TSTP Solution File: SYN443-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN443-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 23:55:26 EDT 2022
% Result : Unsatisfiable 1.61s 1.24s
% Output : Proof 2.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SYN443-1 : TPTP v8.1.0. Released v2.1.0.
% 0.05/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n008.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Sep 5 03:43:55 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 1.61/1.24 % SZS status Unsatisfiable
% 1.61/1.24 % SZS output start Proof
% 1.61/1.24 tff(c1_1_type, type, (
% 1.61/1.24 c1_1: $i > $o)).
% 1.61/1.24 tff(a43_type, type, (
% 1.61/1.24 a43: $i)).
% 1.61/1.24 tff(hskp22_type, type, (
% 1.61/1.24 hskp22: $o)).
% 1.61/1.24 tff(c3_1_type, type, (
% 1.61/1.24 c3_1: $i > $o)).
% 1.61/1.24 tff(a31_type, type, (
% 1.61/1.24 a31: $i)).
% 1.61/1.24 tff(c2_1_type, type, (
% 1.61/1.24 c2_1: $i > $o)).
% 1.61/1.24 tff(a19_type, type, (
% 1.61/1.24 a19: $i)).
% 1.61/1.24 tff(c0_1_type, type, (
% 1.61/1.24 c0_1: $i > $o)).
% 1.61/1.24 tff(ndr1_0_type, type, (
% 1.61/1.24 ndr1_0: $o)).
% 1.61/1.24 tff(hskp11_type, type, (
% 1.61/1.24 hskp11: $o)).
% 1.61/1.24 tff(hskp2_type, type, (
% 1.61/1.24 hskp2: $o)).
% 1.61/1.24 tff(hskp30_type, type, (
% 1.61/1.24 hskp30: $o)).
% 1.61/1.24 tff(hskp18_type, type, (
% 1.61/1.24 hskp18: $o)).
% 1.61/1.24 tff(a3_type, type, (
% 1.61/1.24 a3: $i)).
% 1.61/1.24 tff(a36_type, type, (
% 1.61/1.24 a36: $i)).
% 1.61/1.24 tff(hskp4_type, type, (
% 1.61/1.24 hskp4: $o)).
% 1.61/1.24 tff(hskp19_type, type, (
% 1.61/1.24 hskp19: $o)).
% 1.61/1.24 tff(a58_type, type, (
% 1.61/1.24 a58: $i)).
% 1.61/1.24 tff(a34_type, type, (
% 1.61/1.24 a34: $i)).
% 1.61/1.24 tff(a1_type, type, (
% 1.61/1.24 a1: $i)).
% 1.61/1.24 tff(hskp0_type, type, (
% 1.61/1.24 hskp0: $o)).
% 1.61/1.24 tff(a33_type, type, (
% 1.61/1.24 a33: $i)).
% 1.61/1.24 tff(a4_type, type, (
% 1.61/1.24 a4: $i)).
% 1.61/1.24 tff(hskp3_type, type, (
% 1.61/1.24 hskp3: $o)).
% 1.61/1.24 tff(hskp24_type, type, (
% 1.61/1.24 hskp24: $o)).
% 1.61/1.24 tff(hskp27_type, type, (
% 1.61/1.24 hskp27: $o)).
% 1.61/1.24 tff(hskp28_type, type, (
% 1.61/1.24 hskp28: $o)).
% 1.61/1.24 tff(a9_type, type, (
% 1.61/1.24 a9: $i)).
% 1.61/1.24 tff(hskp7_type, type, (
% 1.61/1.24 hskp7: $o)).
% 1.61/1.24 tff(a25_type, type, (
% 1.61/1.24 a25: $i)).
% 1.61/1.24 tff(hskp29_type, type, (
% 1.61/1.24 hskp29: $o)).
% 1.61/1.24 tff(a5_type, type, (
% 1.61/1.24 a5: $i)).
% 1.61/1.24 tff(a8_type, type, (
% 1.61/1.24 a8: $i)).
% 1.61/1.24 tff(hskp6_type, type, (
% 1.61/1.24 hskp6: $o)).
% 1.61/1.24 tff(hskp5_type, type, (
% 1.61/1.24 hskp5: $o)).
% 1.61/1.24 tff(a6_type, type, (
% 1.61/1.24 a6: $i)).
% 1.61/1.24 tff(a12_type, type, (
% 1.61/1.24 a12: $i)).
% 1.61/1.24 tff(hskp9_type, type, (
% 1.61/1.24 hskp9: $o)).
% 1.61/1.24 tff(a26_type, type, (
% 1.61/1.24 a26: $i)).
% 1.61/1.24 tff(hskp14_type, type, (
% 1.61/1.24 hskp14: $o)).
% 1.61/1.24 tff(a64_type, type, (
% 1.61/1.24 a64: $i)).
% 1.61/1.24 tff(hskp25_type, type, (
% 1.61/1.24 hskp25: $o)).
% 1.61/1.24 tff(a10_type, type, (
% 1.61/1.24 a10: $i)).
% 1.61/1.24 tff(a2_type, type, (
% 1.61/1.24 a2: $i)).
% 1.61/1.24 tff(hskp1_type, type, (
% 1.61/1.24 hskp1: $o)).
% 1.61/1.24 tff(a42_type, type, (
% 1.61/1.24 a42: $i)).
% 1.61/1.24 tff(hskp21_type, type, (
% 1.61/1.24 hskp21: $o)).
% 1.61/1.24 tff(a15_type, type, (
% 1.61/1.24 a15: $i)).
% 1.61/1.24 tff(a27_type, type, (
% 1.61/1.24 a27: $i)).
% 1.61/1.24 tff(hskp15_type, type, (
% 1.61/1.24 hskp15: $o)).
% 1.61/1.24 tff(a32_type, type, (
% 1.61/1.24 a32: $i)).
% 1.61/1.24 tff(hskp17_type, type, (
% 1.61/1.24 hskp17: $o)).
% 1.61/1.24 tff(hskp16_type, type, (
% 1.61/1.24 hskp16: $o)).
% 1.61/1.24 tff(a52_type, type, (
% 1.61/1.24 a52: $i)).
% 1.61/1.24 tff(hskp23_type, type, (
% 1.61/1.24 hskp23: $o)).
% 1.61/1.24 tff(1,assumption,(~hskp22), introduced(assumption)).
% 1.61/1.24 tff(2,assumption,(~c2_1(a19)), introduced(assumption)).
% 1.61/1.24 tff(3,plain,
% 1.61/1.24 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.61/1.24 inference(bind,[status(th)],[])).
% 1.61/1.24 tff(4,plain,
% 1.61/1.24 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.61/1.24 inference(quant_intro,[status(thm)],[3])).
% 1.61/1.24 tff(5,plain,
% 1.61/1.24 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(6,plain,
% 1.61/1.24 (^[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(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.61/1.24 inference(bind,[status(th)],[])).
% 1.61/1.24 tff(7,plain,
% 1.61/1.24 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.61/1.24 inference(quant_intro,[status(thm)],[6])).
% 1.61/1.24 tff(8,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.61/1.24 tff(9,plain,
% 1.61/1.24 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[8, 7])).
% 1.61/1.24 tff(10,plain,
% 1.61/1.24 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[9, 5])).
% 1.61/1.24 tff(11,plain,(
% 1.61/1.24 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.61/1.24 inference(skolemize,[status(sab)],[10])).
% 1.61/1.24 tff(12,plain,
% 1.61/1.24 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[11, 4])).
% 1.61/1.24 tff(13,plain,
% 1.61/1.24 ((hskp11 | hskp22) <=> (hskp11 | hskp22)),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(14,axiom,(hskp11 | hskp22), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.61/1.24 tff(15,plain,
% 1.61/1.24 (hskp11 | hskp22),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.61/1.24 tff(16,plain,
% 1.61/1.24 (hskp11),
% 1.61/1.24 inference(unit_resolution,[status(thm)],[15, 1])).
% 1.61/1.24 tff(17,plain,
% 1.61/1.24 (((~hskp11) | (~c3_1(a19))) <=> ((~hskp11) | (~c3_1(a19)))),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(18,plain,
% 1.61/1.24 (((~c3_1(a19)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a19)))),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(19,axiom,((~c3_1(a19)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.61/1.24 tff(20,plain,
% 1.61/1.24 ((~hskp11) | (~c3_1(a19))),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.61/1.24 tff(21,plain,
% 1.61/1.24 ((~hskp11) | (~c3_1(a19))),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[20, 17])).
% 1.61/1.24 tff(22,plain,
% 1.61/1.24 (~c3_1(a19)),
% 1.61/1.24 inference(unit_resolution,[status(thm)],[21, 16])).
% 1.61/1.24 tff(23,plain,
% 1.61/1.24 (((~hskp11) | c1_1(a19)) <=> ((~hskp11) | c1_1(a19))),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(24,axiom,((~hskp11) | c1_1(a19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.61/1.24 tff(25,plain,
% 1.61/1.24 ((~hskp11) | c1_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.61/1.24 tff(26,plain,
% 1.61/1.24 ((~hskp11) | c1_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[25, 23])).
% 1.61/1.24 tff(27,plain,
% 1.61/1.24 ((~hskp11) | c1_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[26, 23])).
% 1.61/1.24 tff(28,plain,
% 1.61/1.24 ((~hskp11) | c1_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.61/1.24 tff(29,plain,
% 1.61/1.24 ((~hskp11) | c1_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[28, 23])).
% 1.61/1.24 tff(30,plain,
% 1.61/1.24 ((~hskp11) | c1_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[29, 23])).
% 1.61/1.24 tff(31,plain,
% 1.61/1.24 ((~hskp11) | c1_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.61/1.24 tff(32,plain,
% 1.61/1.24 ((~hskp11) | c1_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[31, 23])).
% 1.61/1.24 tff(33,plain,
% 1.61/1.24 (c1_1(a19)),
% 1.61/1.24 inference(unit_resolution,[status(thm)],[32, 16])).
% 1.61/1.24 tff(34,plain,
% 1.61/1.24 (((~hskp11) | c0_1(a19)) <=> ((~hskp11) | c0_1(a19))),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(35,axiom,((~hskp11) | c0_1(a19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.61/1.24 tff(36,plain,
% 1.61/1.24 ((~hskp11) | c0_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.61/1.24 tff(37,plain,
% 1.61/1.24 ((~hskp11) | c0_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[36, 34])).
% 1.61/1.24 tff(38,plain,
% 1.61/1.24 ((~hskp11) | c0_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[37, 34])).
% 1.61/1.24 tff(39,plain,
% 1.61/1.24 ((~hskp11) | c0_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.61/1.24 tff(40,plain,
% 1.61/1.24 ((~hskp11) | c0_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[39, 34])).
% 1.61/1.24 tff(41,plain,
% 1.61/1.24 ((~hskp11) | c0_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[40, 34])).
% 1.61/1.24 tff(42,plain,
% 1.61/1.24 ((~hskp11) | c0_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[41, 34])).
% 1.61/1.24 tff(43,plain,
% 1.61/1.24 ((~hskp11) | c0_1(a19)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[42, 34])).
% 1.61/1.24 tff(44,plain,
% 1.61/1.24 (c0_1(a19)),
% 1.61/1.24 inference(unit_resolution,[status(thm)],[43, 16])).
% 1.61/1.24 tff(45,assumption,(~ndr1_0), introduced(assumption)).
% 1.61/1.24 tff(46,plain,
% 1.61/1.24 ((ndr1_0 | (~hskp2)) <=> (ndr1_0 | (~hskp2))),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(47,plain,
% 1.61/1.24 (((~hskp2) | ndr1_0) <=> (ndr1_0 | (~hskp2))),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(48,axiom,((~hskp2) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause30')).
% 1.61/1.24 tff(49,plain,
% 1.61/1.24 (ndr1_0 | (~hskp2)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.61/1.24 tff(50,plain,
% 1.61/1.24 (ndr1_0 | (~hskp2)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[49, 46])).
% 1.61/1.24 tff(51,plain,
% 1.61/1.24 (~hskp2),
% 1.61/1.24 inference(unit_resolution,[status(thm)],[50, 45])).
% 1.61/1.24 tff(52,plain,
% 1.61/1.24 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(53,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 1.61/1.24 tff(54,plain,
% 1.61/1.24 ((~hskp30) | ndr1_0),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.61/1.24 tff(55,plain,
% 1.61/1.24 ((~hskp30) | ndr1_0),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[54, 52])).
% 1.61/1.24 tff(56,plain,
% 1.61/1.24 ((~hskp30) | ndr1_0),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[55, 52])).
% 1.61/1.24 tff(57,plain,
% 1.61/1.24 ((~hskp30) | ndr1_0),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[56, 52])).
% 1.61/1.24 tff(58,plain,
% 1.61/1.24 ((~hskp30) | ndr1_0),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[57, 52])).
% 1.61/1.24 tff(59,plain,
% 1.61/1.24 ((~hskp30) | ndr1_0),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[58, 52])).
% 1.61/1.24 tff(60,plain,
% 1.61/1.24 ((~hskp30) | ndr1_0),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[59, 52])).
% 1.61/1.24 tff(61,plain,
% 1.61/1.24 ((~hskp30) | ndr1_0),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[60, 52])).
% 1.61/1.24 tff(62,plain,
% 1.61/1.24 (~hskp30),
% 1.61/1.24 inference(unit_resolution,[status(thm)],[61, 45])).
% 1.61/1.24 tff(63,plain,
% 1.61/1.24 ((ndr1_0 | (~hskp18)) <=> (ndr1_0 | (~hskp18))),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(64,plain,
% 1.61/1.24 (((~hskp18) | ndr1_0) <=> (ndr1_0 | (~hskp18))),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(65,axiom,((~hskp18) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause14')).
% 1.61/1.24 tff(66,plain,
% 1.61/1.24 (ndr1_0 | (~hskp18)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.61/1.24 tff(67,plain,
% 1.61/1.24 (ndr1_0 | (~hskp18)),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[66, 63])).
% 1.61/1.24 tff(68,plain,
% 1.61/1.24 (~hskp18),
% 1.61/1.24 inference(unit_resolution,[status(thm)],[67, 45])).
% 1.61/1.24 tff(69,plain,
% 1.61/1.24 ((hskp30 | hskp18 | hskp2) <=> (hskp30 | hskp18 | hskp2)),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(70,plain,
% 1.61/1.24 (((hskp30 | hskp2) | hskp18) <=> (hskp30 | hskp18 | hskp2)),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(71,plain,
% 1.61/1.24 ((hskp30 | hskp2) <=> (hskp30 | hskp2)),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(72,plain,
% 1.61/1.24 (((hskp30 | hskp2) | hskp18) <=> ((hskp30 | hskp2) | hskp18)),
% 1.61/1.24 inference(monotonicity,[status(thm)],[71])).
% 1.61/1.24 tff(73,plain,
% 1.61/1.24 (((hskp30 | hskp2) | hskp18) <=> (hskp30 | hskp18 | hskp2)),
% 1.61/1.24 inference(transitivity,[status(thm)],[72, 70])).
% 1.61/1.24 tff(74,axiom,((hskp30 | hskp2) | hskp18), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 1.61/1.24 tff(75,plain,
% 1.61/1.24 (hskp30 | hskp18 | hskp2),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.61/1.24 tff(76,plain,
% 1.61/1.24 (hskp30 | hskp18 | hskp2),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[75, 69])).
% 1.61/1.24 tff(77,plain,
% 1.61/1.24 (hskp30 | hskp18 | hskp2),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[76, 69])).
% 1.61/1.24 tff(78,plain,
% 1.61/1.24 (hskp30 | hskp18 | hskp2),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[77, 69])).
% 1.61/1.24 tff(79,plain,
% 1.61/1.24 (hskp30 | hskp18 | hskp2),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[78, 69])).
% 1.61/1.24 tff(80,plain,
% 1.61/1.24 (hskp30 | hskp18 | hskp2),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[79, 69])).
% 1.61/1.24 tff(81,plain,
% 1.61/1.24 (hskp30 | hskp18 | hskp2),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[80, 69])).
% 1.61/1.24 tff(82,plain,
% 1.61/1.24 (hskp30 | hskp18 | hskp2),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[81, 69])).
% 1.61/1.24 tff(83,plain,
% 1.61/1.24 ($false),
% 1.61/1.24 inference(unit_resolution,[status(thm)],[82, 68, 62, 51])).
% 1.61/1.24 tff(84,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.61/1.24 tff(85,plain,
% 1.61/1.24 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c3_1(a19) | (~ndr1_0) | c2_1(a19) | (~c0_1(a19)) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c3_1(a19) | (~ndr1_0) | c2_1(a19) | (~c0_1(a19)) | (~c1_1(a19)))),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(86,plain,
% 1.61/1.24 ((hskp22 | (~ndr1_0) | c3_1(a19) | c2_1(a19) | (~c1_1(a19)) | c2_1(a19) | c3_1(a19) | (~c0_1(a19))) <=> (hskp22 | c3_1(a19) | (~ndr1_0) | c2_1(a19) | (~c0_1(a19)) | (~c1_1(a19)))),
% 1.61/1.24 inference(rewrite,[status(thm)],[])).
% 1.61/1.24 tff(87,plain,
% 1.61/1.24 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a19) | c2_1(a19) | (~c1_1(a19)) | c2_1(a19) | c3_1(a19) | (~c0_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c3_1(a19) | (~ndr1_0) | c2_1(a19) | (~c0_1(a19)) | (~c1_1(a19))))),
% 1.61/1.24 inference(monotonicity,[status(thm)],[86])).
% 1.61/1.24 tff(88,plain,
% 1.61/1.24 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a19) | c2_1(a19) | (~c1_1(a19)) | c2_1(a19) | c3_1(a19) | (~c0_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c3_1(a19) | (~ndr1_0) | c2_1(a19) | (~c0_1(a19)) | (~c1_1(a19)))),
% 1.61/1.24 inference(transitivity,[status(thm)],[87, 85])).
% 1.61/1.24 tff(89,plain,
% 1.61/1.24 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a19) | c2_1(a19) | (~c1_1(a19)) | c2_1(a19) | c3_1(a19) | (~c0_1(a19)))),
% 1.61/1.24 inference(quant_inst,[status(thm)],[])).
% 1.61/1.24 tff(90,plain,
% 1.61/1.24 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c3_1(a19) | (~ndr1_0) | c2_1(a19) | (~c0_1(a19)) | (~c1_1(a19))),
% 1.61/1.24 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.61/1.24 tff(91,plain,
% 1.61/1.25 ($false),
% 1.61/1.25 inference(unit_resolution,[status(thm)],[90, 1, 84, 44, 33, 22, 12, 2])).
% 1.61/1.25 tff(92,plain,(c2_1(a19) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.61/1.25 tff(93,plain,
% 1.61/1.25 (c2_1(a19)),
% 1.61/1.25 inference(unit_resolution,[status(thm)],[92, 1])).
% 1.61/1.25 tff(94,plain,
% 1.61/1.25 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))))),
% 1.61/1.25 inference(bind,[status(th)],[])).
% 1.61/1.25 tff(95,plain,
% 1.61/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.61/1.25 inference(quant_intro,[status(thm)],[94])).
% 1.61/1.25 tff(96,plain,
% 1.61/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.61/1.25 inference(rewrite,[status(thm)],[])).
% 1.61/1.25 tff(97,plain,
% 1.61/1.25 (^[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))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))))),
% 1.61/1.25 inference(bind,[status(th)],[])).
% 1.61/1.25 tff(98,plain,
% 1.61/1.25 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.61/1.25 inference(quant_intro,[status(thm)],[97])).
% 1.61/1.25 tff(99,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.61/1.25 tff(100,plain,
% 1.61/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.61/1.25 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.61/1.25 tff(101,plain,
% 1.61/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.61/1.25 inference(modus_ponens,[status(thm)],[100, 96])).
% 1.61/1.25 tff(102,plain,(
% 1.61/1.25 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.61/1.25 inference(skolemize,[status(sab)],[101])).
% 1.61/1.25 tff(103,plain,
% 1.61/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.61/1.25 inference(modus_ponens,[status(thm)],[102, 95])).
% 1.61/1.25 tff(104,plain,
% 1.61/1.25 (^[U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.61/1.25 inference(bind,[status(th)],[])).
% 1.61/1.25 tff(105,plain,
% 1.61/1.25 (![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.61/1.25 inference(quant_intro,[status(thm)],[104])).
% 1.61/1.25 tff(106,plain,
% 1.61/1.25 (![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.61/1.25 inference(rewrite,[status(thm)],[])).
% 1.61/1.25 tff(107,plain,
% 1.61/1.25 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.63/1.25 inference(bind,[status(th)],[])).
% 1.63/1.25 tff(108,plain,
% 1.63/1.25 (![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) <=> ![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.63/1.25 inference(quant_intro,[status(thm)],[107])).
% 1.63/1.25 tff(109,axiom,(![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.63/1.25 tff(110,plain,
% 1.63/1.25 (![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.63/1.25 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.63/1.25 tff(111,plain,
% 1.63/1.25 (![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.63/1.25 inference(modus_ponens,[status(thm)],[110, 106])).
% 1.63/1.25 tff(112,plain,(
% 1.63/1.25 ![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.63/1.25 inference(skolemize,[status(sab)],[111])).
% 1.63/1.25 tff(113,plain,
% 1.63/1.25 (![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.63/1.25 inference(modus_ponens,[status(thm)],[112, 105])).
% 1.63/1.25 tff(114,plain,
% 1.63/1.25 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.63/1.25 inference(bind,[status(th)],[])).
% 1.63/1.25 tff(115,plain,
% 1.63/1.25 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.63/1.25 inference(quant_intro,[status(thm)],[114])).
% 1.63/1.25 tff(116,plain,
% 1.63/1.25 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.63/1.25 inference(rewrite,[status(thm)],[])).
% 1.63/1.25 tff(117,plain,
% 1.63/1.25 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp22))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.63/1.25 inference(bind,[status(th)],[])).
% 1.63/1.25 tff(118,plain,
% 1.63/1.25 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.63/1.25 inference(quant_intro,[status(thm)],[117])).
% 1.63/1.25 tff(119,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 1.63/1.25 tff(120,plain,
% 1.63/1.25 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.63/1.25 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.63/1.25 tff(121,plain,
% 1.63/1.25 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.63/1.25 inference(modus_ponens,[status(thm)],[120, 116])).
