).
% 1.78/1.47 tff(3110,plain,
% 1.78/1.47 (c2_1(a1099)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[462, 3105])).
% 1.78/1.47 tff(3111,plain,
% 1.78/1.47 (c1_1(a1099)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[473, 3105])).
% 1.78/1.47 tff(3112,plain,
% 1.78/1.47 (c1_1(a1104)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[577, 3108])).
% 1.78/1.47 tff(3113,plain,
% 1.78/1.47 (c0_1(a1104)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[549, 3108])).
% 1.78/1.47 tff(3114,plain,
% 1.78/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1147) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1147) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3115,plain,
% 1.78/1.47 (((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099))) <=> (c3_1(a1147) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3116,plain,
% 1.78/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1147) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.78/1.47 inference(monotonicity,[status(thm)],[3115])).
% 1.78/1.47 tff(3117,plain,
% 1.78/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1147) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.78/1.47 inference(transitivity,[status(thm)],[3116, 3114])).
% 1.78/1.47 tff(3118,plain,
% 1.78/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1104) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)) | c0_1(a1099) | (~c2_1(a1099)) | (~c1_1(a1099)))),
% 1.78/1.47 inference(quant_inst,[status(thm)],[])).
% 1.78/1.47 tff(3119,plain,
% 1.78/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1147) | c2_1(a1104) | c0_1(a1099) | (~ndr1_0) | (~c2_1(a1099)) | (~c1_1(a1099)) | (~c1_1(a1104)) | (~c0_1(a1104)) | c1_1(a1147) | (~c0_1(a1147))),
% 1.78/1.47 inference(modus_ponens,[status(thm)],[3118, 3117])).
% 1.78/1.47 tff(3120,plain,
% 1.78/1.47 ($false),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3119, 113, 772, 3113, 3112, 3111, 3110, 771, 3109, 3106, 1418, 3097])).
% 1.78/1.47 tff(3121,plain,(c3_1(a1105) | (~c0_1(a1147)) | c3_1(a1147) | c0_1(a1105) | c1_1(a1105) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.47 tff(3122,plain,
% 1.78/1.47 (c3_1(a1105)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3121, 2988, 771, 772, 669, 819])).
% 1.78/1.47 tff(3123,plain,
% 1.78/1.47 (~hskp3),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[2902, 1269, 772, 771, 2991])).
% 1.78/1.47 tff(3124,assumption,(~c2_1(a1105)), introduced(assumption)).
% 1.78/1.47 tff(3125,plain,
% 1.78/1.47 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1105) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1105) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3126,plain,
% 1.78/1.47 ((hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1105) | c0_1(a1105) | (~c3_1(a1105))) <=> (hskp29 | c0_1(a1105) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3127,plain,
% 1.78/1.47 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1105) | c0_1(a1105) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1105) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147))))),
% 1.78/1.47 inference(monotonicity,[status(thm)],[3126])).
% 1.78/1.47 tff(3128,plain,
% 1.78/1.47 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1105) | c0_1(a1105) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1105) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147)))),
% 1.78/1.47 inference(transitivity,[status(thm)],[3127, 3125])).
% 1.78/1.47 tff(3129,plain,
% 1.78/1.47 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1147) | c2_1(a1147) | (~c1_1(a1147)) | c2_1(a1105) | c0_1(a1105) | (~c3_1(a1105)))),
% 1.78/1.47 inference(quant_inst,[status(thm)],[])).
% 1.78/1.47 tff(3130,plain,
% 1.78/1.47 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1105) | c2_1(a1147) | c3_1(a1147) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c1_1(a1147))),
% 1.78/1.47 inference(modus_ponens,[status(thm)],[3129, 3128])).
% 1.78/1.47 tff(3131,plain,
% 1.78/1.47 ($false),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3130, 113, 770, 2988, 965, 819, 771, 67, 3124, 2584])).
% 1.78/1.47 tff(3132,plain,(c2_1(a1105) | hskp29 | c0_1(a1105) | (~c3_1(a1105)) | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.47 tff(3133,plain,
% 1.78/1.47 (c2_1(a1105)),
% 1.78/1.47 inference(unit_resolution,[status(thm)],[3132, 770, 2988, 3122, 819, 771, 2991])).
% 1.78/1.47 tff(3134,plain,
% 1.78/1.47 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.78/1.47 inference(bind,[status(th)],[])).
% 1.78/1.47 tff(3135,plain,
% 1.78/1.47 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.78/1.47 inference(quant_intro,[status(thm)],[3134])).
% 1.78/1.47 tff(3136,plain,
% 1.78/1.47 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.78/1.47 inference(rewrite,[status(thm)],[])).
% 1.78/1.47 tff(3137,plain,
% 1.78/1.47 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.78/1.47 inference(bind,[status(th)],[])).
% 1.78/1.47 tff(3138,plain,
% 1.78/1.47 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.78/1.47 inference(quant_intro,[status(thm)],[3137])).
% 1.78/1.47 tff(3139,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 1.78/1.47 tff(3140,plain,
% 1.78/1.47 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.78/1.47 inference(modus_ponens,[status(thm)],[3139, 3138])).
% 1.78/1.47 tff(3141,plain,
% 1.78/1.47 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.78/1.47 inference(modus_ponens,[status(thm)],[3140, 3136])).
% 1.78/1.47 tff(3142,plain,(
% 1.78/1.47 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.78/1.47 inference(skolemize,[status(sab)],[3141])).
% 1.78/1.47 tff(3143,plain,
% 1.78/1.47 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.78/1.47 inference(modus_ponens,[status(thm)],[3142, 3135])).
% 1.78/1.47 tff(3144,plain,
% 1.78/1.47 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a1180) | c1_1(a1180) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a1180) | c1_1(a1180) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c3_1(a1180))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3145,plain,
% 1.78/1.48 ((hskp2 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180)) <=> (hskp2 | c0_1(a1180) | c1_1(a1180) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c3_1(a1180))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3146,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a1180) | c1_1(a1180) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c3_1(a1180)))),
% 1.78/1.48 inference(monotonicity,[status(thm)],[3145])).
% 1.78/1.48 tff(3147,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a1180) | c1_1(a1180) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c3_1(a1180))),
% 1.78/1.48 inference(transitivity,[status(thm)],[3146, 3144])).
% 1.78/1.48 tff(3148,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))),
% 1.78/1.48 inference(quant_inst,[status(thm)],[])).
% 1.78/1.48 tff(3149,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a1180) | c1_1(a1180) | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c3_1(a1180)),
% 1.78/1.48 inference(modus_ponens,[status(thm)],[3148, 3147])).
% 1.78/1.48 tff(3150,plain,
% 1.78/1.48 (c3_1(a1180)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3149, 113, 2806, 965, 2776, 2763, 669, 3143, 995])).
% 1.78/1.48 tff(3151,plain,
% 1.78/1.48 ($false),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[2782, 113, 770, 2776, 2757, 819, 771, 67, 3150, 2584])).
% 1.78/1.48 tff(3152,plain,((~hskp26) | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147)) | hskp2 | (~c3_1(a1105)) | c1_1(a1105) | (~c2_1(a1105))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.48 tff(3153,plain,
% 1.78/1.48 (~hskp26),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3152, 770, 819, 771, 2991, 2806, 3122, 669, 3133])).
% 1.78/1.48 tff(3154,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1105) | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3155,plain,
% 1.78/1.48 ((hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130))) <=> (hskp3 | c0_1(a1105) | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3156,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1105) | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130))))),
% 1.78/1.48 inference(monotonicity,[status(thm)],[3155])).
% 1.78/1.48 tff(3157,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))),
% 1.78/1.48 inference(transitivity,[status(thm)],[3156, 3154])).
% 1.78/1.48 tff(3158,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))),
% 1.78/1.48 inference(quant_inst,[status(thm)],[])).
% 1.78/1.48 tff(3159,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c0_1(a1130) | c2_1(a1130) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130))),
% 1.78/1.48 inference(modus_ponens,[status(thm)],[3158, 3157])).
% 1.78/1.48 tff(3160,plain,
% 1.78/1.48 (~c1_1(a1130)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3159, 113, 1357, 2988, 965, 2935, 2927, 2307, 995])).
% 1.78/1.48 tff(3161,plain,
% 1.78/1.48 ($false),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[2933, 113, 2989, 1269, 2927, 2926, 78, 3160])).
% 1.78/1.48 tff(3162,plain,((~hskp20) | hskp5 | hskp3 | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.48 tff(3163,plain,
% 1.78/1.48 (~hskp20),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3162, 3133, 3123, 2988, 3122, 1269])).
% 1.78/1.48 tff(3164,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3165,plain,
% 1.78/1.48 ((hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125))) <=> (hskp20 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3166,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127))))),
% 1.78/1.48 inference(monotonicity,[status(thm)],[3165])).
% 1.78/1.48 tff(3167,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.78/1.48 inference(transitivity,[status(thm)],[3166, 3164])).
% 1.78/1.48 tff(3168,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))),
% 1.78/1.48 inference(quant_inst,[status(thm)],[])).
% 1.78/1.48 tff(3169,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a1127) | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1125)) | (~c2_1(a1125)) | (~c0_1(a1127)) | (~c3_1(a1127))),
% 1.78/1.48 inference(modus_ponens,[status(thm)],[3168, 3167])).
% 1.78/1.48 tff(3170,plain,
% 1.78/1.48 (~c0_1(a1127)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3169, 113, 703, 2868, 2867, 2866, 2865, 2805, 1005])).
% 1.78/1.48 tff(3171,plain,
% 1.78/1.48 ($false),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[2881, 113, 770, 2868, 819, 771, 2865, 67, 2584, 3170])).
% 1.78/1.48 tff(3172,plain,(hskp16 | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147)) | hskp20 | hskp26 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.78/1.48 tff(3173,plain,
% 1.78/1.48 (hskp16),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3172, 3163, 819, 771, 2991, 2806, 770, 3153])).
% 1.78/1.48 tff(3174,plain,
% 1.78/1.48 (~c0_1(a1121)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[1939, 3173])).
% 1.78/1.48 tff(3175,plain,
% 1.78/1.48 (c3_1(a1121)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[1952, 3173])).
% 1.78/1.48 tff(3176,plain,
% 1.78/1.48 (c1_1(a1121)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[1963, 3173])).
% 1.78/1.48 tff(3177,plain,
% 1.78/1.48 (~c2_1(a1121)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[2740, 113, 772, 3176, 3175, 771, 3174, 45, 2991])).
% 1.78/1.48 tff(3178,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1105) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c2_1(a1121) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c2_1(a1121) | (~c1_1(a1121)))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3179,plain,
% 1.78/1.48 ((hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1121) | c0_1(a1121) | (~c1_1(a1121))) <=> (hskp3 | c0_1(a1105) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c2_1(a1121) | (~c1_1(a1121)))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3180,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1121) | c0_1(a1121) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1105) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c2_1(a1121) | (~c1_1(a1121))))),
% 1.78/1.48 inference(monotonicity,[status(thm)],[3179])).
% 1.78/1.48 tff(3181,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1121) | c0_1(a1121) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c2_1(a1121) | (~c1_1(a1121)))),
% 1.78/1.48 inference(transitivity,[status(thm)],[3180, 3178])).
% 1.78/1.48 tff(3182,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1121) | c0_1(a1121) | (~c1_1(a1121)))),
% 1.78/1.48 inference(quant_inst,[status(thm)],[])).
% 1.78/1.48 tff(3183,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c0_1(a1121) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | c2_1(a1121) | (~c1_1(a1121))),
% 1.78/1.48 inference(modus_ponens,[status(thm)],[3182, 3181])).
% 1.78/1.48 tff(3184,plain,
% 1.78/1.48 ($false),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3183, 113, 3123, 3176, 2988, 3122, 3174, 2307, 3133, 3177])).
% 1.78/1.48 tff(3185,plain,(hskp29 | c0_1(a1105) | (~c0_1(a1147)) | c3_1(a1147) | c2_1(a1147) | hskp2 | hskp5 | c1_1(a1105)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.48 tff(3186,plain,
% 1.78/1.48 (hskp29),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3185, 2806, 772, 771, 819, 2988, 1269, 669])).
% 1.78/1.48 tff(3187,plain,
% 1.78/1.48 (c3_1(a1116)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[201, 3186])).
% 1.78/1.48 tff(3188,plain,
% 1.78/1.48 (c2_1(a1116)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[212, 3186])).
% 1.78/1.48 tff(3189,plain,
% 1.78/1.48 (c0_1(a1116)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[223, 3186])).
% 1.78/1.48 tff(3190,plain,
% 1.78/1.48 (c2_1(a1105)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[1143, 113, 3189, 3188, 3187, 772, 3122, 819, 669, 246, 2991])).
% 1.78/1.48 tff(3191,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3192,plain,
% 1.78/1.48 ((hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))) <=> (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3193,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105))))),
% 1.78/1.48 inference(monotonicity,[status(thm)],[3192])).
% 1.78/1.48 tff(3194,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.78/1.48 inference(transitivity,[status(thm)],[3193, 3191])).
% 1.78/1.48 tff(3195,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))),
% 1.78/1.48 inference(quant_inst,[status(thm)],[])).
% 1.78/1.48 tff(3196,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105))),
% 1.78/1.48 inference(modus_ponens,[status(thm)],[3195, 3194])).
% 1.78/1.48 tff(3197,plain,
% 1.78/1.48 ($false),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3196, 113, 2806, 3189, 3188, 3187, 3122, 669, 1065, 3190])).
% 1.78/1.48 tff(3198,plain,(hskp2 | c1_1(a1105) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | c0_1(a1105) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.78/1.48 tff(3199,plain,
% 1.78/1.48 (hskp2),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3198, 1269, 772, 819, 771, 2988, 669])).
% 1.78/1.48 tff(3200,plain,
% 1.78/1.48 (~c3_1(a1100)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[291, 3199])).
% 1.78/1.48 tff(3201,plain,
% 1.78/1.48 (c2_1(a1100)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[302, 3199])).
% 1.78/1.48 tff(3202,plain,
% 1.78/1.48 (c0_1(a1100)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[313, 3199])).
% 1.78/1.48 tff(3203,plain,
% 1.78/1.48 (~hskp12),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[2911, 3202, 3201, 3200, 1269, 772, 771, 2991])).
% 1.78/1.48 tff(3204,assumption,(~hskp12), introduced(assumption)).
% 1.78/1.48 tff(3205,plain,
% 1.78/1.48 (c2_1(a1105)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3132, 770, 2988, 965, 819, 771, 2991])).
% 1.78/1.48 tff(3206,plain,
% 1.78/1.48 (~hskp20),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3162, 3205, 1357, 2988, 965, 1269])).
% 1.78/1.48 tff(3207,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1180) | c1_1(a1180) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1180) | c1_1(a1180) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1180))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3208,plain,
% 1.78/1.48 ((hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180)) <=> (hskp3 | c0_1(a1180) | c1_1(a1180) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1180))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3209,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a1180) | c1_1(a1180) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1180)))),
% 1.78/1.48 inference(monotonicity,[status(thm)],[3208])).
% 1.78/1.48 tff(3210,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1180) | c1_1(a1180) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1180))),
% 1.78/1.48 inference(transitivity,[status(thm)],[3209, 3207])).
% 1.78/1.48 tff(3211,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))),
% 1.78/1.48 inference(quant_inst,[status(thm)],[])).
% 1.78/1.48 tff(3212,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a1180) | c1_1(a1180) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1180)),
% 1.78/1.48 inference(modus_ponens,[status(thm)],[3211, 3210])).
% 1.78/1.48 tff(3213,plain,
% 1.78/1.48 (c3_1(a1180)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3212, 113, 1357, 1388, 1387, 2776, 2763, 1386, 1055])).
% 1.78/1.48 tff(3214,plain,
% 1.78/1.48 ($false),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[2782, 113, 770, 2776, 2757, 819, 771, 67, 3213, 2584])).
% 1.78/1.48 tff(3215,plain,((~hskp26) | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147)) | hskp3 | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.48 tff(3216,plain,
% 1.78/1.48 (~hskp26),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3215, 770, 819, 771, 2991, 1357, 1388, 1387, 1386])).
% 1.78/1.48 tff(3217,plain,
% 1.78/1.48 (hskp18),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[2799, 2802, 2803])).
% 1.78/1.48 tff(3218,plain,
% 1.78/1.48 (~c1_1(a1125)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[2243, 3217])).
% 1.78/1.48 tff(3219,plain,
% 1.78/1.48 (hskp19),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[2863, 2802, 3204])).
% 1.78/1.48 tff(3220,plain,
% 1.78/1.48 (~c2_1(a1127)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[900, 3219])).
% 1.78/1.48 tff(3221,plain,
% 1.78/1.48 (c2_1(a1125)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[2254, 3217])).
% 1.78/1.48 tff(3222,plain,
% 1.78/1.48 (c0_1(a1125)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[2265, 3217])).
% 1.78/1.48 tff(3223,plain,
% 1.78/1.48 (c3_1(a1127)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[912, 3219])).
% 1.78/1.48 tff(3224,plain,
% 1.78/1.48 (~c0_1(a1127)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3169, 113, 703, 3223, 3222, 3221, 3220, 3218, 1005])).
% 1.78/1.48 tff(3225,plain,
% 1.78/1.48 (c1_1(a1127)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[923, 3219])).
% 1.78/1.48 tff(3226,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1105) | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1127)) | c0_1(a1127))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1127)) | c0_1(a1127))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3227,plain,
% 1.78/1.48 ((hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127))) <=> (hskp3 | c0_1(a1105) | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1127)) | c0_1(a1127))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3228,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1105) | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1127)) | c0_1(a1127)))),
% 1.78/1.48 inference(monotonicity,[status(thm)],[3227])).
% 1.78/1.48 tff(3229,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1127)) | c0_1(a1127))),
% 1.78/1.48 inference(transitivity,[status(thm)],[3228, 3226])).
% 1.78/1.48 tff(3230,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127)))),
% 1.78/1.48 inference(quant_inst,[status(thm)],[])).
% 1.78/1.48 tff(3231,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1105) | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1127)) | c0_1(a1127)),
% 1.78/1.48 inference(modus_ponens,[status(thm)],[3230, 3229])).
% 1.78/1.48 tff(3232,plain,
% 1.78/1.48 ($false),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3231, 113, 1357, 3225, 2988, 965, 3220, 2307, 995, 3224])).
% 1.78/1.48 tff(3233,plain,(hskp26 | hskp3 | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)) | hskp20 | hskp12 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.78/1.48 tff(3234,plain,
% 1.78/1.48 (hskp16),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3233, 3216, 2988, 965, 3205, 3206, 3204, 1357])).
% 1.78/1.48 tff(3235,plain,
% 1.78/1.48 (~c0_1(a1121)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[1939, 3234])).
% 1.78/1.48 tff(3236,plain,
% 1.78/1.48 (c3_1(a1121)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[1952, 3234])).
% 1.78/1.48 tff(3237,plain,
% 1.78/1.48 (c1_1(a1121)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[1963, 3234])).
% 1.78/1.48 tff(3238,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c0_1(a1121) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c0_1(a1121) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3239,plain,
% 1.78/1.48 ((hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121))) <=> (hskp20 | c0_1(a1121) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3240,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | c0_1(a1121) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1121)) | (~c3_1(a1121))))),
% 1.78/1.48 inference(monotonicity,[status(thm)],[3239])).
% 1.78/1.48 tff(3241,plain,
% 1.78/1.48 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c0_1(a1121) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.78/1.48 inference(transitivity,[status(thm)],[3240, 3238])).
% 1.78/1.48 tff(3242,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))),
% 1.78/1.48 inference(quant_inst,[status(thm)],[])).
% 1.78/1.48 tff(3243,plain,
% 1.78/1.48 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp20 | c0_1(a1121) | c3_1(a1100) | (~ndr1_0) | (~c0_1(a1100)) | (~c2_1(a1100)) | (~c1_1(a1121)) | (~c3_1(a1121))),
% 1.78/1.48 inference(modus_ponens,[status(thm)],[3242, 3241])).
% 1.78/1.48 tff(3244,plain,
% 1.78/1.48 ($false),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3243, 113, 3206, 3237, 3236, 1388, 1387, 3235, 1386, 268])).
% 1.78/1.48 tff(3245,plain,(hskp29 | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | c0_1(a1105) | (~c3_1(a1105)) | hskp12 | hskp3 | c2_1(a1147) | c3_1(a1147) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.78/1.48 tff(3246,plain,
% 1.78/1.48 (hskp29),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[3245, 3202, 3201, 3200, 2988, 3122, 3203, 3123, 819, 771, 1269])).
% 1.78/1.48 tff(3247,plain,
% 1.78/1.48 (c3_1(a1116)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[201, 3246])).
% 1.78/1.48 tff(3248,plain,
% 1.78/1.48 (c2_1(a1116)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[212, 3246])).
% 1.78/1.48 tff(3249,plain,
% 1.78/1.48 (c0_1(a1116)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[223, 3246])).
% 1.78/1.48 tff(3250,plain,
% 1.78/1.48 (c2_1(a1105)),
% 1.78/1.48 inference(unit_resolution,[status(thm)],[1143, 113, 3249, 3248, 3247, 772, 3122, 819, 669, 246, 2991])).
% 1.78/1.48 tff(3251,plain,
% 1.78/1.48 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.78/1.48 inference(bind,[status(th)],[])).
% 1.78/1.48 tff(3252,plain,
% 1.78/1.48 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.78/1.48 inference(quant_intro,[status(thm)],[3251])).
% 1.78/1.48 tff(3253,plain,
% 1.78/1.48 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.78/1.48 inference(rewrite,[status(thm)],[])).
% 1.78/1.48 tff(3254,plain,
% 1.78/1.48 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp7) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.78/1.49 inference(bind,[status(th)],[])).
% 1.78/1.49 tff(3255,plain,
% 1.78/1.49 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.78/1.49 inference(quant_intro,[status(thm)],[3254])).
% 1.78/1.49 tff(3256,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.78/1.49 tff(3257,plain,
% 1.78/1.49 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.78/1.49 inference(modus_ponens,[status(thm)],[3256, 3255])).