% 1.63/1.25 tff(122,plain,(
% 1.63/1.25 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.63/1.25 inference(skolemize,[status(sab)],[121])).
% 1.63/1.25 tff(123,plain,
% 1.63/1.25 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.63/1.25 inference(modus_ponens,[status(thm)],[122, 115])).
% 1.63/1.25 tff(124,plain,
% 1.63/1.25 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 1.63/1.25 inference(bind,[status(th)],[])).
% 1.63/1.25 tff(125,plain,
% 1.63/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.63/1.25 inference(quant_intro,[status(thm)],[124])).
% 1.63/1.25 tff(126,plain,
% 1.63/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.63/1.25 inference(rewrite,[status(thm)],[])).
% 1.63/1.25 tff(127,plain,
% 1.63/1.25 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_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) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_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) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 1.63/1.25 inference(bind,[status(th)],[])).
% 1.63/1.25 tff(128,plain,
% 1.63/1.25 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_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) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.63/1.25 inference(quant_intro,[status(thm)],[127])).
% 1.63/1.25 tff(129,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.63/1.25 tff(130,plain,
% 1.63/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.63/1.26 tff(131,plain,
% 1.63/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[130, 126])).
% 1.63/1.26 tff(132,plain,(
% 1.63/1.26 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.63/1.26 inference(skolemize,[status(sab)],[131])).
% 1.63/1.26 tff(133,plain,
% 1.63/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[132, 125])).
% 1.63/1.26 tff(134,assumption,(~hskp18), introduced(assumption)).
% 1.63/1.26 tff(135,assumption,(~hskp30), introduced(assumption)).
% 1.63/1.26 tff(136,plain,
% 1.63/1.26 (^[U: $i] : refl((hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.63/1.26 inference(bind,[status(th)],[])).
% 1.63/1.26 tff(137,plain,
% 1.63/1.26 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.63/1.26 inference(quant_intro,[status(thm)],[136])).
% 1.63/1.26 tff(138,plain,
% 1.63/1.26 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(139,plain,
% 1.63/1.26 (^[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) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp27) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp27))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp27) <=> (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp27) <=> (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.63/1.26 inference(bind,[status(th)],[])).
% 1.63/1.26 tff(140,plain,
% 1.63/1.26 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp27) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.63/1.26 inference(quant_intro,[status(thm)],[139])).
% 1.63/1.26 tff(141,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.63/1.26 tff(142,plain,
% 1.63/1.26 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[141, 140])).
% 1.63/1.26 tff(143,plain,
% 1.63/1.26 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[142, 138])).
% 1.63/1.26 tff(144,plain,(
% 1.63/1.26 ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.63/1.26 inference(skolemize,[status(sab)],[143])).
% 1.63/1.26 tff(145,plain,
% 1.63/1.26 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[144, 137])).
% 1.63/1.26 tff(146,plain,
% 1.63/1.26 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.63/1.26 inference(bind,[status(th)],[])).
% 1.63/1.26 tff(147,plain,
% 1.63/1.26 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.26 inference(quant_intro,[status(thm)],[146])).
% 1.63/1.26 tff(148,plain,
% 1.63/1.26 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(149,plain,
% 1.63/1.26 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp19) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp19))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.63/1.26 inference(bind,[status(th)],[])).
% 1.63/1.26 tff(150,plain,
% 1.63/1.26 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.26 inference(quant_intro,[status(thm)],[149])).
% 1.63/1.26 tff(151,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.63/1.26 tff(152,plain,
% 1.63/1.26 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[151, 150])).
% 1.63/1.26 tff(153,plain,
% 1.63/1.26 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[152, 148])).
% 1.63/1.26 tff(154,plain,(
% 1.63/1.26 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.26 inference(skolemize,[status(sab)],[153])).
% 1.63/1.26 tff(155,plain,
% 1.63/1.26 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[154, 147])).
% 1.63/1.26 tff(156,assumption,(hskp4), introduced(assumption)).
% 1.63/1.26 tff(157,plain,
% 1.63/1.26 (((~hskp4) | (~c1_1(a5))) <=> ((~hskp4) | (~c1_1(a5)))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(158,plain,
% 1.63/1.26 (((~c1_1(a5)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a5)))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(159,axiom,((~c1_1(a5)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.63/1.26 tff(160,plain,
% 1.63/1.26 ((~hskp4) | (~c1_1(a5))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[159, 158])).
% 1.63/1.26 tff(161,plain,
% 1.63/1.26 ((~hskp4) | (~c1_1(a5))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[160, 157])).
% 1.63/1.26 tff(162,plain,
% 1.63/1.26 (~c1_1(a5)),
% 1.63/1.26 inference(unit_resolution,[status(thm)],[161, 156])).
% 1.63/1.26 tff(163,plain,
% 1.63/1.26 (hskp2),
% 1.63/1.26 inference(unit_resolution,[status(thm)],[82, 135, 134])).
% 1.63/1.26 tff(164,plain,
% 1.63/1.26 (((~hskp2) | (~c1_1(a3))) <=> ((~hskp2) | (~c1_1(a3)))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(165,plain,
% 1.63/1.26 (((~c1_1(a3)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a3)))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(166,axiom,((~c1_1(a3)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.63/1.26 tff(167,plain,
% 1.63/1.26 ((~hskp2) | (~c1_1(a3))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.63/1.26 tff(168,plain,
% 1.63/1.26 ((~hskp2) | (~c1_1(a3))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[167, 164])).
% 1.63/1.26 tff(169,plain,
% 1.63/1.26 (~c1_1(a3)),
% 1.63/1.26 inference(unit_resolution,[status(thm)],[168, 163])).
% 1.63/1.26 tff(170,plain,
% 1.63/1.26 (((~hskp2) | c2_1(a3)) <=> ((~hskp2) | c2_1(a3))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(171,axiom,((~hskp2) | c2_1(a3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.63/1.26 tff(172,plain,
% 1.63/1.26 ((~hskp2) | c2_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[171, 170])).
% 1.63/1.26 tff(173,plain,
% 1.63/1.26 ((~hskp2) | c2_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[172, 170])).
% 1.63/1.26 tff(174,plain,
% 1.63/1.26 ((~hskp2) | c2_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[173, 170])).
% 1.63/1.26 tff(175,plain,
% 1.63/1.26 ((~hskp2) | c2_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[174, 170])).
% 1.63/1.26 tff(176,plain,
% 1.63/1.26 ((~hskp2) | c2_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[175, 170])).
% 1.63/1.26 tff(177,plain,
% 1.63/1.26 ((~hskp2) | c2_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[176, 170])).
% 1.63/1.26 tff(178,plain,
% 1.63/1.26 ((~hskp2) | c2_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[177, 170])).
% 1.63/1.26 tff(179,plain,
% 1.63/1.26 ((~hskp2) | c2_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[178, 170])).
% 1.63/1.26 tff(180,plain,
% 1.63/1.26 (c2_1(a3)),
% 1.63/1.26 inference(unit_resolution,[status(thm)],[179, 163])).
% 1.63/1.26 tff(181,plain,
% 1.63/1.26 (((~hskp2) | c0_1(a3)) <=> ((~hskp2) | c0_1(a3))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(182,axiom,((~hskp2) | c0_1(a3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.63/1.26 tff(183,plain,
% 1.63/1.26 ((~hskp2) | c0_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[182, 181])).
% 1.63/1.26 tff(184,plain,
% 1.63/1.26 ((~hskp2) | c0_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[183, 181])).
% 1.63/1.26 tff(185,plain,
% 1.63/1.26 ((~hskp2) | c0_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[184, 181])).
% 1.63/1.26 tff(186,plain,
% 1.63/1.26 ((~hskp2) | c0_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[185, 181])).
% 1.63/1.26 tff(187,plain,
% 1.63/1.26 ((~hskp2) | c0_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[186, 181])).
% 1.63/1.26 tff(188,plain,
% 1.63/1.26 ((~hskp2) | c0_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[187, 181])).
% 1.63/1.26 tff(189,plain,
% 1.63/1.26 ((~hskp2) | c0_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[188, 181])).
% 1.63/1.26 tff(190,plain,
% 1.63/1.26 ((~hskp2) | c0_1(a3)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[189, 181])).
% 1.63/1.26 tff(191,plain,
% 1.63/1.26 (c0_1(a3)),
% 1.63/1.26 inference(unit_resolution,[status(thm)],[190, 163])).
% 1.63/1.26 tff(192,plain,
% 1.63/1.26 (((~hskp4) | c3_1(a5)) <=> ((~hskp4) | c3_1(a5))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(193,axiom,((~hskp4) | c3_1(a5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.63/1.26 tff(194,plain,
% 1.63/1.26 ((~hskp4) | c3_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.63/1.26 tff(195,plain,
% 1.63/1.26 ((~hskp4) | c3_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[194, 192])).
% 1.63/1.26 tff(196,plain,
% 1.63/1.26 ((~hskp4) | c3_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[195, 192])).
% 1.63/1.26 tff(197,plain,
% 1.63/1.26 ((~hskp4) | c3_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[196, 192])).
% 1.63/1.26 tff(198,plain,
% 1.63/1.26 ((~hskp4) | c3_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[197, 192])).
% 1.63/1.26 tff(199,plain,
% 1.63/1.26 ((~hskp4) | c3_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[198, 192])).
% 1.63/1.26 tff(200,plain,
% 1.63/1.26 ((~hskp4) | c3_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[199, 192])).
% 1.63/1.26 tff(201,plain,
% 1.63/1.26 ((~hskp4) | c3_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[200, 192])).
% 1.63/1.26 tff(202,plain,
% 1.63/1.26 (c3_1(a5)),
% 1.63/1.26 inference(unit_resolution,[status(thm)],[201, 156])).
% 1.63/1.26 tff(203,plain,
% 1.63/1.26 (((~hskp4) | c2_1(a5)) <=> ((~hskp4) | c2_1(a5))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(204,axiom,((~hskp4) | c2_1(a5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.63/1.26 tff(205,plain,
% 1.63/1.26 ((~hskp4) | c2_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[204, 203])).
% 1.63/1.26 tff(206,plain,
% 1.63/1.26 ((~hskp4) | c2_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[205, 203])).
% 1.63/1.26 tff(207,plain,
% 1.63/1.26 ((~hskp4) | c2_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[206, 203])).
% 1.63/1.26 tff(208,plain,
% 1.63/1.26 ((~hskp4) | c2_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[207, 203])).
% 1.63/1.26 tff(209,plain,
% 1.63/1.26 ((~hskp4) | c2_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[208, 203])).
% 1.63/1.26 tff(210,plain,
% 1.63/1.26 ((~hskp4) | c2_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[209, 203])).
% 1.63/1.26 tff(211,plain,
% 1.63/1.26 ((~hskp4) | c2_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[210, 203])).
% 1.63/1.26 tff(212,plain,
% 1.63/1.26 ((~hskp4) | c2_1(a5)),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[211, 203])).
% 1.63/1.26 tff(213,plain,
% 1.63/1.26 (c2_1(a5)),
% 1.63/1.26 inference(unit_resolution,[status(thm)],[212, 156])).
% 1.63/1.26 tff(214,assumption,(~c1_1(a5)), introduced(assumption)).
% 1.63/1.26 tff(215,assumption,(hskp3), introduced(assumption)).
% 1.63/1.26 tff(216,plain,
% 1.63/1.26 (((~hskp3) | (~c0_1(a4))) <=> ((~hskp3) | (~c0_1(a4)))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(217,plain,
% 1.63/1.26 (((~c0_1(a4)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a4)))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(218,axiom,((~c0_1(a4)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.63/1.26 tff(219,plain,
% 1.63/1.26 ((~hskp3) | (~c0_1(a4))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[218, 217])).
% 1.63/1.26 tff(220,plain,
% 1.63/1.26 ((~hskp3) | (~c0_1(a4))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[219, 216])).
% 1.63/1.26 tff(221,plain,
% 1.63/1.26 (~c0_1(a4)),
% 1.63/1.26 inference(unit_resolution,[status(thm)],[220, 215])).
% 1.63/1.26 tff(222,plain,
% 1.63/1.26 (((~hskp3) | (~c1_1(a4))) <=> ((~hskp3) | (~c1_1(a4)))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(223,plain,
% 1.63/1.26 (((~c1_1(a4)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a4)))),
% 1.63/1.26 inference(rewrite,[status(thm)],[])).
% 1.63/1.26 tff(224,axiom,((~c1_1(a4)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.63/1.26 tff(225,plain,
% 1.63/1.26 ((~hskp3) | (~c1_1(a4))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.63/1.26 tff(226,plain,
% 1.63/1.26 ((~hskp3) | (~c1_1(a4))),
% 1.63/1.26 inference(modus_ponens,[status(thm)],[225, 222])).
% 1.63/1.26 tff(227,plain,
% 1.63/1.26 (~c1_1(a4)),
% 1.63/1.26 inference(unit_resolution,[status(thm)],[226, 215])).
% 1.63/1.26 tff(228,assumption,(~c1_1(a4)), introduced(assumption)).
% 1.63/1.26 tff(229,assumption,(~c0_1(a4)), introduced(assumption)).
% 1.63/1.26 tff(230,assumption,(~c3_1(a6)), introduced(assumption)).
% 1.63/1.26 tff(231,assumption,(~c3_1(a4)), introduced(assumption)).
% 1.63/1.27 tff(232,plain,
% 1.63/1.27 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c3_1(a4) | c0_1(a4) | c1_1(a4) | (~ndr1_0))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c3_1(a4) | c0_1(a4) | c1_1(a4) | (~ndr1_0))),
% 1.63/1.27 inference(rewrite,[status(thm)],[])).
% 1.63/1.27 tff(233,plain,
% 1.63/1.27 ((hskp4 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c0_1(a4)) <=> (hskp4 | c3_1(a4) | c0_1(a4) | c1_1(a4) | (~ndr1_0))),
% 1.63/1.27 inference(rewrite,[status(thm)],[])).
% 1.63/1.27 tff(234,plain,
% 1.63/1.27 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c3_1(a4) | c0_1(a4) | c1_1(a4) | (~ndr1_0)))),
% 1.63/1.27 inference(monotonicity,[status(thm)],[233])).
% 1.63/1.27 tff(235,plain,
% 1.63/1.27 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c3_1(a4) | c0_1(a4) | c1_1(a4) | (~ndr1_0))),
% 1.63/1.27 inference(transitivity,[status(thm)],[234, 232])).
% 1.63/1.27 tff(236,plain,
% 1.63/1.27 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c0_1(a4))),
% 1.63/1.27 inference(quant_inst,[status(thm)],[])).
% 1.63/1.27 tff(237,plain,
% 1.63/1.27 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c3_1(a4) | c0_1(a4) | c1_1(a4) | (~ndr1_0)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[236, 235])).
% 1.63/1.27 tff(238,plain,
% 1.63/1.27 (hskp4 | c3_1(a4) | c0_1(a4)),
% 1.63/1.27 inference(unit_resolution,[status(thm)],[237, 84, 228, 113])).
% 1.63/1.27 tff(239,plain,
% 1.63/1.27 (hskp4),
% 1.63/1.27 inference(unit_resolution,[status(thm)],[238, 231, 229])).
% 1.63/1.27 tff(240,plain,
% 1.63/1.27 (c3_1(a5)),
% 1.63/1.27 inference(unit_resolution,[status(thm)],[201, 239])).
% 1.63/1.27 tff(241,plain,
% 1.63/1.27 (c2_1(a5)),
% 1.63/1.27 inference(unit_resolution,[status(thm)],[212, 239])).
% 1.63/1.27 tff(242,assumption,(~c0_1(a5)), introduced(assumption)).
% 1.63/1.27 tff(243,plain,
% 1.63/1.27 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.63/1.27 inference(bind,[status(th)],[])).
% 1.63/1.27 tff(244,plain,
% 1.63/1.27 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.27 inference(quant_intro,[status(thm)],[243])).
% 1.63/1.27 tff(245,plain,
% 1.63/1.27 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.27 inference(rewrite,[status(thm)],[])).
% 1.63/1.27 tff(246,plain,
% 1.63/1.27 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.63/1.27 inference(bind,[status(th)],[])).
% 1.63/1.27 tff(247,plain,
% 1.63/1.27 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.27 inference(quant_intro,[status(thm)],[246])).
% 1.63/1.27 tff(248,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 1.63/1.27 tff(249,plain,
% 1.63/1.27 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[248, 247])).
% 1.63/1.27 tff(250,plain,
% 1.63/1.27 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[249, 245])).
% 1.63/1.27 tff(251,plain,(
% 1.63/1.27 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.27 inference(skolemize,[status(sab)],[250])).
% 1.63/1.27 tff(252,plain,
% 1.63/1.27 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[251, 244])).
% 1.63/1.27 tff(253,assumption,(~c1_1(a3)), introduced(assumption)).
% 1.63/1.27 tff(254,assumption,(c2_1(a3)), introduced(assumption)).
% 1.63/1.27 tff(255,assumption,(c0_1(a3)), introduced(assumption)).
% 1.63/1.27 tff(256,assumption,(c3_1(a5)), introduced(assumption)).
% 1.63/1.27 tff(257,assumption,(c2_1(a5)), introduced(assumption)).
% 1.63/1.27 tff(258,plain,
% 1.63/1.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)))),
% 1.63/1.27 inference(rewrite,[status(thm)],[])).
% 1.63/1.27 tff(259,plain,
% 1.63/1.27 ((hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5))) <=> (hskp5 | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)))),
% 1.63/1.27 inference(rewrite,[status(thm)],[])).
% 1.63/1.27 tff(260,plain,
% 1.63/1.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5))))),
% 1.63/1.27 inference(monotonicity,[status(thm)],[259])).
% 1.63/1.27 tff(261,plain,
% 1.63/1.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)))),
% 1.63/1.27 inference(transitivity,[status(thm)],[260, 258])).
% 1.63/1.27 tff(262,plain,
% 1.63/1.27 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))),
% 1.63/1.27 inference(quant_inst,[status(thm)],[])).
% 1.63/1.27 tff(263,plain,
% 1.63/1.27 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5))),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[262, 261])).
% 1.63/1.27 tff(264,plain,
% 1.63/1.27 (hskp5),
% 1.63/1.27 inference(unit_resolution,[status(thm)],[263, 84, 257, 256, 255, 254, 253, 252, 242])).
% 1.63/1.27 tff(265,plain,
% 1.63/1.27 (((~hskp5) | c0_1(a6)) <=> ((~hskp5) | c0_1(a6))),
% 1.63/1.27 inference(rewrite,[status(thm)],[])).
% 1.63/1.27 tff(266,axiom,((~hskp5) | c0_1(a6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.63/1.27 tff(267,plain,
% 1.63/1.27 ((~hskp5) | c0_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[266, 265])).
% 1.63/1.27 tff(268,plain,
% 1.63/1.27 ((~hskp5) | c0_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[267, 265])).
% 1.63/1.27 tff(269,plain,
% 1.63/1.27 ((~hskp5) | c0_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[268, 265])).
% 1.63/1.27 tff(270,plain,
% 1.63/1.27 ((~hskp5) | c0_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[269, 265])).
% 1.63/1.27 tff(271,plain,
% 1.63/1.27 ((~hskp5) | c0_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[270, 265])).
% 1.63/1.27 tff(272,plain,
% 1.63/1.27 ((~hskp5) | c0_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[271, 265])).
% 1.63/1.27 tff(273,plain,
% 1.63/1.27 ((~hskp5) | c0_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[272, 265])).
% 1.63/1.27 tff(274,plain,
% 1.63/1.27 ((~hskp5) | c0_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[273, 265])).
% 1.63/1.27 tff(275,plain,
% 1.63/1.27 (c0_1(a6)),
% 1.63/1.27 inference(unit_resolution,[status(thm)],[274, 264])).
% 1.63/1.27 tff(276,plain,
% 1.63/1.27 (((~hskp5) | c2_1(a6)) <=> ((~hskp5) | c2_1(a6))),
% 1.63/1.27 inference(rewrite,[status(thm)],[])).
% 1.63/1.27 tff(277,axiom,((~hskp5) | c2_1(a6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.63/1.27 tff(278,plain,
% 1.63/1.27 ((~hskp5) | c2_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[277, 276])).
% 1.63/1.27 tff(279,plain,
% 1.63/1.27 ((~hskp5) | c2_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[278, 276])).
% 1.63/1.27 tff(280,plain,
% 1.63/1.27 ((~hskp5) | c2_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[279, 276])).
% 1.63/1.27 tff(281,plain,
% 1.63/1.27 ((~hskp5) | c2_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[280, 276])).
% 1.63/1.27 tff(282,plain,
% 1.63/1.27 ((~hskp5) | c2_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[281, 276])).
% 1.63/1.27 tff(283,plain,
% 1.63/1.27 ((~hskp5) | c2_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[282, 276])).
% 1.63/1.27 tff(284,plain,
% 1.63/1.27 ((~hskp5) | c2_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[283, 276])).
% 1.63/1.27 tff(285,plain,
% 1.63/1.27 ((~hskp5) | c2_1(a6)),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[284, 276])).
% 1.63/1.27 tff(286,plain,
% 1.63/1.27 (c2_1(a6)),
% 1.63/1.27 inference(unit_resolution,[status(thm)],[285, 264])).
% 1.63/1.27 tff(287,plain,
% 1.63/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a6) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a6)) | (~c0_1(a6)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a6) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a6)) | (~c0_1(a6)))),
% 1.63/1.27 inference(rewrite,[status(thm)],[])).
% 1.63/1.27 tff(288,plain,
% 1.63/1.27 (((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5))) <=> (c3_1(a6) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a6)) | (~c0_1(a6)))),
% 1.63/1.27 inference(rewrite,[status(thm)],[])).
% 1.63/1.27 tff(289,plain,
% 1.63/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a6) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a6)) | (~c0_1(a6))))),
% 1.63/1.27 inference(monotonicity,[status(thm)],[288])).
% 1.63/1.27 tff(290,plain,
% 1.63/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a6) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a6)) | (~c0_1(a6)))),
% 1.63/1.27 inference(transitivity,[status(thm)],[289, 287])).
% 1.63/1.27 tff(291,plain,
% 1.63/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.63/1.27 inference(quant_inst,[status(thm)],[])).
% 1.63/1.27 tff(292,plain,
% 1.63/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a6) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a6)) | (~c0_1(a6))),
% 1.63/1.27 inference(modus_ponens,[status(thm)],[291, 290])).
% 1.63/1.27 tff(293,plain,
% 1.63/1.27 ((~c2_1(a6)) | (~c0_1(a6))),
% 1.63/1.27 inference(unit_resolution,[status(thm)],[292, 84, 257, 256, 255, 254, 230, 253, 103, 242])).
% 1.63/1.27 tff(294,plain,
% 1.63/1.27 ($false),
% 1.63/1.27 inference(unit_resolution,[status(thm)],[293, 286, 275])).
% 1.63/1.27 tff(295,plain,(c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | (~c0_1(a3)) | (~c2_1(a3)) | c3_1(a6) | c1_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.27 tff(296,plain,
% 1.63/1.27 (c0_1(a5)),
% 1.63/1.27 inference(unit_resolution,[status(thm)],[295, 241, 240, 191, 180, 230, 169])).
% 1.63/1.27 tff(297,plain,
% 1.63/1.27 (^[U: $i] : refl((hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))),
% 1.63/1.27 inference(bind,[status(th)],[])).
% 1.63/1.27 tff(298,plain,
% 1.63/1.27 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.63/1.27 inference(quant_intro,[status(thm)],[297])).
% 1.63/1.27 tff(299,plain,
% 1.63/1.27 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.63/1.27 inference(rewrite,[status(thm)],[])).
% 1.63/1.27 tff(300,plain,
% 1.63/1.27 (^[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) | c1_1(U) | c2_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp30) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp30))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp30) | hskp18) <=> ((hskp30 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp18))), rewrite(((hskp30 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp18) <=> (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp30) | hskp18) <=> (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))))),
% 1.63/1.28 inference(bind,[status(th)],[])).
% 1.63/1.28 tff(301,plain,
% 1.63/1.28 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp30) | hskp18) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.63/1.28 inference(quant_intro,[status(thm)],[300])).
% 1.63/1.28 tff(302,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp30) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.63/1.28 tff(303,plain,
% 1.63/1.28 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.63/1.28 inference(modus_ponens,[status(thm)],[302, 301])).
% 1.63/1.28 tff(304,plain,
% 1.63/1.28 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.63/1.28 inference(modus_ponens,[status(thm)],[303, 299])).
% 1.63/1.28 tff(305,plain,(
% 1.63/1.28 ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.63/1.28 inference(skolemize,[status(sab)],[304])).
% 1.63/1.28 tff(306,plain,
% 1.63/1.28 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.63/1.28 inference(modus_ponens,[status(thm)],[305, 298])).
% 1.63/1.28 tff(307,assumption,(~hskp14), introduced(assumption)).
% 1.63/1.28 tff(308,plain,
% 1.63/1.28 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c3_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c3_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4))),
% 1.63/1.28 inference(rewrite,[status(thm)],[])).
% 1.63/1.28 tff(309,plain,
% 1.63/1.28 ((hskp30 | hskp18 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c2_1(a4)) <=> (hskp30 | hskp18 | c3_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4))),
% 1.63/1.28 inference(rewrite,[status(thm)],[])).
% 1.63/1.28 tff(310,plain,
% 1.63/1.28 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c2_1(a4))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c3_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4)))),
% 1.63/1.28 inference(monotonicity,[status(thm)],[309])).
% 1.63/1.28 tff(311,plain,
% 1.63/1.28 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c2_1(a4))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c3_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4))),
% 1.63/1.28 inference(transitivity,[status(thm)],[310, 308])).
% 1.63/1.28 tff(312,plain,
% 1.63/1.28 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c2_1(a4))),
% 1.63/1.28 inference(quant_inst,[status(thm)],[])).
% 1.63/1.28 tff(313,plain,
% 1.63/1.28 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c3_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4)),
% 1.63/1.28 inference(modus_ponens,[status(thm)],[312, 311])).
% 1.63/1.28 tff(314,plain,
% 1.63/1.28 (c3_1(a4) | c2_1(a4)),
% 1.63/1.28 inference(unit_resolution,[status(thm)],[313, 135, 84, 134, 228, 306])).
% 1.63/1.28 tff(315,plain,
% 1.63/1.28 (c2_1(a4)),
% 1.63/1.28 inference(unit_resolution,[status(thm)],[314, 231])).
% 1.63/1.28 tff(316,plain,
% 1.63/1.28 (^[U: $i] : refl((hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.63/1.28 inference(bind,[status(th)],[])).
% 1.63/1.28 tff(317,plain,
% 1.63/1.28 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.28 inference(quant_intro,[status(thm)],[316])).
% 1.63/1.28 tff(318,plain,
% 1.63/1.28 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.28 inference(rewrite,[status(thm)],[])).
% 1.63/1.28 tff(319,plain,
% 1.63/1.28 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) | hskp14) <=> ((hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14))), rewrite(((hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) | hskp14) <=> (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.63/1.28 inference(bind,[status(th)],[])).
% 1.63/1.28 tff(320,plain,
% 1.63/1.28 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) | hskp14) <=> ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.28 inference(quant_intro,[status(thm)],[319])).
% 1.63/1.28 tff(321,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.63/1.28 tff(322,plain,
% 1.63/1.28 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.28 inference(modus_ponens,[status(thm)],[321, 320])).
% 1.63/1.28 tff(323,plain,
% 1.63/1.28 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.28 inference(modus_ponens,[status(thm)],[322, 318])).
% 1.63/1.28 tff(324,plain,(
% 1.63/1.28 ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.28 inference(skolemize,[status(sab)],[323])).
% 1.63/1.28 tff(325,plain,
% 1.63/1.28 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.63/1.28 inference(modus_ponens,[status(thm)],[324, 317])).
% 1.63/1.28 tff(326,assumption,(c2_1(a4)), introduced(assumption)).
% 1.63/1.28 tff(327,plain,
% 1.63/1.28 (^[U: $i] : refl((hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.63/1.28 inference(bind,[status(th)],[])).
% 1.63/1.28 tff(328,plain,
% 1.63/1.28 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.28 inference(quant_intro,[status(thm)],[327])).
% 1.63/1.28 tff(329,plain,
% 1.63/1.28 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.28 inference(rewrite,[status(thm)],[])).
% 1.63/1.28 tff(330,plain,
% 1.63/1.28 (^[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)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp14) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp14))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp14) <=> (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp14) <=> (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.63/1.28 inference(bind,[status(th)],[])).
% 1.63/1.28 tff(331,plain,
% 1.63/1.28 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp14) <=> ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.28 inference(quant_intro,[status(thm)],[330])).
% 1.63/1.28 tff(332,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 1.63/1.28 tff(333,plain,
% 1.63/1.28 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.28 inference(modus_ponens,[status(thm)],[332, 331])).
% 1.63/1.28 tff(334,plain,
% 1.63/1.28 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.28 inference(modus_ponens,[status(thm)],[333, 329])).
% 1.63/1.28 tff(335,plain,(
% 1.63/1.28 ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.28 inference(skolemize,[status(sab)],[334])).
% 1.63/1.28 tff(336,plain,
% 1.63/1.28 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.28 inference(modus_ponens,[status(thm)],[335, 328])).
% 1.63/1.28 tff(337,plain,
% 1.63/1.28 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | c3_1(a4) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c3_1(a4) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)))),
% 1.63/1.28 inference(rewrite,[status(thm)],[])).
% 1.63/1.28 tff(338,plain,
% 1.63/1.28 ((hskp29 | hskp14 | (~ndr1_0) | c3_1(a4) | c0_1(a4) | (~c2_1(a4))) <=> (hskp29 | hskp14 | c3_1(a4) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)))),
% 1.63/1.28 inference(rewrite,[status(thm)],[])).
% 1.63/1.28 tff(339,plain,
% 1.63/1.28 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a4) | c0_1(a4) | (~c2_1(a4)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | c3_1(a4) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4))))),
% 1.63/1.28 inference(monotonicity,[status(thm)],[338])).
% 1.63/1.28 tff(340,plain,
% 1.63/1.28 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a4) | c0_1(a4) | (~c2_1(a4)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c3_1(a4) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)))),
% 1.63/1.28 inference(transitivity,[status(thm)],[339, 337])).
% 1.63/1.28 tff(341,plain,
% 1.63/1.28 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a4) | c0_1(a4) | (~c2_1(a4)))),
% 1.63/1.28 inference(quant_inst,[status(thm)],[])).
% 1.63/1.28 tff(342,plain,
% 1.63/1.28 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c3_1(a4) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4))),
% 1.63/1.28 inference(modus_ponens,[status(thm)],[341, 340])).
% 1.63/1.28 tff(343,plain,
% 1.63/1.28 (hskp29 | hskp14 | c3_1(a4) | (~c2_1(a4))),
% 1.63/1.28 inference(unit_resolution,[status(thm)],[342, 84, 229, 336])).
% 1.63/1.28 tff(344,plain,
% 1.63/1.28 (hskp29),
% 1.63/1.28 inference(unit_resolution,[status(thm)],[343, 307, 231, 326])).
% 1.63/1.28 tff(345,plain,
% 1.63/1.28 (((~hskp29) | c0_1(a25)) <=> ((~hskp29) | c0_1(a25))),
% 1.63/1.28 inference(rewrite,[status(thm)],[])).
% 1.63/1.28 tff(346,axiom,((~hskp29) | c0_1(a25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.63/1.28 tff(347,plain,
% 1.63/1.29 ((~hskp29) | c0_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[346, 345])).
% 1.63/1.29 tff(348,plain,
% 1.63/1.29 ((~hskp29) | c0_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[347, 345])).
% 1.63/1.29 tff(349,plain,
% 1.63/1.29 ((~hskp29) | c0_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[348, 345])).
% 1.63/1.29 tff(350,plain,
% 1.63/1.29 ((~hskp29) | c0_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[349, 345])).
% 1.63/1.29 tff(351,plain,
% 1.63/1.29 ((~hskp29) | c0_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[350, 345])).
% 1.63/1.29 tff(352,plain,
% 1.63/1.29 ((~hskp29) | c0_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[351, 345])).
% 1.63/1.29 tff(353,plain,
% 1.63/1.29 ((~hskp29) | c0_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[352, 345])).
% 1.63/1.29 tff(354,plain,
% 1.63/1.29 ((~hskp29) | c0_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[353, 345])).
% 1.63/1.29 tff(355,plain,
% 1.63/1.29 (c0_1(a25)),
% 1.63/1.29 inference(unit_resolution,[status(thm)],[354, 344])).
% 1.63/1.29 tff(356,plain,
% 1.63/1.29 (((~hskp29) | c2_1(a25)) <=> ((~hskp29) | c2_1(a25))),
% 1.63/1.29 inference(rewrite,[status(thm)],[])).
% 1.63/1.29 tff(357,axiom,((~hskp29) | c2_1(a25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.63/1.29 tff(358,plain,
% 1.63/1.29 ((~hskp29) | c2_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[357, 356])).
% 1.63/1.29 tff(359,plain,
% 1.63/1.29 ((~hskp29) | c2_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[358, 356])).
% 1.63/1.29 tff(360,plain,
% 1.63/1.29 ((~hskp29) | c2_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[359, 356])).
% 1.63/1.29 tff(361,plain,
% 1.63/1.29 ((~hskp29) | c2_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[360, 356])).
% 1.63/1.29 tff(362,plain,
% 1.63/1.29 ((~hskp29) | c2_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[361, 356])).
% 1.63/1.29 tff(363,plain,
% 1.63/1.29 ((~hskp29) | c2_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[362, 356])).
% 1.63/1.29 tff(364,plain,
% 1.63/1.29 ((~hskp29) | c2_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[363, 356])).
% 1.63/1.29 tff(365,plain,
% 1.63/1.29 ((~hskp29) | c2_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[364, 356])).
% 1.63/1.29 tff(366,plain,
% 1.63/1.29 (c2_1(a25)),
% 1.63/1.29 inference(unit_resolution,[status(thm)],[365, 344])).
% 1.63/1.29 tff(367,plain,
% 1.63/1.29 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W))))),
% 1.63/1.29 inference(bind,[status(th)],[])).
% 1.63/1.29 tff(368,plain,
% 1.63/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.29 inference(quant_intro,[status(thm)],[367])).
% 1.63/1.29 tff(369,plain,
% 1.63/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.29 inference(rewrite,[status(thm)],[])).
% 1.63/1.29 tff(370,plain,
% 1.63/1.29 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))))),
% 1.63/1.29 inference(bind,[status(th)],[])).
% 1.63/1.29 tff(371,plain,
% 1.63/1.29 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.29 inference(quant_intro,[status(thm)],[370])).
% 1.63/1.29 tff(372,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 1.63/1.29 tff(373,plain,
% 1.63/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[372, 371])).
% 1.63/1.29 tff(374,plain,
% 1.63/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[373, 369])).
% 1.63/1.29 tff(375,plain,(
% 1.63/1.29 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.29 inference(skolemize,[status(sab)],[374])).
% 1.63/1.29 tff(376,plain,
% 1.63/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[375, 368])).
% 1.63/1.29 tff(377,plain,
% 1.63/1.29 (((~hskp29) | c1_1(a25)) <=> ((~hskp29) | c1_1(a25))),
% 1.63/1.29 inference(rewrite,[status(thm)],[])).
% 1.63/1.29 tff(378,axiom,((~hskp29) | c1_1(a25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.63/1.29 tff(379,plain,
% 1.63/1.29 ((~hskp29) | c1_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[378, 377])).
% 1.63/1.29 tff(380,plain,
% 1.63/1.29 ((~hskp29) | c1_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[379, 377])).
% 1.63/1.29 tff(381,plain,
% 1.63/1.29 ((~hskp29) | c1_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[380, 377])).
% 1.63/1.29 tff(382,plain,
% 1.63/1.29 ((~hskp29) | c1_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[381, 377])).
% 1.63/1.29 tff(383,plain,
% 1.63/1.29 ((~hskp29) | c1_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[382, 377])).
% 1.63/1.29 tff(384,plain,
% 1.63/1.29 ((~hskp29) | c1_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[383, 377])).
% 1.63/1.29 tff(385,plain,
% 1.63/1.29 ((~hskp29) | c1_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[384, 377])).
% 1.63/1.29 tff(386,plain,
% 1.63/1.29 ((~hskp29) | c1_1(a25)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[385, 377])).
% 1.63/1.29 tff(387,plain,
% 1.63/1.29 (c1_1(a25)),
% 1.63/1.29 inference(unit_resolution,[status(thm)],[386, 344])).
% 1.63/1.29 tff(388,plain,
% 1.63/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c2_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.63/1.29 inference(rewrite,[status(thm)],[])).
% 1.63/1.29 tff(389,plain,
% 1.63/1.29 (((~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)) | (~c0_1(a25))) <=> ((~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.63/1.29 inference(rewrite,[status(thm)],[])).
% 1.63/1.29 tff(390,plain,
% 1.63/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c2_1(a25))))),
% 1.63/1.29 inference(monotonicity,[status(thm)],[389])).
% 1.63/1.29 tff(391,plain,
% 1.63/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.63/1.29 inference(transitivity,[status(thm)],[390, 388])).
% 1.63/1.29 tff(392,plain,
% 1.63/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)) | (~c0_1(a25)))),
% 1.63/1.29 inference(quant_inst,[status(thm)],[])).
% 1.63/1.29 tff(393,plain,
% 1.63/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c2_1(a25))),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[392, 391])).
% 1.63/1.29 tff(394,plain,
% 1.63/1.29 (~c3_1(a25)),
% 1.63/1.29 inference(unit_resolution,[status(thm)],[393, 84, 355, 387, 366, 376])).
% 1.63/1.29 tff(395,assumption,(hskp27), introduced(assumption)).
% 1.63/1.29 tff(396,plain,
% 1.63/1.29 (((~hskp27) | c3_1(a10)) <=> ((~hskp27) | c3_1(a10))),
% 1.63/1.29 inference(rewrite,[status(thm)],[])).
% 1.63/1.29 tff(397,axiom,((~hskp27) | c3_1(a10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 1.63/1.29 tff(398,plain,
% 1.63/1.29 ((~hskp27) | c3_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[397, 396])).
% 1.63/1.29 tff(399,plain,
% 1.63/1.29 ((~hskp27) | c3_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[398, 396])).
% 1.63/1.29 tff(400,plain,
% 1.63/1.29 ((~hskp27) | c3_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[399, 396])).
% 1.63/1.29 tff(401,plain,
% 1.63/1.29 ((~hskp27) | c3_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[400, 396])).
% 1.63/1.29 tff(402,plain,
% 1.63/1.29 ((~hskp27) | c3_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[401, 396])).
% 1.63/1.29 tff(403,plain,
% 1.63/1.29 ((~hskp27) | c3_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[402, 396])).
% 1.63/1.29 tff(404,plain,
% 1.63/1.29 ((~hskp27) | c3_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[403, 396])).
% 1.63/1.29 tff(405,plain,
% 1.63/1.29 ((~hskp27) | c3_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[404, 396])).
% 1.63/1.29 tff(406,plain,
% 1.63/1.29 (c3_1(a10)),
% 1.63/1.29 inference(unit_resolution,[status(thm)],[405, 395])).
% 1.63/1.29 tff(407,plain,
% 1.63/1.29 (((~hskp27) | c2_1(a10)) <=> ((~hskp27) | c2_1(a10))),
% 1.63/1.29 inference(rewrite,[status(thm)],[])).
% 1.63/1.29 tff(408,axiom,((~hskp27) | c2_1(a10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 1.63/1.29 tff(409,plain,
% 1.63/1.29 ((~hskp27) | c2_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[408, 407])).
% 1.63/1.29 tff(410,plain,
% 1.63/1.29 ((~hskp27) | c2_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[409, 407])).
% 1.63/1.29 tff(411,plain,
% 1.63/1.29 ((~hskp27) | c2_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[410, 407])).
% 1.63/1.29 tff(412,plain,
% 1.63/1.29 ((~hskp27) | c2_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[411, 407])).
% 1.63/1.29 tff(413,plain,
% 1.63/1.29 ((~hskp27) | c2_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[412, 407])).
% 1.63/1.29 tff(414,plain,
% 1.63/1.29 ((~hskp27) | c2_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[413, 407])).
% 1.63/1.29 tff(415,plain,
% 1.63/1.29 ((~hskp27) | c2_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[414, 407])).
% 1.63/1.29 tff(416,plain,
% 1.63/1.29 ((~hskp27) | c2_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[415, 407])).
% 1.63/1.29 tff(417,plain,
% 1.63/1.29 (c2_1(a10)),
% 1.63/1.29 inference(unit_resolution,[status(thm)],[416, 395])).
% 1.63/1.29 tff(418,plain,
% 1.63/1.29 (((~hskp27) | c1_1(a10)) <=> ((~hskp27) | c1_1(a10))),
% 1.63/1.29 inference(rewrite,[status(thm)],[])).
% 1.63/1.29 tff(419,axiom,((~hskp27) | c1_1(a10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.63/1.29 tff(420,plain,
% 1.63/1.29 ((~hskp27) | c1_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[419, 418])).
% 1.63/1.29 tff(421,plain,
% 1.63/1.29 ((~hskp27) | c1_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[420, 418])).
% 1.63/1.29 tff(422,plain,
% 1.63/1.29 ((~hskp27) | c1_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[421, 418])).
% 1.63/1.29 tff(423,plain,
% 1.63/1.29 ((~hskp27) | c1_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[422, 418])).
% 1.63/1.29 tff(424,plain,
% 1.63/1.29 ((~hskp27) | c1_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[423, 418])).
% 1.63/1.29 tff(425,plain,
% 1.63/1.29 ((~hskp27) | c1_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[424, 418])).
% 1.63/1.29 tff(426,plain,
% 1.63/1.29 ((~hskp27) | c1_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[425, 418])).
% 1.63/1.29 tff(427,plain,
% 1.63/1.29 ((~hskp27) | c1_1(a10)),
% 1.63/1.29 inference(modus_ponens,[status(thm)],[426, 418])).
% 1.63/1.30 tff(428,plain,
% 1.63/1.30 (c1_1(a10)),
% 1.63/1.30 inference(unit_resolution,[status(thm)],[427, 395])).
% 1.63/1.30 tff(429,plain,
% 1.63/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)))),
% 1.63/1.30 inference(rewrite,[status(thm)],[])).
% 1.63/1.30 tff(430,plain,
% 1.63/1.30 (((~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c0_1(a10))) <=> ((~ndr1_0) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)))),
% 1.63/1.30 inference(rewrite,[status(thm)],[])).
% 1.63/1.30 tff(431,plain,
% 1.63/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c0_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c0_1(a10))))),
% 1.63/1.30 inference(monotonicity,[status(thm)],[430])).
% 1.63/1.30 tff(432,plain,
% 1.63/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c0_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)))),
% 1.63/1.30 inference(transitivity,[status(thm)],[431, 429])).
% 1.63/1.30 tff(433,plain,
% 1.63/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c0_1(a10)))),
% 1.63/1.30 inference(quant_inst,[status(thm)],[])).
% 1.63/1.30 tff(434,plain,
% 1.63/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c0_1(a10))),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[433, 432])).
% 1.63/1.30 tff(435,plain,
% 1.63/1.30 (~c0_1(a10)),
% 1.63/1.30 inference(unit_resolution,[status(thm)],[434, 84, 428, 417, 406, 376])).
% 1.63/1.30 tff(436,assumption,(~c3_1(a25)), introduced(assumption)).
% 1.63/1.30 tff(437,assumption,(c2_1(a25)), introduced(assumption)).
% 1.63/1.30 tff(438,assumption,(c0_1(a25)), introduced(assumption)).
% 1.63/1.30 tff(439,plain,
% 1.63/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25) | (~c2_1(a10)) | (~c3_1(a10)) | c0_1(a10))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25) | (~c2_1(a10)) | (~c3_1(a10)) | c0_1(a10))),
% 1.63/1.30 inference(rewrite,[status(thm)],[])).
% 1.63/1.30 tff(440,plain,
% 1.63/1.30 (((~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a10) | (~c2_1(a10)) | (~c3_1(a10))) <=> (c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25) | (~c2_1(a10)) | (~c3_1(a10)) | c0_1(a10))),
% 1.63/1.30 inference(rewrite,[status(thm)],[])).