% 1.78/1.49 tff(3258,plain,
% 1.78/1.49 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.78/1.49 inference(modus_ponens,[status(thm)],[3257, 3253])).
% 1.78/1.49 tff(3259,plain,(
% 1.78/1.49 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.78/1.49 inference(skolemize,[status(sab)],[3258])).
% 1.78/1.49 tff(3260,plain,
% 1.78/1.49 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.78/1.49 inference(modus_ponens,[status(thm)],[3259, 3252])).
% 1.78/1.49 tff(3261,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3262,plain,
% 1.78/1.49 ((hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))) <=> (hskp7 | c0_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3263,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105))))),
% 1.78/1.49 inference(monotonicity,[status(thm)],[3262])).
% 1.78/1.49 tff(3264,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.78/1.49 inference(transitivity,[status(thm)],[3263, 3261])).
% 1.78/1.49 tff(3265,plain,
% 1.78/1.49 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))),
% 1.78/1.49 inference(quant_inst,[status(thm)],[])).
% 1.78/1.49 tff(3266,plain,
% 1.78/1.49 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c2_1(a1105)) | (~c3_1(a1105))),
% 1.78/1.49 inference(modus_ponens,[status(thm)],[3265, 3264])).
% 1.78/1.49 tff(3267,plain,
% 1.78/1.49 ($false),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3266, 113, 2989, 3249, 3248, 3247, 2988, 3122, 3260, 3250])).
% 1.78/1.49 tff(3268,plain,(hskp5 | c0_1(a1105) | (~c0_1(a1147)) | c2_1(a1147) | c1_1(a1105) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.49 tff(3269,plain,
% 1.78/1.49 (hskp5),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3268, 2988, 772, 819, 669, 771])).
% 1.78/1.49 tff(3270,plain,
% 1.78/1.49 (~c2_1(a1103)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[126, 3269])).
% 1.78/1.49 tff(3271,plain,
% 1.78/1.49 (~c0_1(a1103)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[132, 3269])).
% 1.78/1.49 tff(3272,plain,
% 1.78/1.49 (c3_1(a1103)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[153, 3269])).
% 1.78/1.49 tff(3273,plain,
% 1.78/1.49 (c1_1(a1103)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2528, 113, 2454, 3272, 3271, 3270, 2126])).
% 1.78/1.49 tff(3274,plain,
% 1.78/1.49 (hskp21 | (~c1_1(a1103))),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2520, 113, 2454, 3272, 3271, 33])).
% 1.78/1.49 tff(3275,plain,
% 1.78/1.49 (hskp21),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3274, 3273])).
% 1.78/1.49 tff(3276,plain,
% 1.78/1.49 (~c3_1(a1131)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[811, 3275])).
% 1.78/1.49 tff(3277,plain,
% 1.78/1.49 (~c0_1(a1131)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[817, 3275])).
% 1.78/1.49 tff(3278,plain,
% 1.78/1.49 (c1_1(a1131)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[829, 3275])).
% 1.78/1.49 tff(3279,plain,
% 1.78/1.49 (hskp14),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[160, 113, 2989, 3272, 3271, 3270, 143])).
% 1.78/1.49 tff(3280,plain,
% 1.78/1.49 (~c3_1(a1118)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[166, 3279])).
% 1.78/1.49 tff(3281,plain,
% 1.78/1.49 (~c2_1(a1118)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[172, 3279])).
% 1.78/1.49 tff(3282,plain,
% 1.78/1.49 (c1_1(a1118)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[183, 3279])).
% 1.78/1.49 tff(3283,plain,
% 1.78/1.49 (hskp29),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[190, 113, 3282, 3272, 3281, 3280, 3271, 3270, 67])).
% 1.78/1.49 tff(3284,plain,
% 1.78/1.49 (c3_1(a1116)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[201, 3283])).
% 1.78/1.49 tff(3285,plain,
% 1.78/1.49 (c2_1(a1116)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[212, 3283])).
% 1.78/1.49 tff(3286,plain,
% 1.78/1.49 (c0_1(a1116)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[223, 3283])).
% 1.78/1.49 tff(3287,plain,
% 1.78/1.49 ($false),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2726, 113, 3286, 3285, 3284, 772, 3278, 819, 771, 3277, 3276, 344])).
% 1.78/1.49 tff(3288,plain,(c0_1(a1105) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | hskp0 | c1_1(a1105)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.49 tff(3289,plain,
% 1.78/1.49 (c0_1(a1105)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3288, 669, 2457, 2456, 2454, 2458])).
% 1.78/1.49 tff(3290,plain,
% 1.78/1.49 (~hskp7),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[657, 2992])).
% 1.78/1.49 tff(3291,plain,
% 1.78/1.49 (c2_1(a1105)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2999, 1269, 3290, 2992])).
% 1.78/1.49 tff(3292,plain,
% 1.78/1.49 (c1_1(a1147)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2990, 1269, 3290])).
% 1.78/1.49 tff(3293,plain,
% 1.78/1.49 (c0_1(a1105)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3288, 669, 819, 771, 2454, 772])).
% 1.78/1.49 tff(3294,plain,
% 1.78/1.49 (~hskp3),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2902, 1269, 772, 771, 3292])).
% 1.78/1.49 tff(3295,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c3_1(a1105) | c0_1(a1180) | c1_1(a1180) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a1105) | c0_1(a1180) | c1_1(a1180) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | c3_1(a1180))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3296,plain,
% 1.78/1.49 ((hskp3 | (~ndr1_0) | c3_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180)) <=> (hskp3 | c3_1(a1105) | c0_1(a1180) | c1_1(a1180) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | c3_1(a1180))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3297,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c3_1(a1105) | c0_1(a1180) | c1_1(a1180) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | c3_1(a1180)))),
% 1.78/1.49 inference(monotonicity,[status(thm)],[3296])).
% 1.78/1.49 tff(3298,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a1105) | c0_1(a1180) | c1_1(a1180) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | c3_1(a1180))),
% 1.78/1.49 inference(transitivity,[status(thm)],[3297, 3295])).
% 1.78/1.49 tff(3299,plain,
% 1.78/1.49 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1180) | c0_1(a1180) | c3_1(a1180))),
% 1.78/1.49 inference(quant_inst,[status(thm)],[])).
% 1.78/1.49 tff(3300,plain,
% 1.78/1.49 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a1105) | c0_1(a1180) | c1_1(a1180) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | c3_1(a1180)),
% 1.78/1.49 inference(modus_ponens,[status(thm)],[3299, 3298])).
% 1.78/1.49 tff(3301,plain,
% 1.78/1.49 (c3_1(a1180)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3300, 113, 1357, 992, 2992, 2776, 2763, 1055, 995])).
% 1.78/1.49 tff(3302,plain,
% 1.78/1.49 ($false),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2782, 113, 770, 2776, 2757, 819, 771, 67, 3301, 2584])).
% 1.78/1.49 tff(3303,plain,((~hskp26) | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147)) | hskp3 | (~c0_1(a1105)) | c3_1(a1105) | (~c2_1(a1105))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.49 tff(3304,plain,
% 1.78/1.49 (~hskp26),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3303, 770, 819, 771, 3292, 3294, 992, 2992, 995])).
% 1.78/1.49 tff(3305,plain,
% 1.78/1.49 (~hskp16),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2749, 770, 819, 771, 3292, 772])).
% 1.78/1.49 tff(3306,plain,
% 1.78/1.49 (hskp18),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2799, 3305, 3304])).
% 1.78/1.49 tff(3307,plain,
% 1.78/1.49 (~c1_1(a1125)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2243, 3306])).
% 1.78/1.49 tff(3308,plain,
% 1.78/1.49 (hskp2),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2883, 3305, 819, 771, 3292, 3290, 3304, 770])).
% 1.78/1.49 tff(3309,plain,
% 1.78/1.49 (~c3_1(a1100)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[291, 3308])).
% 1.78/1.49 tff(3310,plain,
% 1.78/1.49 (c2_1(a1100)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[302, 3308])).
% 1.78/1.49 tff(3311,plain,
% 1.78/1.49 (c0_1(a1100)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[313, 3308])).
% 1.78/1.49 tff(3312,plain,
% 1.78/1.49 (~hskp12),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2911, 3311, 3310, 3309, 1269, 772, 771, 3292])).
% 1.78/1.49 tff(3313,plain,
% 1.78/1.49 (hskp19),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2863, 3312, 3304])).
% 1.78/1.49 tff(3314,plain,
% 1.78/1.49 (~c2_1(a1127)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[900, 3313])).
% 1.78/1.49 tff(3315,plain,
% 1.78/1.49 (c2_1(a1125)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2254, 3306])).
% 1.78/1.49 tff(3316,plain,
% 1.78/1.49 (c0_1(a1125)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2265, 3306])).
% 1.78/1.49 tff(3317,plain,
% 1.78/1.49 (c3_1(a1127)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[912, 3313])).
% 1.78/1.49 tff(3318,plain,
% 1.78/1.49 (~c0_1(a1127)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2874, 113, 3290, 3317, 3316, 3315, 3314, 3307, 2220])).
% 1.78/1.49 tff(3319,plain,
% 1.78/1.49 ($false),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2881, 113, 770, 3317, 819, 771, 3314, 67, 3292, 3318])).
% 1.78/1.49 tff(3320,plain,(hskp29 | c2_1(a1147) | c3_1(a1147) | hskp5 | (~c0_1(a1147)) | (~c0_1(a1105)) | c3_1(a1105) | (~c2_1(a1105))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.49 tff(3321,plain,
% 1.78/1.49 (hskp29),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3320, 1269, 771, 819, 772, 3293, 2992, 3291])).
% 1.78/1.49 tff(3322,plain,
% 1.78/1.49 (c3_1(a1116)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[201, 3321])).
% 1.78/1.49 tff(3323,plain,
% 1.78/1.49 (c2_1(a1116)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[212, 3321])).
% 1.78/1.49 tff(3324,plain,
% 1.78/1.49 (c0_1(a1116)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[223, 3321])).
% 1.78/1.49 tff(3325,plain,
% 1.78/1.49 (~c3_1(a1180)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2980, 113, 249, 248, 247, 772, 2763, 2757, 819, 246, 2584])).
% 1.78/1.49 tff(3326,plain,
% 1.78/1.49 ($false),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3300, 113, 1357, 992, 2992, 2776, 2763, 1055, 3325, 995])).
% 1.78/1.49 tff(3327,plain,((~hskp26) | hskp3 | (~c0_1(a1105)) | c3_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1147)) | c2_1(a1147) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.49 tff(3328,plain,
% 1.78/1.49 (~hskp26),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3327, 3294, 3293, 2992, 3291, 3324, 3323, 3322, 772, 819, 3292])).
% 1.78/1.49 tff(3329,plain,
% 1.78/1.49 (c2_1(a1114)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2839, 2943])).
% 1.78/1.49 tff(3330,plain,
% 1.78/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1105) | c2_1(a1147) | c0_1(a1114) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1105) | c2_1(a1147) | c0_1(a1114) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3331,plain,
% 1.78/1.49 (((~ndr1_0) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c3_1(a1105) | (~c0_1(a1105)) | c0_1(a1114) | (~c2_1(a1114)) | (~c1_1(a1114))) <=> (c3_1(a1105) | c2_1(a1147) | c0_1(a1114) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3332,plain,
% 1.78/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c3_1(a1105) | (~c0_1(a1105)) | c0_1(a1114) | (~c2_1(a1114)) | (~c1_1(a1114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a1105) | c2_1(a1147) | c0_1(a1114) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.78/1.49 inference(monotonicity,[status(thm)],[3331])).
% 1.78/1.49 tff(3333,plain,
% 1.78/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c3_1(a1105) | (~c0_1(a1105)) | c0_1(a1114) | (~c2_1(a1114)) | (~c1_1(a1114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1105) | c2_1(a1147) | c0_1(a1114) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.78/1.49 inference(transitivity,[status(thm)],[3332, 3330])).
% 1.78/1.49 tff(3334,plain,
% 1.78/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c3_1(a1105) | (~c0_1(a1105)) | c0_1(a1114) | (~c2_1(a1114)) | (~c1_1(a1114)))),
% 1.78/1.49 inference(quant_inst,[status(thm)],[])).
% 1.78/1.49 tff(3335,plain,
% 1.78/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a1105) | c2_1(a1147) | c0_1(a1114) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c1_1(a1114)) | (~c2_1(a1114)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.78/1.49 inference(modus_ponens,[status(thm)],[3334, 3333])).
% 1.78/1.49 tff(3336,plain,
% 1.78/1.49 (~c1_1(a1114)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3335, 113, 772, 3329, 992, 2992, 819, 2945, 669, 1418, 2584])).
% 1.78/1.49 tff(3337,plain,
% 1.78/1.49 ($false),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2962, 113, 772, 2956, 2955, 771, 2954, 2945, 2944, 363, 2584, 3336])).
% 1.78/1.49 tff(3338,plain,(hskp2 | (~c0_1(a1147)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1105)) | c3_1(a1105) | c2_1(a1147) | c1_1(a1105) | hskp26 | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.49 tff(3339,plain,
% 1.78/1.49 (hskp2),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3338, 3292, 771, 772, 3293, 2992, 819, 669, 3328, 3324, 3323, 3322])).
% 1.78/1.49 tff(3340,plain,
% 1.78/1.49 (~c3_1(a1100)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[291, 3339])).
% 1.78/1.49 tff(3341,plain,
% 1.78/1.49 (c0_1(a1100)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[313, 3339])).
% 1.78/1.49 tff(3342,plain,
% 1.78/1.49 (c2_1(a1100)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[302, 3339])).
% 1.78/1.49 tff(3343,plain,
% 1.78/1.49 (~hskp12),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2911, 3342, 3341, 3340, 1269, 772, 771, 3292])).
% 1.78/1.49 tff(3344,plain,
% 1.78/1.49 (hskp19),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2863, 3343, 3328])).
% 1.78/1.49 tff(3345,plain,
% 1.78/1.49 (~c2_1(a1127)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[900, 3344])).
% 1.78/1.49 tff(3346,plain,
% 1.78/1.49 (c3_1(a1127)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[912, 3344])).
% 1.78/1.49 tff(3347,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3348,plain,
% 1.78/1.49 ((hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105))) <=> (hskp7 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3349,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127))))),
% 1.78/1.49 inference(monotonicity,[status(thm)],[3348])).
% 1.78/1.49 tff(3350,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127)))),
% 1.78/1.49 inference(transitivity,[status(thm)],[3349, 3347])).
% 1.78/1.49 tff(3351,plain,
% 1.78/1.49 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1127) | (~c3_1(a1127)) | (~c0_1(a1127)) | c1_1(a1105) | (~c2_1(a1105)) | (~c0_1(a1105)))),
% 1.78/1.49 inference(quant_inst,[status(thm)],[])).
% 1.78/1.49 tff(3352,plain,
% 1.78/1.49 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1127) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1127)) | (~c3_1(a1127))),
% 1.78/1.49 inference(modus_ponens,[status(thm)],[3351, 3350])).
% 1.78/1.49 tff(3353,plain,
% 1.78/1.49 (~c0_1(a1127)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3352, 113, 3290, 3346, 3293, 3345, 669, 2220, 3291])).
% 1.78/1.49 tff(3354,plain,
% 1.78/1.49 (hskp20),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[1305, 3344, 1269, 3324, 3323, 3322])).
% 1.78/1.49 tff(3355,plain,
% 1.78/1.49 (~c2_1(a1130)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2287, 3354])).
% 1.78/1.49 tff(3356,plain,
% 1.78/1.49 (~c0_1(a1130)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[326, 3354])).
% 1.78/1.49 tff(3357,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1130) | c2_1(a1130) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | c1_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1130) | c2_1(a1130) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | c1_1(a1130))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3358,plain,
% 1.78/1.49 ((hskp0 | (~ndr1_0) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130)) <=> (hskp0 | c0_1(a1130) | c2_1(a1130) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | c1_1(a1130))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3359,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1130) | c2_1(a1130) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | c1_1(a1130)))),
% 1.78/1.49 inference(monotonicity,[status(thm)],[3358])).
% 1.78/1.49 tff(3360,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1130) | c2_1(a1130) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | c1_1(a1130))),
% 1.78/1.49 inference(transitivity,[status(thm)],[3359, 3357])).
% 1.78/1.49 tff(3361,plain,
% 1.78/1.49 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1127) | c0_1(a1127) | (~c3_1(a1127)) | c2_1(a1130) | c1_1(a1130) | c0_1(a1130))),
% 1.78/1.49 inference(quant_inst,[status(thm)],[])).
% 1.78/1.49 tff(3362,plain,
% 1.78/1.49 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1130) | c2_1(a1130) | c2_1(a1127) | (~ndr1_0) | c0_1(a1127) | (~c3_1(a1127)) | c1_1(a1130)),
% 1.78/1.49 inference(modus_ponens,[status(thm)],[3361, 3360])).
% 1.78/1.49 tff(3363,plain,
% 1.78/1.49 (c1_1(a1130)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3362, 113, 2454, 3346, 3356, 3355, 3345, 2126, 3353])).
% 1.78/1.49 tff(3364,plain,
% 1.78/1.49 (~c3_1(a1130)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[332, 3354])).
% 1.78/1.49 tff(3365,plain,
% 1.78/1.49 ($false),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[1325, 113, 3324, 3323, 3322, 772, 819, 771, 3356, 3364, 344, 3363])).
% 1.78/1.49 tff(3366,plain,(hskp5 | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | hskp0 | c1_1(a1105) | c3_1(a1105)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.49 tff(3367,plain,
% 1.78/1.49 (hskp5),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3366, 2992, 819, 771, 2454, 669, 772])).
% 1.78/1.49 tff(3368,plain,
% 1.78/1.49 (~c2_1(a1103)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[126, 3367])).
% 1.78/1.49 tff(3369,plain,
% 1.78/1.49 (~c0_1(a1103)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[132, 3367])).
% 1.78/1.49 tff(3370,plain,
% 1.78/1.49 (c3_1(a1103)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[153, 3367])).
% 1.78/1.49 tff(3371,plain,
% 1.78/1.49 (c1_1(a1103)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2528, 113, 2454, 3370, 3369, 3368, 2126])).
% 1.78/1.49 tff(3372,plain,
% 1.78/1.49 (hskp21 | (~c1_1(a1103))),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2520, 113, 2454, 3370, 3369, 33])).
% 1.78/1.49 tff(3373,plain,
% 1.78/1.49 (hskp21),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3372, 3371])).
% 1.78/1.49 tff(3374,plain,
% 1.78/1.49 (~c3_1(a1131)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[811, 3373])).
% 1.78/1.49 tff(3375,plain,
% 1.78/1.49 (~c0_1(a1131)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[817, 3373])).
% 1.78/1.49 tff(3376,plain,
% 1.78/1.49 (c1_1(a1131)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[829, 3373])).
% 1.78/1.49 tff(3377,plain,
% 1.78/1.49 (hskp14),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[160, 113, 3290, 3370, 3369, 3368, 143])).
% 1.78/1.49 tff(3378,plain,
% 1.78/1.49 (~c3_1(a1118)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[166, 3377])).
% 1.78/1.49 tff(3379,plain,
% 1.78/1.49 (~c2_1(a1118)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[172, 3377])).
% 1.78/1.49 tff(3380,plain,
% 1.78/1.49 (c1_1(a1118)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[183, 3377])).
% 1.78/1.49 tff(3381,plain,
% 1.78/1.49 (hskp29),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[190, 113, 3380, 3370, 3379, 3378, 3369, 3368, 67])).
% 1.78/1.49 tff(3382,plain,
% 1.78/1.49 (c3_1(a1116)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[201, 3381])).
% 1.78/1.49 tff(3383,plain,
% 1.78/1.49 (c2_1(a1116)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[212, 3381])).
% 1.78/1.49 tff(3384,plain,
% 1.78/1.49 (c0_1(a1116)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[223, 3381])).
% 1.78/1.49 tff(3385,plain,
% 1.78/1.49 ($false),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2726, 113, 3384, 3383, 3382, 772, 3376, 819, 771, 3375, 3374, 344])).
% 1.78/1.49 tff(3386,plain,(c3_1(a1105) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147) | hskp0 | c1_1(a1105)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.49 tff(3387,plain,
% 1.78/1.49 (c3_1(a1105)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3386, 669, 2457, 2456, 2454, 2458])).
% 1.78/1.49 tff(3388,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3389,plain,
% 1.78/1.49 ((hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147)) <=> (hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3390,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147)))),
% 1.78/1.49 inference(monotonicity,[status(thm)],[3389])).
% 1.78/1.49 tff(3391,plain,
% 1.78/1.49 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))),
% 1.78/1.49 inference(transitivity,[status(thm)],[3390, 3388])).
% 1.78/1.49 tff(3392,plain,
% 1.78/1.49 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp30 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c2_1(a1147) | c1_1(a1147) | c3_1(a1147))),
% 1.78/1.49 inference(quant_inst,[status(thm)],[])).
% 1.78/1.49 tff(3393,plain,
% 1.78/1.49 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp30 | c2_1(a1147) | c3_1(a1147) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147)),
% 1.78/1.49 inference(modus_ponens,[status(thm)],[3392, 3391])).
% 1.78/1.49 tff(3394,plain,
% 1.78/1.49 ((~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3393, 113, 670, 2457, 2456, 669, 668])).
% 1.78/1.49 tff(3395,plain,
% 1.78/1.49 (c1_1(a1147)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3394, 3387, 3289])).
% 1.78/1.49 tff(3396,plain,
% 1.78/1.49 ($false),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2344, 113, 770, 2075, 819, 771, 2076, 2077, 67, 2584])).
% 1.78/1.49 tff(3397,plain,((~hskp5) | hskp29 | c2_1(a1147) | c3_1(a1147) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.49 tff(3398,plain,
% 1.78/1.49 (~hskp5),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3397, 770, 2457, 2456, 3395])).
% 1.78/1.49 tff(3399,plain,
% 1.78/1.49 (~hskp3),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2902, 3398, 2458, 2456, 3395])).