% 1.63/1.30 tff(441,plain,
% 1.63/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a10) | (~c2_1(a10)) | (~c3_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25) | (~c2_1(a10)) | (~c3_1(a10)) | c0_1(a10)))),
% 1.63/1.30 inference(monotonicity,[status(thm)],[440])).
% 1.63/1.30 tff(442,plain,
% 1.63/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a10) | (~c2_1(a10)) | (~c3_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25) | (~c2_1(a10)) | (~c3_1(a10)) | c0_1(a10))),
% 1.63/1.30 inference(transitivity,[status(thm)],[441, 439])).
% 1.63/1.30 tff(443,plain,
% 1.63/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a10) | (~c2_1(a10)) | (~c3_1(a10)))),
% 1.63/1.30 inference(quant_inst,[status(thm)],[])).
% 1.63/1.30 tff(444,plain,
% 1.63/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25) | (~c2_1(a10)) | (~c3_1(a10)) | c0_1(a10)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[443, 442])).
% 1.63/1.30 tff(445,plain,
% 1.63/1.30 ($false),
% 1.63/1.30 inference(unit_resolution,[status(thm)],[444, 84, 438, 437, 417, 406, 255, 254, 253, 103, 436, 435])).
% 1.63/1.30 tff(446,plain,((~hskp27) | (~c0_1(a25)) | (~c2_1(a25)) | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3) | c3_1(a25)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.30 tff(447,plain,
% 1.63/1.30 (~hskp27),
% 1.63/1.30 inference(unit_resolution,[status(thm)],[446, 394, 366, 255, 254, 253, 355])).
% 1.63/1.30 tff(448,plain,
% 1.63/1.30 (^[U: $i] : refl((hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.63/1.30 inference(bind,[status(th)],[])).
% 1.63/1.30 tff(449,plain,
% 1.63/1.30 (![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.30 inference(quant_intro,[status(thm)],[448])).
% 1.63/1.30 tff(450,plain,
% 1.63/1.30 (![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.30 inference(rewrite,[status(thm)],[])).
% 1.63/1.30 tff(451,plain,
% 1.63/1.30 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp25) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp25))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp25) <=> (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp25) <=> (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.63/1.30 inference(bind,[status(th)],[])).
% 1.63/1.30 tff(452,plain,
% 1.63/1.30 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp25) <=> ![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.30 inference(quant_intro,[status(thm)],[451])).
% 1.63/1.30 tff(453,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.63/1.30 tff(454,plain,
% 1.63/1.30 (![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[453, 452])).
% 1.63/1.30 tff(455,plain,
% 1.63/1.30 (![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[454, 450])).
% 1.63/1.30 tff(456,plain,(
% 1.63/1.30 ![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.30 inference(skolemize,[status(sab)],[455])).
% 1.63/1.30 tff(457,plain,
% 1.63/1.30 (![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[456, 449])).
% 1.63/1.30 tff(458,plain,
% 1.63/1.30 (((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | c3_1(a25))) <=> ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp25 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | c3_1(a25))),
% 1.63/1.30 inference(rewrite,[status(thm)],[])).
% 1.63/1.30 tff(459,plain,
% 1.63/1.30 ((hskp27 | hskp25 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25))) <=> (hskp27 | hskp25 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | c3_1(a25))),
% 1.63/1.30 inference(rewrite,[status(thm)],[])).
% 1.63/1.30 tff(460,plain,
% 1.63/1.30 (((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)))) <=> ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | c3_1(a25)))),
% 1.63/1.30 inference(monotonicity,[status(thm)],[459])).
% 1.63/1.30 tff(461,plain,
% 1.63/1.30 (((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)))) <=> ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp25 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | c3_1(a25))),
% 1.63/1.30 inference(transitivity,[status(thm)],[460, 458])).
% 1.63/1.30 tff(462,plain,
% 1.63/1.30 ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)))),
% 1.63/1.30 inference(quant_inst,[status(thm)],[])).
% 1.63/1.30 tff(463,plain,
% 1.63/1.30 ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp25 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | c3_1(a25)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[462, 461])).
% 1.63/1.30 tff(464,plain,
% 1.63/1.30 (hskp27 | hskp25),
% 1.63/1.30 inference(unit_resolution,[status(thm)],[463, 84, 387, 366, 457, 394])).
% 1.63/1.30 tff(465,plain,
% 1.63/1.30 (hskp25),
% 1.63/1.30 inference(unit_resolution,[status(thm)],[464, 447])).
% 1.63/1.30 tff(466,plain,
% 1.63/1.30 (((~hskp25) | (~c2_1(a64))) <=> ((~hskp25) | (~c2_1(a64)))),
% 1.63/1.30 inference(rewrite,[status(thm)],[])).
% 1.63/1.30 tff(467,plain,
% 1.63/1.30 (((~c2_1(a64)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a64)))),
% 1.63/1.30 inference(rewrite,[status(thm)],[])).
% 1.63/1.30 tff(468,axiom,((~c2_1(a64)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.63/1.30 tff(469,plain,
% 1.63/1.30 ((~hskp25) | (~c2_1(a64))),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[468, 467])).
% 1.63/1.30 tff(470,plain,
% 1.63/1.30 ((~hskp25) | (~c2_1(a64))),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[469, 466])).
% 1.63/1.30 tff(471,plain,
% 1.63/1.30 (~c2_1(a64)),
% 1.63/1.30 inference(unit_resolution,[status(thm)],[470, 465])).
% 1.63/1.30 tff(472,plain,
% 1.63/1.30 (((~hskp25) | c3_1(a64)) <=> ((~hskp25) | c3_1(a64))),
% 1.63/1.30 inference(rewrite,[status(thm)],[])).
% 1.63/1.30 tff(473,axiom,((~hskp25) | c3_1(a64)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.63/1.30 tff(474,plain,
% 1.63/1.30 ((~hskp25) | c3_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[473, 472])).
% 1.63/1.30 tff(475,plain,
% 1.63/1.30 ((~hskp25) | c3_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[474, 472])).
% 1.63/1.30 tff(476,plain,
% 1.63/1.30 ((~hskp25) | c3_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[475, 472])).
% 1.63/1.30 tff(477,plain,
% 1.63/1.30 ((~hskp25) | c3_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[476, 472])).
% 1.63/1.30 tff(478,plain,
% 1.63/1.30 ((~hskp25) | c3_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[477, 472])).
% 1.63/1.30 tff(479,plain,
% 1.63/1.30 ((~hskp25) | c3_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[478, 472])).
% 1.63/1.30 tff(480,plain,
% 1.63/1.30 ((~hskp25) | c3_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[479, 472])).
% 1.63/1.30 tff(481,plain,
% 1.63/1.30 ((~hskp25) | c3_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[480, 472])).
% 1.63/1.30 tff(482,plain,
% 1.63/1.30 (c3_1(a64)),
% 1.63/1.30 inference(unit_resolution,[status(thm)],[481, 465])).
% 1.63/1.30 tff(483,plain,
% 1.63/1.30 (((~hskp25) | c1_1(a64)) <=> ((~hskp25) | c1_1(a64))),
% 1.63/1.30 inference(rewrite,[status(thm)],[])).
% 1.63/1.30 tff(484,axiom,((~hskp25) | c1_1(a64)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 1.63/1.30 tff(485,plain,
% 1.63/1.30 ((~hskp25) | c1_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[484, 483])).
% 1.63/1.30 tff(486,plain,
% 1.63/1.30 ((~hskp25) | c1_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[485, 483])).
% 1.63/1.30 tff(487,plain,
% 1.63/1.30 ((~hskp25) | c1_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[486, 483])).
% 1.63/1.30 tff(488,plain,
% 1.63/1.30 ((~hskp25) | c1_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[487, 483])).
% 1.63/1.30 tff(489,plain,
% 1.63/1.30 ((~hskp25) | c1_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[488, 483])).
% 1.63/1.30 tff(490,plain,
% 1.63/1.30 ((~hskp25) | c1_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[489, 483])).
% 1.63/1.30 tff(491,plain,
% 1.63/1.30 ((~hskp25) | c1_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[490, 483])).
% 1.63/1.30 tff(492,plain,
% 1.63/1.30 ((~hskp25) | c1_1(a64)),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[491, 483])).
% 1.63/1.30 tff(493,plain,
% 1.63/1.30 (c1_1(a64)),
% 1.63/1.30 inference(unit_resolution,[status(thm)],[492, 465])).
% 1.63/1.30 tff(494,plain,
% 1.63/1.30 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | c2_1(a64) | (~ndr1_0) | (~c3_1(a64)) | (~c1_1(a64)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c2_1(a64) | (~ndr1_0) | (~c3_1(a64)) | (~c1_1(a64)))),
% 1.63/1.30 inference(rewrite,[status(thm)],[])).
% 1.63/1.30 tff(495,plain,
% 1.63/1.30 ((hskp18 | hskp14 | (~ndr1_0) | c2_1(a64) | (~c3_1(a64)) | (~c1_1(a64))) <=> (hskp18 | hskp14 | c2_1(a64) | (~ndr1_0) | (~c3_1(a64)) | (~c1_1(a64)))),
% 1.63/1.30 inference(rewrite,[status(thm)],[])).
% 1.63/1.30 tff(496,plain,
% 1.63/1.30 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a64) | (~c3_1(a64)) | (~c1_1(a64)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | c2_1(a64) | (~ndr1_0) | (~c3_1(a64)) | (~c1_1(a64))))),
% 1.63/1.30 inference(monotonicity,[status(thm)],[495])).
% 1.63/1.30 tff(497,plain,
% 1.63/1.30 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a64) | (~c3_1(a64)) | (~c1_1(a64)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c2_1(a64) | (~ndr1_0) | (~c3_1(a64)) | (~c1_1(a64)))),
% 1.63/1.30 inference(transitivity,[status(thm)],[496, 494])).
% 1.63/1.30 tff(498,plain,
% 1.63/1.30 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a64) | (~c3_1(a64)) | (~c1_1(a64)))),
% 1.63/1.30 inference(quant_inst,[status(thm)],[])).
% 1.63/1.30 tff(499,plain,
% 1.63/1.30 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c2_1(a64) | (~ndr1_0) | (~c3_1(a64)) | (~c1_1(a64))),
% 1.63/1.30 inference(modus_ponens,[status(thm)],[498, 497])).
% 1.63/1.30 tff(500,plain,
% 1.63/1.30 ($false),
% 1.63/1.30 inference(unit_resolution,[status(thm)],[499, 84, 134, 307, 493, 482, 471, 325])).
% 1.63/1.31 tff(501,plain,(hskp14 | hskp18 | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3) | c3_1(a4) | (~c2_1(a4)) | c0_1(a4)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.31 tff(502,plain,
% 1.63/1.31 ($false),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[501, 315, 231, 191, 180, 169, 134, 307, 229])).
% 1.63/1.31 tff(503,plain,(c3_1(a4) | hskp18 | hskp14 | c0_1(a4) | hskp30 | c1_1(a4)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.31 tff(504,plain,
% 1.63/1.31 (hskp14),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[503, 231, 134, 229, 135, 228])).
% 1.63/1.31 tff(505,plain,
% 1.63/1.31 (((~hskp14) | (~c2_1(a26))) <=> ((~hskp14) | (~c2_1(a26)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(506,plain,
% 1.63/1.31 (((~c2_1(a26)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a26)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(507,axiom,((~c2_1(a26)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.63/1.31 tff(508,plain,
% 1.63/1.31 ((~hskp14) | (~c2_1(a26))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[507, 506])).
% 1.63/1.31 tff(509,plain,
% 1.63/1.31 ((~hskp14) | (~c2_1(a26))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[508, 505])).
% 1.63/1.31 tff(510,plain,
% 1.63/1.31 (~c2_1(a26)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[509, 504])).
% 1.63/1.31 tff(511,plain,
% 1.63/1.31 (((~hskp14) | (~c1_1(a26))) <=> ((~hskp14) | (~c1_1(a26)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(512,plain,
% 1.63/1.31 (((~c1_1(a26)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a26)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(513,axiom,((~c1_1(a26)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.63/1.31 tff(514,plain,
% 1.63/1.31 ((~hskp14) | (~c1_1(a26))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[513, 512])).
% 1.63/1.31 tff(515,plain,
% 1.63/1.31 ((~hskp14) | (~c1_1(a26))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[514, 511])).
% 1.63/1.31 tff(516,plain,
% 1.63/1.31 (~c1_1(a26)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[515, 504])).
% 1.63/1.31 tff(517,plain,
% 1.63/1.31 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c3_1(a26))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c3_1(a26))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(518,plain,
% 1.63/1.31 ((hskp30 | hskp18 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c2_1(a26)) <=> (hskp30 | hskp18 | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c3_1(a26))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(519,plain,
% 1.63/1.31 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c2_1(a26))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c3_1(a26)))),
% 1.63/1.31 inference(monotonicity,[status(thm)],[518])).
% 1.63/1.31 tff(520,plain,
% 1.63/1.31 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c2_1(a26))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c3_1(a26))),
% 1.63/1.31 inference(transitivity,[status(thm)],[519, 517])).
% 1.63/1.31 tff(521,plain,
% 1.63/1.31 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c2_1(a26))),
% 1.63/1.31 inference(quant_inst,[status(thm)],[])).
% 1.63/1.31 tff(522,plain,
% 1.63/1.31 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c3_1(a26)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[521, 520])).
% 1.63/1.31 tff(523,plain,
% 1.63/1.31 (c3_1(a26)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[522, 135, 84, 134, 516, 510, 306])).
% 1.63/1.31 tff(524,plain,
% 1.63/1.31 (^[U: $i] : refl((hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.63/1.31 inference(bind,[status(th)],[])).
% 1.63/1.31 tff(525,plain,
% 1.63/1.31 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.31 inference(quant_intro,[status(thm)],[524])).
% 1.63/1.31 tff(526,plain,
% 1.63/1.31 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(527,plain,
% 1.63/1.31 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp3) <=> ((hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp3))), rewrite(((hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp3) <=> (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp3) <=> (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.63/1.31 inference(bind,[status(th)],[])).
% 1.63/1.31 tff(528,plain,
% 1.63/1.31 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp3) <=> ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.31 inference(quant_intro,[status(thm)],[527])).
% 1.63/1.31 tff(529,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 1.63/1.31 tff(530,plain,
% 1.63/1.31 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[529, 528])).
% 1.63/1.31 tff(531,plain,
% 1.63/1.31 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[530, 526])).
% 1.63/1.31 tff(532,plain,(
% 1.63/1.31 ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.31 inference(skolemize,[status(sab)],[531])).
% 1.63/1.31 tff(533,plain,
% 1.63/1.31 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[532, 525])).
% 1.63/1.31 tff(534,plain,
% 1.63/1.31 (((~hskp14) | (~c0_1(a26))) <=> ((~hskp14) | (~c0_1(a26)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(535,plain,
% 1.63/1.31 (((~c0_1(a26)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a26)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(536,axiom,((~c0_1(a26)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.63/1.31 tff(537,plain,
% 1.63/1.31 ((~hskp14) | (~c0_1(a26))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[536, 535])).
% 1.63/1.31 tff(538,plain,
% 1.63/1.31 ((~hskp14) | (~c0_1(a26))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[537, 534])).
% 1.63/1.31 tff(539,plain,
% 1.63/1.31 (~c0_1(a26)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[538, 504])).
% 1.63/1.31 tff(540,plain,
% 1.63/1.31 (((~hskp3) | c3_1(a4)) <=> ((~hskp3) | c3_1(a4))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(541,axiom,((~hskp3) | c3_1(a4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.63/1.31 tff(542,plain,
% 1.63/1.31 ((~hskp3) | c3_1(a4)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[541, 540])).
% 1.63/1.31 tff(543,plain,
% 1.63/1.31 ((~hskp3) | c3_1(a4)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[542, 540])).
% 1.63/1.31 tff(544,plain,
% 1.63/1.31 ((~hskp3) | c3_1(a4)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[543, 540])).
% 1.63/1.31 tff(545,plain,
% 1.63/1.31 ((~hskp3) | c3_1(a4)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[544, 540])).
% 1.63/1.31 tff(546,plain,
% 1.63/1.31 ((~hskp3) | c3_1(a4)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[545, 540])).
% 1.63/1.31 tff(547,plain,
% 1.63/1.31 ((~hskp3) | c3_1(a4)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[546, 540])).
% 1.63/1.31 tff(548,plain,
% 1.63/1.31 ((~hskp3) | c3_1(a4)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[547, 540])).
% 1.63/1.31 tff(549,plain,
% 1.63/1.31 ((~hskp3) | c3_1(a4)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[548, 540])).
% 1.63/1.31 tff(550,plain,
% 1.63/1.31 (~hskp3),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[549, 231])).
% 1.63/1.31 tff(551,assumption,(~hskp9), introduced(assumption)).
% 1.63/1.31 tff(552,plain,
% 1.63/1.31 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp3 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp9 | hskp3 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(553,plain,
% 1.63/1.31 ((hskp9 | hskp3 | (~ndr1_0) | c1_1(a26) | c0_1(a26) | (~c3_1(a26))) <=> (hskp9 | hskp3 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(554,plain,
% 1.63/1.31 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp3 | (~ndr1_0) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp3 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26))))),
% 1.63/1.31 inference(monotonicity,[status(thm)],[553])).
% 1.63/1.31 tff(555,plain,
% 1.63/1.31 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp3 | (~ndr1_0) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp9 | hskp3 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)))),
% 1.63/1.31 inference(transitivity,[status(thm)],[554, 552])).
% 1.63/1.31 tff(556,plain,
% 1.63/1.31 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp3 | (~ndr1_0) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))),
% 1.63/1.31 inference(quant_inst,[status(thm)],[])).
% 1.63/1.31 tff(557,plain,
% 1.63/1.31 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp9 | hskp3 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[556, 555])).
% 1.63/1.31 tff(558,plain,
% 1.63/1.31 ($false),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[557, 84, 551, 550, 539, 516, 533, 523])).
% 1.63/1.31 tff(559,plain,(c3_1(a4) | hskp9 | hskp30 | hskp18 | c0_1(a4) | c1_1(a4)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.31 tff(560,plain,
% 1.63/1.31 (hskp9),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[559, 231, 135, 134, 229, 228])).
% 1.63/1.31 tff(561,plain,
% 1.63/1.31 (((~hskp9) | c1_1(a12)) <=> ((~hskp9) | c1_1(a12))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(562,axiom,((~hskp9) | c1_1(a12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.63/1.31 tff(563,plain,
% 1.63/1.31 ((~hskp9) | c1_1(a12)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[562, 561])).
% 1.63/1.31 tff(564,plain,
% 1.63/1.31 ((~hskp9) | c1_1(a12)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[563, 561])).
% 1.63/1.31 tff(565,plain,
% 1.63/1.31 ((~hskp9) | c1_1(a12)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[564, 561])).
% 1.63/1.31 tff(566,plain,
% 1.63/1.31 ((~hskp9) | c1_1(a12)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[565, 561])).
% 1.63/1.31 tff(567,plain,
% 1.63/1.31 ((~hskp9) | c1_1(a12)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[566, 561])).
% 1.63/1.31 tff(568,plain,
% 1.63/1.31 ((~hskp9) | c1_1(a12)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[567, 561])).
% 1.63/1.31 tff(569,plain,
% 1.63/1.31 ((~hskp9) | c1_1(a12)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[568, 561])).
% 1.63/1.31 tff(570,plain,
% 1.63/1.31 ((~hskp9) | c1_1(a12)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[569, 561])).
% 1.63/1.31 tff(571,plain,
% 1.63/1.31 (c1_1(a12)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[570, 560])).
% 1.63/1.31 tff(572,plain,
% 1.63/1.31 (((~hskp9) | (~c3_1(a12))) <=> ((~hskp9) | (~c3_1(a12)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(573,plain,
% 1.63/1.31 (((~c3_1(a12)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a12)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(574,axiom,((~c3_1(a12)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.63/1.31 tff(575,plain,
% 1.63/1.31 ((~hskp9) | (~c3_1(a12))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[574, 573])).
% 1.63/1.31 tff(576,plain,
% 1.63/1.31 ((~hskp9) | (~c3_1(a12))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[575, 572])).
% 1.63/1.31 tff(577,plain,
% 1.63/1.31 (~c3_1(a12)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[576, 560])).
% 1.63/1.31 tff(578,plain,
% 1.63/1.31 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))))),
% 1.63/1.31 inference(bind,[status(th)],[])).
% 1.63/1.31 tff(579,plain,
% 1.63/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.31 inference(quant_intro,[status(thm)],[578])).
% 1.63/1.31 tff(580,plain,
% 1.63/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(581,plain,
% 1.63/1.31 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))))),
% 1.63/1.32 inference(bind,[status(th)],[])).
% 1.63/1.32 tff(582,plain,
% 1.63/1.32 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.32 inference(quant_intro,[status(thm)],[581])).
% 1.63/1.32 tff(583,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.63/1.32 tff(584,plain,
% 1.63/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[583, 582])).
% 1.63/1.32 tff(585,plain,
% 1.63/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[584, 580])).
% 1.63/1.32 tff(586,plain,(
% 1.63/1.32 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.32 inference(skolemize,[status(sab)],[585])).
% 1.63/1.32 tff(587,plain,
% 1.63/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[586, 579])).
% 1.63/1.32 tff(588,assumption,(~hskp0), introduced(assumption)).
% 1.63/1.32 tff(589,plain,
% 1.63/1.32 (^[U: $i] : refl((hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.63/1.32 inference(bind,[status(th)],[])).
% 1.63/1.32 tff(590,plain,
% 1.63/1.32 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.63/1.32 inference(quant_intro,[status(thm)],[589])).
% 1.63/1.32 tff(591,plain,
% 1.63/1.32 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(592,plain,
% 1.63/1.32 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp0) <=> ((hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp0))), rewrite(((hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp0) <=> (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp0) <=> (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.70/1.32 inference(bind,[status(th)],[])).
% 1.70/1.32 tff(593,plain,
% 1.70/1.32 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp0) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.70/1.32 inference(quant_intro,[status(thm)],[592])).
% 1.70/1.32 tff(594,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.70/1.32 tff(595,plain,
% 1.70/1.32 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[594, 593])).
% 1.70/1.32 tff(596,plain,
% 1.70/1.32 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[595, 591])).
% 1.70/1.32 tff(597,plain,(
% 1.70/1.32 ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.70/1.32 inference(skolemize,[status(sab)],[596])).
% 1.70/1.32 tff(598,plain,
% 1.70/1.32 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[597, 590])).
% 1.70/1.32 tff(599,plain,
% 1.70/1.32 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.70/1.32 inference(rewrite,[status(thm)],[])).
% 1.70/1.32 tff(600,plain,
% 1.70/1.32 ((hskp1 | hskp0 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5))) <=> (hskp1 | hskp0 | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.70/1.32 inference(rewrite,[status(thm)],[])).
% 1.70/1.32 tff(601,plain,
% 1.70/1.32 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))))),
% 1.70/1.32 inference(monotonicity,[status(thm)],[600])).
% 1.70/1.32 tff(602,plain,
% 1.70/1.32 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.70/1.32 inference(transitivity,[status(thm)],[601, 599])).
% 1.70/1.32 tff(603,plain,
% 1.70/1.32 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.70/1.32 inference(quant_inst,[status(thm)],[])).
% 1.70/1.32 tff(604,plain,
% 1.70/1.32 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[603, 602])).
% 1.70/1.32 tff(605,plain,
% 1.70/1.32 (hskp1 | hskp0 | (~c2_1(a5)) | (~c3_1(a5))),
% 1.70/1.32 inference(unit_resolution,[status(thm)],[604, 84, 214, 598])).
% 1.70/1.32 tff(606,plain,
% 1.70/1.32 (hskp1),
% 1.70/1.32 inference(unit_resolution,[status(thm)],[605, 588, 257, 256])).
% 1.70/1.32 tff(607,plain,
% 1.70/1.32 (((~hskp1) | (~c2_1(a2))) <=> ((~hskp1) | (~c2_1(a2)))),
% 1.70/1.32 inference(rewrite,[status(thm)],[])).
% 1.70/1.32 tff(608,plain,
% 1.70/1.32 (((~c2_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a2)))),
% 1.70/1.32 inference(rewrite,[status(thm)],[])).
% 1.70/1.32 tff(609,axiom,((~c2_1(a2)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.70/1.32 tff(610,plain,
% 1.70/1.32 ((~hskp1) | (~c2_1(a2))),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[609, 608])).
% 1.70/1.32 tff(611,plain,
% 1.70/1.32 ((~hskp1) | (~c2_1(a2))),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[610, 607])).
% 1.70/1.32 tff(612,plain,
% 1.70/1.32 (~c2_1(a2)),
% 1.70/1.32 inference(unit_resolution,[status(thm)],[611, 606])).
% 1.70/1.32 tff(613,plain,
% 1.70/1.32 (((~hskp1) | c3_1(a2)) <=> ((~hskp1) | c3_1(a2))),
% 1.70/1.32 inference(rewrite,[status(thm)],[])).
% 1.70/1.32 tff(614,axiom,((~hskp1) | c3_1(a2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.70/1.32 tff(615,plain,
% 1.70/1.32 ((~hskp1) | c3_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[614, 613])).
% 1.70/1.32 tff(616,plain,
% 1.70/1.32 ((~hskp1) | c3_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[615, 613])).
% 1.70/1.32 tff(617,plain,
% 1.70/1.32 ((~hskp1) | c3_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[616, 613])).
% 1.70/1.32 tff(618,plain,
% 1.70/1.32 ((~hskp1) | c3_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[617, 613])).
% 1.70/1.32 tff(619,plain,
% 1.70/1.32 ((~hskp1) | c3_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[618, 613])).
% 1.70/1.32 tff(620,plain,
% 1.70/1.32 ((~hskp1) | c3_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[619, 613])).
% 1.70/1.32 tff(621,plain,
% 1.70/1.32 ((~hskp1) | c3_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[620, 613])).
% 1.70/1.32 tff(622,plain,
% 1.70/1.32 ((~hskp1) | c3_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[621, 613])).
% 1.70/1.32 tff(623,plain,
% 1.70/1.32 (c3_1(a2)),
% 1.70/1.32 inference(unit_resolution,[status(thm)],[622, 606])).
% 1.70/1.32 tff(624,plain,
% 1.70/1.32 (((~hskp1) | c0_1(a2)) <=> ((~hskp1) | c0_1(a2))),
% 1.70/1.32 inference(rewrite,[status(thm)],[])).
% 1.70/1.32 tff(625,axiom,((~hskp1) | c0_1(a2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.70/1.32 tff(626,plain,
% 1.70/1.32 ((~hskp1) | c0_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[625, 624])).
% 1.70/1.32 tff(627,plain,
% 1.70/1.32 ((~hskp1) | c0_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[626, 624])).
% 1.70/1.32 tff(628,plain,
% 1.70/1.32 ((~hskp1) | c0_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[627, 624])).
% 1.70/1.32 tff(629,plain,
% 1.70/1.32 ((~hskp1) | c0_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[628, 624])).
% 1.70/1.32 tff(630,plain,
% 1.70/1.32 ((~hskp1) | c0_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[629, 624])).
% 1.70/1.32 tff(631,plain,
% 1.70/1.32 ((~hskp1) | c0_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[630, 624])).
% 1.70/1.32 tff(632,plain,
% 1.70/1.32 ((~hskp1) | c0_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[631, 624])).
% 1.70/1.32 tff(633,plain,
% 1.70/1.32 ((~hskp1) | c0_1(a2)),
% 1.70/1.32 inference(modus_ponens,[status(thm)],[632, 624])).
% 1.70/1.32 tff(634,plain,
% 1.70/1.32 (c0_1(a2)),
% 1.70/1.32 inference(unit_resolution,[status(thm)],[633, 606])).
% 1.70/1.32 tff(635,plain,
% 1.70/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a3) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a3)) | (~c0_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a3) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a3)) | (~c0_1(a3)))),
% 1.70/1.32 inference(rewrite,[status(thm)],[])).
% 1.70/1.32 tff(636,plain,
% 1.70/1.32 (((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3))) <=> (c1_1(a3) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a3)) | (~c0_1(a3)))),
% 1.70/1.32 inference(rewrite,[status(thm)],[])).
% 1.70/1.32 tff(637,plain,
% 1.70/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a3) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a3)) | (~c0_1(a3))))),
% 1.70/1.33 inference(monotonicity,[status(thm)],[636])).
% 1.70/1.33 tff(638,plain,
% 1.70/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a3) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a3)) | (~c0_1(a3)))),
% 1.70/1.33 inference(transitivity,[status(thm)],[637, 635])).
% 1.70/1.33 tff(639,plain,
% 1.70/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)))),
% 1.70/1.33 inference(quant_inst,[status(thm)],[])).
% 1.70/1.33 tff(640,plain,
% 1.70/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a3) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a3)) | (~c0_1(a3))),
% 1.70/1.33 inference(modus_ponens,[status(thm)],[639, 638])).
% 1.70/1.33 tff(641,plain,
% 1.70/1.33 (~c1_1(a2)),
% 1.70/1.33 inference(unit_resolution,[status(thm)],[640, 84, 255, 254, 634, 623, 253, 612, 587])).
% 1.70/1.33 tff(642,plain,
% 1.70/1.33 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.70/1.33 inference(bind,[status(th)],[])).
% 1.70/1.33 tff(643,plain,
% 1.70/1.33 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.70/1.33 inference(quant_intro,[status(thm)],[642])).
% 1.70/1.33 tff(644,plain,
% 1.70/1.33 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.70/1.33 inference(rewrite,[status(thm)],[])).
% 1.70/1.33 tff(645,plain,
% 1.70/1.33 (^[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(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.70/1.33 inference(bind,[status(th)],[])).
% 1.70/1.33 tff(646,plain,
% 1.70/1.33 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.70/1.33 inference(quant_intro,[status(thm)],[645])).
% 1.70/1.33 tff(647,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 1.70/1.33 tff(648,plain,
% 1.70/1.33 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.70/1.33 inference(modus_ponens,[status(thm)],[647, 646])).
% 1.70/1.33 tff(649,plain,
% 1.70/1.33 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.70/1.33 inference(modus_ponens,[status(thm)],[648, 644])).
% 1.70/1.33 tff(650,plain,(
% 1.70/1.33 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.70/1.33 inference(skolemize,[status(sab)],[649])).
% 1.70/1.33 tff(651,plain,
% 1.70/1.33 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.70/1.33 inference(modus_ponens,[status(thm)],[650, 643])).
% 1.70/1.33 tff(652,assumption,(~c3_1(a12)), introduced(assumption)).
% 1.70/1.33 tff(653,assumption,(c1_1(a12)), introduced(assumption)).
% 1.70/1.33 tff(654,plain,
% 1.70/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c3_1(a12) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a12)) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a12) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a12)) | (~c1_1(a12)))),
% 1.70/1.33 inference(rewrite,[status(thm)],[])).
% 1.70/1.33 tff(655,plain,
% 1.70/1.33 ((hskp0 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2))) <=> (hskp0 | c3_1(a12) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a12)) | (~c1_1(a12)))),
% 1.70/1.33 inference(rewrite,[status(thm)],[])).
% 1.70/1.33 tff(656,plain,
% 1.70/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c3_1(a12) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a12)) | (~c1_1(a12))))),
% 1.70/1.33 inference(monotonicity,[status(thm)],[655])).
% 1.70/1.33 tff(657,plain,
% 1.70/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a12) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a12)) | (~c1_1(a12)))),
% 1.70/1.33 inference(transitivity,[status(thm)],[656, 654])).
% 1.70/1.33 tff(658,plain,
% 1.70/1.33 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))),
% 1.70/1.33 inference(quant_inst,[status(thm)],[])).
% 1.70/1.33 tff(659,plain,
% 1.70/1.33 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a12) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a12)) | (~c1_1(a12))),
% 1.70/1.33 inference(modus_ponens,[status(thm)],[658, 657])).
% 1.70/1.33 tff(660,plain,
% 1.70/1.33 (~c0_1(a12)),
% 1.70/1.33 inference(unit_resolution,[status(thm)],[659, 84, 588, 653, 623, 652, 612, 651, 641])).
% 1.70/1.33 tff(661,plain,
% 1.70/1.33 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.70/1.33 inference(bind,[status(th)],[])).
% 1.70/1.33 tff(662,plain,
% 1.70/1.33 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.70/1.33 inference(quant_intro,[status(thm)],[661])).
% 1.70/1.33 tff(663,plain,
% 1.70/1.33 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.70/1.33 inference(rewrite,[status(thm)],[])).
% 1.70/1.33 tff(664,plain,
% 1.70/1.33 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.70/1.33 inference(bind,[status(th)],[])).
% 1.70/1.33 tff(665,plain,
% 1.70/1.33 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.70/1.33 inference(quant_intro,[status(thm)],[664])).
% 1.70/1.33 tff(666,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 1.70/1.33 tff(667,plain,
% 1.70/1.33 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.70/1.33 inference(modus_ponens,[status(thm)],[666, 665])).
% 1.70/1.33 tff(668,plain,
% 1.70/1.33 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.70/1.33 inference(modus_ponens,[status(thm)],[667, 663])).
% 1.70/1.33 tff(669,plain,(
% 1.70/1.33 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.70/1.33 inference(skolemize,[status(sab)],[668])).
% 1.70/1.33 tff(670,plain,
% 1.70/1.33 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.70/1.33 inference(modus_ponens,[status(thm)],[669, 662])).
% 1.70/1.33 tff(671,plain,
% 1.70/1.33 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.70/1.33 inference(rewrite,[status(thm)],[])).
% 1.70/1.33 tff(672,plain,
% 1.70/1.33 ((hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2))) <=> (hskp22 | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.70/1.33 inference(rewrite,[status(thm)],[])).
% 1.70/1.33 tff(673,plain,
% 1.70/1.33 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a5))))),
% 1.70/1.33 inference(monotonicity,[status(thm)],[672])).
% 1.70/1.33 tff(674,plain,
% 1.70/1.33 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.70/1.33 inference(transitivity,[status(thm)],[673, 671])).
% 1.70/1.33 tff(675,plain,
% 1.70/1.33 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))),
% 1.70/1.33 inference(quant_inst,[status(thm)],[])).
% 1.70/1.33 tff(676,plain,
% 1.70/1.33 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a5))),
% 1.70/1.33 inference(modus_ponens,[status(thm)],[675, 674])).
% 1.70/1.33 tff(677,plain,
% 1.70/1.33 (hskp22),
% 1.70/1.33 inference(unit_resolution,[status(thm)],[676, 84, 257, 256, 623, 214, 612, 123, 641])).
% 1.70/1.33 tff(678,plain,
% 1.70/1.33 (((~hskp22) | (~c3_1(a43))) <=> ((~hskp22) | (~c3_1(a43)))),
% 1.70/1.33 inference(rewrite,[status(thm)],[])).
% 1.70/1.33 tff(679,plain,
% 1.70/1.33 (((~c3_1(a43)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a43)))),
% 1.70/1.33 inference(rewrite,[status(thm)],[])).
% 1.70/1.33 tff(680,axiom,((~c3_1(a43)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.70/1.34 tff(681,plain,
% 1.70/1.34 ((~hskp22) | (~c3_1(a43))),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[680, 679])).
% 1.70/1.34 tff(682,plain,
% 1.70/1.34 ((~hskp22) | (~c3_1(a43))),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[681, 678])).
% 1.70/1.34 tff(683,plain,
% 1.70/1.34 (~c3_1(a43)),
% 1.70/1.34 inference(unit_resolution,[status(thm)],[682, 677])).
% 1.70/1.34 tff(684,plain,
% 1.70/1.34 (((~hskp22) | (~c1_1(a43))) <=> ((~hskp22) | (~c1_1(a43)))),
% 1.70/1.34 inference(rewrite,[status(thm)],[])).
% 1.70/1.34 tff(685,plain,
% 1.70/1.34 (((~c1_1(a43)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a43)))),
% 1.70/1.34 inference(rewrite,[status(thm)],[])).
% 1.70/1.34 tff(686,axiom,((~c1_1(a43)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.70/1.34 tff(687,plain,
% 1.70/1.34 ((~hskp22) | (~c1_1(a43))),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[686, 685])).
% 1.70/1.34 tff(688,plain,
% 1.70/1.34 ((~hskp22) | (~c1_1(a43))),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[687, 684])).
% 1.70/1.34 tff(689,plain,
% 1.70/1.34 (~c1_1(a43)),
% 1.70/1.34 inference(unit_resolution,[status(thm)],[688, 677])).
% 1.70/1.34 tff(690,plain,
% 1.70/1.34 (((~hskp22) | c2_1(a43)) <=> ((~hskp22) | c2_1(a43))),
% 1.70/1.34 inference(rewrite,[status(thm)],[])).
% 1.70/1.34 tff(691,axiom,((~hskp22) | c2_1(a43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.70/1.34 tff(692,plain,
% 1.70/1.34 ((~hskp22) | c2_1(a43)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[691, 690])).
% 1.70/1.34 tff(693,plain,
% 1.70/1.34 ((~hskp22) | c2_1(a43)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[692, 690])).
% 1.70/1.34 tff(694,plain,
% 1.70/1.34 ((~hskp22) | c2_1(a43)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[693, 690])).
% 1.70/1.34 tff(695,plain,
% 1.70/1.34 ((~hskp22) | c2_1(a43)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[694, 690])).
% 1.70/1.34 tff(696,plain,
% 1.70/1.34 ((~hskp22) | c2_1(a43)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[695, 690])).
% 1.70/1.34 tff(697,plain,
% 1.70/1.34 ((~hskp22) | c2_1(a43)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[696, 690])).
% 1.70/1.34 tff(698,plain,
% 1.70/1.34 ((~hskp22) | c2_1(a43)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[697, 690])).
% 1.70/1.34 tff(699,plain,
% 1.70/1.34 ((~hskp22) | c2_1(a43)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[698, 690])).
% 1.70/1.34 tff(700,plain,
% 1.70/1.34 (c2_1(a43)),
% 1.70/1.34 inference(unit_resolution,[status(thm)],[699, 677])).
% 1.70/1.34 tff(701,plain,
% 1.70/1.34 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp0 | c1_1(a43) | c3_1(a43) | c3_1(a12) | (~ndr1_0) | c0_1(a12) | (~c1_1(a12)) | (~c2_1(a43)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp0 | c1_1(a43) | c3_1(a43) | c3_1(a12) | (~ndr1_0) | c0_1(a12) | (~c1_1(a12)) | (~c2_1(a43)))),
% 1.70/1.34 inference(rewrite,[status(thm)],[])).
% 1.70/1.34 tff(702,plain,
% 1.70/1.34 ((hskp0 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c2_1(a43)) | c0_1(a12) | c3_1(a12) | (~c1_1(a12))) <=> (hskp0 | c1_1(a43) | c3_1(a43) | c3_1(a12) | (~ndr1_0) | c0_1(a12) | (~c1_1(a12)) | (~c2_1(a43)))),
% 1.70/1.34 inference(rewrite,[status(thm)],[])).
% 1.70/1.34 tff(703,plain,
% 1.70/1.34 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c2_1(a43)) | c0_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp0 | c1_1(a43) | c3_1(a43) | c3_1(a12) | (~ndr1_0) | c0_1(a12) | (~c1_1(a12)) | (~c2_1(a43))))),
% 1.70/1.34 inference(monotonicity,[status(thm)],[702])).
% 1.70/1.34 tff(704,plain,
% 1.70/1.34 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c2_1(a43)) | c0_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp0 | c1_1(a43) | c3_1(a43) | c3_1(a12) | (~ndr1_0) | c0_1(a12) | (~c1_1(a12)) | (~c2_1(a43)))),
% 1.70/1.34 inference(transitivity,[status(thm)],[703, 701])).
% 1.70/1.34 tff(705,plain,
% 1.70/1.34 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c2_1(a43)) | c0_1(a12) | c3_1(a12) | (~c1_1(a12)))),
% 1.70/1.34 inference(quant_inst,[status(thm)],[])).
% 1.70/1.34 tff(706,plain,
% 1.70/1.34 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp0 | c1_1(a43) | c3_1(a43) | c3_1(a12) | (~ndr1_0) | c0_1(a12) | (~c1_1(a12)) | (~c2_1(a43))),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[705, 704])).
% 1.70/1.34 tff(707,plain,
% 1.70/1.34 ($false),
% 1.70/1.34 inference(unit_resolution,[status(thm)],[706, 84, 588, 700, 653, 689, 683, 652, 670, 660])).
% 1.70/1.34 tff(708,plain,(hskp0 | (~c1_1(a12)) | c3_1(a12) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.70/1.34 tff(709,plain,
% 1.70/1.34 (hskp0),
% 1.70/1.34 inference(unit_resolution,[status(thm)],[708, 241, 577, 571, 240, 214, 191, 180, 169])).
% 1.70/1.34 tff(710,plain,
% 1.70/1.34 (((~hskp0) | (~c0_1(a1))) <=> ((~hskp0) | (~c0_1(a1)))),
% 1.70/1.34 inference(rewrite,[status(thm)],[])).
% 1.70/1.34 tff(711,plain,
% 1.70/1.34 (((~c0_1(a1)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a1)))),
% 1.70/1.34 inference(rewrite,[status(thm)],[])).
% 1.70/1.34 tff(712,axiom,((~c0_1(a1)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 1.70/1.34 tff(713,plain,
% 1.70/1.34 ((~hskp0) | (~c0_1(a1))),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[712, 711])).
% 1.70/1.34 tff(714,plain,
% 1.70/1.34 ((~hskp0) | (~c0_1(a1))),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[713, 710])).
% 1.70/1.34 tff(715,plain,
% 1.70/1.34 (~c0_1(a1)),
% 1.70/1.34 inference(unit_resolution,[status(thm)],[714, 709])).
% 1.70/1.34 tff(716,plain,
% 1.70/1.34 (((~hskp0) | c1_1(a1)) <=> ((~hskp0) | c1_1(a1))),
% 1.70/1.34 inference(rewrite,[status(thm)],[])).
% 1.70/1.34 tff(717,axiom,((~hskp0) | c1_1(a1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 1.70/1.34 tff(718,plain,
% 1.70/1.34 ((~hskp0) | c1_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[717, 716])).
% 1.70/1.34 tff(719,plain,
% 1.70/1.34 ((~hskp0) | c1_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[718, 716])).
% 1.70/1.34 tff(720,plain,
% 1.70/1.34 ((~hskp0) | c1_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[719, 716])).
% 1.70/1.34 tff(721,plain,
% 1.70/1.34 ((~hskp0) | c1_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[720, 716])).
% 1.70/1.34 tff(722,plain,
% 1.70/1.34 ((~hskp0) | c1_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[721, 716])).
% 1.70/1.34 tff(723,plain,
% 1.70/1.34 ((~hskp0) | c1_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[722, 716])).
% 1.70/1.34 tff(724,plain,
% 1.70/1.34 ((~hskp0) | c1_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[723, 716])).
% 1.70/1.34 tff(725,plain,
% 1.70/1.34 ((~hskp0) | c1_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[724, 716])).
% 1.70/1.34 tff(726,plain,
% 1.70/1.34 (c1_1(a1)),
% 1.70/1.34 inference(unit_resolution,[status(thm)],[725, 709])).
% 1.70/1.34 tff(727,plain,
% 1.70/1.34 (((~hskp0) | c2_1(a1)) <=> ((~hskp0) | c2_1(a1))),
% 1.70/1.34 inference(rewrite,[status(thm)],[])).
% 1.70/1.34 tff(728,axiom,((~hskp0) | c2_1(a1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 1.70/1.34 tff(729,plain,
% 1.70/1.34 ((~hskp0) | c2_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[728, 727])).
% 1.70/1.34 tff(730,plain,
% 1.70/1.34 ((~hskp0) | c2_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[729, 727])).
% 1.70/1.34 tff(731,plain,
% 1.70/1.34 ((~hskp0) | c2_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[730, 727])).
% 1.70/1.34 tff(732,plain,
% 1.70/1.34 ((~hskp0) | c2_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[731, 727])).
% 1.70/1.34 tff(733,plain,
% 1.70/1.34 ((~hskp0) | c2_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[732, 727])).