% 1.78/1.49 tff(3400,plain,
% 1.78/1.49 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3401,plain,
% 1.78/1.49 ((hskp22 | hskp0 | (~ndr1_0) | c2_1(a1105) | c1_1(a1105) | (~c3_1(a1105))) <=> (hskp22 | hskp0 | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.78/1.49 inference(rewrite,[status(thm)],[])).
% 1.78/1.49 tff(3402,plain,
% 1.78/1.49 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1105) | c1_1(a1105) | (~c3_1(a1105)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105))))),
% 1.78/1.49 inference(monotonicity,[status(thm)],[3401])).
% 1.78/1.49 tff(3403,plain,
% 1.78/1.49 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1105) | c1_1(a1105) | (~c3_1(a1105)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.78/1.49 inference(transitivity,[status(thm)],[3402, 3400])).
% 1.78/1.49 tff(3404,plain,
% 1.78/1.49 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1105) | c1_1(a1105) | (~c3_1(a1105)))),
% 1.78/1.49 inference(quant_inst,[status(thm)],[])).
% 1.78/1.49 tff(3405,plain,
% 1.78/1.49 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105))),
% 1.78/1.49 inference(modus_ponens,[status(thm)],[3404, 3403])).
% 1.78/1.49 tff(3406,plain,
% 1.78/1.49 (hskp22 | c2_1(a1105) | (~c3_1(a1105))),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3405, 113, 2454, 669, 2144])).
% 1.78/1.49 tff(3407,plain,
% 1.78/1.49 (hskp22),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[3406, 3124, 3387])).
% 1.78/1.49 tff(3408,plain,
% 1.78/1.49 (c3_1(a1145)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2200, 3407])).
% 1.78/1.49 tff(3409,plain,
% 1.78/1.49 (c2_1(a1145)),
% 1.78/1.49 inference(unit_resolution,[status(thm)],[2168, 3407])).
% 1.78/1.49 tff(3410,plain,
% 1.78/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.78/1.50 inference(rewrite,[status(thm)],[])).
% 1.78/1.50 tff(3411,plain,
% 1.78/1.50 (((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105))) <=> (c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.78/1.50 inference(rewrite,[status(thm)],[])).
% 1.78/1.50 tff(3412,plain,
% 1.78/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.78/1.50 inference(monotonicity,[status(thm)],[3411])).
% 1.78/1.50 tff(3413,plain,
% 1.78/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.78/1.50 inference(transitivity,[status(thm)],[3412, 3410])).
% 1.78/1.50 tff(3414,plain,
% 1.78/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1145)) | c2_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.78/1.50 inference(quant_inst,[status(thm)],[])).
% 1.78/1.50 tff(3415,plain,
% 1.78/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1147) | c1_1(a1105) | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c3_1(a1145)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.78/1.50 inference(modus_ponens,[status(thm)],[3414, 3413])).
% 1.78/1.50 tff(3416,plain,
% 1.78/1.50 (~c0_1(a1145)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3415, 113, 2458, 3409, 3408, 3387, 2457, 669, 246, 3124, 3395])).
% 1.78/1.50 tff(3417,plain,
% 1.78/1.50 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp18 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))),
% 1.78/1.50 inference(rewrite,[status(thm)],[])).
% 1.78/1.50 tff(3418,plain,
% 1.78/1.50 ((hskp30 | hskp18 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105))) <=> (hskp30 | hskp18 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))),
% 1.78/1.50 inference(rewrite,[status(thm)],[])).
% 1.78/1.50 tff(3419,plain,
% 1.78/1.50 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105))))),
% 1.78/1.50 inference(monotonicity,[status(thm)],[3418])).
% 1.78/1.50 tff(3420,plain,
% 1.78/1.50 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp18 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105)))),
% 1.78/1.50 inference(transitivity,[status(thm)],[3419, 3417])).
% 1.78/1.50 tff(3421,plain,
% 1.78/1.50 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp30 | hskp18 | (~ndr1_0) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)))),
% 1.78/1.50 inference(quant_inst,[status(thm)],[])).
% 1.78/1.50 tff(3422,plain,
% 1.78/1.50 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp30 | hskp18 | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c3_1(a1105))),
% 1.78/1.50 inference(modus_ponens,[status(thm)],[3421, 3420])).
% 1.78/1.50 tff(3423,plain,
% 1.78/1.50 (hskp18 | (~c0_1(a1105)) | (~c3_1(a1105))),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3422, 113, 670, 669, 2230])).
% 1.78/1.50 tff(3424,plain,
% 1.78/1.50 (hskp18),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3423, 3387, 3289])).
% 1.78/1.50 tff(3425,plain,
% 1.78/1.50 (~c1_1(a1125)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2243, 3424])).
% 1.78/1.50 tff(3426,plain,
% 1.78/1.50 (c2_1(a1125)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2254, 3424])).
% 1.78/1.50 tff(3427,plain,
% 1.78/1.50 (c0_1(a1125)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2265, 3424])).
% 1.78/1.50 tff(3428,plain,
% 1.78/1.50 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1125)) | (~c2_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.78/1.50 inference(rewrite,[status(thm)],[])).
% 1.78/1.50 tff(3429,plain,
% 1.78/1.50 ((hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125))) <=> (hskp20 | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.78/1.50 inference(rewrite,[status(thm)],[])).
% 1.78/1.50 tff(3430,plain,
% 1.78/1.50 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1125)) | (~c2_1(a1125))))),
% 1.78/1.50 inference(monotonicity,[status(thm)],[3429])).
% 1.78/1.50 tff(3431,plain,
% 1.78/1.50 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1125)) | (~c2_1(a1125)))),
% 1.78/1.50 inference(transitivity,[status(thm)],[3430, 3428])).
% 1.78/1.50 tff(3432,plain,
% 1.78/1.50 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1125) | (~c2_1(a1125)) | (~c0_1(a1125)))),
% 1.78/1.50 inference(quant_inst,[status(thm)],[])).
% 1.78/1.50 tff(3433,plain,
% 1.78/1.50 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a1125) | (~ndr1_0) | (~c0_1(a1105)) | c2_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1125)) | (~c2_1(a1125))),
% 1.78/1.50 inference(modus_ponens,[status(thm)],[3432, 3431])).
% 1.78/1.50 tff(3434,plain,
% 1.78/1.50 (hskp20),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3433, 113, 3427, 3426, 3289, 3387, 3425, 1005, 3124])).
% 1.78/1.50 tff(3435,plain,
% 1.78/1.50 (~c2_1(a1130)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2287, 3434])).
% 1.78/1.50 tff(3436,plain,
% 1.78/1.50 (~c0_1(a1130)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[326, 3434])).
% 1.78/1.50 tff(3437,plain,
% 1.78/1.50 (~c1_1(a1130)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2314, 113, 1357, 3409, 3408, 3436, 3435, 2307, 3416])).
% 1.78/1.50 tff(3438,plain,
% 1.78/1.50 (~c3_1(a1130)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[332, 3434])).
% 1.78/1.50 tff(3439,plain,
% 1.78/1.50 ($false),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2296, 113, 670, 3289, 3387, 3435, 3438, 669, 668, 3437])).
% 1.78/1.50 tff(3440,plain,(c2_1(a1105) | hskp30 | c1_1(a1105) | hskp3 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.78/1.50 tff(3441,plain,
% 1.78/1.50 (c2_1(a1105)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3440, 3399, 669, 670, 2454])).
% 1.78/1.50 tff(3442,plain,
% 1.78/1.50 (hskp2 | (~c2_1(a1105))),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1071, 113, 3289, 3387, 669, 1065])).
% 1.78/1.50 tff(3443,plain,
% 1.78/1.50 (hskp2),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3442, 3441])).
% 1.78/1.50 tff(3444,plain,
% 1.78/1.50 (~c3_1(a1100)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[291, 3443])).
% 1.78/1.50 tff(3445,plain,
% 1.78/1.50 (c0_1(a1100)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[313, 3443])).
% 1.78/1.50 tff(3446,plain,
% 1.78/1.50 (c2_1(a1100)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[302, 3443])).
% 1.78/1.50 tff(3447,plain,
% 1.78/1.50 (~hskp26),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3215, 3446, 2457, 2456, 3395, 770, 3399, 3445, 3444])).
% 1.78/1.50 tff(3448,plain,
% 1.78/1.50 ((hskp26 | hskp4 | hskp3) <=> (hskp26 | hskp4 | hskp3)),
% 1.78/1.50 inference(rewrite,[status(thm)],[])).
% 1.78/1.50 tff(3449,plain,
% 1.78/1.50 (((hskp4 | hskp3) | hskp26) <=> (hskp26 | hskp4 | hskp3)),
% 1.78/1.50 inference(rewrite,[status(thm)],[])).
% 1.78/1.50 tff(3450,plain,
% 1.78/1.50 ((hskp4 | hskp3) <=> (hskp4 | hskp3)),
% 1.78/1.50 inference(rewrite,[status(thm)],[])).
% 1.78/1.50 tff(3451,plain,
% 1.78/1.50 (((hskp4 | hskp3) | hskp26) <=> ((hskp4 | hskp3) | hskp26)),
% 1.78/1.50 inference(monotonicity,[status(thm)],[3450])).
% 1.78/1.50 tff(3452,plain,
% 1.78/1.50 (((hskp4 | hskp3) | hskp26) <=> (hskp26 | hskp4 | hskp3)),
% 1.78/1.50 inference(transitivity,[status(thm)],[3451, 3449])).
% 1.78/1.50 tff(3453,axiom,((hskp4 | hskp3) | hskp26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 1.78/1.50 tff(3454,plain,
% 1.78/1.50 (hskp26 | hskp4 | hskp3),
% 1.78/1.50 inference(modus_ponens,[status(thm)],[3453, 3452])).
% 1.78/1.50 tff(3455,plain,
% 1.78/1.50 (hskp26 | hskp4 | hskp3),
% 1.78/1.50 inference(modus_ponens,[status(thm)],[3454, 3448])).
% 1.78/1.50 tff(3456,plain,
% 1.78/1.50 (hskp26 | hskp4 | hskp3),
% 1.78/1.50 inference(modus_ponens,[status(thm)],[3455, 3448])).
% 1.78/1.50 tff(3457,plain,
% 1.78/1.50 (hskp26 | hskp4 | hskp3),
% 1.78/1.50 inference(modus_ponens,[status(thm)],[3456, 3448])).
% 1.78/1.50 tff(3458,plain,
% 1.78/1.50 (hskp26 | hskp4 | hskp3),
% 1.78/1.50 inference(modus_ponens,[status(thm)],[3457, 3448])).
% 1.78/1.50 tff(3459,plain,
% 1.78/1.50 (hskp26 | hskp4 | hskp3),
% 1.78/1.50 inference(modus_ponens,[status(thm)],[3458, 3448])).
% 1.78/1.50 tff(3460,plain,
% 1.78/1.50 (hskp26 | hskp4 | hskp3),
% 1.78/1.50 inference(modus_ponens,[status(thm)],[3459, 3448])).
% 1.78/1.50 tff(3461,plain,
% 1.78/1.50 (hskp26 | hskp4 | hskp3),
% 1.78/1.50 inference(modus_ponens,[status(thm)],[3460, 3448])).
% 1.78/1.50 tff(3462,plain,
% 1.78/1.50 (hskp4),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3461, 3447, 3399])).
% 1.78/1.50 tff(3463,plain,
% 1.78/1.50 (~c3_1(a1102)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1529, 3462])).
% 1.78/1.50 tff(3464,plain,
% 1.78/1.50 (c1_1(a1102)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1549, 3462])).
% 1.78/1.50 tff(3465,plain,
% 1.78/1.50 (c0_1(a1102)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1560, 3462])).
% 1.78/1.50 tff(3466,plain,
% 1.78/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c2_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c2_1(a1102)))),
% 1.78/1.50 inference(rewrite,[status(thm)],[])).
% 1.78/1.50 tff(3467,plain,
% 1.78/1.50 ((hskp5 | (~ndr1_0) | c3_1(a1102) | (~c1_1(a1102)) | (~c2_1(a1102)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102))) <=> (hskp5 | c3_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c2_1(a1102)))),
% 1.78/1.50 inference(rewrite,[status(thm)],[])).
% 1.78/1.50 tff(3468,plain,
% 1.78/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1102) | (~c1_1(a1102)) | (~c2_1(a1102)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c3_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c2_1(a1102))))),
% 1.78/1.50 inference(monotonicity,[status(thm)],[3467])).
% 1.78/1.50 tff(3469,plain,
% 1.78/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1102) | (~c1_1(a1102)) | (~c2_1(a1102)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c2_1(a1102)))),
% 1.78/1.50 inference(transitivity,[status(thm)],[3468, 3466])).
% 1.78/1.50 tff(3470,plain,
% 1.78/1.50 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1102) | (~c1_1(a1102)) | (~c2_1(a1102)) | c3_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)))),
% 1.78/1.50 inference(quant_inst,[status(thm)],[])).
% 1.78/1.50 tff(3471,plain,
% 1.78/1.50 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c3_1(a1102) | (~ndr1_0) | (~c1_1(a1102)) | (~c0_1(a1102)) | (~c2_1(a1102))),
% 1.78/1.50 inference(modus_ponens,[status(thm)],[3470, 3469])).
% 1.78/1.50 tff(3472,plain,
% 1.78/1.50 (~c2_1(a1102)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3471, 113, 3398, 3465, 3464, 3463, 1279])).
% 1.78/1.50 tff(3473,plain,
% 1.78/1.50 (~hskp12),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2911, 3446, 3445, 3444, 3398, 2458, 2456, 3395])).
% 1.78/1.50 tff(3474,plain,
% 1.78/1.50 (hskp19),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2863, 3447, 3473])).
% 1.78/1.50 tff(3475,plain,
% 1.78/1.50 (~c2_1(a1127)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[900, 3474])).
% 1.78/1.50 tff(3476,plain,
% 1.78/1.50 (c3_1(a1127)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[912, 3474])).
% 1.78/1.50 tff(3477,plain,
% 1.78/1.50 (c0_1(a1127)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2881, 113, 770, 3476, 2457, 2456, 3475, 67, 3395])).
% 1.78/1.50 tff(3478,plain,
% 1.78/1.50 (hskp20 | (~c0_1(a1127))),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3169, 113, 3476, 3427, 3426, 3475, 3425, 1005])).
% 1.78/1.50 tff(3479,plain,
% 1.78/1.50 (hskp20),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3478, 3477])).
% 1.78/1.50 tff(3480,plain,
% 1.78/1.50 (~c3_1(a1130)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[332, 3479])).
% 1.78/1.50 tff(3481,plain,
% 1.78/1.50 (~c0_1(a1130)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[326, 3479])).
% 1.78/1.50 tff(3482,plain,
% 1.78/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a1130) | c3_1(a1130) | c3_1(a1102) | (~ndr1_0) | (~c0_1(a1102)) | c2_1(a1102) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a1130) | c3_1(a1130) | c3_1(a1102) | (~ndr1_0) | (~c0_1(a1102)) | c2_1(a1102) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))),
% 1.78/1.50 inference(rewrite,[status(thm)],[])).
% 1.78/1.50 tff(3483,plain,
% 1.78/1.50 (((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c2_1(a1102) | c3_1(a1102) | (~c0_1(a1102)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130))) <=> (c0_1(a1130) | c3_1(a1130) | c3_1(a1102) | (~ndr1_0) | (~c0_1(a1102)) | c2_1(a1102) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))),
% 1.78/1.50 inference(rewrite,[status(thm)],[])).
% 1.78/1.50 tff(3484,plain,
% 1.78/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c2_1(a1102) | c3_1(a1102) | (~c0_1(a1102)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a1130) | c3_1(a1130) | c3_1(a1102) | (~ndr1_0) | (~c0_1(a1102)) | c2_1(a1102) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130))))),
% 1.78/1.50 inference(monotonicity,[status(thm)],[3483])).
% 1.78/1.50 tff(3485,plain,
% 1.78/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c2_1(a1102) | c3_1(a1102) | (~c0_1(a1102)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a1130) | c3_1(a1130) | c3_1(a1102) | (~ndr1_0) | (~c0_1(a1102)) | c2_1(a1102) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130)))),
% 1.78/1.50 inference(transitivity,[status(thm)],[3484, 3482])).
% 1.78/1.50 tff(3486,plain,
% 1.78/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c2_1(a1102) | c3_1(a1102) | (~c0_1(a1102)) | c3_1(a1130) | c0_1(a1130) | (~c1_1(a1130)))),
% 1.78/1.50 inference(quant_inst,[status(thm)],[])).
% 1.78/1.50 tff(3487,plain,
% 1.78/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a1130) | c3_1(a1130) | c3_1(a1102) | (~ndr1_0) | (~c0_1(a1102)) | c2_1(a1102) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | (~c1_1(a1130))),
% 1.78/1.50 inference(modus_ponens,[status(thm)],[3486, 3485])).
% 1.78/1.50 tff(3488,plain,
% 1.78/1.50 (~c1_1(a1130)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3487, 113, 3289, 3387, 3465, 3481, 3480, 3463, 344, 3441, 3472])).
% 1.78/1.50 tff(3489,plain,
% 1.78/1.50 (~c2_1(a1130)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2287, 3479])).
% 1.78/1.50 tff(3490,plain,
% 1.78/1.50 ($false),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2296, 113, 670, 3289, 3387, 3489, 3480, 669, 668, 3488])).
% 1.78/1.50 tff(3491,plain,(hskp29 | hskp30 | c1_1(a1105) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.78/1.50 tff(3492,plain,
% 1.78/1.50 (hskp29),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3491, 669, 670, 2454])).
% 1.78/1.50 tff(3493,plain,
% 1.78/1.50 (c3_1(a1116)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[201, 3492])).
% 1.78/1.50 tff(3494,plain,
% 1.78/1.50 (c2_1(a1116)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[212, 3492])).
% 1.78/1.50 tff(3495,plain,
% 1.78/1.50 (c0_1(a1116)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[223, 3492])).
% 1.78/1.50 tff(3496,plain,
% 1.78/1.50 (c2_1(a1105)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1143, 113, 3495, 3494, 3493, 2458, 3387, 2457, 669, 246, 3395])).
% 1.78/1.50 tff(3497,plain,
% 1.78/1.50 (hskp2),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3196, 113, 3495, 3494, 3493, 3387, 669, 1065, 3496])).
% 1.78/1.50 tff(3498,plain,
% 1.78/1.50 (~c3_1(a1100)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[291, 3497])).
% 1.78/1.50 tff(3499,plain,
% 1.78/1.50 (~c1_1(a1130)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1325, 113, 249, 248, 247, 772, 819, 771, 2935, 2926, 344])).
% 1.78/1.50 tff(3500,plain,
% 1.78/1.50 ($false),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2296, 113, 670, 992, 965, 2927, 2926, 669, 668, 3499])).
% 1.78/1.50 tff(3501,plain,((~hskp20) | hskp30 | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.50 tff(3502,plain,
% 1.78/1.50 (~hskp20),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3501, 3289, 670, 3387, 669, 3495, 3494, 3493, 2458, 2457, 2456])).
% 1.78/1.50 tff(3503,plain,
% 1.78/1.50 (c2_1(a1100)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[302, 3497])).
% 1.78/1.50 tff(3504,plain,
% 1.78/1.50 (c0_1(a1100)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[313, 3497])).
% 1.78/1.50 tff(3505,plain,
% 1.78/1.50 (~hskp12),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2911, 1269, 1388, 1386, 1387, 772, 771, 2584])).
% 1.78/1.50 tff(3506,plain,
% 1.78/1.50 (~hskp19),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1305, 1269, 249, 703, 248, 247])).
% 1.78/1.50 tff(3507,plain,
% 1.78/1.50 (hskp26),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2863, 3506, 3505])).
% 1.78/1.50 tff(3508,plain,
% 1.78/1.50 (~c2_1(a1180)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2756, 3507])).
% 1.78/1.50 tff(3509,plain,
% 1.78/1.50 (~c1_1(a1180)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2762, 3507])).
% 1.78/1.50 tff(3510,plain,
% 1.78/1.50 (~c3_1(a1180)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2980, 113, 249, 248, 247, 772, 3509, 3508, 819, 246, 2584])).
% 1.78/1.50 tff(3511,plain,
% 1.78/1.50 (~c0_1(a1180)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2775, 3507])).
% 1.78/1.50 tff(3512,plain,
% 1.78/1.50 ($false),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3212, 113, 2903, 1388, 1387, 3511, 3509, 1386, 1055, 3510])).
% 1.78/1.50 tff(3513,plain,(hskp5 | (~c0_1(a1100)) | (~c2_1(a1100)) | c3_1(a1100) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116)) | (~c0_1(a1147)) | c2_1(a1147) | (~c1_1(a1147)) | hskp20 | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.50 tff(3514,plain,
% 1.78/1.50 (hskp5),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3513, 3504, 3503, 3498, 3495, 3494, 3493, 2458, 2457, 3395, 3502, 2456])).
% 1.78/1.50 tff(3515,plain,
% 1.78/1.50 (~c0_1(a1103)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[132, 3514])).
% 1.78/1.50 tff(3516,plain,
% 1.78/1.50 (c3_1(a1103)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[153, 3514])).
% 1.78/1.50 tff(3517,plain,
% 1.78/1.50 (~c1_1(a1103)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[320, 113, 3502, 3516, 3504, 3503, 3515, 3498, 268])).
% 1.78/1.50 tff(3518,plain,
% 1.78/1.50 (~c2_1(a1103)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[126, 3514])).
% 1.78/1.50 tff(3519,plain,
% 1.78/1.50 ($false),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2528, 113, 2454, 3516, 3515, 3518, 2126, 3517])).
% 1.78/1.50 tff(3520,plain,(c1_1(a1105) | hskp0 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.78/1.50 tff(3521,plain,
% 1.78/1.50 (hskp30),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3520, 2987, 2532])).
% 1.78/1.50 tff(3522,plain,
% 1.78/1.50 (c1_1(a1136)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[690, 3521])).