% 1.70/1.34 tff(734,plain,
% 1.70/1.34 ((~hskp0) | c2_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[733, 727])).
% 1.70/1.34 tff(735,plain,
% 1.70/1.34 ((~hskp0) | c2_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[734, 727])).
% 1.70/1.34 tff(736,plain,
% 1.70/1.34 ((~hskp0) | c2_1(a1)),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[735, 727])).
% 1.70/1.34 tff(737,plain,
% 1.70/1.34 (c2_1(a1)),
% 1.70/1.34 inference(unit_resolution,[status(thm)],[736, 709])).
% 1.70/1.34 tff(738,assumption,(~c0_1(a1)), introduced(assumption)).
% 1.70/1.34 tff(739,assumption,(c0_1(a5)), introduced(assumption)).
% 1.70/1.34 tff(740,plain,
% 1.70/1.34 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.70/1.34 inference(bind,[status(th)],[])).
% 1.70/1.34 tff(741,plain,
% 1.70/1.34 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.70/1.34 inference(quant_intro,[status(thm)],[740])).
% 1.70/1.34 tff(742,plain,
% 1.70/1.34 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.70/1.34 inference(rewrite,[status(thm)],[])).
% 1.70/1.34 tff(743,plain,
% 1.70/1.34 (^[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(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)) | 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)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | 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)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.70/1.34 inference(bind,[status(th)],[])).
% 1.70/1.34 tff(744,plain,
% 1.70/1.34 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.70/1.34 inference(quant_intro,[status(thm)],[743])).
% 1.70/1.34 tff(745,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 1.70/1.34 tff(746,plain,
% 1.70/1.34 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[745, 744])).
% 1.70/1.34 tff(747,plain,
% 1.70/1.34 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[746, 742])).
% 1.70/1.34 tff(748,plain,(
% 1.70/1.34 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.70/1.34 inference(skolemize,[status(sab)],[747])).
% 1.70/1.34 tff(749,plain,
% 1.70/1.34 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.70/1.34 inference(modus_ponens,[status(thm)],[748, 741])).
% 1.70/1.35 tff(750,assumption,(hskp14), introduced(assumption)).
% 1.70/1.35 tff(751,plain,
% 1.70/1.35 (~c2_1(a26)),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[509, 750])).
% 1.70/1.35 tff(752,plain,
% 1.70/1.35 (~c1_1(a26)),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[515, 750])).
% 1.70/1.35 tff(753,plain,
% 1.70/1.35 (~c0_1(a26)),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[538, 750])).
% 1.70/1.35 tff(754,plain,
% 1.70/1.35 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.70/1.35 inference(rewrite,[status(thm)],[])).
% 1.70/1.35 tff(755,plain,
% 1.70/1.35 ((hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a26) | c1_1(a26) | c0_1(a26)) <=> (hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.70/1.35 inference(rewrite,[status(thm)],[])).
% 1.70/1.35 tff(756,plain,
% 1.70/1.35 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a26) | c1_1(a26) | c0_1(a26))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5))))),
% 1.70/1.35 inference(monotonicity,[status(thm)],[755])).
% 1.70/1.35 tff(757,plain,
% 1.70/1.35 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a26) | c1_1(a26) | c0_1(a26))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.70/1.35 inference(transitivity,[status(thm)],[756, 754])).
% 1.70/1.35 tff(758,plain,
% 1.70/1.35 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a26) | c1_1(a26) | c0_1(a26))),
% 1.70/1.35 inference(quant_inst,[status(thm)],[])).
% 1.70/1.35 tff(759,plain,
% 1.70/1.35 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5))),
% 1.70/1.35 inference(modus_ponens,[status(thm)],[758, 757])).
% 1.70/1.35 tff(760,plain,
% 1.70/1.35 (hskp1),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[759, 84, 257, 753, 752, 751, 214, 749, 739])).
% 1.70/1.35 tff(761,plain,
% 1.70/1.35 (~c2_1(a2)),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[611, 760])).
% 1.70/1.35 tff(762,plain,
% 1.70/1.35 (c3_1(a26)),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[522, 135, 84, 134, 752, 751, 306])).
% 1.70/1.35 tff(763,plain,
% 1.70/1.35 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a26)))),
% 1.70/1.35 inference(rewrite,[status(thm)],[])).
% 1.70/1.35 tff(764,plain,
% 1.70/1.35 ((hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26))) <=> (hskp22 | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a26)))),
% 1.70/1.35 inference(rewrite,[status(thm)],[])).
% 1.70/1.35 tff(765,plain,
% 1.70/1.35 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a26))))),
% 1.70/1.35 inference(monotonicity,[status(thm)],[764])).
% 1.70/1.35 tff(766,plain,
% 1.70/1.35 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a26)))),
% 1.70/1.35 inference(transitivity,[status(thm)],[765, 763])).
% 1.70/1.35 tff(767,plain,
% 1.70/1.35 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26)))),
% 1.70/1.35 inference(quant_inst,[status(thm)],[])).
% 1.70/1.35 tff(768,plain,
% 1.70/1.35 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a26))),
% 1.70/1.35 inference(modus_ponens,[status(thm)],[767, 766])).
% 1.70/1.35 tff(769,plain,
% 1.70/1.35 (hskp22 | (~c3_1(a26))),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[768, 84, 257, 256, 752, 751, 214, 123])).
% 1.70/1.35 tff(770,plain,
% 1.70/1.35 (hskp22),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[769, 762])).
% 1.70/1.35 tff(771,plain,
% 1.70/1.35 (~c3_1(a43)),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[682, 770])).
% 1.70/1.35 tff(772,plain,
% 1.70/1.35 (~c1_1(a43)),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[688, 770])).
% 1.70/1.35 tff(773,assumption,(c2_1(a1)), introduced(assumption)).
% 1.70/1.35 tff(774,assumption,(c1_1(a1)), introduced(assumption)).
% 1.70/1.35 tff(775,plain,
% 1.70/1.35 (c3_1(a2)),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[622, 760])).
% 1.70/1.35 tff(776,plain,
% 1.70/1.35 (c0_1(a2)),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[633, 760])).
% 1.70/1.35 tff(777,plain,
% 1.70/1.35 (c2_1(a43)),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[699, 770])).
% 1.70/1.35 tff(778,plain,
% 1.70/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c2_1(a2) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a2) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)))),
% 1.70/1.35 inference(rewrite,[status(thm)],[])).
% 1.70/1.35 tff(779,plain,
% 1.70/1.35 (((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1))) <=> (c1_1(a43) | c3_1(a43) | c2_1(a2) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)))),
% 1.70/1.35 inference(rewrite,[status(thm)],[])).
% 1.70/1.35 tff(780,plain,
% 1.70/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c2_1(a2) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43))))),
% 1.70/1.35 inference(monotonicity,[status(thm)],[779])).
% 1.70/1.35 tff(781,plain,
% 1.70/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a2) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)))),
% 1.70/1.35 inference(transitivity,[status(thm)],[780, 778])).
% 1.70/1.35 tff(782,plain,
% 1.70/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))),
% 1.70/1.35 inference(quant_inst,[status(thm)],[])).
% 1.70/1.35 tff(783,plain,
% 1.70/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a2) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43))),
% 1.70/1.35 inference(modus_ponens,[status(thm)],[782, 781])).
% 1.70/1.35 tff(784,plain,
% 1.70/1.35 ($false),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[783, 84, 777, 776, 775, 774, 773, 772, 771, 761, 738, 133])).
% 1.70/1.35 tff(785,plain,((~hskp14) | (~c1_1(a1)) | (~c2_1(a1)) | c0_1(a1) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | hskp30 | hskp18 | (~c0_1(a5))), inference(lemma,lemma(discharge,[]))).
% 1.70/1.35 tff(786,plain,
% 1.70/1.35 ($false),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[785, 737, 726, 504, 715, 241, 240, 214, 135, 134, 296])).
% 1.70/1.35 tff(787,plain,(c3_1(a4) | c1_1(a5) | hskp30 | hskp18 | c3_1(a6) | c0_1(a4) | c1_1(a4)), inference(lemma,lemma(discharge,[]))).
% 1.70/1.35 tff(788,plain,
% 1.70/1.35 (c3_1(a4)),
% 1.70/1.35 inference(unit_resolution,[status(thm)],[787, 230, 135, 134, 214, 229, 228])).
% 1.70/1.35 tff(789,plain,
% 1.70/1.35 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.70/1.35 inference(bind,[status(th)],[])).
% 1.70/1.35 tff(790,plain,
% 1.70/1.35 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.70/1.35 inference(quant_intro,[status(thm)],[789])).
% 1.70/1.35 tff(791,plain,
% 1.70/1.35 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.70/1.35 inference(rewrite,[status(thm)],[])).
% 1.70/1.35 tff(792,plain,
% 1.70/1.35 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.70/1.35 inference(bind,[status(th)],[])).
% 1.70/1.35 tff(793,plain,
% 1.70/1.35 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.70/1.35 inference(quant_intro,[status(thm)],[792])).
% 1.70/1.35 tff(794,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 1.70/1.35 tff(795,plain,
% 1.70/1.35 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.70/1.35 inference(modus_ponens,[status(thm)],[794, 793])).
% 1.70/1.35 tff(796,plain,
% 1.70/1.35 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.70/1.35 inference(modus_ponens,[status(thm)],[795, 791])).
% 1.70/1.35 tff(797,plain,(
% 1.70/1.35 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.70/1.35 inference(skolemize,[status(sab)],[796])).
% 1.70/1.35 tff(798,plain,
% 1.70/1.35 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.70/1.35 inference(modus_ponens,[status(thm)],[797, 790])).
% 1.70/1.35 tff(799,assumption,(~hskp6), introduced(assumption)).
% 1.70/1.35 tff(800,assumption,(c3_1(a4)), introduced(assumption)).
% 1.70/1.35 tff(801,plain,
% 1.70/1.35 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.70/1.35 inference(bind,[status(th)],[])).
% 1.70/1.35 tff(802,plain,
% 1.70/1.35 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.70/1.35 inference(quant_intro,[status(thm)],[801])).
% 1.70/1.35 tff(803,plain,
% 1.70/1.35 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.70/1.35 inference(rewrite,[status(thm)],[])).
% 1.70/1.35 tff(804,plain,
% 1.70/1.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.70/1.36 inference(bind,[status(th)],[])).
% 1.70/1.36 tff(805,plain,
% 1.70/1.36 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.70/1.36 inference(quant_intro,[status(thm)],[804])).
% 1.70/1.36 tff(806,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.70/1.36 tff(807,plain,
% 1.70/1.36 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[806, 805])).
% 1.70/1.36 tff(808,plain,
% 1.70/1.36 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[807, 803])).
% 1.70/1.36 tff(809,plain,(
% 1.70/1.36 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.70/1.36 inference(skolemize,[status(sab)],[808])).
% 1.70/1.36 tff(810,plain,
% 1.70/1.36 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[809, 802])).
% 1.70/1.36 tff(811,plain,
% 1.70/1.36 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c3_1(a4)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c3_1(a4)))),
% 1.70/1.36 inference(rewrite,[status(thm)],[])).
% 1.70/1.36 tff(812,plain,
% 1.70/1.36 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c3_1(a4))) <=> (hskp7 | hskp6 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c3_1(a4)))),
% 1.70/1.36 inference(rewrite,[status(thm)],[])).
% 1.70/1.36 tff(813,plain,
% 1.70/1.36 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c3_1(a4)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c3_1(a4))))),
% 1.70/1.36 inference(monotonicity,[status(thm)],[812])).
% 1.70/1.36 tff(814,plain,
% 1.70/1.36 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c3_1(a4)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c3_1(a4)))),
% 1.70/1.36 inference(transitivity,[status(thm)],[813, 811])).
% 1.70/1.36 tff(815,plain,
% 1.70/1.36 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c3_1(a4)))),
% 1.70/1.36 inference(quant_inst,[status(thm)],[])).
% 1.70/1.36 tff(816,plain,
% 1.70/1.36 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c3_1(a4))),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[815, 814])).
% 1.70/1.36 tff(817,plain,
% 1.70/1.36 (hskp7 | hskp6 | c0_1(a4) | (~c3_1(a4))),
% 1.70/1.36 inference(unit_resolution,[status(thm)],[816, 84, 228, 810])).
% 1.70/1.36 tff(818,plain,
% 1.70/1.36 (hskp7),
% 1.70/1.36 inference(unit_resolution,[status(thm)],[817, 800, 799, 229])).
% 1.70/1.36 tff(819,plain,
% 1.70/1.36 (((~hskp7) | (~c2_1(a9))) <=> ((~hskp7) | (~c2_1(a9)))),
% 1.70/1.36 inference(rewrite,[status(thm)],[])).
% 1.70/1.36 tff(820,plain,
% 1.70/1.36 (((~c2_1(a9)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a9)))),
% 1.70/1.36 inference(rewrite,[status(thm)],[])).
% 1.70/1.36 tff(821,axiom,((~c2_1(a9)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.70/1.36 tff(822,plain,
% 1.70/1.36 ((~hskp7) | (~c2_1(a9))),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[821, 820])).
% 1.70/1.36 tff(823,plain,
% 1.70/1.36 ((~hskp7) | (~c2_1(a9))),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[822, 819])).
% 1.70/1.36 tff(824,plain,
% 1.70/1.36 (~c2_1(a9)),
% 1.70/1.36 inference(unit_resolution,[status(thm)],[823, 818])).
% 1.70/1.36 tff(825,plain,
% 1.70/1.36 (((~hskp7) | (~c0_1(a9))) <=> ((~hskp7) | (~c0_1(a9)))),
% 1.70/1.36 inference(rewrite,[status(thm)],[])).
% 1.70/1.36 tff(826,plain,
% 1.70/1.36 (((~c0_1(a9)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a9)))),
% 1.70/1.36 inference(rewrite,[status(thm)],[])).
% 1.70/1.36 tff(827,axiom,((~c0_1(a9)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.70/1.36 tff(828,plain,
% 1.70/1.36 ((~hskp7) | (~c0_1(a9))),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[827, 826])).
% 1.70/1.36 tff(829,plain,
% 1.70/1.36 ((~hskp7) | (~c0_1(a9))),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[828, 825])).
% 1.70/1.36 tff(830,plain,
% 1.70/1.36 (~c0_1(a9)),
% 1.70/1.36 inference(unit_resolution,[status(thm)],[829, 818])).
% 1.70/1.36 tff(831,plain,
% 1.70/1.36 (((~hskp7) | c1_1(a9)) <=> ((~hskp7) | c1_1(a9))),
% 1.70/1.36 inference(rewrite,[status(thm)],[])).
% 1.70/1.36 tff(832,axiom,((~hskp7) | c1_1(a9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.70/1.36 tff(833,plain,
% 1.70/1.36 ((~hskp7) | c1_1(a9)),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[832, 831])).
% 1.70/1.36 tff(834,plain,
% 1.70/1.36 ((~hskp7) | c1_1(a9)),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[833, 831])).
% 1.70/1.36 tff(835,plain,
% 1.70/1.36 ((~hskp7) | c1_1(a9)),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[834, 831])).
% 1.70/1.36 tff(836,plain,
% 1.70/1.36 ((~hskp7) | c1_1(a9)),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[835, 831])).
% 1.70/1.36 tff(837,plain,
% 1.70/1.36 ((~hskp7) | c1_1(a9)),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[836, 831])).
% 1.70/1.36 tff(838,plain,
% 1.70/1.36 ((~hskp7) | c1_1(a9)),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[837, 831])).
% 1.70/1.36 tff(839,plain,
% 1.70/1.36 ((~hskp7) | c1_1(a9)),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[838, 831])).
% 1.70/1.36 tff(840,plain,
% 1.70/1.36 ((~hskp7) | c1_1(a9)),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[839, 831])).
% 1.70/1.36 tff(841,plain,
% 1.70/1.36 (c1_1(a9)),
% 1.70/1.36 inference(unit_resolution,[status(thm)],[840, 818])).
% 1.70/1.36 tff(842,plain,
% 1.70/1.36 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a9) | c2_1(a9) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a9)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a9) | c2_1(a9) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a9)))),
% 1.70/1.36 inference(rewrite,[status(thm)],[])).
% 1.70/1.36 tff(843,plain,
% 1.70/1.36 ((hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a9) | c0_1(a9) | (~c1_1(a9))) <=> (hskp6 | c0_1(a9) | c2_1(a9) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a9)))),
% 1.70/1.36 inference(rewrite,[status(thm)],[])).
% 1.70/1.36 tff(844,plain,
% 1.70/1.36 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a9) | c0_1(a9) | (~c1_1(a9)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a9) | c2_1(a9) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a9))))),
% 1.70/1.36 inference(monotonicity,[status(thm)],[843])).
% 1.70/1.36 tff(845,plain,
% 1.70/1.36 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a9) | c0_1(a9) | (~c1_1(a9)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a9) | c2_1(a9) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a9)))),
% 1.70/1.36 inference(transitivity,[status(thm)],[844, 842])).
% 1.70/1.36 tff(846,plain,
% 1.70/1.36 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a9) | c0_1(a9) | (~c1_1(a9)))),
% 1.70/1.36 inference(quant_inst,[status(thm)],[])).
% 1.70/1.36 tff(847,plain,
% 1.70/1.36 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a9) | c2_1(a9) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a9))),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[846, 845])).
% 1.70/1.36 tff(848,plain,
% 1.70/1.36 (c2_1(a4)),
% 1.70/1.36 inference(unit_resolution,[status(thm)],[847, 84, 799, 841, 800, 830, 824, 229, 798])).
% 1.70/1.36 tff(849,plain,
% 1.70/1.36 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)))),
% 1.70/1.36 inference(rewrite,[status(thm)],[])).
% 1.70/1.36 tff(850,plain,
% 1.70/1.36 ((hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c3_1(a4)) | (~c2_1(a4))) <=> (hskp5 | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)))),
% 1.70/1.36 inference(rewrite,[status(thm)],[])).
% 1.70/1.36 tff(851,plain,
% 1.70/1.36 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c3_1(a4)) | (~c2_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4))))),
% 1.70/1.36 inference(monotonicity,[status(thm)],[850])).
% 1.70/1.36 tff(852,plain,
% 1.70/1.36 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c3_1(a4)) | (~c2_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)))),
% 1.70/1.36 inference(transitivity,[status(thm)],[851, 849])).
% 1.70/1.36 tff(853,plain,
% 1.70/1.36 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c3_1(a4)) | (~c2_1(a4)))),
% 1.70/1.36 inference(quant_inst,[status(thm)],[])).
% 1.70/1.36 tff(854,plain,
% 1.70/1.36 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4))),
% 1.70/1.36 inference(modus_ponens,[status(thm)],[853, 852])).
% 1.70/1.36 tff(855,plain,
% 1.70/1.36 (hskp5 | (~c2_1(a4)) | (~c3_1(a4))),
% 1.70/1.36 inference(unit_resolution,[status(thm)],[854, 84, 255, 254, 229, 253, 252])).
% 1.70/1.36 tff(856,plain,
% 1.70/1.36 (hskp5),
% 1.70/1.36 inference(unit_resolution,[status(thm)],[855, 848, 800])).
% 1.70/1.36 tff(857,plain,
% 1.70/1.36 (c0_1(a6)),
% 1.70/1.36 inference(unit_resolution,[status(thm)],[274, 856])).
% 1.70/1.36 tff(858,plain,
% 1.70/1.36 (c2_1(a6)),
% 1.70/1.36 inference(unit_resolution,[status(thm)],[285, 856])).
% 1.70/1.36 tff(859,plain,
% 1.70/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a6) | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a6) | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6)))),
% 1.70/1.36 inference(rewrite,[status(thm)],[])).
% 1.70/1.36 tff(860,plain,
% 1.70/1.36 (((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4))) <=> (c3_1(a6) | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6)))),
% 1.70/1.36 inference(rewrite,[status(thm)],[])).
% 1.70/1.36 tff(861,plain,
% 1.70/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a6) | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6))))),
% 1.75/1.37 inference(monotonicity,[status(thm)],[860])).
% 1.75/1.37 tff(862,plain,
% 1.75/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a6) | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6)))),
% 1.75/1.37 inference(transitivity,[status(thm)],[861, 859])).
% 1.75/1.37 tff(863,plain,
% 1.75/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4)))),
% 1.75/1.37 inference(quant_inst,[status(thm)],[])).
% 1.75/1.37 tff(864,plain,
% 1.75/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a6) | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6))),
% 1.75/1.37 inference(modus_ponens,[status(thm)],[863, 862])).
% 1.75/1.37 tff(865,plain,
% 1.75/1.37 ((~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6))),
% 1.75/1.37 inference(unit_resolution,[status(thm)],[864, 84, 255, 254, 230, 229, 253, 103])).
% 1.75/1.37 tff(866,plain,
% 1.75/1.37 ($false),
% 1.75/1.37 inference(unit_resolution,[status(thm)],[865, 858, 857, 800, 848])).
% 1.75/1.37 tff(867,plain,((~c3_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | c3_1(a6) | c0_1(a4) | c1_1(a3) | hskp6 | c1_1(a4)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.37 tff(868,plain,
% 1.75/1.37 (hskp6),
% 1.75/1.37 inference(unit_resolution,[status(thm)],[867, 788, 180, 230, 229, 169, 191, 228])).
% 1.75/1.37 tff(869,plain,
% 1.75/1.37 (((~hskp6) | (~c2_1(a8))) <=> ((~hskp6) | (~c2_1(a8)))),
% 1.75/1.37 inference(rewrite,[status(thm)],[])).
% 1.75/1.37 tff(870,plain,
% 1.75/1.37 (((~c2_1(a8)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a8)))),
% 1.75/1.37 inference(rewrite,[status(thm)],[])).
% 1.75/1.37 tff(871,axiom,((~c2_1(a8)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.75/1.37 tff(872,plain,
% 1.75/1.37 ((~hskp6) | (~c2_1(a8))),
% 1.75/1.37 inference(modus_ponens,[status(thm)],[871, 870])).
% 1.75/1.37 tff(873,plain,
% 1.75/1.37 ((~hskp6) | (~c2_1(a8))),
% 1.75/1.37 inference(modus_ponens,[status(thm)],[872, 869])).