% 1.78/1.50 tff(3523,plain,
% 1.78/1.50 (c3_1(a1136)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[726, 3521])).
% 1.78/1.50 tff(3524,plain,
% 1.78/1.50 (c2_1(a1136)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[737, 3521])).
% 1.78/1.50 tff(3525,plain,
% 1.78/1.50 (hskp14),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1123, 770, 2987, 3524, 3523, 3522, 2986, 2985])).
% 1.78/1.50 tff(3526,plain,
% 1.78/1.50 (~c2_1(a1118)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[172, 3525])).
% 1.78/1.50 tff(3527,plain,
% 1.78/1.50 (c0_1(a1136)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[797, 770, 2706, 3524, 3523, 771, 3522])).
% 1.78/1.50 tff(3528,plain,
% 1.78/1.50 (~c3_1(a1118)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[166, 3525])).
% 1.78/1.50 tff(3529,plain,
% 1.78/1.50 (c1_1(a1118)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[183, 3525])).
% 1.78/1.50 tff(3530,plain,
% 1.78/1.50 (c0_1(a1118)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1774, 113, 3524, 3523, 2706, 3529, 819, 771, 3528, 344, 3527])).
% 1.78/1.50 tff(3531,plain,
% 1.78/1.50 (c2_1(a1105) | (~c0_1(a1118))),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1801, 113, 3524, 3523, 3529, 2985, 3526, 2987, 246, 3527])).
% 1.78/1.50 tff(3532,plain,
% 1.78/1.50 (c2_1(a1105)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3531, 3530])).
% 1.78/1.50 tff(3533,plain,
% 1.78/1.50 (hskp2 | (~c2_1(a1105))),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1071, 113, 2986, 2985, 2987, 1065])).
% 1.78/1.50 tff(3534,plain,
% 1.78/1.50 (hskp2),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3533, 3532])).
% 1.78/1.50 tff(3535,plain,
% 1.78/1.50 (c2_1(a1100)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[302, 3534])).
% 1.78/1.50 tff(3536,plain,
% 1.78/1.50 (c0_1(a1100)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[313, 3534])).
% 1.78/1.50 tff(3537,plain,
% 1.78/1.50 (~c3_1(a1100)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[291, 3534])).
% 1.78/1.50 tff(3538,plain,
% 1.78/1.50 (~hskp8),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1790, 3530, 3523, 2986, 2985, 2987, 3527, 3529, 3526, 3524])).
% 1.78/1.50 tff(3539,plain,
% 1.78/1.50 (hskp19 | hskp8 | (~c2_1(a1105))),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[2681, 113, 2985, 2987, 2675])).
% 1.78/1.50 tff(3540,plain,
% 1.78/1.50 (hskp19),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3539, 3538, 3532])).
% 1.78/1.50 tff(3541,plain,
% 1.78/1.50 (~c2_1(a1127)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[900, 3540])).
% 1.78/1.50 tff(3542,plain,
% 1.78/1.50 (c3_1(a1127)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[912, 3540])).
% 1.78/1.50 tff(3543,plain,
% 1.78/1.50 (c0_1(a1127)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1681, 113, 770, 3542, 3529, 3541, 3526, 3528, 67])).
% 1.78/1.50 tff(3544,plain,
% 1.78/1.50 (hskp20 | (~c0_1(a1127))),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1013, 113, 3542, 2986, 3541, 2987, 1005, 3532])).
% 1.78/1.50 tff(3545,plain,
% 1.78/1.50 (hskp20),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[3544, 3543])).
% 1.78/1.50 tff(3546,plain,
% 1.78/1.50 (~c0_1(a1130)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[326, 3545])).
% 1.78/1.50 tff(3547,plain,
% 1.78/1.50 (~c3_1(a1130)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[332, 3545])).
% 1.78/1.50 tff(3548,plain,
% 1.78/1.50 (hskp5),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[1407, 334, 805, 345, 1387, 1386, 768, 739, 992, 965, 669, 1388, 772, 819, 771])).
% 1.78/1.50 tff(3549,plain,
% 1.78/1.50 (~c2_1(a1103)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[126, 3548])).
% 1.78/1.50 tff(3550,plain,
% 1.78/1.50 (c3_1(a1103)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[153, 3548])).
% 1.78/1.50 tff(3551,plain,
% 1.78/1.50 (~c0_1(a1103)),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[132, 3548])).
% 1.78/1.50 tff(3552,plain,
% 1.78/1.50 ($false),
% 1.78/1.50 inference(unit_resolution,[status(thm)],[373, 3551, 3550, 230, 227, 3549, 334, 345, 226, 228])).
% 1.78/1.50 tff(3553,plain,(c0_1(a1130) | c2_1(a1118) | (~c0_1(a1118)) | c3_1(a1130) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1136)) | (~c2_1(a1100)) | c3_1(a1100) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c0_1(a1105)) | (~c3_1(a1105)) | c1_1(a1105) | (~c0_1(a1100)) | (~c0_1(a1147)) | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.50 tff(3554,plain,
% 1.82/1.50 ($false),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[3553, 3547, 3546, 771, 2706, 3528, 3529, 3527, 3530, 3537, 3524, 3523, 2986, 2985, 2987, 3536, 3535, 819, 3526])).
% 1.82/1.50 tff(3555,plain,(hskp29 | c3_1(a1147) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.50 tff(3556,plain,
% 1.82/1.50 (hskp29),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[3555, 771, 819])).
% 1.82/1.50 tff(3557,plain,
% 1.82/1.50 (c3_1(a1116)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[201, 3556])).
% 1.82/1.50 tff(3558,plain,
% 1.82/1.50 (c2_1(a1116)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[212, 3556])).
% 1.82/1.50 tff(3559,plain,
% 1.82/1.50 (c0_1(a1116)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[223, 3556])).
% 1.82/1.50 tff(3560,plain,
% 1.82/1.50 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.82/1.50 inference(bind,[status(th)],[])).
% 1.82/1.50 tff(3561,plain,
% 1.82/1.50 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/1.50 inference(quant_intro,[status(thm)],[3560])).
% 1.82/1.50 tff(3562,plain,
% 1.82/1.50 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(3563,plain,
% 1.82/1.50 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.82/1.50 inference(bind,[status(th)],[])).
% 1.82/1.50 tff(3564,plain,
% 1.82/1.50 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/1.50 inference(quant_intro,[status(thm)],[3563])).
% 1.82/1.50 tff(3565,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 1.82/1.50 tff(3566,plain,
% 1.82/1.50 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[3565, 3564])).
% 1.82/1.50 tff(3567,plain,
% 1.82/1.50 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[3566, 3562])).
% 1.82/1.50 tff(3568,plain,(
% 1.82/1.50 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/1.50 inference(skolemize,[status(sab)],[3567])).
% 1.82/1.50 tff(3569,plain,
% 1.82/1.50 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[3568, 3561])).
% 1.82/1.50 tff(3570,plain,
% 1.82/1.50 (~c2_1(a1105)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1072, 2806])).
% 1.82/1.50 tff(3571,plain,
% 1.82/1.50 (hskp22 | c2_1(a1105)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[3405, 113, 2532, 965, 669, 2144])).
% 1.82/1.50 tff(3572,plain,
% 1.82/1.50 (hskp22),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[3571, 3570])).
% 1.82/1.50 tff(3573,plain,
% 1.82/1.50 (~c1_1(a1145)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[2157, 3572])).
% 1.82/1.50 tff(3574,plain,
% 1.82/1.50 (c3_1(a1145)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[2200, 3572])).
% 1.82/1.50 tff(3575,plain,
% 1.82/1.50 (c2_1(a1145)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[2168, 3572])).
% 1.82/1.50 tff(3576,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c1_1(a1145) | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1145)) | (~c3_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c1_1(a1145) | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(3577,plain,
% 1.82/1.50 ((hskp19 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121))) <=> (hskp19 | c1_1(a1145) | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3578,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c1_1(a1145) | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1145)) | (~c3_1(a1145))))),
% 1.82/1.51 inference(monotonicity,[status(thm)],[3577])).
% 1.82/1.51 tff(3579,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c1_1(a1145) | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1145)) | (~c3_1(a1145)))),
% 1.82/1.51 inference(transitivity,[status(thm)],[3578, 3576])).
% 1.82/1.51 tff(3580,plain,
% 1.82/1.51 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a1145) | (~c3_1(a1145)) | (~c2_1(a1145)) | c0_1(a1121) | (~c3_1(a1121)) | (~c1_1(a1121)))),
% 1.82/1.51 inference(quant_inst,[status(thm)],[])).
% 1.82/1.51 tff(3581,plain,
% 1.82/1.51 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c1_1(a1145) | c0_1(a1121) | (~ndr1_0) | (~c1_1(a1121)) | (~c3_1(a1121)) | (~c2_1(a1145)) | (~c3_1(a1145))),
% 1.82/1.51 inference(modus_ponens,[status(thm)],[3580, 3579])).
% 1.82/1.51 tff(3582,plain,
% 1.82/1.51 ($false),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3581, 113, 2942, 3575, 3574, 2956, 2955, 3573, 2954, 3569])).
% 1.82/1.51 tff(3583,plain,(hskp2 | (~c3_1(a1105)) | c1_1(a1105) | hskp26 | (~c0_1(a1105)) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.51 tff(3584,plain,
% 1.82/1.51 (hskp2),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3583, 2802, 2987, 2985, 2986, 3559, 3558, 3557])).
% 1.82/1.51 tff(3585,plain,
% 1.82/1.51 (~c3_1(a1100)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[291, 3584])).
% 1.82/1.51 tff(3586,plain,
% 1.82/1.51 (c2_1(a1100)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[302, 3584])).
% 1.82/1.51 tff(3587,plain,
% 1.82/1.51 (c0_1(a1100)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[313, 3584])).
% 1.82/1.51 tff(3588,plain,
% 1.82/1.51 (~c1_1(a1100)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1289, 113, 1269, 3587, 3586, 3585, 1279])).
% 1.82/1.51 tff(3589,plain,
% 1.82/1.51 (~hskp8),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[2651, 3558, 2986, 3557, 3559, 2985, 2987])).
% 1.82/1.51 tff(3590,plain,
% 1.82/1.51 (~hskp3),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1346, 1269, 2706, 3558, 3557, 3559, 819, 771])).
% 1.82/1.51 tff(3591,plain,
% 1.82/1.51 (hskp4),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3461, 2802, 3590])).
% 1.82/1.51 tff(3592,plain,
% 1.82/1.51 (~c3_1(a1102)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1529, 3591])).
% 1.82/1.51 tff(3593,plain,
% 1.82/1.51 (c1_1(a1102)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1549, 3591])).
% 1.82/1.51 tff(3594,plain,
% 1.82/1.51 (c0_1(a1102)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1560, 3591])).
% 1.82/1.51 tff(3595,plain,
% 1.82/1.51 (~c2_1(a1102)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3471, 113, 1269, 3594, 3593, 3592, 1279])).
% 1.82/1.51 tff(3596,plain,
% 1.82/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1102)) | (~c0_1(a1102)) | c2_1(a1102) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1102)) | (~c0_1(a1102)) | c2_1(a1102) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3597,plain,
% 1.82/1.51 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105))) <=> (c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1102)) | (~c0_1(a1102)) | c2_1(a1102) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3598,plain,
% 1.82/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1102)) | (~c0_1(a1102)) | c2_1(a1102) | c2_1(a1105) | (~c3_1(a1105))))),
% 1.82/1.51 inference(monotonicity,[status(thm)],[3597])).
% 1.82/1.51 tff(3599,plain,
% 1.82/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1102)) | (~c0_1(a1102)) | c2_1(a1102) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.82/1.51 inference(transitivity,[status(thm)],[3598, 3596])).
% 1.82/1.51 tff(3600,plain,
% 1.82/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1102) | (~c1_1(a1102)) | (~c0_1(a1102)) | c1_1(a1105) | c2_1(a1105) | (~c3_1(a1105)))),
% 1.82/1.51 inference(quant_inst,[status(thm)],[])).
% 1.82/1.51 tff(3601,plain,
% 1.82/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a1105) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1102)) | (~c0_1(a1102)) | c2_1(a1102) | c2_1(a1105) | (~c3_1(a1105))),
% 1.82/1.51 inference(modus_ponens,[status(thm)],[3600, 3599])).
% 1.82/1.51 tff(3602,plain,
% 1.82/1.51 (c2_1(a1105)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3601, 113, 3559, 3558, 3557, 2985, 3594, 3593, 2987, 246, 3595])).
% 1.82/1.51 tff(3603,plain,
% 1.82/1.51 (hskp19),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3539, 3602, 3589])).
% 1.82/1.51 tff(3604,plain,
% 1.82/1.51 (hskp20),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1305, 3603, 3559, 1269, 3558, 3557])).
% 1.82/1.51 tff(3605,plain,
% 1.82/1.51 (~c0_1(a1130)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[326, 3604])).
% 1.82/1.51 tff(3606,plain,
% 1.82/1.51 (~c3_1(a1130)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[332, 3604])).
% 1.82/1.51 tff(3607,plain,
% 1.82/1.51 (~c0_1(a1136)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1407, 3606, 771, 2706, 3524, 3605, 3586, 3523, 2986, 2985, 2987, 3587, 3585, 819, 1269])).
% 1.82/1.51 tff(3608,plain,
% 1.82/1.51 (~c2_1(a1127)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[900, 3603])).
% 1.82/1.51 tff(3609,plain,
% 1.82/1.51 (c1_1(a1127)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[923, 3603])).
% 1.82/1.51 tff(3610,plain,
% 1.82/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a1127) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)) | (~c1_1(a1127)) | (~c0_1(a1127)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1127) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)) | (~c1_1(a1127)) | (~c0_1(a1127)))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3611,plain,
% 1.82/1.51 (((~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136))) <=> (c2_1(a1127) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)) | (~c1_1(a1127)) | (~c0_1(a1127)))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3612,plain,
% 1.82/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a1127) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)) | (~c1_1(a1127)) | (~c0_1(a1127))))),
% 1.82/1.51 inference(monotonicity,[status(thm)],[3611])).
% 1.82/1.51 tff(3613,plain,
% 1.82/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1127) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)) | (~c1_1(a1127)) | (~c0_1(a1127)))),
% 1.82/1.51 inference(transitivity,[status(thm)],[3612, 3610])).
% 1.82/1.51 tff(3614,plain,
% 1.82/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1127) | (~c1_1(a1127)) | (~c0_1(a1127)) | c1_1(a1100) | c3_1(a1100) | (~c0_1(a1100)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))),
% 1.82/1.51 inference(quant_inst,[status(thm)],[])).
% 1.82/1.51 tff(3615,plain,
% 1.82/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a1127) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | c1_1(a1100) | (~c0_1(a1100)) | (~c1_1(a1127)) | (~c0_1(a1127))),
% 1.82/1.51 inference(modus_ponens,[status(thm)],[3614, 3613])).
% 1.82/1.51 tff(3616,plain,
% 1.82/1.51 (~c0_1(a1127)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3615, 113, 3522, 3524, 3609, 3587, 3608, 3585, 1418, 3607, 3588])).
% 1.82/1.51 tff(3617,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1127)) | c0_1(a1127))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1127)) | c0_1(a1127))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3618,plain,
% 1.82/1.51 ((hskp3 | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127))) <=> (hskp3 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1127)) | c0_1(a1127))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3619,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1127)) | c0_1(a1127)))),
% 1.82/1.51 inference(monotonicity,[status(thm)],[3618])).
% 1.82/1.51 tff(3620,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1127)) | c0_1(a1127))),
% 1.82/1.51 inference(transitivity,[status(thm)],[3619, 3617])).
% 1.82/1.51 tff(3621,plain,
% 1.82/1.51 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1136) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1127) | c0_1(a1127) | (~c1_1(a1127)))),
% 1.82/1.51 inference(quant_inst,[status(thm)],[])).
% 1.82/1.51 tff(3622,plain,
% 1.82/1.51 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c3_1(a1136)) | (~c1_1(a1127)) | c0_1(a1127)),
% 1.82/1.51 inference(modus_ponens,[status(thm)],[3621, 3620])).
% 1.82/1.51 tff(3623,plain,
% 1.82/1.51 ($false),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3622, 113, 3590, 3524, 3523, 3609, 3608, 2307, 3607, 3616])).
% 1.82/1.51 tff(3624,plain,(hskp26 | c3_1(a1147) | c2_1(a1147) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.82/1.51 tff(3625,plain,
% 1.82/1.51 (hskp26),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3624, 1269, 819, 771])).
% 1.82/1.51 tff(3626,plain,
% 1.82/1.51 (~c2_1(a1180)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[2756, 3625])).
% 1.82/1.51 tff(3627,plain,
% 1.82/1.51 (~c1_1(a1180)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[2762, 3625])).
% 1.82/1.51 tff(3628,plain,
% 1.82/1.51 (~c0_1(a1180)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[2775, 3625])).
% 1.82/1.51 tff(3629,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1180) | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | (~c3_1(a1180)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1180) | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | (~c3_1(a1180)))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3630,plain,
% 1.82/1.51 ((hskp0 | (~ndr1_0) | c2_1(a1180) | c0_1(a1180) | (~c3_1(a1180)) | c2_1(a1180) | c1_1(a1180) | c0_1(a1180)) <=> (hskp0 | c0_1(a1180) | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | (~c3_1(a1180)))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3631,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1180) | c0_1(a1180) | (~c3_1(a1180)) | c2_1(a1180) | c1_1(a1180) | c0_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1180) | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | (~c3_1(a1180))))),
% 1.82/1.51 inference(monotonicity,[status(thm)],[3630])).
% 1.82/1.51 tff(3632,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1180) | c0_1(a1180) | (~c3_1(a1180)) | c2_1(a1180) | c1_1(a1180) | c0_1(a1180))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1180) | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | (~c3_1(a1180)))),
% 1.82/1.51 inference(transitivity,[status(thm)],[3631, 3629])).
% 1.82/1.51 tff(3633,plain,
% 1.82/1.51 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1180) | c0_1(a1180) | (~c3_1(a1180)) | c2_1(a1180) | c1_1(a1180) | c0_1(a1180))),
% 1.82/1.51 inference(quant_inst,[status(thm)],[])).
% 1.82/1.51 tff(3634,plain,
% 1.82/1.51 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1180) | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | (~c3_1(a1180))),
% 1.82/1.51 inference(modus_ponens,[status(thm)],[3633, 3632])).
% 1.82/1.51 tff(3635,plain,
% 1.82/1.51 (~c3_1(a1180)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3634, 113, 2532, 3628, 3627, 3626, 2126])).
% 1.82/1.51 tff(3636,plain,
% 1.82/1.51 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp8 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3637,plain,
% 1.82/1.51 ((hskp19 | hskp8 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180)) <=> (hskp19 | hskp8 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3638,plain,
% 1.82/1.51 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180)))),
% 1.82/1.51 inference(monotonicity,[status(thm)],[3637])).
% 1.82/1.51 tff(3639,plain,
% 1.82/1.51 (((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180))) <=> ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp8 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180))),
% 1.82/1.51 inference(transitivity,[status(thm)],[3638, 3636])).
% 1.82/1.51 tff(3640,plain,
% 1.82/1.51 ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp8 | (~ndr1_0) | c3_1(a1180) | c2_1(a1180) | c1_1(a1180))),
% 1.82/1.51 inference(quant_inst,[status(thm)],[])).
% 1.82/1.51 tff(3641,plain,
% 1.82/1.51 ((~![U: $i] : (hskp19 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp8 | c1_1(a1180) | c2_1(a1180) | (~ndr1_0) | c3_1(a1180)),
% 1.82/1.51 inference(modus_ponens,[status(thm)],[3640, 3639])).
% 1.82/1.51 tff(3642,plain,
% 1.82/1.51 (hskp19 | c3_1(a1180)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3641, 113, 3589, 3627, 3626, 1165])).
% 1.82/1.51 tff(3643,plain,
% 1.82/1.51 (hskp19),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3642, 3635])).
% 1.82/1.51 tff(3644,plain,
% 1.82/1.51 (hskp2),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[2941, 3643, 3559, 3558, 3557])).
% 1.82/1.51 tff(3645,plain,
% 1.82/1.51 (~c3_1(a1100)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[291, 3644])).
% 1.82/1.51 tff(3646,plain,
% 1.82/1.51 (c2_1(a1100)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[302, 3644])).
% 1.82/1.51 tff(3647,plain,
% 1.82/1.51 (c0_1(a1100)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[313, 3644])).
% 1.82/1.51 tff(3648,plain,
% 1.82/1.51 ($false),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3212, 113, 3590, 3647, 3646, 3628, 3627, 3645, 1055, 3635])).
% 1.82/1.51 tff(3649,plain,(hskp5 | c2_1(a1147) | c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.51 tff(3650,plain,
% 1.82/1.51 (hskp5),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3649, 771, 819])).
% 1.82/1.51 tff(3651,plain,
% 1.82/1.51 (~c2_1(a1103)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[126, 3650])).
% 1.82/1.51 tff(3652,plain,
% 1.82/1.51 (~c0_1(a1103)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[132, 3650])).
% 1.82/1.51 tff(3653,plain,
% 1.82/1.51 (c3_1(a1103)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[153, 3650])).
% 1.82/1.51 tff(3654,plain,
% 1.82/1.51 (c1_1(a1103)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[2528, 113, 2532, 3653, 3652, 3651, 2126])).
% 1.82/1.51 tff(3655,plain,
% 1.82/1.51 (hskp21 | (~c1_1(a1103))),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[2520, 113, 2532, 3653, 3652, 33])).
% 1.82/1.51 tff(3656,plain,
% 1.82/1.51 (hskp21),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3655, 3654])).
% 1.82/1.51 tff(3657,plain,
% 1.82/1.51 (~c3_1(a1131)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[811, 3656])).
% 1.82/1.51 tff(3658,plain,
% 1.82/1.51 (~c0_1(a1131)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[817, 3656])).
% 1.82/1.51 tff(3659,plain,
% 1.82/1.51 (c1_1(a1131)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[829, 3656])).
% 1.82/1.51 tff(3660,plain,
% 1.82/1.51 ($false),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[2726, 113, 3559, 3558, 3557, 2706, 3659, 819, 771, 3658, 3657, 344])).
% 1.82/1.51 tff(3661,plain,(c3_1(a1147) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.51 tff(3662,plain,
% 1.82/1.51 (c3_1(a1147)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3661, 819])).
% 1.82/1.51 tff(3663,plain,
% 1.82/1.51 (~hskp23),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[755, 3662])).
% 1.82/1.51 tff(3664,plain,
% 1.82/1.51 (hskp30),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[2180, 3663, 2532])).
% 1.82/1.51 tff(3665,plain,
% 1.82/1.51 (c1_1(a1136)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[690, 3664])).
% 1.82/1.51 tff(3666,plain,
% 1.82/1.51 (c2_1(a1136)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[737, 3664])).
% 1.82/1.51 tff(3667,plain,
% 1.82/1.51 (~hskp9),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1653, 770, 3663, 3665, 3666])).
% 1.82/1.51 tff(3668,plain,
% 1.82/1.51 (c3_1(a1136)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[726, 3664])).
% 1.82/1.51 tff(3669,plain,
% 1.82/1.51 (hskp19 | hskp9),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1670, 113, 3665, 3666, 3668, 1664])).
% 1.82/1.51 tff(3670,plain,
% 1.82/1.51 (hskp19),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3669, 3667])).
% 1.82/1.51 tff(3671,plain,
% 1.82/1.51 (~c2_1(a1127)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[900, 3670])).
% 1.82/1.51 tff(3672,plain,
% 1.82/1.51 (c3_1(a1127)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[912, 3670])).
% 1.82/1.51 tff(3673,plain,
% 1.82/1.51 (c1_1(a1127)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[923, 3670])).
% 1.82/1.51 tff(3674,plain,
% 1.82/1.51 (hskp14),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[749, 3663])).
% 1.82/1.51 tff(3675,plain,
% 1.82/1.51 (~c3_1(a1118)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[166, 3674])).
% 1.82/1.51 tff(3676,plain,
% 1.82/1.51 (~c2_1(a1118)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[172, 3674])).
% 1.82/1.51 tff(3677,plain,
% 1.82/1.51 (c1_1(a1118)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[183, 3674])).
% 1.82/1.51 tff(3678,plain,
% 1.82/1.51 (c0_1(a1127)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1681, 113, 770, 3672, 3677, 3671, 3676, 3675, 67])).
% 1.82/1.51 tff(3679,plain,
% 1.82/1.51 (hskp28 | (~c0_1(a1127))),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1688, 113, 3673, 3672, 3671, 567])).
% 1.82/1.51 tff(3680,plain,
% 1.82/1.51 (hskp28),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3679, 3678])).
% 1.82/1.51 tff(3681,plain,
% 1.82/1.51 (c2_1(a1111)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[596, 3680])).
% 1.82/1.51 tff(3682,plain,
% 1.82/1.51 (c0_1(a1111)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[618, 3680])).
% 1.82/1.51 tff(3683,plain,
% 1.82/1.51 (hskp13),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1728, 3682, 3667, 3681, 3673, 3672, 3671])).
% 1.82/1.51 tff(3684,plain,
% 1.82/1.51 (~c3_1(a1115)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1354, 3683])).
% 1.82/1.51 tff(3685,plain,
% 1.82/1.51 (~c1_1(a1115)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1229, 3683])).
% 1.82/1.51 tff(3686,plain,
% 1.82/1.51 (c1_1(a1111)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[607, 3680])).
% 1.82/1.51 tff(3687,plain,
% 1.82/1.51 (~c0_1(a1115)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1738, 3663, 113, 3682, 3686, 3681, 3685, 3684, 1633])).
% 1.82/1.51 tff(3688,plain,
% 1.82/1.51 (c2_1(a1115)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1240, 3683])).
% 1.82/1.51 tff(3689,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3690,plain,
% 1.82/1.51 ((hskp0 | (~ndr1_0) | c2_1(a1147) | c0_1(a1147) | (~c3_1(a1147)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147)) <=> (hskp0 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3691,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1147) | c0_1(a1147) | (~c3_1(a1147)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147)))),
% 1.82/1.51 inference(monotonicity,[status(thm)],[3690])).
% 1.82/1.51 tff(3692,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1147) | c0_1(a1147) | (~c3_1(a1147)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))),
% 1.82/1.51 inference(transitivity,[status(thm)],[3691, 3689])).
% 1.82/1.51 tff(3693,plain,
% 1.82/1.51 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1147) | c0_1(a1147) | (~c3_1(a1147)) | c2_1(a1147) | c1_1(a1147) | c0_1(a1147))),
% 1.82/1.51 inference(quant_inst,[status(thm)],[])).
% 1.82/1.51 tff(3694,plain,
% 1.82/1.51 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147)),
% 1.82/1.51 inference(modus_ponens,[status(thm)],[3693, 3692])).
% 1.82/1.51 tff(3695,plain,
% 1.82/1.51 (c0_1(a1147) | (~c3_1(a1147)) | c1_1(a1147)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3694, 113, 2532, 819, 2126])).
% 1.82/1.51 tff(3696,plain,
% 1.82/1.51 (c1_1(a1147)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3695, 2533, 3662])).
% 1.82/1.51 tff(3697,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3698,plain,
% 1.82/1.51 ((hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1147) | c0_1(a1147) | (~c3_1(a1147))) <=> (hskp29 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(3699,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1147) | c0_1(a1147) | (~c3_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118))))),
% 1.82/1.51 inference(monotonicity,[status(thm)],[3698])).
% 1.82/1.51 tff(3700,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1147) | c0_1(a1147) | (~c3_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118)))),
% 1.82/1.51 inference(transitivity,[status(thm)],[3699, 3697])).
% 1.82/1.51 tff(3701,plain,
% 1.82/1.51 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1147) | c0_1(a1147) | (~c3_1(a1147)))),
% 1.82/1.51 inference(quant_inst,[status(thm)],[])).
% 1.82/1.51 tff(3702,plain,
% 1.82/1.51 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a1147) | c2_1(a1147) | (~c3_1(a1147)) | c2_1(a1118) | c3_1(a1118) | (~ndr1_0) | (~c1_1(a1118))),
% 1.82/1.51 inference(modus_ponens,[status(thm)],[3701, 3700])).
% 1.82/1.51 tff(3703,plain,
% 1.82/1.51 (hskp29 | c0_1(a1147)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3702, 113, 3677, 819, 3662, 3676, 3675, 67])).
% 1.82/1.51 tff(3704,plain,
% 1.82/1.51 (hskp29),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[3703, 2533])).
% 1.82/1.51 tff(3705,plain,
% 1.82/1.51 (c3_1(a1116)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[201, 3704])).
% 1.82/1.51 tff(3706,plain,
% 1.82/1.51 (c2_1(a1116)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[212, 3704])).
% 1.82/1.51 tff(3707,plain,
% 1.82/1.51 (c0_1(a1116)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[223, 3704])).
% 1.82/1.51 tff(3708,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3709,plain,
% 1.82/1.52 ((hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147))) <=> (hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3710,plain,
% 1.82/1.52 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147))))),
% 1.82/1.52 inference(monotonicity,[status(thm)],[3709])).
% 1.82/1.52 tff(3711,plain,
% 1.82/1.52 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(transitivity,[status(thm)],[3710, 3708])).
% 1.82/1.52 tff(3712,plain,
% 1.82/1.52 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(quant_inst,[status(thm)],[])).
% 1.82/1.52 tff(3713,plain,
% 1.82/1.52 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c1_1(a1147))),
% 1.82/1.52 inference(modus_ponens,[status(thm)],[3712, 3711])).
% 1.82/1.52 tff(3714,plain,
% 1.82/1.52 (hskp2),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3713, 113, 3707, 3706, 3705, 819, 3662, 278, 3696])).
% 1.82/1.52 tff(3715,plain,
% 1.82/1.52 (~c3_1(a1100)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[291, 3714])).
% 1.82/1.52 tff(3716,plain,
% 1.82/1.52 (c0_1(a1100)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[313, 3714])).
% 1.82/1.52 tff(3717,plain,
% 1.82/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c1_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3718,plain,
% 1.82/1.52 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147))) <=> (c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3719,plain,
% 1.82/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c1_1(a1147))))),
% 1.82/1.52 inference(monotonicity,[status(thm)],[3718])).
% 1.82/1.52 tff(3720,plain,
% 1.82/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(transitivity,[status(thm)],[3719, 3717])).
% 1.82/1.52 tff(3721,plain,
% 1.82/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1100) | (~c1_1(a1100)) | (~c0_1(a1100)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147)))),
% 1.82/1.52 inference(quant_inst,[status(thm)],[])).
% 1.82/1.52 tff(3722,plain,
% 1.82/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1100) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1100)) | (~c0_1(a1100)) | (~c1_1(a1147))),
% 1.82/1.52 inference(modus_ponens,[status(thm)],[3721, 3720])).
% 1.82/1.52 tff(3723,plain,
% 1.82/1.52 (~c1_1(a1100)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3722, 113, 3665, 3666, 3668, 2533, 3716, 3662, 3715, 45, 3696])).
% 1.82/1.52 tff(3724,plain,
% 1.82/1.52 (c2_1(a1100)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[302, 3714])).
% 1.82/1.52 tff(3725,plain,
% 1.82/1.52 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3726,plain,
% 1.82/1.52 ((hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100))) <=> (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3727,plain,
% 1.82/1.52 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100))))),
% 1.82/1.52 inference(monotonicity,[status(thm)],[3726])).
% 1.82/1.52 tff(3728,plain,
% 1.82/1.52 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100)))),
% 1.82/1.52 inference(transitivity,[status(thm)],[3727, 3725])).
% 1.82/1.52 tff(3729,plain,
% 1.82/1.52 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c2_1(a1100)) | (~c0_1(a1100)))),
% 1.82/1.52 inference(quant_inst,[status(thm)],[])).
% 1.82/1.52 tff(3730,plain,
% 1.82/1.52 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | (~ndr1_0) | c1_1(a1100) | (~c0_1(a1100)) | (~c2_1(a1100))),
% 1.82/1.52 inference(modus_ponens,[status(thm)],[3729, 3728])).
% 1.82/1.52 tff(3731,plain,
% 1.82/1.52 (hskp7),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3730, 3663, 113, 3716, 3724, 2574, 3723])).
% 1.82/1.52 tff(3732,plain,
% 1.82/1.52 (~c1_1(a1105)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[633, 3731])).
% 1.82/1.52 tff(3733,plain,
% 1.82/1.52 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a1147) | c2_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a1147) | c2_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3734,plain,
% 1.82/1.52 ((hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147))) <=> (hskp10 | c0_1(a1147) | c2_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3735,plain,
% 1.82/1.52 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a1147) | c2_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147))))),
% 1.82/1.52 inference(monotonicity,[status(thm)],[3734])).
% 1.82/1.52 tff(3736,plain,
% 1.82/1.52 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a1147) | c2_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(transitivity,[status(thm)],[3735, 3733])).
% 1.82/1.52 tff(3737,plain,
% 1.82/1.52 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c0_1(a1147) | (~c1_1(a1147)))),
% 1.82/1.52 inference(quant_inst,[status(thm)],[])).
% 1.82/1.52 tff(3738,plain,
% 1.82/1.52 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a1147) | c2_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1147))),
% 1.82/1.52 inference(modus_ponens,[status(thm)],[3737, 3736])).
% 1.82/1.52 tff(3739,plain,
% 1.82/1.52 (hskp10 | c0_1(a1147) | (~c1_1(a1147))),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3738, 113, 3665, 3666, 3668, 819, 1993])).
% 1.82/1.52 tff(3740,plain,
% 1.82/1.52 (hskp10),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3739, 2533, 3696])).
% 1.82/1.52 tff(3741,plain,
% 1.82/1.52 (~c2_1(a1110)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[2006, 3740])).
% 1.82/1.52 tff(3742,plain,
% 1.82/1.52 (~c1_1(a1110)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[2012, 3740])).
% 1.82/1.52 tff(3743,plain,
% 1.82/1.52 (c3_1(a1110)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[2025, 3740])).
% 1.82/1.52 tff(3744,plain,
% 1.82/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c3_1(a1110)) | (~c1_1(a1118)) | (~c0_1(a1118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c3_1(a1110)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3745,plain,
% 1.82/1.52 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110))) <=> (c2_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c3_1(a1110)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3746,plain,
% 1.82/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c3_1(a1110)) | (~c1_1(a1118)) | (~c0_1(a1118))))),
% 1.82/1.52 inference(monotonicity,[status(thm)],[3745])).
% 1.82/1.52 tff(3747,plain,
% 1.82/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c3_1(a1110)) | (~c1_1(a1118)) | (~c0_1(a1118)))),
% 1.82/1.52 inference(transitivity,[status(thm)],[3746, 3744])).
% 1.82/1.52 tff(3748,plain,
% 1.82/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c2_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c1_1(a1110) | c2_1(a1110) | (~c3_1(a1110)))),
% 1.82/1.52 inference(quant_inst,[status(thm)],[])).
% 1.82/1.52 tff(3749,plain,
% 1.82/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c3_1(a1110)) | (~c1_1(a1118)) | (~c0_1(a1118))),
% 1.82/1.52 inference(modus_ponens,[status(thm)],[3748, 3747])).
% 1.82/1.52 tff(3750,plain,
% 1.82/1.52 (~c0_1(a1118)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3749, 113, 3707, 3706, 3705, 3677, 3743, 3676, 3742, 3741, 246])).
% 1.82/1.52 tff(3751,plain,
% 1.82/1.52 (hskp8),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[2034, 3750, 3677, 3665, 3706, 3676, 3675, 3705, 3666, 3668, 3707])).
% 1.82/1.52 tff(3752,plain,
% 1.82/1.52 (c0_1(a1105)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[646, 3731])).
% 1.82/1.52 tff(3753,plain,
% 1.82/1.52 (c3_1(a1105)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[657, 3731])).
% 1.82/1.52 tff(3754,plain,
% 1.82/1.52 ($false),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[2651, 3753, 3752, 3706, 3705, 3707, 3751, 3732])).
% 1.82/1.52 tff(3755,plain,(c0_1(a1147) | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.52 tff(3756,plain,
% 1.82/1.52 (c0_1(a1147)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3755, 819])).
% 1.82/1.52 tff(3757,plain,
% 1.82/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3758,plain,
% 1.82/1.52 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115))) <=> (c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3759,plain,
% 1.82/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.82/1.52 inference(monotonicity,[status(thm)],[3758])).
% 1.82/1.52 tff(3760,plain,
% 1.82/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.82/1.52 inference(transitivity,[status(thm)],[3759, 3757])).
% 1.82/1.52 tff(3761,plain,
% 1.82/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.82/1.52 inference(quant_inst,[status(thm)],[])).
% 1.82/1.52 tff(3762,plain,
% 1.82/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a1147) | c1_1(a1115) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | c0_1(a1115) | (~c2_1(a1115)) | c1_1(a1147) | (~c0_1(a1147))),
% 1.82/1.52 inference(modus_ponens,[status(thm)],[3761, 3760])).
% 1.82/1.52 tff(3763,plain,
% 1.82/1.52 (c1_1(a1147)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3762, 113, 3665, 3666, 3668, 3756, 3688, 819, 3685, 1155, 3687])).
% 1.82/1.52 tff(3764,assumption,(hskp10), introduced(assumption)).
% 1.82/1.52 tff(3765,plain,
% 1.82/1.52 (~c2_1(a1110)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[2006, 3764])).
% 1.82/1.52 tff(3766,plain,
% 1.82/1.52 (~c1_1(a1110)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[2012, 3764])).
% 1.82/1.52 tff(3767,assumption,(c2_1(a1115)), introduced(assumption)).
% 1.82/1.52 tff(3768,plain,
% 1.82/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1115) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1110)) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1110)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3769,plain,
% 1.82/1.52 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1110) | c1_1(a1110) | (~c0_1(a1110)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115))) <=> (c1_1(a1115) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1110)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3770,plain,
% 1.82/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1110) | c1_1(a1110) | (~c0_1(a1110)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1115) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1110)) | c0_1(a1115) | (~c2_1(a1115))))),
% 1.82/1.52 inference(monotonicity,[status(thm)],[3769])).
% 1.82/1.52 tff(3771,plain,
% 1.82/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1110) | c1_1(a1110) | (~c0_1(a1110)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1110)) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.82/1.52 inference(transitivity,[status(thm)],[3770, 3768])).
% 1.82/1.52 tff(3772,plain,
% 1.82/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1110) | c1_1(a1110) | (~c0_1(a1110)) | c1_1(a1115) | c0_1(a1115) | (~c2_1(a1115)))),
% 1.82/1.52 inference(quant_inst,[status(thm)],[])).
% 1.82/1.52 tff(3773,plain,
% 1.82/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1115) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1110)) | c0_1(a1115) | (~c2_1(a1115))),
% 1.82/1.52 inference(modus_ponens,[status(thm)],[3772, 3771])).
% 1.82/1.52 tff(3774,plain,
% 1.82/1.52 (~c0_1(a1110)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3773, 113, 769, 768, 739, 3767, 2586, 3766, 3765, 1155, 2583])).
% 1.82/1.52 tff(3775,plain,
% 1.82/1.52 (c3_1(a1110)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[2025, 3764])).
% 1.82/1.52 tff(3776,plain,
% 1.82/1.52 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1118) | c3_1(a1118) | c2_1(a1110) | (~ndr1_0) | c0_1(a1110) | (~c3_1(a1110)) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1118) | c3_1(a1118) | c2_1(a1110) | (~ndr1_0) | c0_1(a1110) | (~c3_1(a1110)) | (~c1_1(a1118)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3777,plain,
% 1.82/1.52 ((hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c0_1(a1110) | (~c3_1(a1110))) <=> (hskp29 | c2_1(a1118) | c3_1(a1118) | c2_1(a1110) | (~ndr1_0) | c0_1(a1110) | (~c3_1(a1110)) | (~c1_1(a1118)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3778,plain,
% 1.82/1.52 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c0_1(a1110) | (~c3_1(a1110)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | c2_1(a1118) | c3_1(a1118) | c2_1(a1110) | (~ndr1_0) | c0_1(a1110) | (~c3_1(a1110)) | (~c1_1(a1118))))),
% 1.82/1.52 inference(monotonicity,[status(thm)],[3777])).
% 1.82/1.52 tff(3779,plain,
% 1.82/1.52 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c0_1(a1110) | (~c3_1(a1110)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1118) | c3_1(a1118) | c2_1(a1110) | (~ndr1_0) | c0_1(a1110) | (~c3_1(a1110)) | (~c1_1(a1118)))),
% 1.82/1.52 inference(transitivity,[status(thm)],[3778, 3776])).
% 1.82/1.52 tff(3780,plain,
% 1.82/1.52 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c0_1(a1110) | (~c3_1(a1110)))),
% 1.82/1.52 inference(quant_inst,[status(thm)],[])).
% 1.82/1.52 tff(3781,plain,
% 1.82/1.52 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp29 | c2_1(a1118) | c3_1(a1118) | c2_1(a1110) | (~ndr1_0) | c0_1(a1110) | (~c3_1(a1110)) | (~c1_1(a1118))),
% 1.82/1.52 inference(modus_ponens,[status(thm)],[3780, 3779])).
% 1.82/1.52 tff(3782,plain,
% 1.82/1.52 ($false),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3781, 113, 770, 228, 3775, 230, 226, 3765, 67, 3774])).
% 1.82/1.52 tff(3783,plain,((~hskp10) | hskp29 | (~c1_1(a1118)) | c2_1(a1118) | c3_1(a1118) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1115)) | c1_1(a1115) | c0_1(a1115)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.52 tff(3784,plain,
% 1.82/1.52 (~hskp10),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3783, 770, 3677, 3676, 3675, 3665, 3666, 3668, 3688, 3685, 3687])).
% 1.82/1.52 tff(3785,plain,
% 1.82/1.52 (hskp10 | c0_1(a1118)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[1999, 113, 3665, 3666, 3668, 3677, 3676, 1993])).
% 1.82/1.52 tff(3786,plain,
% 1.82/1.52 (c0_1(a1118)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3785, 3784])).
% 1.82/1.52 tff(3787,plain,
% 1.82/1.52 (c0_1(a1136)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[2037, 3786, 3666, 3668, 3677, 3675, 3665])).
% 1.82/1.52 tff(3788,plain,
% 1.82/1.52 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3789,plain,
% 1.82/1.52 ((hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147))) <=> (hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(rewrite,[status(thm)],[])).
% 1.82/1.52 tff(3790,plain,
% 1.82/1.52 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1147))))),
% 1.82/1.52 inference(monotonicity,[status(thm)],[3789])).
% 1.82/1.52 tff(3791,plain,
% 1.82/1.52 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(transitivity,[status(thm)],[3790, 3788])).
% 1.82/1.52 tff(3792,plain,
% 1.82/1.52 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1147) | (~c3_1(a1147)) | (~c1_1(a1147)))),
% 1.82/1.52 inference(quant_inst,[status(thm)],[])).
% 1.82/1.52 tff(3793,plain,
% 1.82/1.52 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1147))),
% 1.82/1.52 inference(modus_ponens,[status(thm)],[3792, 3791])).
% 1.82/1.52 tff(3794,plain,
% 1.82/1.52 (hskp2 | (~c0_1(a1136)) | (~c1_1(a1147))),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3793, 113, 3666, 3668, 819, 3662, 278])).
% 1.82/1.52 tff(3795,plain,
% 1.82/1.52 (hskp2),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[3794, 3787, 3763])).
% 1.82/1.52 tff(3796,plain,
% 1.82/1.52 (~c3_1(a1100)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[291, 3795])).
% 1.82/1.52 tff(3797,plain,
% 1.82/1.52 (c2_1(a1100)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[302, 3795])).
% 1.82/1.52 tff(3798,plain,
% 1.82/1.52 (c0_1(a1100)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[313, 3795])).