% 1.75/1.37 tff(874,plain,
% 1.75/1.37 (~c2_1(a8)),
% 1.75/1.37 inference(unit_resolution,[status(thm)],[873, 868])).
% 1.75/1.37 tff(875,plain,
% 1.75/1.37 (((~hskp6) | (~c3_1(a8))) <=> ((~hskp6) | (~c3_1(a8)))),
% 1.75/1.37 inference(rewrite,[status(thm)],[])).
% 1.75/1.37 tff(876,plain,
% 1.75/1.37 (((~c3_1(a8)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a8)))),
% 1.75/1.37 inference(rewrite,[status(thm)],[])).
% 1.75/1.37 tff(877,axiom,((~c3_1(a8)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.75/1.37 tff(878,plain,
% 1.75/1.37 ((~hskp6) | (~c3_1(a8))),
% 1.75/1.37 inference(modus_ponens,[status(thm)],[877, 876])).
% 1.75/1.37 tff(879,plain,
% 1.75/1.37 ((~hskp6) | (~c3_1(a8))),
% 1.75/1.37 inference(modus_ponens,[status(thm)],[878, 875])).
% 1.75/1.37 tff(880,plain,
% 1.75/1.37 (~c3_1(a8)),
% 1.75/1.37 inference(unit_resolution,[status(thm)],[879, 868])).
% 1.75/1.37 tff(881,assumption,(~c3_1(a8)), introduced(assumption)).
% 1.75/1.37 tff(882,assumption,(~c2_1(a8)), introduced(assumption)).
% 1.75/1.37 tff(883,assumption,(~c3_1(a5)), introduced(assumption)).
% 1.75/1.37 tff(884,plain,
% 1.75/1.37 (~hskp4),
% 1.75/1.37 inference(unit_resolution,[status(thm)],[201, 883])).
% 1.75/1.37 tff(885,plain,
% 1.75/1.37 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c3_1(a5) | c1_1(a5) | (~ndr1_0) | c0_1(a5))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c3_1(a5) | c1_1(a5) | (~ndr1_0) | c0_1(a5))),
% 1.75/1.37 inference(rewrite,[status(thm)],[])).
% 1.75/1.37 tff(886,plain,
% 1.75/1.37 ((hskp4 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c0_1(a5)) <=> (hskp4 | c3_1(a5) | c1_1(a5) | (~ndr1_0) | c0_1(a5))),
% 1.75/1.37 inference(rewrite,[status(thm)],[])).
% 1.75/1.37 tff(887,plain,
% 1.75/1.37 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c3_1(a5) | c1_1(a5) | (~ndr1_0) | c0_1(a5)))),
% 1.75/1.37 inference(monotonicity,[status(thm)],[886])).
% 1.75/1.37 tff(888,plain,
% 1.75/1.37 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c3_1(a5) | c1_1(a5) | (~ndr1_0) | c0_1(a5))),
% 1.75/1.37 inference(transitivity,[status(thm)],[887, 885])).
% 1.75/1.37 tff(889,plain,
% 1.75/1.37 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c0_1(a5))),
% 1.75/1.37 inference(quant_inst,[status(thm)],[])).
% 1.75/1.37 tff(890,plain,
% 1.75/1.37 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c3_1(a5) | c1_1(a5) | (~ndr1_0) | c0_1(a5)),
% 1.75/1.37 inference(modus_ponens,[status(thm)],[889, 888])).
% 1.75/1.37 tff(891,plain,
% 1.75/1.37 (hskp4 | c3_1(a5) | c0_1(a5)),
% 1.75/1.37 inference(unit_resolution,[status(thm)],[890, 84, 214, 113])).
% 1.75/1.37 tff(892,plain,
% 1.75/1.37 (c0_1(a5)),
% 1.75/1.37 inference(unit_resolution,[status(thm)],[891, 883, 884])).
% 1.75/1.37 tff(893,plain,
% 1.75/1.37 (c3_1(a4)),
% 1.75/1.37 inference(unit_resolution,[status(thm)],[238, 884, 229])).
% 1.75/1.37 tff(894,plain,
% 1.75/1.37 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c2_1(a5) | c3_1(a5) | c1_1(a5) | (~ndr1_0))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c2_1(a5) | c3_1(a5) | c1_1(a5) | (~ndr1_0))),
% 1.75/1.37 inference(rewrite,[status(thm)],[])).
% 1.75/1.37 tff(895,plain,
% 1.75/1.37 ((hskp30 | hskp18 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c2_1(a5)) <=> (hskp30 | hskp18 | c2_1(a5) | c3_1(a5) | c1_1(a5) | (~ndr1_0))),
% 1.75/1.37 inference(rewrite,[status(thm)],[])).
% 1.75/1.37 tff(896,plain,
% 1.75/1.37 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c2_1(a5))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c2_1(a5) | c3_1(a5) | c1_1(a5) | (~ndr1_0)))),
% 1.75/1.37 inference(monotonicity,[status(thm)],[895])).
% 1.75/1.37 tff(897,plain,
% 1.75/1.37 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c2_1(a5))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c2_1(a5) | c3_1(a5) | c1_1(a5) | (~ndr1_0))),
% 1.75/1.37 inference(transitivity,[status(thm)],[896, 894])).
% 1.75/1.37 tff(898,plain,
% 1.75/1.37 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c2_1(a5))),
% 1.75/1.37 inference(quant_inst,[status(thm)],[])).
% 1.75/1.37 tff(899,plain,
% 1.75/1.37 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c2_1(a5) | c3_1(a5) | c1_1(a5) | (~ndr1_0)),
% 1.75/1.37 inference(modus_ponens,[status(thm)],[898, 897])).
% 1.75/1.37 tff(900,plain,
% 1.75/1.37 (c2_1(a5) | c3_1(a5)),
% 1.75/1.37 inference(unit_resolution,[status(thm)],[899, 135, 84, 134, 214, 306])).
% 1.75/1.37 tff(901,plain,
% 1.75/1.37 (c2_1(a5)),
% 1.75/1.37 inference(unit_resolution,[status(thm)],[900, 883])).
% 1.75/1.37 tff(902,plain,
% 1.75/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.75/1.37 inference(rewrite,[status(thm)],[])).
% 1.75/1.37 tff(903,plain,
% 1.75/1.37 (((~ndr1_0) | c3_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4))) <=> (c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.75/1.37 inference(rewrite,[status(thm)],[])).
% 1.75/1.37 tff(904,plain,
% 1.75/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a5)) | (~c0_1(a5))))),
% 1.75/1.37 inference(monotonicity,[status(thm)],[903])).
% 1.75/1.37 tff(905,plain,
% 1.75/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.75/1.37 inference(transitivity,[status(thm)],[904, 902])).
% 1.75/1.37 tff(906,plain,
% 1.75/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4)))),
% 1.75/1.37 inference(quant_inst,[status(thm)],[])).
% 1.75/1.37 tff(907,plain,
% 1.75/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a5)) | (~c0_1(a5))),
% 1.75/1.37 inference(modus_ponens,[status(thm)],[906, 905])).
% 1.75/1.37 tff(908,plain,
% 1.75/1.37 (~c2_1(a4)),
% 1.75/1.37 inference(unit_resolution,[status(thm)],[907, 84, 901, 883, 893, 214, 229, 103, 892])).
% 1.75/1.37 tff(909,plain,
% 1.75/1.37 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.75/1.37 inference(bind,[status(th)],[])).
% 1.75/1.37 tff(910,plain,
% 1.75/1.37 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.75/1.37 inference(quant_intro,[status(thm)],[909])).
% 1.75/1.37 tff(911,plain,
% 1.75/1.37 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.75/1.37 inference(rewrite,[status(thm)],[])).
% 1.75/1.37 tff(912,plain,
% 1.75/1.37 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_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) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(913,plain,
% 1.75/1.38 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[912])).
% 1.75/1.38 tff(914,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 1.75/1.38 tff(915,plain,
% 1.75/1.38 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[914, 913])).
% 1.75/1.38 tff(916,plain,
% 1.75/1.38 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[915, 911])).
% 1.75/1.38 tff(917,plain,(
% 1.75/1.38 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.75/1.38 inference(skolemize,[status(sab)],[916])).
% 1.75/1.38 tff(918,plain,
% 1.75/1.38 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[917, 910])).
% 1.75/1.38 tff(919,plain,
% 1.75/1.38 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a5)))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(920,plain,
% 1.75/1.38 ((hskp9 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c0_1(a4) | (~c3_1(a4))) <=> (hskp9 | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a5)))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(921,plain,
% 1.75/1.38 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c0_1(a4) | (~c3_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a5))))),
% 1.75/1.38 inference(monotonicity,[status(thm)],[920])).
% 1.75/1.38 tff(922,plain,
% 1.75/1.38 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c0_1(a4) | (~c3_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a5)))),
% 1.75/1.38 inference(transitivity,[status(thm)],[921, 919])).
% 1.75/1.38 tff(923,plain,
% 1.75/1.38 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c0_1(a4) | (~c3_1(a4)))),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(924,plain,
% 1.75/1.38 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a5))),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[923, 922])).
% 1.75/1.38 tff(925,plain,
% 1.75/1.38 ($false),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[924, 84, 551, 883, 893, 214, 229, 918, 908, 892])).
% 1.75/1.38 tff(926,plain,(c3_1(a5) | hskp9 | c1_1(a5) | c0_1(a4) | c1_1(a4) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.75/1.38 tff(927,plain,
% 1.75/1.38 (c3_1(a5)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[926, 551, 214, 229, 228, 135, 134])).
% 1.75/1.38 tff(928,plain,
% 1.75/1.38 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | c1_1(a8))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | c1_1(a8))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(929,plain,
% 1.75/1.38 ((hskp30 | hskp18 | (~ndr1_0) | c3_1(a8) | c1_1(a8) | c2_1(a8)) <=> (hskp30 | hskp18 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | c1_1(a8))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(930,plain,
% 1.75/1.38 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a8) | c1_1(a8) | c2_1(a8))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | c1_1(a8)))),
% 1.75/1.38 inference(monotonicity,[status(thm)],[929])).
% 1.75/1.38 tff(931,plain,
% 1.75/1.38 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a8) | c1_1(a8) | c2_1(a8))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | c1_1(a8))),
% 1.75/1.38 inference(transitivity,[status(thm)],[930, 928])).
% 1.75/1.38 tff(932,plain,
% 1.75/1.38 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a8) | c1_1(a8) | c2_1(a8))),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(933,plain,
% 1.75/1.38 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | c1_1(a8)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[932, 931])).
% 1.75/1.38 tff(934,plain,
% 1.75/1.38 (c2_1(a8) | c1_1(a8)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[933, 135, 84, 134, 881, 306])).
% 1.75/1.38 tff(935,plain,
% 1.75/1.38 (c1_1(a8)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[934, 882])).
% 1.75/1.38 tff(936,assumption,(c1_1(a8)), introduced(assumption)).
% 1.75/1.38 tff(937,assumption,(~c2_1(a5)), introduced(assumption)).
% 1.75/1.38 tff(938,plain,
% 1.75/1.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c2_1(a5) | c1_1(a5) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a5) | c1_1(a5) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(939,plain,
% 1.75/1.38 ((hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a5) | c1_1(a5) | c0_1(a5)) <=> (hskp1 | c2_1(a5) | c1_1(a5) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(940,plain,
% 1.75/1.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c2_1(a5) | c1_1(a5) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5)))),
% 1.75/1.38 inference(monotonicity,[status(thm)],[939])).
% 1.75/1.38 tff(941,plain,
% 1.75/1.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a5) | c1_1(a5) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5))),
% 1.75/1.38 inference(transitivity,[status(thm)],[940, 938])).
% 1.75/1.38 tff(942,plain,
% 1.75/1.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a5) | c1_1(a5) | c0_1(a5))),
% 1.75/1.38 inference(quant_inst,[status(thm)],[])).
% 1.75/1.38 tff(943,plain,
% 1.75/1.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a5) | c1_1(a5) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5)),
% 1.75/1.38 inference(modus_ponens,[status(thm)],[942, 941])).
% 1.75/1.38 tff(944,plain,
% 1.75/1.38 (hskp1 | c0_1(a5)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[943, 84, 937, 255, 254, 214, 253, 749])).
% 1.75/1.38 tff(945,plain,
% 1.75/1.38 (hskp1),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[944, 242])).
% 1.75/1.38 tff(946,plain,
% 1.75/1.38 (~c2_1(a2)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[611, 945])).
% 1.75/1.38 tff(947,plain,
% 1.75/1.38 (c3_1(a2)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[622, 945])).
% 1.75/1.38 tff(948,plain,
% 1.75/1.38 (c0_1(a2)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[633, 945])).
% 1.75/1.38 tff(949,plain,
% 1.75/1.38 (~c1_1(a2)),
% 1.75/1.38 inference(unit_resolution,[status(thm)],[640, 84, 255, 254, 948, 947, 253, 946, 587])).
% 1.75/1.38 tff(950,plain,
% 1.75/1.38 (^[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)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.75/1.38 inference(bind,[status(th)],[])).
% 1.75/1.38 tff(951,plain,
% 1.75/1.38 (![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)) | c2_1(W) | c1_1(W) | c0_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)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.75/1.38 inference(quant_intro,[status(thm)],[950])).
% 1.75/1.38 tff(952,plain,
% 1.75/1.38 (![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)) | c2_1(W) | c1_1(W) | c0_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)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.75/1.38 inference(rewrite,[status(thm)],[])).
% 1.75/1.38 tff(953,plain,
% 1.75/1.38 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_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)) | c0_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)) | c0_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) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_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) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | 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) | c0_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) | c0_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)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | 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)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.75/1.39 inference(bind,[status(th)],[])).
% 1.75/1.39 tff(954,plain,
% 1.75/1.39 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.75/1.39 inference(quant_intro,[status(thm)],[953])).
% 1.75/1.39 tff(955,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.75/1.39 tff(956,plain,
% 1.75/1.39 (![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)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[955, 954])).
% 1.75/1.39 tff(957,plain,
% 1.75/1.39 (![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)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[956, 952])).
% 1.75/1.39 tff(958,plain,(
% 1.75/1.39 ![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)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.75/1.39 inference(skolemize,[status(sab)],[957])).
% 1.75/1.39 tff(959,plain,
% 1.75/1.39 (![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)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[958, 951])).
% 1.75/1.39 tff(960,plain,
% 1.75/1.39 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c0_1(a5) | (~c0_1(a8)))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c0_1(a5) | (~c0_1(a8)))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(961,plain,
% 1.75/1.39 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a5) | c1_1(a5) | c0_1(a5)) <=> (c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c0_1(a5) | (~c0_1(a8)))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(962,plain,
% 1.75/1.39 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c0_1(a5) | (~c0_1(a8))))),
% 1.75/1.39 inference(monotonicity,[status(thm)],[961])).
% 1.75/1.39 tff(963,plain,
% 1.75/1.39 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c0_1(a5) | (~c0_1(a8)))),
% 1.75/1.39 inference(transitivity,[status(thm)],[962, 960])).
% 1.75/1.39 tff(964,plain,
% 1.75/1.39 ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a5) | c1_1(a5) | c0_1(a5))),
% 1.75/1.39 inference(quant_inst,[status(thm)],[])).
% 1.75/1.39 tff(965,plain,
% 1.75/1.39 ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c0_1(a5) | (~c0_1(a8))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[964, 963])).
% 1.75/1.39 tff(966,plain,
% 1.75/1.39 (~c0_1(a8)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[965, 84, 937, 948, 882, 881, 214, 946, 959, 242, 949])).
% 1.75/1.39 tff(967,plain,
% 1.75/1.39 (((~hskp6) | c0_1(a8)) <=> ((~hskp6) | c0_1(a8))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(968,axiom,((~hskp6) | c0_1(a8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.75/1.39 tff(969,plain,
% 1.75/1.39 ((~hskp6) | c0_1(a8)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[968, 967])).
% 1.75/1.39 tff(970,plain,
% 1.75/1.39 ((~hskp6) | c0_1(a8)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[969, 967])).
% 1.75/1.39 tff(971,plain,
% 1.75/1.39 ((~hskp6) | c0_1(a8)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[970, 967])).
% 1.75/1.39 tff(972,plain,
% 1.75/1.39 ((~hskp6) | c0_1(a8)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[971, 967])).
% 1.75/1.39 tff(973,plain,
% 1.75/1.39 ((~hskp6) | c0_1(a8)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[972, 967])).
% 1.75/1.39 tff(974,plain,
% 1.75/1.39 ((~hskp6) | c0_1(a8)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[973, 967])).
% 1.75/1.39 tff(975,plain,
% 1.75/1.39 ((~hskp6) | c0_1(a8)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[974, 967])).
% 1.75/1.39 tff(976,plain,
% 1.75/1.39 ((~hskp6) | c0_1(a8)),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[975, 967])).
% 1.75/1.39 tff(977,plain,
% 1.75/1.39 (~hskp6),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[976, 966])).
% 1.75/1.39 tff(978,plain,
% 1.75/1.39 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a8) | c2_1(a5) | c2_1(a8) | (~ndr1_0) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a8) | c2_1(a5) | c2_1(a8) | (~ndr1_0) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a8)))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(979,plain,
% 1.75/1.39 ((hskp6 | (~ndr1_0) | c0_1(a5) | c2_1(a5) | (~c3_1(a5)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8))) <=> (hskp6 | c0_1(a8) | c2_1(a5) | c2_1(a8) | (~ndr1_0) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a8)))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(980,plain,
% 1.75/1.39 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a5) | c2_1(a5) | (~c3_1(a5)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a8) | c2_1(a5) | c2_1(a8) | (~ndr1_0) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a8))))),
% 1.75/1.39 inference(monotonicity,[status(thm)],[979])).
% 1.75/1.39 tff(981,plain,
% 1.75/1.39 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a5) | c2_1(a5) | (~c3_1(a5)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a8) | c2_1(a5) | c2_1(a8) | (~ndr1_0) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a8)))),
% 1.75/1.39 inference(transitivity,[status(thm)],[980, 978])).
% 1.75/1.39 tff(982,plain,
% 1.75/1.39 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a5) | c2_1(a5) | (~c3_1(a5)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))),
% 1.75/1.39 inference(quant_inst,[status(thm)],[])).
% 1.75/1.39 tff(983,plain,
% 1.75/1.39 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a8) | c2_1(a5) | c2_1(a8) | (~ndr1_0) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a8))),
% 1.75/1.39 inference(modus_ponens,[status(thm)],[982, 981])).
% 1.75/1.39 tff(984,plain,
% 1.75/1.39 (hskp6 | c0_1(a8)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[983, 84, 937, 256, 882, 798, 242, 936])).
% 1.75/1.39 tff(985,plain,
% 1.75/1.39 ($false),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[984, 977, 966])).
% 1.75/1.39 tff(986,plain,(c0_1(a5) | c2_1(a5) | (~c3_1(a5)) | c2_1(a8) | (~c1_1(a8)) | c3_1(a8) | c1_1(a5) | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.39 tff(987,plain,
% 1.75/1.39 (c0_1(a5)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[986, 937, 256, 882, 936, 881, 214, 255, 254, 253])).
% 1.75/1.39 tff(988,assumption,(~c2_1(a4)), introduced(assumption)).
% 1.75/1.39 tff(989,plain,
% 1.75/1.39 (~hskp4),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[212, 937])).
% 1.75/1.39 tff(990,plain,
% 1.75/1.39 (c3_1(a4)),
% 1.75/1.39 inference(unit_resolution,[status(thm)],[238, 989, 229])).
% 1.75/1.39 tff(991,plain,
% 1.75/1.39 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a5)) | (~c0_1(a8)))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a5)) | (~c0_1(a8)))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(992,plain,
% 1.75/1.39 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4)) <=> (c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a5)) | (~c0_1(a8)))),
% 1.75/1.39 inference(rewrite,[status(thm)],[])).
% 1.75/1.39 tff(993,plain,
% 1.75/1.39 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a5)) | (~c0_1(a8))))),
% 1.75/1.40 inference(monotonicity,[status(thm)],[992])).
% 1.75/1.40 tff(994,plain,
% 1.75/1.40 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a5)) | (~c0_1(a8)))),
% 1.75/1.40 inference(transitivity,[status(thm)],[993, 991])).
% 1.75/1.40 tff(995,plain,
% 1.75/1.40 ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4))),
% 1.75/1.40 inference(quant_inst,[status(thm)],[])).
% 1.75/1.40 tff(996,plain,
% 1.75/1.40 ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a5)) | (~c0_1(a8))),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[995, 994])).
% 1.75/1.40 tff(997,plain,
% 1.75/1.40 (~c0_1(a8)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[996, 84, 937, 882, 881, 214, 229, 228, 959, 988, 739])).
% 1.75/1.40 tff(998,plain,
% 1.75/1.40 (~hskp6),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[976, 997])).
% 1.75/1.40 tff(999,plain,
% 1.75/1.40 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a8) | c2_1(a8) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a8) | c2_1(a8) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a8)))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(1000,plain,
% 1.75/1.40 ((hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8))) <=> (hskp6 | c0_1(a8) | c2_1(a8) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a8)))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(1001,plain,
% 1.75/1.40 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a8) | c2_1(a8) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a8))))),
% 1.75/1.40 inference(monotonicity,[status(thm)],[1000])).
% 1.75/1.40 tff(1002,plain,
% 1.75/1.40 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a8) | c2_1(a8) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a8)))),
% 1.75/1.40 inference(transitivity,[status(thm)],[1001, 999])).
% 1.75/1.40 tff(1003,plain,
% 1.75/1.40 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))),
% 1.75/1.40 inference(quant_inst,[status(thm)],[])).
% 1.75/1.40 tff(1004,plain,
% 1.75/1.40 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a8) | c2_1(a8) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a8))),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 1.75/1.40 tff(1005,plain,
% 1.75/1.40 (hskp6 | c0_1(a8) | c2_1(a4) | (~c3_1(a4))),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[1004, 84, 882, 229, 798, 936])).
% 1.75/1.40 tff(1006,plain,
% 1.75/1.40 ($false),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[1005, 998, 997, 990, 988])).