% 1.82/1.52 tff(3799,plain,
% 1.82/1.52 (~c1_1(a1100)),
% 1.82/1.52 inference(unit_resolution,[status(thm)],[1289, 113, 1269, 3798, 3797, 3796, 1279])).
% 1.82/1.53 tff(3800,plain,
% 1.82/1.53 (hskp7 | c1_1(a1100)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3730, 3663, 113, 3798, 3797, 2574])).
% 1.82/1.53 tff(3801,plain,
% 1.82/1.53 (hskp7),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3800, 3799])).
% 1.82/1.53 tff(3802,plain,
% 1.82/1.53 (~c1_1(a1105)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[633, 3801])).
% 1.82/1.53 tff(3803,plain,
% 1.82/1.53 (c0_1(a1105)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[646, 3801])).
% 1.82/1.53 tff(3804,plain,
% 1.82/1.53 (c3_1(a1105)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[657, 3801])).
% 1.82/1.53 tff(3805,plain,
% 1.82/1.53 ($false),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[1763, 3804, 3803, 3663, 3677, 3676, 3666, 3675, 3668, 770, 3802, 3665])).
% 1.82/1.53 tff(3806,plain,(hskp29 | hskp5 | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.53 tff(3807,plain,
% 1.82/1.53 (hskp29),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3806, 1269, 819])).
% 1.82/1.53 tff(3808,plain,
% 1.82/1.53 (c3_1(a1116)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[201, 3807])).
% 1.82/1.53 tff(3809,plain,
% 1.82/1.53 (c2_1(a1116)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[212, 3807])).
% 1.82/1.53 tff(3810,plain,
% 1.82/1.53 (c0_1(a1116)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[223, 3807])).
% 1.82/1.53 tff(3811,plain,
% 1.82/1.53 (hskp2 | (~c1_1(a1147))),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3713, 113, 249, 248, 247, 819, 3662, 278])).
% 1.82/1.53 tff(3812,plain,
% 1.82/1.53 (~c1_1(a1147)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3811, 2806])).
% 1.82/1.53 tff(3813,plain,
% 1.82/1.53 (^[U: $i] : refl((hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.82/1.53 inference(bind,[status(th)],[])).
% 1.82/1.53 tff(3814,plain,
% 1.82/1.53 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.82/1.53 inference(quant_intro,[status(thm)],[3813])).
% 1.82/1.53 tff(3815,plain,
% 1.82/1.53 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3816,plain,
% 1.82/1.53 (^[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)) | 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)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp17) | hskp19) <=> ((hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp17) | hskp19) <=> (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.82/1.53 inference(bind,[status(th)],[])).
% 1.82/1.53 tff(3817,plain,
% 1.82/1.53 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp17) | hskp19) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.82/1.53 inference(quant_intro,[status(thm)],[3816])).
% 1.82/1.53 tff(3818,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp17) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.82/1.53 tff(3819,plain,
% 1.82/1.53 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3818, 3817])).
% 1.82/1.53 tff(3820,plain,
% 1.82/1.53 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3819, 3815])).
% 1.82/1.53 tff(3821,plain,(
% 1.82/1.53 ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.82/1.53 inference(skolemize,[status(sab)],[3820])).
% 1.82/1.53 tff(3822,plain,
% 1.82/1.53 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3821, 3814])).
% 1.82/1.53 tff(3823,plain,
% 1.82/1.53 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c2_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c2_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3824,plain,
% 1.82/1.53 ((hskp19 | hskp17 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147))) <=> (hskp19 | hskp17 | c2_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3825,plain,
% 1.82/1.53 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c2_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.82/1.53 inference(monotonicity,[status(thm)],[3824])).
% 1.82/1.53 tff(3826,plain,
% 1.82/1.53 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c2_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.82/1.53 inference(transitivity,[status(thm)],[3825, 3823])).
% 1.82/1.53 tff(3827,plain,
% 1.82/1.53 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.82/1.53 inference(quant_inst,[status(thm)],[])).
% 1.82/1.53 tff(3828,plain,
% 1.82/1.53 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c2_1(a1147) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147))),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3827, 3826])).
% 1.82/1.53 tff(3829,plain,
% 1.82/1.53 (hskp19 | hskp17 | c1_1(a1147) | (~c0_1(a1147))),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3828, 113, 819, 3822])).
% 1.82/1.53 tff(3830,plain,
% 1.82/1.53 (hskp17),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3829, 2942, 3756, 3812])).
% 1.82/1.53 tff(3831,plain,
% 1.82/1.53 (((~hskp17) | (~c2_1(a1124))) <=> ((~hskp17) | (~c2_1(a1124)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3832,plain,
% 1.82/1.53 (((~c2_1(a1124)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a1124)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3833,axiom,((~c2_1(a1124)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.82/1.53 tff(3834,plain,
% 1.82/1.53 ((~hskp17) | (~c2_1(a1124))),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3833, 3832])).
% 1.82/1.53 tff(3835,plain,
% 1.82/1.53 ((~hskp17) | (~c2_1(a1124))),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3834, 3831])).
% 1.82/1.53 tff(3836,plain,
% 1.82/1.53 (~c2_1(a1124)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3835, 3830])).
% 1.82/1.53 tff(3837,plain,
% 1.82/1.53 (((~hskp17) | (~c1_1(a1124))) <=> ((~hskp17) | (~c1_1(a1124)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3838,plain,
% 1.82/1.53 (((~c1_1(a1124)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1124)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3839,axiom,((~c1_1(a1124)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 1.82/1.53 tff(3840,plain,
% 1.82/1.53 ((~hskp17) | (~c1_1(a1124))),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3839, 3838])).
% 1.82/1.53 tff(3841,plain,
% 1.82/1.53 ((~hskp17) | (~c1_1(a1124))),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3840, 3837])).
% 1.82/1.53 tff(3842,plain,
% 1.82/1.53 (~c1_1(a1124)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3841, 3830])).
% 1.82/1.53 tff(3843,plain,
% 1.82/1.53 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3844,plain,
% 1.82/1.53 ((hskp22 | hskp0 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c3_1(a1147))) <=> (hskp22 | hskp0 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3845,plain,
% 1.82/1.53 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c3_1(a1147)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147)))),
% 1.82/1.53 inference(monotonicity,[status(thm)],[3844])).
% 1.82/1.53 tff(3846,plain,
% 1.82/1.53 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c3_1(a1147)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147))),
% 1.82/1.53 inference(transitivity,[status(thm)],[3845, 3843])).
% 1.82/1.53 tff(3847,plain,
% 1.82/1.53 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1147) | c1_1(a1147) | (~c3_1(a1147)))),
% 1.82/1.53 inference(quant_inst,[status(thm)],[])).
% 1.82/1.53 tff(3848,plain,
% 1.82/1.53 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c2_1(a1147) | (~c3_1(a1147)) | (~ndr1_0) | c1_1(a1147)),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3847, 3846])).
% 1.82/1.53 tff(3849,plain,
% 1.82/1.53 (hskp22 | (~c3_1(a1147)) | c1_1(a1147)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3848, 113, 2532, 819, 2144])).
% 1.82/1.53 tff(3850,plain,
% 1.82/1.53 (hskp22),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3849, 3812, 3662])).
% 1.82/1.53 tff(3851,plain,
% 1.82/1.53 (~c1_1(a1145)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2157, 3850])).
% 1.82/1.53 tff(3852,plain,
% 1.82/1.53 (((~hskp17) | c0_1(a1124)) <=> ((~hskp17) | c0_1(a1124))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3853,axiom,((~hskp17) | c0_1(a1124)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.82/1.53 tff(3854,plain,
% 1.82/1.53 ((~hskp17) | c0_1(a1124)),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3853, 3852])).
% 1.82/1.53 tff(3855,plain,
% 1.82/1.53 ((~hskp17) | c0_1(a1124)),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3854, 3852])).
% 1.82/1.53 tff(3856,plain,
% 1.82/1.53 ((~hskp17) | c0_1(a1124)),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3855, 3852])).
% 1.82/1.53 tff(3857,plain,
% 1.82/1.53 ((~hskp17) | c0_1(a1124)),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3856, 3852])).
% 1.82/1.53 tff(3858,plain,
% 1.82/1.53 ((~hskp17) | c0_1(a1124)),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3857, 3852])).
% 1.82/1.53 tff(3859,plain,
% 1.82/1.53 ((~hskp17) | c0_1(a1124)),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3858, 3852])).
% 1.82/1.53 tff(3860,plain,
% 1.82/1.53 ((~hskp17) | c0_1(a1124)),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3859, 3852])).
% 1.82/1.53 tff(3861,plain,
% 1.82/1.53 ((~hskp17) | c0_1(a1124)),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3860, 3852])).
% 1.82/1.53 tff(3862,plain,
% 1.82/1.53 (c0_1(a1124)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3861, 3830])).
% 1.82/1.53 tff(3863,plain,
% 1.82/1.53 (c2_1(a1145)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2168, 3850])).
% 1.82/1.53 tff(3864,plain,
% 1.82/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1124) | c2_1(a1124) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1124)) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1124) | c2_1(a1124) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1124)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3865,plain,
% 1.82/1.53 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1124) | c1_1(a1124) | (~c0_1(a1124)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145))) <=> (c1_1(a1145) | c1_1(a1124) | c2_1(a1124) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1124)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3866,plain,
% 1.82/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1124) | c1_1(a1124) | (~c0_1(a1124)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1124) | c2_1(a1124) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1124)) | c0_1(a1145) | (~c2_1(a1145))))),
% 1.82/1.53 inference(monotonicity,[status(thm)],[3865])).
% 1.82/1.53 tff(3867,plain,
% 1.82/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1124) | c1_1(a1124) | (~c0_1(a1124)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1124) | c2_1(a1124) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1124)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.82/1.53 inference(transitivity,[status(thm)],[3866, 3864])).
% 1.82/1.53 tff(3868,plain,
% 1.82/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c2_1(a1124) | c1_1(a1124) | (~c0_1(a1124)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.82/1.53 inference(quant_inst,[status(thm)],[])).
% 1.82/1.53 tff(3869,plain,
% 1.82/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1124) | c2_1(a1124) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c0_1(a1124)) | c0_1(a1145) | (~c2_1(a1145))),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3868, 3867])).
% 1.82/1.53 tff(3870,plain,
% 1.82/1.53 (c0_1(a1145)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3869, 113, 3665, 3666, 3668, 3863, 3862, 3851, 3842, 3836, 1155])).
% 1.82/1.53 tff(3871,plain,
% 1.82/1.53 (c3_1(a1145)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2200, 3850])).
% 1.82/1.53 tff(3872,plain,
% 1.82/1.53 ($false),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2385, 113, 2806, 3863, 3871, 3851, 1065, 3870])).
% 1.82/1.53 tff(3873,plain,(hskp2 | c2_1(a1147) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.53 tff(3874,plain,
% 1.82/1.53 (hskp2),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3873, 3810, 819, 3809, 3808])).
% 1.82/1.53 tff(3875,plain,
% 1.82/1.53 (~c3_1(a1100)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[291, 3874])).
% 1.82/1.53 tff(3876,plain,
% 1.82/1.53 (c2_1(a1100)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[302, 3874])).
% 1.82/1.53 tff(3877,plain,
% 1.82/1.53 (c0_1(a1100)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[313, 3874])).
% 1.82/1.53 tff(3878,plain,
% 1.82/1.53 (~c1_1(a1100)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[1289, 113, 1269, 3877, 3876, 3875, 1279])).
% 1.82/1.53 tff(3879,plain,
% 1.82/1.53 (hskp7 | c1_1(a1100)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3730, 3663, 113, 3877, 3876, 2574])).
% 1.82/1.53 tff(3880,plain,
% 1.82/1.53 (hskp7),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3879, 3878])).
% 1.82/1.53 tff(3881,plain,
% 1.82/1.53 (~c1_1(a1105)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[633, 3880])).
% 1.82/1.53 tff(3882,plain,
% 1.82/1.53 (c0_1(a1105)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[646, 3880])).
% 1.82/1.53 tff(3883,plain,
% 1.82/1.53 (c3_1(a1105)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[657, 3880])).
% 1.82/1.53 tff(3884,plain,
% 1.82/1.53 (~hskp8),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2651, 3883, 3809, 3808, 3810, 3882, 3881])).
% 1.82/1.53 tff(3885,plain,
% 1.82/1.53 (c0_1(a1118)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2034, 3884, 3677, 3665, 3809, 3676, 3675, 3808, 3666, 3668, 3810])).
% 1.82/1.53 tff(3886,plain,
% 1.82/1.53 (c0_1(a1136)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2037, 3885, 3666, 3668, 3677, 3675, 3665])).
% 1.82/1.53 tff(3887,plain,
% 1.82/1.53 ($false),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2703, 3663, 113, 3665, 3666, 3877, 3875, 1633, 3886, 3878])).
% 1.82/1.53 tff(3888,plain,(hskp5 | c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.53 tff(3889,plain,
% 1.82/1.53 (hskp5),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3888, 819])).
% 1.82/1.53 tff(3890,plain,
% 1.82/1.53 (~c2_1(a1103)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[126, 3889])).
% 1.82/1.53 tff(3891,plain,
% 1.82/1.53 (~c0_1(a1103)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[132, 3889])).
% 1.82/1.53 tff(3892,plain,
% 1.82/1.53 (~c0_1(a1118)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2079, 3889, 3677, 3675, 3676])).
% 1.82/1.53 tff(3893,plain,
% 1.82/1.53 (hskp10),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3785, 3892])).
% 1.82/1.53 tff(3894,plain,
% 1.82/1.53 (~c2_1(a1110)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2006, 3893])).
% 1.82/1.53 tff(3895,plain,
% 1.82/1.53 (~c1_1(a1110)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2012, 3893])).
% 1.82/1.53 tff(3896,plain,
% 1.82/1.53 (c3_1(a1103)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[153, 3889])).
% 1.82/1.53 tff(3897,plain,
% 1.82/1.53 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1110) | c2_1(a1110) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c0_1(a1110))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1110) | c2_1(a1110) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c0_1(a1110))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3898,plain,
% 1.82/1.53 ((hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1110) | c1_1(a1110) | c0_1(a1110)) <=> (hskp0 | c1_1(a1110) | c2_1(a1110) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c0_1(a1110))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3899,plain,
% 1.82/1.53 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1110) | c1_1(a1110) | c0_1(a1110))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1110) | c2_1(a1110) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c0_1(a1110)))),
% 1.82/1.53 inference(monotonicity,[status(thm)],[3898])).
% 1.82/1.53 tff(3900,plain,
% 1.82/1.53 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1110) | c1_1(a1110) | c0_1(a1110))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1110) | c2_1(a1110) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c0_1(a1110))),
% 1.82/1.53 inference(transitivity,[status(thm)],[3899, 3897])).
% 1.82/1.53 tff(3901,plain,
% 1.82/1.53 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1103) | c0_1(a1103) | (~c3_1(a1103)) | c2_1(a1110) | c1_1(a1110) | c0_1(a1110))),
% 1.82/1.53 inference(quant_inst,[status(thm)],[])).
% 1.82/1.53 tff(3902,plain,
% 1.82/1.53 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1110) | c2_1(a1110) | c0_1(a1103) | c2_1(a1103) | (~ndr1_0) | (~c3_1(a1103)) | c0_1(a1110)),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3901, 3900])).
% 1.82/1.53 tff(3903,plain,
% 1.82/1.53 (c0_1(a1110)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3902, 113, 2532, 3896, 3895, 3894, 3891, 3890, 2126])).
% 1.82/1.53 tff(3904,plain,
% 1.82/1.53 (c3_1(a1110)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2025, 3893])).
% 1.82/1.53 tff(3905,plain,
% 1.82/1.53 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3906,plain,
% 1.82/1.53 ((hskp22 | hskp0 | (~ndr1_0) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110))) <=> (hskp22 | hskp0 | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3907,plain,
% 1.82/1.53 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110))))),
% 1.82/1.53 inference(monotonicity,[status(thm)],[3906])).
% 1.82/1.53 tff(3908,plain,
% 1.82/1.53 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)))),
% 1.82/1.53 inference(transitivity,[status(thm)],[3907, 3905])).
% 1.82/1.53 tff(3909,plain,
% 1.82/1.53 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110)))),
% 1.82/1.53 inference(quant_inst,[status(thm)],[])).
% 1.82/1.53 tff(3910,plain,
% 1.82/1.53 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp22 | hskp0 | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110))),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3909, 3908])).
% 1.82/1.53 tff(3911,plain,
% 1.82/1.53 (hskp22),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3910, 113, 2532, 3904, 3895, 3894, 2144])).
% 1.82/1.53 tff(3912,plain,
% 1.82/1.53 (~c1_1(a1145)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2157, 3911])).
% 1.82/1.53 tff(3913,plain,
% 1.82/1.53 (c2_1(a1145)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[2168, 3911])).
% 1.82/1.53 tff(3914,plain,
% 1.82/1.53 (hskp29),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[190, 113, 3677, 3896, 3676, 3675, 3891, 3890, 67])).
% 1.82/1.53 tff(3915,plain,
% 1.82/1.53 (c3_1(a1116)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[201, 3914])).
% 1.82/1.53 tff(3916,plain,
% 1.82/1.53 (c2_1(a1116)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[212, 3914])).
% 1.82/1.53 tff(3917,plain,
% 1.82/1.53 (c0_1(a1116)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[223, 3914])).
% 1.82/1.53 tff(3918,plain,
% 1.82/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1110)) | (~c3_1(a1110)) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1110)) | (~c3_1(a1110)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3919,plain,
% 1.82/1.53 (((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1110) | (~c3_1(a1110)) | (~c0_1(a1110)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145))) <=> (c1_1(a1145) | c1_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1110)) | (~c3_1(a1110)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3920,plain,
% 1.82/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1110) | (~c3_1(a1110)) | (~c0_1(a1110)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1145) | c1_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1110)) | (~c3_1(a1110)) | c0_1(a1145) | (~c2_1(a1145))))),
% 1.82/1.53 inference(monotonicity,[status(thm)],[3919])).
% 1.82/1.53 tff(3921,plain,
% 1.82/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1110) | (~c3_1(a1110)) | (~c0_1(a1110)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1110)) | (~c3_1(a1110)) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.82/1.53 inference(transitivity,[status(thm)],[3920, 3918])).
% 1.82/1.53 tff(3922,plain,
% 1.82/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c1_1(a1110) | (~c3_1(a1110)) | (~c0_1(a1110)) | c1_1(a1145) | c0_1(a1145) | (~c2_1(a1145)))),
% 1.82/1.53 inference(quant_inst,[status(thm)],[])).
% 1.82/1.53 tff(3923,plain,
% 1.82/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1145) | c1_1(a1110) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | (~c0_1(a1110)) | (~c3_1(a1110)) | c0_1(a1145) | (~c2_1(a1145))),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3922, 3921])).
% 1.82/1.53 tff(3924,plain,
% 1.82/1.53 (c0_1(a1145)),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3923, 113, 3917, 3916, 3915, 3913, 3904, 3912, 3895, 702, 3903])).
% 1.82/1.53 tff(3925,plain,
% 1.82/1.53 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a1147) | (~c3_1(a1147)) | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1147) | (~c3_1(a1147)) | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1147)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3926,plain,
% 1.82/1.53 ((hskp7 | (~ndr1_0) | c2_1(a1147) | (~c3_1(a1147)) | (~c0_1(a1147)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145))) <=> (hskp7 | c2_1(a1147) | (~c3_1(a1147)) | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1147)))),
% 1.82/1.53 inference(rewrite,[status(thm)],[])).
% 1.82/1.53 tff(3927,plain,
% 1.82/1.53 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1147) | (~c3_1(a1147)) | (~c0_1(a1147)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a1147) | (~c3_1(a1147)) | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1147))))),
% 1.82/1.53 inference(monotonicity,[status(thm)],[3926])).
% 1.82/1.53 tff(3928,plain,
% 1.82/1.53 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1147) | (~c3_1(a1147)) | (~c0_1(a1147)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1147) | (~c3_1(a1147)) | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1147)))),
% 1.82/1.53 inference(transitivity,[status(thm)],[3927, 3925])).
% 1.82/1.53 tff(3929,plain,
% 1.82/1.53 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1147) | (~c3_1(a1147)) | (~c0_1(a1147)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))),
% 1.82/1.53 inference(quant_inst,[status(thm)],[])).
% 1.82/1.53 tff(3930,plain,
% 1.82/1.53 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a1147) | (~c3_1(a1147)) | c1_1(a1145) | (~ndr1_0) | (~c0_1(a1145)) | (~c2_1(a1145)) | (~c0_1(a1147))),
% 1.82/1.53 inference(modus_ponens,[status(thm)],[3929, 3928])).
% 1.82/1.53 tff(3931,plain,
% 1.82/1.53 (hskp7),
% 1.82/1.53 inference(unit_resolution,[status(thm)],[3930, 113, 3756, 3913, 819, 3662, 3912, 2220, 3924])).
% 1.82/1.53 tff(3932,plain,
% 1.82/1.53 (~c1_1(a1105)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[633, 3931])).
% 1.85/1.53 tff(3933,plain,
% 1.85/1.53 (hskp8),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[2034, 3916, 3677, 3665, 3892, 3676, 3675, 3915, 3666, 3668, 3917])).
% 1.85/1.53 tff(3934,plain,
% 1.85/1.53 (c0_1(a1105)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[646, 3931])).
% 1.85/1.53 tff(3935,plain,
% 1.85/1.53 (c3_1(a1105)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[657, 3931])).
% 1.85/1.53 tff(3936,plain,
% 1.85/1.53 ($false),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[2651, 3935, 3934, 3916, 3915, 3917, 3933, 3932])).
% 1.85/1.53 tff(3937,plain,(c2_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.53 tff(3938,plain,
% 1.85/1.53 (~hskp23),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[803, 3937])).
% 1.85/1.53 tff(3939,plain,
% 1.85/1.53 (hskp30),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[2180, 3938, 2532])).
% 1.85/1.53 tff(3940,plain,
% 1.85/1.53 (c1_1(a1136)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[690, 3939])).
% 1.85/1.53 tff(3941,plain,
% 1.85/1.53 (hskp14),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[749, 3938])).
% 1.85/1.53 tff(3942,plain,
% 1.85/1.53 (~c3_1(a1118)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[166, 3941])).
% 1.85/1.53 tff(3943,plain,
% 1.85/1.53 (c1_1(a1118)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[183, 3941])).
% 1.85/1.53 tff(3944,plain,
% 1.85/1.53 (c3_1(a1136)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[726, 3939])).
% 1.85/1.53 tff(3945,plain,
% 1.85/1.53 (c2_1(a1136)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[737, 3939])).
% 1.85/1.53 tff(3946,plain,
% 1.85/1.53 (~c2_1(a1118)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[172, 3941])).
% 1.85/1.53 tff(3947,plain,
% 1.85/1.53 (~c0_1(a1118)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[2079, 2074, 3943, 3942, 3946])).
% 1.85/1.53 tff(3948,plain,
% 1.85/1.53 (hskp10 | c0_1(a1118)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[1999, 113, 3940, 3945, 3944, 3943, 3946, 1993])).
% 1.85/1.53 tff(3949,plain,
% 1.85/1.53 (hskp10),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[3948, 3947])).
% 1.85/1.53 tff(3950,plain,
% 1.85/1.53 (~c2_1(a1110)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[2006, 3949])).
% 1.85/1.53 tff(3951,plain,
% 1.85/1.53 (~c1_1(a1110)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[2012, 3949])).
% 1.85/1.53 tff(3952,plain,
% 1.85/1.53 (c0_1(a1110)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[3902, 113, 2532, 2075, 3951, 3950, 2076, 2077, 2126])).
% 1.85/1.53 tff(3953,plain,
% 1.85/1.53 (c3_1(a1110)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[2025, 3949])).
% 1.85/1.53 tff(3954,plain,
% 1.85/1.53 (hskp22),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[3910, 113, 2532, 3953, 3951, 3950, 2144])).
% 1.85/1.53 tff(3955,plain,
% 1.85/1.53 (~c1_1(a1145)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[2157, 3954])).
% 1.85/1.53 tff(3956,plain,
% 1.85/1.53 (c2_1(a1145)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[2168, 3954])).
% 1.85/1.53 tff(3957,plain,
% 1.85/1.53 (hskp29),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[190, 113, 3943, 2075, 3946, 3942, 2076, 2077, 67])).
% 1.85/1.53 tff(3958,plain,
% 1.85/1.53 (c3_1(a1116)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[201, 3957])).
% 1.85/1.53 tff(3959,plain,
% 1.85/1.53 (c2_1(a1116)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[212, 3957])).
% 1.85/1.53 tff(3960,plain,
% 1.85/1.53 (c0_1(a1116)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[223, 3957])).
% 1.85/1.53 tff(3961,plain,
% 1.85/1.53 (c0_1(a1145)),
% 1.85/1.53 inference(unit_resolution,[status(thm)],[3923, 113, 3960, 3959, 3958, 3956, 3953, 3955, 3951, 702, 3952])).
% 1.85/1.53 tff(3962,plain,
% 1.85/1.54 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)) | (~c1_1(a1118)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)) | (~c1_1(a1118)))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(3963,plain,
% 1.85/1.54 ((hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110))) <=> (hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)) | (~c1_1(a1118)))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(3964,plain,
% 1.85/1.54 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)) | (~c1_1(a1118))))),
% 1.85/1.54 inference(monotonicity,[status(thm)],[3963])).
% 1.85/1.54 tff(3965,plain,
% 1.85/1.54 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)) | (~c1_1(a1118)))),
% 1.85/1.54 inference(transitivity,[status(thm)],[3964, 3962])).
% 1.85/1.54 tff(3966,plain,
% 1.85/1.54 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1118) | c2_1(a1118) | (~c1_1(a1118)) | c2_1(a1110) | c1_1(a1110) | (~c3_1(a1110)))),
% 1.85/1.54 inference(quant_inst,[status(thm)],[])).
% 1.85/1.54 tff(3967,plain,
% 1.85/1.54 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1118) | c3_1(a1118) | c1_1(a1110) | c2_1(a1110) | (~ndr1_0) | (~c3_1(a1110)) | (~c1_1(a1118))),
% 1.85/1.54 inference(modus_ponens,[status(thm)],[3966, 3965])).
% 1.85/1.54 tff(3968,plain,
% 1.85/1.54 (hskp11),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[3967, 113, 3943, 3953, 3946, 3942, 3951, 3950, 1857])).
% 1.85/1.54 tff(3969,plain,
% 1.85/1.54 (~c2_1(a1113)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1869, 3968])).
% 1.85/1.54 tff(3970,plain,
% 1.85/1.54 (c3_1(a1113)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1926, 3968])).
% 1.85/1.54 tff(3971,plain,
% 1.85/1.54 (c0_1(a1113)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1880, 3968])).
% 1.85/1.54 tff(3972,plain,
% 1.85/1.54 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a1145) | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c3_1(a1113)) | (~c0_1(a1145)) | (~c2_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1145) | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c3_1(a1113)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(3973,plain,
% 1.85/1.54 ((hskp7 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145))) <=> (hskp7 | c1_1(a1145) | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c3_1(a1113)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(3974,plain,
% 1.85/1.54 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a1145) | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c3_1(a1113)) | (~c0_1(a1145)) | (~c2_1(a1145))))),
% 1.85/1.54 inference(monotonicity,[status(thm)],[3973])).
% 1.85/1.54 tff(3975,plain,
% 1.85/1.54 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1145) | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c3_1(a1113)) | (~c0_1(a1145)) | (~c2_1(a1145)))),
% 1.85/1.54 inference(transitivity,[status(thm)],[3974, 3972])).
% 1.85/1.54 tff(3976,plain,
% 1.85/1.54 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1113) | (~c3_1(a1113)) | (~c0_1(a1113)) | c1_1(a1145) | (~c2_1(a1145)) | (~c0_1(a1145)))),
% 1.85/1.54 inference(quant_inst,[status(thm)],[])).
% 1.85/1.54 tff(3977,plain,
% 1.85/1.54 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a1145) | c2_1(a1113) | (~ndr1_0) | (~c0_1(a1113)) | (~c3_1(a1113)) | (~c0_1(a1145)) | (~c2_1(a1145))),
% 1.85/1.54 inference(modus_ponens,[status(thm)],[3976, 3975])).
% 1.85/1.54 tff(3978,plain,
% 1.85/1.54 (hskp7),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[3977, 113, 3956, 3971, 3970, 3955, 3969, 2220, 3961])).
% 1.85/1.54 tff(3979,plain,
% 1.85/1.54 (~c1_1(a1105)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[633, 3978])).
% 1.85/1.54 tff(3980,plain,
% 1.85/1.54 (hskp8),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[2034, 3959, 3943, 3940, 3947, 3946, 3942, 3958, 3945, 3944, 3960])).
% 1.85/1.54 tff(3981,plain,
% 1.85/1.54 (c0_1(a1105)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[646, 3978])).
% 1.85/1.54 tff(3982,plain,
% 1.85/1.54 (c3_1(a1105)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[657, 3978])).
% 1.85/1.54 tff(3983,plain,
% 1.85/1.54 ($false),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[2651, 3982, 3981, 3959, 3958, 3960, 3980, 3979])).
% 1.85/1.54 tff(3984,plain,(~hskp5), inference(lemma,lemma(discharge,[]))).
% 1.85/1.54 tff(3985,plain,
% 1.85/1.54 (~hskp9),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1653, 770, 3938, 3940, 3945])).
% 1.85/1.54 tff(3986,plain,
% 1.85/1.54 (hskp19 | hskp9),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1670, 113, 3940, 3945, 3944, 1664])).
% 1.85/1.54 tff(3987,plain,
% 1.85/1.54 (hskp19),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[3986, 3985])).
% 1.85/1.54 tff(3988,plain,
% 1.85/1.54 (~c2_1(a1127)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[900, 3987])).
% 1.85/1.54 tff(3989,plain,
% 1.85/1.54 (c3_1(a1127)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[912, 3987])).
% 1.85/1.54 tff(3990,plain,
% 1.85/1.54 (c1_1(a1127)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[923, 3987])).
% 1.85/1.54 tff(3991,plain,
% 1.85/1.54 (c0_1(a1127)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1681, 113, 770, 3989, 3943, 3988, 3946, 3942, 67])).
% 1.85/1.54 tff(3992,plain,
% 1.85/1.54 (hskp28 | (~c0_1(a1127))),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1688, 113, 3990, 3989, 3988, 567])).
% 1.85/1.54 tff(3993,plain,
% 1.85/1.54 (hskp28),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[3992, 3991])).
% 1.85/1.54 tff(3994,plain,
% 1.85/1.54 (c2_1(a1111)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[596, 3993])).
% 1.85/1.54 tff(3995,plain,
% 1.85/1.54 (c0_1(a1111)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[618, 3993])).
% 1.85/1.54 tff(3996,plain,
% 1.85/1.54 (hskp13),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1728, 3995, 3985, 3994, 3990, 3989, 3988])).
% 1.85/1.54 tff(3997,plain,
% 1.85/1.54 (c2_1(a1115)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1240, 3996])).
% 1.85/1.54 tff(3998,plain,
% 1.85/1.54 (~c1_1(a1115)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1229, 3996])).
% 1.85/1.54 tff(3999,plain,
% 1.85/1.54 (~c3_1(a1115)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1354, 3996])).
% 1.85/1.54 tff(4000,plain,
% 1.85/1.54 (c1_1(a1111)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[607, 3993])).
% 1.85/1.54 tff(4001,plain,
% 1.85/1.54 (~c0_1(a1115)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1738, 3938, 113, 3995, 4000, 3994, 3998, 3999, 1633])).
% 1.85/1.54 tff(4002,plain,
% 1.85/1.54 (~hskp10),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[3783, 4001, 3943, 3946, 3942, 3940, 3945, 3944, 770, 3998, 3997])).
% 1.85/1.54 tff(4003,plain,
% 1.85/1.54 (c0_1(a1118)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[3948, 4002])).
% 1.85/1.54 tff(4004,plain,
% 1.85/1.54 (c0_1(a1136)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[2037, 4003, 3945, 3944, 3943, 3942, 3940])).
% 1.85/1.54 tff(4005,plain,
% 1.85/1.54 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(4006,plain,
% 1.85/1.54 ((hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127))) <=> (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(4007,plain,
% 1.85/1.54 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127))))),
% 1.85/1.54 inference(monotonicity,[status(thm)],[4006])).
% 1.85/1.54 tff(4008,plain,
% 1.85/1.54 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127)))),
% 1.85/1.54 inference(transitivity,[status(thm)],[4007, 4005])).
% 1.85/1.54 tff(4009,plain,
% 1.85/1.54 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c2_1(a1127) | (~c3_1(a1127)) | (~c1_1(a1127)))),
% 1.85/1.54 inference(quant_inst,[status(thm)],[])).
% 1.85/1.54 tff(4010,plain,
% 1.85/1.54 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a1127) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1127)) | (~c3_1(a1127))),
% 1.85/1.54 inference(modus_ponens,[status(thm)],[4009, 4008])).
% 1.85/1.54 tff(4011,plain,
% 1.85/1.54 (hskp2 | (~c0_1(a1136))),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[4010, 113, 3945, 3944, 3990, 3989, 3988, 278])).
% 1.85/1.54 tff(4012,plain,
% 1.85/1.54 (hskp2),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[4011, 4004])).
% 1.85/1.54 tff(4013,plain,
% 1.85/1.54 (~c3_1(a1100)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[291, 4012])).
% 1.85/1.54 tff(4014,plain,
% 1.85/1.54 (c2_1(a1100)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[302, 4012])).
% 1.85/1.54 tff(4015,plain,
% 1.85/1.54 (c0_1(a1100)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[313, 4012])).
% 1.85/1.54 tff(4016,plain,
% 1.85/1.54 (~c1_1(a1100)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1289, 113, 1269, 4015, 4014, 4013, 1279])).
% 1.85/1.54 tff(4017,plain,
% 1.85/1.54 (hskp7 | c1_1(a1100)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[3730, 3938, 113, 4015, 4014, 2574])).
% 1.85/1.54 tff(4018,plain,
% 1.85/1.54 (hskp7),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[4017, 4016])).
% 1.85/1.54 tff(4019,plain,
% 1.85/1.54 (~c1_1(a1105)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[633, 4018])).
% 1.85/1.54 tff(4020,plain,
% 1.85/1.54 (c0_1(a1105)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[646, 4018])).
% 1.85/1.54 tff(4021,plain,
% 1.85/1.54 (c3_1(a1105)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[657, 4018])).
% 1.85/1.54 tff(4022,plain,
% 1.85/1.54 ($false),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1763, 4021, 4020, 3938, 3943, 3946, 3945, 3942, 3944, 770, 4019, 3940])).
% 1.85/1.54 tff(4023,plain,(hskp29 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.85/1.54 tff(4024,plain,
% 1.85/1.54 (hskp29),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[4023, 3984])).
% 1.85/1.54 tff(4025,plain,
% 1.85/1.54 (c0_1(a1116)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[223, 4024])).
% 1.85/1.54 tff(4026,plain,
% 1.85/1.54 (c3_1(a1116)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[201, 4024])).
% 1.85/1.54 tff(4027,plain,
% 1.85/1.54 (c2_1(a1116)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[212, 4024])).
% 1.85/1.54 tff(4028,plain,
% 1.85/1.54 (hskp29),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[4023, 1269])).
% 1.85/1.54 tff(4029,plain,
% 1.85/1.54 (c3_1(a1116)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[201, 4028])).
% 1.85/1.54 tff(4030,plain,
% 1.85/1.54 (c2_1(a1116)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[212, 4028])).
% 1.85/1.54 tff(4031,plain,
% 1.85/1.54 (c0_1(a1116)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[223, 4028])).
% 1.85/1.54 tff(4032,plain,
% 1.85/1.54 (hskp9),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[3986, 2942])).
% 1.85/1.54 tff(4033,plain,
% 1.85/1.54 (~c3_1(a1108)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[497, 4032])).
% 1.85/1.54 tff(4034,plain,
% 1.85/1.54 (~c1_1(a1108)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[503, 4032])).
% 1.85/1.54 tff(4035,plain,
% 1.85/1.54 (c0_1(a1108)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[514, 4032])).
% 1.85/1.54 tff(4036,plain,
% 1.85/1.54 (~c0_1(a1136)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1644, 3938, 113, 3940, 3945, 4035, 4034, 4033, 1633])).
% 1.85/1.54 tff(4037,plain,
% 1.85/1.54 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | c0_1(a1147) | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1147) | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(4038,plain,
% 1.85/1.54 ((hskp16 | hskp2 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c2_1(a1147))) <=> (hskp16 | hskp2 | c0_1(a1147) | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(4039,plain,
% 1.85/1.54 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c2_1(a1147)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | c0_1(a1147) | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0)))),
% 1.85/1.54 inference(monotonicity,[status(thm)],[4038])).
% 1.85/1.54 tff(4040,plain,
% 1.85/1.54 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c2_1(a1147)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1147) | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0))),
% 1.85/1.54 inference(transitivity,[status(thm)],[4039, 4037])).
% 1.85/1.54 tff(4041,plain,
% 1.85/1.54 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c3_1(a1147) | c0_1(a1147) | (~c2_1(a1147)))),
% 1.85/1.54 inference(quant_inst,[status(thm)],[])).
% 1.85/1.54 tff(4042,plain,
% 1.85/1.54 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp16 | hskp2 | c0_1(a1147) | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0)),
% 1.85/1.54 inference(modus_ponens,[status(thm)],[4041, 4040])).
% 1.85/1.54 tff(4043,plain,
% 1.85/1.54 (hskp16 | hskp2 | c0_1(a1147) | c3_1(a1147)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[4042, 113, 3937, 2816])).
% 1.85/1.54 tff(4044,plain,
% 1.85/1.54 (hskp16),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[4043, 2806, 2533, 771])).
% 1.85/1.54 tff(4045,plain,
% 1.85/1.54 (~c0_1(a1121)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1939, 4044])).
% 1.85/1.54 tff(4046,plain,
% 1.85/1.54 (c3_1(a1121)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1952, 4044])).
% 1.85/1.54 tff(4047,plain,
% 1.85/1.54 (c1_1(a1121)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1963, 4044])).
% 1.85/1.54 tff(4048,plain,
% 1.85/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1121) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1121) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(4049,plain,
% 1.85/1.54 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121))) <=> (c0_1(a1121) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(4050,plain,
% 1.85/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1121) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1121)) | (~c3_1(a1121))))),
% 1.85/1.54 inference(monotonicity,[status(thm)],[4049])).
% 1.85/1.54 tff(4051,plain,
% 1.85/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1121) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.85/1.54 inference(transitivity,[status(thm)],[4050, 4048])).
% 1.85/1.54 tff(4052,plain,
% 1.85/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1121) | (~c1_1(a1121)) | (~c3_1(a1121)))),
% 1.85/1.54 inference(quant_inst,[status(thm)],[])).
% 1.85/1.54 tff(4053,plain,
% 1.85/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1121) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1121)) | (~c3_1(a1121))),
% 1.85/1.54 inference(modus_ponens,[status(thm)],[4052, 4051])).
% 1.85/1.54 tff(4054,plain,
% 1.85/1.54 (~c0_1(a1118)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[4053, 113, 3940, 3945, 3944, 4047, 4046, 3943, 4045, 3942, 45])).
% 1.85/1.54 tff(4055,plain,
% 1.85/1.54 (^[U: $i] : refl((hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.85/1.54 inference(bind,[status(th)],[])).
% 1.85/1.54 tff(4056,plain,
% 1.85/1.54 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.85/1.54 inference(quant_intro,[status(thm)],[4055])).
% 1.85/1.54 tff(4057,plain,
% 1.85/1.54 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(4058,plain,
% 1.85/1.54 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp2) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp2))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp2) <=> (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp2) <=> (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.85/1.54 inference(bind,[status(th)],[])).
% 1.85/1.54 tff(4059,plain,
% 1.85/1.54 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp2) <=> ![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.85/1.54 inference(quant_intro,[status(thm)],[4058])).
% 1.85/1.54 tff(4060,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 1.85/1.54 tff(4061,plain,
% 1.85/1.54 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.85/1.54 inference(modus_ponens,[status(thm)],[4060, 4059])).
% 1.85/1.54 tff(4062,plain,
% 1.85/1.54 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.85/1.54 inference(modus_ponens,[status(thm)],[4061, 4057])).
% 1.85/1.54 tff(4063,plain,(
% 1.85/1.54 ![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.85/1.54 inference(skolemize,[status(sab)],[4062])).
% 1.85/1.54 tff(4064,plain,
% 1.85/1.54 (![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.85/1.54 inference(modus_ponens,[status(thm)],[4063, 4056])).
% 1.85/1.54 tff(4065,plain,
% 1.85/1.54 (((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp2 | c2_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))) <=> ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp28 | hskp2 | c2_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(4066,plain,
% 1.85/1.54 ((hskp28 | hskp2 | (~ndr1_0) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118))) <=> (hskp28 | hskp2 | c2_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(4067,plain,
% 1.85/1.54 (((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp2 | (~ndr1_0) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp2 | c2_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118)))),
% 1.85/1.54 inference(monotonicity,[status(thm)],[4066])).
% 1.85/1.54 tff(4068,plain,
% 1.85/1.54 (((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp2 | (~ndr1_0) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))) <=> ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp28 | hskp2 | c2_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118))),
% 1.85/1.54 inference(transitivity,[status(thm)],[4067, 4065])).
% 1.85/1.54 tff(4069,plain,
% 1.85/1.54 ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp2 | (~ndr1_0) | c2_1(a1118) | c0_1(a1118) | (~c1_1(a1118)))),
% 1.85/1.54 inference(quant_inst,[status(thm)],[])).
% 1.85/1.54 tff(4070,plain,
% 1.85/1.54 ((~![U: $i] : (hskp28 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp28 | hskp2 | c2_1(a1118) | (~ndr1_0) | (~c1_1(a1118)) | c0_1(a1118)),
% 1.85/1.54 inference(modus_ponens,[status(thm)],[4069, 4068])).
% 1.85/1.54 tff(4071,plain,
% 1.85/1.54 (hskp28 | hskp2 | c0_1(a1118)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[4070, 113, 3943, 3946, 4064])).
% 1.85/1.54 tff(4072,plain,
% 1.85/1.54 (hskp28),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[4071, 4054, 2806])).
% 1.85/1.54 tff(4073,plain,
% 1.85/1.54 (c2_1(a1111)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[596, 4072])).
% 1.85/1.54 tff(4074,plain,
% 1.85/1.54 (c1_1(a1111)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[607, 4072])).
% 1.85/1.54 tff(4075,plain,
% 1.85/1.54 (c0_1(a1111)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[618, 4072])).
% 1.85/1.54 tff(4076,plain,
% 1.85/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(4077,plain,
% 1.85/1.54 (((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136))) <=> (c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.85/1.54 inference(rewrite,[status(thm)],[])).
% 1.85/1.54 tff(4078,plain,
% 1.85/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111))))),
% 1.85/1.54 inference(monotonicity,[status(thm)],[4077])).
% 1.85/1.54 tff(4079,plain,
% 1.85/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111)))),
% 1.85/1.54 inference(transitivity,[status(thm)],[4078, 4076])).
% 1.85/1.54 tff(4080,plain,
% 1.85/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1111)) | (~c2_1(a1111)) | (~c0_1(a1111)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)) | c0_1(a1136) | (~c2_1(a1136)) | (~c1_1(a1136)))),
% 1.85/1.54 inference(quant_inst,[status(thm)],[])).
% 1.85/1.54 tff(4081,plain,
% 1.85/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c2_1(a1136)) | c0_1(a1136) | (~c1_1(a1136)) | (~c0_1(a1108)) | (~c2_1(a1111)) | (~c0_1(a1111)) | (~c1_1(a1111))),
% 1.85/1.54 inference(modus_ponens,[status(thm)],[4080, 4079])).
% 1.85/1.54 tff(4082,plain,
% 1.85/1.54 ($false),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[4081, 113, 3940, 3945, 4075, 4074, 4073, 4035, 4034, 4033, 57, 4036])).
% 1.85/1.54 tff(4083,plain,(hskp2 | c0_1(a1147) | c3_1(a1147) | (~c0_1(a1116)) | (~c2_1(a1116)) | (~c3_1(a1116))), inference(lemma,lemma(discharge,[]))).
% 1.85/1.54 tff(4084,plain,
% 1.85/1.54 (hskp2),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[4083, 4031, 771, 2533, 4030, 4029])).
% 1.85/1.54 tff(4085,plain,
% 1.85/1.54 (~c3_1(a1100)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[291, 4084])).
% 1.85/1.54 tff(4086,plain,
% 1.85/1.54 (c2_1(a1100)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[302, 4084])).
% 1.85/1.54 tff(4087,plain,
% 1.85/1.54 (c0_1(a1100)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[313, 4084])).
% 1.85/1.54 tff(4088,plain,
% 1.85/1.54 (~c1_1(a1100)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[1289, 113, 1269, 4087, 4086, 4085, 1279])).
% 1.85/1.54 tff(4089,plain,
% 1.85/1.54 (hskp7 | c1_1(a1100)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[3730, 3938, 113, 4087, 4086, 2574])).
% 1.85/1.54 tff(4090,plain,
% 1.85/1.54 (hskp7),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[4089, 4088])).
% 1.85/1.54 tff(4091,plain,
% 1.85/1.54 (~c1_1(a1105)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[633, 4090])).
% 1.85/1.54 tff(4092,plain,
% 1.85/1.54 (c0_1(a1105)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[646, 4090])).
% 1.85/1.54 tff(4093,plain,
% 1.85/1.54 (c3_1(a1105)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[657, 4090])).
% 1.85/1.54 tff(4094,plain,
% 1.85/1.54 (~hskp8),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[2651, 4093, 4030, 4029, 4031, 4092, 4091])).
% 1.85/1.54 tff(4095,plain,
% 1.85/1.54 (c0_1(a1118)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[2034, 4094, 3943, 3940, 4030, 3946, 3942, 4029, 3945, 3944, 4031])).
% 1.85/1.54 tff(4096,plain,
% 1.85/1.54 (c0_1(a1136)),
% 1.85/1.54 inference(unit_resolution,[status(thm)],[2037, 4095, 3945, 3944, 3943, 3942, 3940])).
% 1.85/1.54 tff(4097,plain,
% 1.85/1.55 ($false),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[2703, 3938, 113, 3940, 3945, 4087, 4085, 1633, 4096, 4088])).
% 1.85/1.55 tff(4098,plain,(hskp5 | c3_1(a1147) | c0_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.55 tff(4099,plain,
% 1.85/1.55 (c0_1(a1147)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[4098, 771, 3984])).
% 1.85/1.55 tff(4100,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4101,plain,
% 1.85/1.55 ((hskp5 | (~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c2_1(a1147)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147))) <=> (hskp5 | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4102,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c2_1(a1147)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.85/1.55 inference(monotonicity,[status(thm)],[4101])).
% 1.85/1.55 tff(4103,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c2_1(a1147)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.85/1.55 inference(transitivity,[status(thm)],[4102, 4100])).
% 1.85/1.55 tff(4104,plain,
% 1.85/1.55 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a1147) | (~c1_1(a1147)) | (~c2_1(a1147)) | c3_1(a1147) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.85/1.55 inference(quant_inst,[status(thm)],[])).
% 1.85/1.55 tff(4105,plain,
% 1.85/1.55 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | (~c2_1(a1147)) | c3_1(a1147) | (~ndr1_0) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.85/1.55 inference(modus_ponens,[status(thm)],[4104, 4103])).
% 1.85/1.55 tff(4106,plain,
% 1.85/1.55 (~c1_1(a1147)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[4105, 113, 3984, 4099, 3937, 771, 1279])).
% 1.85/1.55 tff(4107,plain,
% 1.85/1.55 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~c2_1(a1147)) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | (~c2_1(a1147)) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4108,plain,
% 1.85/1.55 ((hskp23 | hskp7 | (~ndr1_0) | c1_1(a1147) | (~c2_1(a1147)) | (~c0_1(a1147))) <=> (hskp23 | hskp7 | (~c2_1(a1147)) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4109,plain,
% 1.85/1.55 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1147) | (~c2_1(a1147)) | (~c0_1(a1147)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~c2_1(a1147)) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.85/1.55 inference(monotonicity,[status(thm)],[4108])).
% 1.85/1.55 tff(4110,plain,
% 1.85/1.55 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1147) | (~c2_1(a1147)) | (~c0_1(a1147)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | (~c2_1(a1147)) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.85/1.55 inference(transitivity,[status(thm)],[4109, 4107])).
% 1.85/1.55 tff(4111,plain,
% 1.85/1.55 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c1_1(a1147) | (~c2_1(a1147)) | (~c0_1(a1147)))),
% 1.85/1.55 inference(quant_inst,[status(thm)],[])).
% 1.85/1.55 tff(4112,plain,
% 1.85/1.55 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp7 | (~c2_1(a1147)) | (~ndr1_0) | c1_1(a1147) | (~c0_1(a1147))),
% 1.85/1.55 inference(modus_ponens,[status(thm)],[4111, 4110])).
% 1.85/1.55 tff(4113,plain,
% 1.85/1.55 (hskp7 | c1_1(a1147) | (~c0_1(a1147))),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[4112, 3938, 113, 3937, 2574])).
% 1.85/1.55 tff(4114,plain,
% 1.85/1.55 (hskp7),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[4113, 4106, 4099])).
% 1.85/1.55 tff(4115,plain,
% 1.85/1.55 (~c1_1(a1105)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[633, 4114])).
% 1.85/1.55 tff(4116,plain,
% 1.85/1.55 (c0_1(a1105)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[646, 4114])).
% 1.85/1.55 tff(4117,plain,
% 1.85/1.55 (c3_1(a1105)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[657, 4114])).
% 1.85/1.55 tff(4118,plain,
% 1.85/1.55 (~hskp8),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[2651, 4117, 4027, 4026, 4025, 4116, 4115])).
% 1.85/1.55 tff(4119,plain,
% 1.85/1.55 (c0_1(a1118)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[2034, 4118, 3943, 3940, 4027, 3946, 3942, 4026, 3945, 3944, 4025])).
% 1.85/1.55 tff(4120,plain,
% 1.85/1.55 (c0_1(a1136)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[2037, 4119, 3945, 3944, 3943, 3942, 3940])).
% 1.85/1.55 tff(4121,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4122,plain,
% 1.85/1.55 ((hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147))) <=> (hskp23 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4123,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147))))),
% 1.85/1.55 inference(monotonicity,[status(thm)],[4122])).
% 1.85/1.55 tff(4124,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147)))),
% 1.85/1.55 inference(transitivity,[status(thm)],[4123, 4121])).
% 1.85/1.55 tff(4125,plain,
% 1.85/1.55 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1147) | c3_1(a1147) | (~c0_1(a1147)))),
% 1.85/1.55 inference(quant_inst,[status(thm)],[])).
% 1.85/1.55 tff(4126,plain,
% 1.85/1.55 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a1147) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c1_1(a1136)) | c1_1(a1147) | (~c0_1(a1147))),
% 1.85/1.55 inference(modus_ponens,[status(thm)],[4125, 4124])).
% 1.85/1.55 tff(4127,plain,
% 1.85/1.55 ($false),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[4126, 3938, 113, 3940, 3945, 4099, 771, 1633, 4120, 4106])).
% 1.85/1.55 tff(4128,plain,(c3_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.55 tff(4129,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a1147) | (~c2_1(a1147)) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1147) | (~c2_1(a1147)) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4130,plain,
% 1.85/1.55 ((hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1147) | (~c3_1(a1147)) | (~c2_1(a1147))) <=> (hskp7 | c0_1(a1147) | (~c2_1(a1147)) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4131,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1147) | (~c3_1(a1147)) | (~c2_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a1147) | (~c2_1(a1147)) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116))))),
% 1.85/1.55 inference(monotonicity,[status(thm)],[4130])).
% 1.85/1.55 tff(4132,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1147) | (~c3_1(a1147)) | (~c2_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1147) | (~c2_1(a1147)) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)))),
% 1.85/1.55 inference(transitivity,[status(thm)],[4131, 4129])).
% 1.85/1.55 tff(4133,plain,
% 1.85/1.55 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116)) | c0_1(a1147) | (~c3_1(a1147)) | (~c2_1(a1147)))),
% 1.85/1.55 inference(quant_inst,[status(thm)],[])).
% 1.85/1.55 tff(4134,plain,
% 1.85/1.55 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a1147) | (~c2_1(a1147)) | (~c3_1(a1147)) | (~ndr1_0) | (~c3_1(a1116)) | (~c2_1(a1116)) | (~c0_1(a1116))),
% 1.85/1.55 inference(modus_ponens,[status(thm)],[4133, 4132])).
% 1.85/1.55 tff(4135,plain,
% 1.85/1.55 (hskp7),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[4134, 113, 4025, 4027, 4026, 2533, 3937, 4128, 3260])).
% 1.85/1.55 tff(4136,plain,
% 1.85/1.55 (~c1_1(a1105)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[633, 4135])).
% 1.85/1.55 tff(4137,plain,
% 1.85/1.55 (c0_1(a1105)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[646, 4135])).
% 1.85/1.55 tff(4138,plain,
% 1.85/1.55 (c3_1(a1105)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[657, 4135])).
% 1.85/1.55 tff(4139,plain,
% 1.85/1.55 (~hskp8),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[2651, 4138, 4027, 4026, 4025, 4137, 4136])).
% 1.85/1.55 tff(4140,plain,
% 1.85/1.55 (c0_1(a1118)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[2034, 4139, 3943, 3940, 4027, 3946, 3942, 4026, 3945, 3944, 4025])).
% 1.85/1.55 tff(4141,plain,
% 1.85/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1147)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4142,plain,
% 1.85/1.55 (((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147))) <=> (c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1147)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4143,plain,
% 1.85/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1147))))),
% 1.85/1.55 inference(monotonicity,[status(thm)],[4142])).
% 1.85/1.55 tff(4144,plain,
% 1.85/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1147)))),
% 1.85/1.55 inference(transitivity,[status(thm)],[4143, 4141])).
% 1.85/1.55 tff(4145,plain,
% 1.85/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1136)) | c3_1(a1118) | (~c1_1(a1118)) | (~c0_1(a1118)) | c0_1(a1147) | (~c1_1(a1147)) | (~c3_1(a1147)))),
% 1.85/1.55 inference(quant_inst,[status(thm)],[])).
% 1.85/1.55 tff(4146,plain,
% 1.85/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a1147) | (~c3_1(a1147)) | c3_1(a1118) | (~ndr1_0) | (~c2_1(a1136)) | (~c3_1(a1136)) | (~c1_1(a1136)) | (~c1_1(a1118)) | (~c0_1(a1118)) | (~c1_1(a1147))),
% 1.85/1.55 inference(modus_ponens,[status(thm)],[4145, 4144])).
% 1.85/1.55 tff(4147,plain,
% 1.85/1.55 ((~c0_1(a1118)) | (~c1_1(a1147))),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[4146, 113, 3940, 3945, 3944, 2533, 3943, 4128, 3942, 45])).
% 1.85/1.55 tff(4148,plain,
% 1.85/1.55 (~c1_1(a1147)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[4147, 4140])).
% 1.85/1.55 tff(4149,plain,
% 1.85/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1147) | (~c2_1(a1147)) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1147) | (~c2_1(a1147)) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4150,plain,
% 1.85/1.55 (((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1147) | c0_1(a1147) | (~c2_1(a1147))) <=> (c0_1(a1147) | (~c2_1(a1147)) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4151,plain,
% 1.85/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1147) | c0_1(a1147) | (~c2_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1147) | (~c2_1(a1147)) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147)))),
% 1.85/1.55 inference(monotonicity,[status(thm)],[4150])).
% 1.85/1.55 tff(4152,plain,
% 1.85/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1147) | c0_1(a1147) | (~c2_1(a1147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1147) | (~c2_1(a1147)) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147))),
% 1.85/1.55 inference(transitivity,[status(thm)],[4151, 4149])).
% 1.85/1.55 tff(4153,plain,
% 1.85/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a1105)) | (~c2_1(a1105)) | (~c0_1(a1105)) | c1_1(a1105) | (~c3_1(a1105)) | (~c0_1(a1105)) | c1_1(a1147) | c0_1(a1147) | (~c2_1(a1147)))),
% 1.85/1.55 inference(quant_inst,[status(thm)],[])).
% 1.85/1.55 tff(4154,plain,
% 1.85/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1147) | (~c2_1(a1147)) | c1_1(a1105) | (~ndr1_0) | (~c0_1(a1105)) | (~c2_1(a1105)) | (~c3_1(a1105)) | c1_1(a1147)),
% 1.85/1.55 inference(modus_ponens,[status(thm)],[4153, 4152])).
% 1.85/1.55 tff(4155,plain,
% 1.85/1.55 (~c2_1(a1105)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[4154, 113, 2533, 4137, 4138, 3937, 4136, 702, 4148])).
% 1.85/1.55 tff(4156,plain,
% 1.85/1.55 (c0_1(a1136)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[2037, 4140, 3945, 3944, 3943, 3942, 3940])).
% 1.85/1.55 tff(4157,plain,
% 1.85/1.55 ($false),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[1801, 113, 3945, 3944, 3943, 4138, 3946, 4136, 246, 4140, 4156, 4155])).
% 1.85/1.55 tff(4158,plain,(c0_1(a1147)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.55 tff(4159,plain,
% 1.85/1.55 (c1_1(a1147)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[4113, 68, 4158])).
% 1.85/1.55 tff(4160,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~c2_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c0_1(a1108)) | (~c1_1(a1147)) | (~c0_1(a1147)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | (~c2_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c0_1(a1108)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4161,plain,
% 1.85/1.55 ((hskp23 | (~ndr1_0) | (~c1_1(a1147)) | (~c2_1(a1147)) | (~c0_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108))) <=> (hskp23 | (~c2_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c0_1(a1108)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4162,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1147)) | (~c2_1(a1147)) | (~c0_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~c2_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c0_1(a1108)) | (~c1_1(a1147)) | (~c0_1(a1147))))),
% 1.85/1.55 inference(monotonicity,[status(thm)],[4161])).
% 1.85/1.55 tff(4163,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1147)) | (~c2_1(a1147)) | (~c0_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | (~c2_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c0_1(a1108)) | (~c1_1(a1147)) | (~c0_1(a1147)))),
% 1.85/1.55 inference(transitivity,[status(thm)],[4162, 4160])).
% 1.85/1.55 tff(4164,plain,
% 1.85/1.55 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1147)) | (~c2_1(a1147)) | (~c0_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~c0_1(a1108)))),
% 1.85/1.55 inference(quant_inst,[status(thm)],[])).
% 1.85/1.55 tff(4165,plain,
% 1.85/1.55 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | (~c2_1(a1147)) | c1_1(a1108) | c3_1(a1108) | (~ndr1_0) | (~c0_1(a1108)) | (~c1_1(a1147)) | (~c0_1(a1147))),
% 1.85/1.55 inference(modus_ponens,[status(thm)],[4164, 4163])).
% 1.85/1.55 tff(4166,plain,
% 1.85/1.55 ($false),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[4165, 3938, 113, 4158, 1638, 3937, 1637, 1636, 1633, 2584])).
% 1.85/1.55 tff(4167,plain,((~hskp9) | (~c1_1(a1147))), inference(lemma,lemma(discharge,[]))).
% 1.85/1.55 tff(4168,plain,
% 1.85/1.55 (~hskp9),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[4167, 4159])).
% 1.85/1.55 tff(4169,plain,
% 1.85/1.55 (hskp19),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[3986, 4168])).
% 1.85/1.55 tff(4170,plain,
% 1.85/1.55 (hskp2),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[2941, 4169, 4025, 4027, 4026])).
% 1.85/1.55 tff(4171,plain,
% 1.85/1.55 (~c3_1(a1100)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[291, 4170])).
% 1.85/1.55 tff(4172,plain,
% 1.85/1.55 (c2_1(a1100)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[302, 4170])).
% 1.85/1.55 tff(4173,plain,
% 1.85/1.55 (c0_1(a1100)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[313, 4170])).
% 1.85/1.55 tff(4174,plain,
% 1.85/1.55 (~c1_1(a1100)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[1289, 113, 3984, 4173, 4172, 4171, 1279])).
% 1.85/1.55 tff(4175,plain,
% 1.85/1.55 ($false),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[3730, 3938, 113, 68, 4173, 4172, 2574, 4174])).
% 1.85/1.55 tff(4176,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 1.85/1.55 tff(4177,plain,
% 1.85/1.55 (~c1_1(a1105)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[633, 4176])).
% 1.85/1.55 tff(4178,plain,
% 1.85/1.55 (c0_1(a1105)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[646, 4176])).
% 1.85/1.55 tff(4179,plain,
% 1.85/1.55 (c3_1(a1105)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[657, 4176])).
% 1.85/1.55 tff(4180,plain,
% 1.85/1.55 (~hskp8),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[2651, 4179, 4027, 4026, 4025, 4178, 4177])).
% 1.85/1.55 tff(4181,plain,
% 1.85/1.55 (c0_1(a1118)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[2034, 4180, 3943, 3940, 4027, 3946, 3942, 4026, 3945, 3944, 4025])).
% 1.85/1.55 tff(4182,plain,
% 1.85/1.55 (c0_1(a1136)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[2037, 4181, 3945, 3944, 3943, 3942, 3940])).
% 1.85/1.55 tff(4183,plain,
% 1.85/1.55 (c2_1(a1105)),
% 1.85/1.55 inference(unit_resolution,[status(thm)],[1801, 113, 3945, 3944, 3943, 4179, 3946, 4177, 246, 4181, 4182])).
% 1.85/1.55 tff(4184,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4185,plain,
% 1.85/1.55 ((hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105))) <=> (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.85/1.55 inference(rewrite,[status(thm)],[])).
% 1.85/1.55 tff(4186,plain,
% 1.85/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1105)) | (~c3_1(a1105))))),
% 1.85/1.55 inference(monotonicity,[status(thm)],[4185])).
% 1.85/1.56 tff(4187,plain,
% 1.85/1.56 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1105)) | (~c3_1(a1105)))),
% 1.85/1.56 inference(transitivity,[status(thm)],[4186, 4184])).
% 1.85/1.56 tff(4188,plain,
% 1.85/1.56 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | (~c3_1(a1136)) | (~c2_1(a1136)) | (~c0_1(a1136)) | c1_1(a1105) | (~c3_1(a1105)) | (~c2_1(a1105)))),
% 1.85/1.56 inference(quant_inst,[status(thm)],[])).
% 1.85/1.56 tff(4189,plain,
% 1.85/1.56 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp2 | c1_1(a1105) | (~ndr1_0) | (~c2_1(a1136)) | (~c0_1(a1136)) | (~c3_1(a1136)) | (~c2_1(a1105)) | (~c3_1(a1105))),
% 1.85/1.56 inference(modus_ponens,[status(thm)],[4188, 4187])).
% 1.85/1.56 tff(4190,plain,
% 1.85/1.56 (hskp2),
% 1.85/1.56 inference(unit_resolution,[status(thm)],[4189, 113, 3945, 3944, 4179, 4177, 1065, 4182, 4183])).
% 1.85/1.56 tff(4191,plain,
% 1.85/1.56 (~c3_1(a1100)),
% 1.85/1.56 inference(unit_resolution,[status(thm)],[291, 4190])).
% 1.85/1.56 tff(4192,plain,
% 1.85/1.56 (hskp19 | (~c2_1(a1105))),
% 1.85/1.56 inference(unit_resolution,[status(thm)],[2681, 113, 4180, 4179, 4177, 2675])).
% 1.85/1.56 tff(4193,plain,
% 1.85/1.56 (hskp19),
% 1.85/1.56 inference(unit_resolution,[status(thm)],[4192, 4183])).
% 1.85/1.56 tff(4194,plain,
% 1.85/1.56 (hskp20),
% 1.85/1.56 inference(unit_resolution,[status(thm)],[1305, 4193, 3984, 4025, 4027, 4026])).
% 1.85/1.56 tff(4195,plain,
% 1.85/1.56 (~c3_1(a1130)),
% 1.85/1.56 inference(unit_resolution,[status(thm)],[332, 4194])).
% 1.85/1.56 tff(4196,plain,
% 1.85/1.56 (~c2_1(a1130)),
% 1.85/1.56 inference(unit_resolution,[status(thm)],[2287, 4194])).
% 1.85/1.56 tff(4197,plain,
% 1.85/1.56 (~c0_1(a1130)),
% 1.85/1.56 inference(unit_resolution,[status(thm)],[326, 4194])).
% 1.85/1.56 tff(4198,plain,
% 1.85/1.56 (c2_1(a1100)),
% 1.85/1.56 inference(unit_resolution,[status(thm)],[302, 4190])).
% 1.85/1.56 tff(4199,plain,
% 1.85/1.56 (~c1_1(a1100)),
% 1.85/1.56 inference(unit_resolution,[status(thm)],[2694, 113, 3984, 4198, 4197, 4196, 4195, 4191, 10])).
% 1.85/1.56 tff(4200,plain,
% 1.85/1.56 (c0_1(a1100)),
% 1.85/1.56 inference(unit_resolution,[status(thm)],[313, 4190])).
% 1.85/1.56 tff(4201,plain,
% 1.85/1.56 ($false),
% 1.85/1.56 inference(unit_resolution,[status(thm)],[2703, 3938, 113, 3940, 3945, 4200, 4191, 1633, 4182, 4199])).
% 1.85/1.56 % SZS output end Proof
%------------------------------------------------------------------------------