% 1.75/1.40 tff(1007,plain,(c2_1(a4) | c2_1(a8) | c0_1(a4) | (~c1_1(a8)) | c2_1(a5) | c3_1(a8) | c1_1(a5) | c1_1(a4) | (~c0_1(a5))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.40 tff(1008,plain,
% 1.75/1.40 (c2_1(a4)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[1007, 937, 229, 936, 882, 881, 214, 228, 987])).
% 1.75/1.40 tff(1009,plain,
% 1.75/1.40 (hskp5),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[855, 1008, 990])).
% 1.75/1.40 tff(1010,plain,
% 1.75/1.40 (c0_1(a6)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[274, 1009])).
% 1.75/1.40 tff(1011,plain,
% 1.75/1.40 (c2_1(a6)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[285, 1009])).
% 1.75/1.40 tff(1012,plain,
% 1.75/1.40 ($false),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[865, 1011, 1010, 990, 1008])).
% 1.75/1.40 tff(1013,plain,(c2_1(a5) | (~c0_1(a3)) | (~c2_1(a3)) | c3_1(a6) | c0_1(a4) | c1_1(a3) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c1_1(a4) | (~c3_1(a5))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.40 tff(1014,plain,
% 1.75/1.40 (c2_1(a5)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[1013, 927, 180, 230, 229, 169, 935, 882, 881, 214, 228, 191])).
% 1.75/1.40 tff(1015,plain,
% 1.75/1.40 (c0_1(a5)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[295, 1014, 927, 191, 180, 230, 169])).
% 1.75/1.40 tff(1016,plain,
% 1.75/1.40 (c3_1(a4)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[559, 551, 135, 134, 229, 228])).
% 1.75/1.40 tff(1017,plain,
% 1.75/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(1018,plain,
% 1.75/1.40 ((hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4)) <=> (hskp1 | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(1019,plain,
% 1.75/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c2_1(a5)) | (~c0_1(a5))))),
% 1.75/1.40 inference(monotonicity,[status(thm)],[1018])).
% 1.75/1.40 tff(1020,plain,
% 1.75/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.75/1.40 inference(transitivity,[status(thm)],[1019, 1017])).
% 1.75/1.40 tff(1021,plain,
% 1.75/1.40 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4))),
% 1.75/1.40 inference(quant_inst,[status(thm)],[])).
% 1.75/1.40 tff(1022,plain,
% 1.75/1.40 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c2_1(a5)) | (~c0_1(a5))),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 1.75/1.40 tff(1023,plain,
% 1.75/1.40 (hskp1),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[1022, 84, 257, 214, 229, 228, 749, 988, 739])).
% 1.75/1.40 tff(1024,plain,
% 1.75/1.40 (~c2_1(a2)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[611, 1023])).
% 1.75/1.40 tff(1025,plain,
% 1.75/1.40 (c3_1(a2)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[622, 1023])).
% 1.75/1.40 tff(1026,plain,
% 1.75/1.40 (c0_1(a2)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[633, 1023])).
% 1.75/1.40 tff(1027,plain,
% 1.75/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(1028,plain,
% 1.75/1.40 (((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5))) <=> (c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(1029,plain,
% 1.75/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a5)) | (~c0_1(a5))))),
% 1.75/1.40 inference(monotonicity,[status(thm)],[1028])).
% 1.75/1.40 tff(1030,plain,
% 1.75/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.75/1.40 inference(transitivity,[status(thm)],[1029, 1027])).
% 1.75/1.40 tff(1031,plain,
% 1.75/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.75/1.40 inference(quant_inst,[status(thm)],[])).
% 1.75/1.40 tff(1032,plain,
% 1.75/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a5)) | (~c0_1(a5))),
% 1.75/1.40 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 1.75/1.40 tff(1033,plain,
% 1.75/1.40 (~c1_1(a2)),
% 1.75/1.40 inference(unit_resolution,[status(thm)],[1032, 84, 257, 1026, 1025, 214, 1024, 587, 739])).
% 1.75/1.40 tff(1034,plain,
% 1.75/1.40 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a8)))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a8)))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(1035,plain,
% 1.75/1.40 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4)) <=> (c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a8)))),
% 1.75/1.40 inference(rewrite,[status(thm)],[])).
% 1.75/1.40 tff(1036,plain,
% 1.75/1.40 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a8))))),
% 1.75/1.41 inference(monotonicity,[status(thm)],[1035])).
% 1.75/1.41 tff(1037,plain,
% 1.75/1.41 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a8)))),
% 1.75/1.41 inference(transitivity,[status(thm)],[1036, 1034])).
% 1.75/1.41 tff(1038,plain,
% 1.75/1.41 ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4))),
% 1.75/1.41 inference(quant_inst,[status(thm)],[])).
% 1.75/1.41 tff(1039,plain,
% 1.75/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a8))),
% 1.75/1.41 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 1.75/1.41 tff(1040,plain,
% 1.75/1.41 (~c0_1(a8)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1039, 84, 1026, 882, 881, 229, 228, 1024, 959, 988, 1033])).
% 1.75/1.41 tff(1041,plain,
% 1.75/1.41 (~hskp6),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[976, 1040])).
% 1.75/1.41 tff(1042,plain,
% 1.75/1.41 ($false),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1005, 1041, 1040, 800, 988])).
% 1.75/1.41 tff(1043,plain,(c2_1(a4) | (~c3_1(a4)) | c2_1(a8) | c0_1(a4) | (~c1_1(a8)) | c3_1(a8) | c1_1(a4) | (~c2_1(a5)) | c1_1(a5) | (~c0_1(a5))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.41 tff(1044,plain,
% 1.75/1.41 (c2_1(a4)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1043, 1016, 882, 229, 935, 881, 228, 1014, 214, 1015])).
% 1.75/1.41 tff(1045,plain,
% 1.75/1.41 (hskp5 | (~c2_1(a4)) | (~c3_1(a4))),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[854, 84, 191, 180, 229, 169, 252])).
% 1.75/1.41 tff(1046,plain,
% 1.75/1.41 (hskp5),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1045, 1044, 1016])).
% 1.75/1.41 tff(1047,plain,
% 1.75/1.41 (c0_1(a6)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[274, 1046])).
% 1.75/1.41 tff(1048,plain,
% 1.75/1.41 (c2_1(a6)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[285, 1046])).
% 1.75/1.41 tff(1049,plain,
% 1.75/1.41 ((~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6))),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[864, 84, 191, 180, 230, 229, 169, 103])).
% 1.75/1.41 tff(1050,plain,
% 1.75/1.41 ($false),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1049, 1048, 1047, 1016, 1044])).
% 1.75/1.41 tff(1051,plain,(hskp9 | c3_1(a6) | c0_1(a4) | c2_1(a8) | c3_1(a8) | c1_1(a4) | c1_1(a5) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.75/1.41 tff(1052,plain,
% 1.75/1.41 (hskp9),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1051, 882, 229, 230, 881, 228, 214, 135, 134])).
% 1.75/1.41 tff(1053,plain,
% 1.75/1.41 (~c3_1(a12)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[576, 1052])).
% 1.75/1.41 tff(1054,plain,
% 1.75/1.41 (((~hskp9) | (~c2_1(a12))) <=> ((~hskp9) | (~c2_1(a12)))),
% 1.75/1.41 inference(rewrite,[status(thm)],[])).
% 1.75/1.41 tff(1055,plain,
% 1.75/1.41 (((~c2_1(a12)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a12)))),
% 1.75/1.41 inference(rewrite,[status(thm)],[])).
% 1.75/1.41 tff(1056,axiom,((~c2_1(a12)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.75/1.41 tff(1057,plain,
% 1.75/1.41 ((~hskp9) | (~c2_1(a12))),
% 1.75/1.41 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 1.75/1.41 tff(1058,plain,
% 1.75/1.41 ((~hskp9) | (~c2_1(a12))),
% 1.75/1.41 inference(modus_ponens,[status(thm)],[1057, 1054])).
% 1.75/1.41 tff(1059,plain,
% 1.75/1.41 (~c2_1(a12)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1058, 1052])).
% 1.75/1.41 tff(1060,plain,
% 1.75/1.41 (hskp1),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1022, 84, 901, 214, 229, 228, 749, 908, 892])).
% 1.75/1.41 tff(1061,plain,
% 1.75/1.41 (~c2_1(a2)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[611, 1060])).
% 1.75/1.41 tff(1062,plain,
% 1.75/1.41 (c3_1(a2)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[622, 1060])).
% 1.75/1.41 tff(1063,plain,
% 1.75/1.41 (c0_1(a2)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[633, 1060])).
% 1.75/1.41 tff(1064,plain,
% 1.75/1.41 (~c1_1(a2)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1032, 84, 901, 1063, 1062, 214, 1061, 587, 892])).
% 1.75/1.41 tff(1065,plain,
% 1.75/1.41 (~c0_1(a8)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1039, 84, 1063, 882, 881, 229, 228, 1061, 959, 908, 1064])).
% 1.75/1.41 tff(1066,assumption,(~c2_1(a12)), introduced(assumption)).
% 1.75/1.41 tff(1067,plain,
% 1.75/1.41 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a12) | c3_1(a12) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a12)))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a12) | c3_1(a12) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a12)))),
% 1.75/1.41 inference(rewrite,[status(thm)],[])).
% 1.75/1.41 tff(1068,plain,
% 1.75/1.41 (((~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4)) <=> (c2_1(a12) | c3_1(a12) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a12)))),
% 1.75/1.41 inference(rewrite,[status(thm)],[])).
% 1.75/1.41 tff(1069,plain,
% 1.75/1.41 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a12) | c3_1(a12) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a12))))),
% 1.75/1.41 inference(monotonicity,[status(thm)],[1068])).
% 1.75/1.41 tff(1070,plain,
% 1.75/1.41 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a12) | c3_1(a12) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a12)))),
% 1.75/1.41 inference(transitivity,[status(thm)],[1069, 1067])).
% 1.75/1.41 tff(1071,plain,
% 1.75/1.41 ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4))),
% 1.75/1.41 inference(quant_inst,[status(thm)],[])).
% 1.75/1.41 tff(1072,plain,
% 1.75/1.41 ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a12) | c3_1(a12) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a12))),
% 1.75/1.41 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 1.75/1.41 tff(1073,plain,
% 1.75/1.41 (~c0_1(a12)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1072, 84, 1063, 1066, 652, 229, 228, 1061, 959, 908, 1064])).
% 1.75/1.41 tff(1074,plain,
% 1.75/1.41 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))),
% 1.75/1.41 inference(rewrite,[status(thm)],[])).
% 1.75/1.41 tff(1075,plain,
% 1.75/1.41 ((hskp30 | hskp18 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12)) <=> (hskp30 | hskp18 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))),
% 1.75/1.41 inference(rewrite,[status(thm)],[])).
% 1.75/1.41 tff(1076,plain,
% 1.75/1.41 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0)))),
% 1.75/1.41 inference(monotonicity,[status(thm)],[1075])).
% 1.75/1.41 tff(1077,plain,
% 1.75/1.41 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))),
% 1.75/1.41 inference(transitivity,[status(thm)],[1076, 1074])).
% 1.75/1.41 tff(1078,plain,
% 1.75/1.41 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12))),
% 1.75/1.41 inference(quant_inst,[status(thm)],[])).
% 1.75/1.41 tff(1079,plain,
% 1.75/1.41 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0)),
% 1.75/1.41 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 1.75/1.41 tff(1080,plain,
% 1.75/1.41 (c1_1(a12) | c2_1(a12)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1079, 135, 84, 134, 652, 306])).
% 1.75/1.41 tff(1081,plain,
% 1.75/1.41 (c1_1(a12)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1080, 1066])).
% 1.75/1.41 tff(1082,plain,
% 1.75/1.41 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a12) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | c0_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a12) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | c0_1(a12) | (~c1_1(a12)))),
% 1.75/1.41 inference(rewrite,[status(thm)],[])).
% 1.75/1.41 tff(1083,plain,
% 1.75/1.41 ((hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12))) <=> (hskp6 | c2_1(a12) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | c0_1(a12) | (~c1_1(a12)))),
% 1.75/1.41 inference(rewrite,[status(thm)],[])).
% 1.75/1.41 tff(1084,plain,
% 1.75/1.41 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a12) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | c0_1(a12) | (~c1_1(a12))))),
% 1.75/1.41 inference(monotonicity,[status(thm)],[1083])).
% 1.75/1.41 tff(1085,plain,
% 1.75/1.41 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a12) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | c0_1(a12) | (~c1_1(a12)))),
% 1.75/1.41 inference(transitivity,[status(thm)],[1084, 1082])).
% 1.75/1.41 tff(1086,plain,
% 1.75/1.41 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12)))),
% 1.75/1.41 inference(quant_inst,[status(thm)],[])).
% 1.75/1.41 tff(1087,plain,
% 1.75/1.41 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a12) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | c0_1(a12) | (~c1_1(a12))),
% 1.75/1.41 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 1.75/1.41 tff(1088,plain,
% 1.75/1.41 (hskp6 | c2_1(a4) | (~c3_1(a4)) | c0_1(a12)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1087, 84, 1081, 1066, 229, 798])).
% 1.75/1.41 tff(1089,plain,
% 1.75/1.41 (hskp6),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1088, 1073, 893, 908])).
% 1.75/1.41 tff(1090,plain,
% 1.75/1.41 ($false),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[976, 1089, 1065])).
% 1.75/1.41 tff(1091,plain,(c3_1(a5) | c2_1(a12) | c0_1(a4) | c2_1(a8) | c3_1(a8) | c1_1(a4) | c3_1(a12) | c1_1(a5) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.75/1.41 tff(1092,plain,
% 1.75/1.41 (c3_1(a5)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1091, 1059, 229, 882, 881, 228, 1053, 214, 135, 134])).
% 1.75/1.41 tff(1093,plain,
% 1.75/1.41 (c2_1(a5)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1013, 1092, 180, 230, 229, 169, 935, 882, 881, 214, 228, 191])).
% 1.75/1.41 tff(1094,plain,
% 1.75/1.41 (c0_1(a5)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[295, 1093, 1092, 191, 180, 230, 169])).
% 1.75/1.41 tff(1095,plain,
% 1.75/1.41 (c1_1(a12)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[570, 1052])).
% 1.75/1.41 tff(1096,plain,
% 1.75/1.41 (hskp0),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[708, 1093, 1053, 1095, 1092, 214, 191, 180, 169])).
% 1.75/1.41 tff(1097,plain,
% 1.75/1.41 (~c0_1(a1)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[714, 1096])).
% 1.75/1.41 tff(1098,plain,
% 1.75/1.41 (c2_1(a1)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[736, 1096])).
% 1.75/1.41 tff(1099,plain,
% 1.75/1.41 (c1_1(a1)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[725, 1096])).
% 1.75/1.41 tff(1100,plain,
% 1.75/1.41 (~hskp14),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[785, 1099, 1098, 1097, 1093, 1092, 214, 135, 134, 1094])).
% 1.75/1.41 tff(1101,plain,
% 1.75/1.41 (c3_1(a4)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[503, 1100, 134, 229, 135, 228])).
% 1.75/1.41 tff(1102,plain,
% 1.75/1.41 (c2_1(a4)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1043, 1101, 882, 229, 935, 881, 228, 1093, 214, 1094])).
% 1.75/1.41 tff(1103,plain,
% 1.75/1.41 (hskp5),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1045, 1101, 1102])).
% 1.75/1.41 tff(1104,plain,
% 1.75/1.41 (c0_1(a6)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[274, 1103])).
% 1.75/1.41 tff(1105,plain,
% 1.75/1.41 (c2_1(a6)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[285, 1103])).
% 1.75/1.41 tff(1106,plain,
% 1.75/1.41 ($false),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1049, 1105, 1104, 1101, 1102])).
% 1.75/1.41 tff(1107,plain,(c2_1(a8) | c3_1(a6) | c0_1(a4) | c3_1(a8) | c1_1(a4) | c1_1(a5) | hskp18 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.75/1.41 tff(1108,plain,
% 1.75/1.41 ($false),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1107, 880, 874, 229, 230, 228, 214, 134, 135])).
% 1.75/1.41 tff(1109,plain,(c3_1(a6) | c0_1(a4) | c1_1(a4) | c1_1(a5) | hskp18 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.75/1.41 tff(1110,plain,
% 1.75/1.41 (c3_1(a6)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1109, 214, 228, 229, 134, 135])).
% 1.75/1.41 tff(1111,plain,
% 1.75/1.41 (((~hskp5) | (~c3_1(a6))) <=> ((~hskp5) | (~c3_1(a6)))),
% 1.75/1.41 inference(rewrite,[status(thm)],[])).
% 1.75/1.41 tff(1112,plain,
% 1.75/1.41 (((~c3_1(a6)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a6)))),
% 1.75/1.41 inference(rewrite,[status(thm)],[])).
% 1.75/1.41 tff(1113,axiom,((~c3_1(a6)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.75/1.41 tff(1114,plain,
% 1.75/1.41 ((~hskp5) | (~c3_1(a6))),
% 1.75/1.41 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 1.75/1.41 tff(1115,plain,
% 1.75/1.41 ((~hskp5) | (~c3_1(a6))),
% 1.75/1.41 inference(modus_ponens,[status(thm)],[1114, 1111])).
% 1.75/1.41 tff(1116,plain,
% 1.75/1.41 (~hskp5),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1115, 1110])).
% 1.75/1.41 tff(1117,plain,
% 1.75/1.41 (~c2_1(a4)),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[1045, 990, 1116])).
% 1.75/1.41 tff(1118,plain,
% 1.75/1.41 (hskp7),
% 1.75/1.41 inference(unit_resolution,[status(thm)],[817, 799, 800, 229])).
% 1.75/1.42 tff(1119,plain,
% 1.75/1.42 (~c2_1(a9)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[823, 1118])).
% 1.75/1.42 tff(1120,plain,
% 1.75/1.42 (~c0_1(a9)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[829, 1118])).
% 1.75/1.42 tff(1121,plain,
% 1.75/1.42 (c1_1(a9)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[840, 1118])).
% 1.75/1.42 tff(1122,plain,
% 1.75/1.42 ($false),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[847, 84, 799, 1121, 800, 1120, 1119, 229, 798, 988])).
% 1.75/1.42 tff(1123,plain,(hskp6 | (~c3_1(a4)) | c0_1(a4) | c2_1(a4) | c1_1(a4)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.42 tff(1124,plain,
% 1.75/1.42 (hskp6),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1123, 990, 229, 1117, 228])).
% 1.75/1.42 tff(1125,plain,
% 1.75/1.42 (~c2_1(a8)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[873, 1124])).
% 1.75/1.42 tff(1126,plain,
% 1.75/1.42 (~c3_1(a8)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[879, 1124])).
% 1.75/1.42 tff(1127,plain,
% 1.75/1.42 (c3_1(a5)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[900, 937])).
% 1.75/1.42 tff(1128,plain,
% 1.75/1.42 (~c1_1(a8)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[986, 882, 1127, 242, 881, 937, 214, 191, 180, 169])).
% 1.75/1.42 tff(1129,plain,
% 1.75/1.42 ($false),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[934, 1128, 882])).
% 1.75/1.42 tff(1130,plain,(c2_1(a8) | hskp30 | hskp18 | c3_1(a8) | c0_1(a5) | c2_1(a5) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.42 tff(1131,plain,
% 1.75/1.42 (c0_1(a5)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1130, 1126, 134, 135, 1125, 937, 214])).
% 1.75/1.42 tff(1132,plain,
% 1.75/1.42 (~c1_1(a8)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1007, 1131, 229, 1117, 937, 1126, 214, 228, 1125])).
% 1.75/1.42 tff(1133,plain,
% 1.75/1.42 (c0_1(a8)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[976, 1124])).
% 1.75/1.42 tff(1134,plain,
% 1.75/1.42 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a8)) | c1_1(a8))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a8)) | c1_1(a8))),
% 1.75/1.42 inference(rewrite,[status(thm)],[])).
% 1.75/1.42 tff(1135,plain,
% 1.75/1.42 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a8) | c1_1(a8) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | c0_1(a4)) <=> (c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a8)) | c1_1(a8))),
% 1.75/1.42 inference(rewrite,[status(thm)],[])).
% 1.75/1.42 tff(1136,plain,
% 1.75/1.42 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a8) | c1_1(a8) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a8)) | c1_1(a8)))),
% 1.75/1.42 inference(monotonicity,[status(thm)],[1135])).
% 1.75/1.42 tff(1137,plain,
% 1.75/1.42 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a8) | c1_1(a8) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a8)) | c1_1(a8))),
% 1.75/1.42 inference(transitivity,[status(thm)],[1136, 1134])).
% 1.75/1.42 tff(1138,plain,
% 1.75/1.42 ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a8) | c1_1(a8) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | c0_1(a4))),
% 1.75/1.42 inference(quant_inst,[status(thm)],[])).
% 1.75/1.42 tff(1139,plain,
% 1.75/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a8)) | c1_1(a8)),
% 1.75/1.42 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 1.75/1.42 tff(1140,plain,
% 1.75/1.42 ($false),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1139, 84, 1133, 1125, 1126, 229, 228, 959, 1117, 1132])).
% 1.75/1.42 tff(1141,plain,(c2_1(a5) | c0_1(a4) | c1_1(a4) | c1_1(a5) | hskp18 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.75/1.42 tff(1142,plain,
% 1.75/1.42 (c2_1(a5)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1141, 214, 228, 229, 134, 135])).
% 1.75/1.42 tff(1143,assumption,(~hskp5), introduced(assumption)).
% 1.75/1.42 tff(1144,plain,
% 1.75/1.42 (~c3_1(a5)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[263, 84, 1143, 257, 255, 254, 253, 252, 242])).
% 1.75/1.42 tff(1145,plain,
% 1.75/1.42 (~hskp4),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[201, 1144])).
% 1.75/1.42 tff(1146,plain,
% 1.75/1.42 ($false),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[891, 1145, 1144, 242])).
% 1.75/1.42 tff(1147,plain,(c0_1(a5) | c1_1(a5) | hskp5 | (~c2_1(a5)) | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.42 tff(1148,plain,
% 1.75/1.42 (c0_1(a5)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1147, 214, 1116, 1142, 191, 180, 169])).
% 1.75/1.42 tff(1149,plain,
% 1.75/1.42 (^[U: $i] : refl((hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.75/1.42 inference(bind,[status(th)],[])).
% 1.75/1.42 tff(1150,plain,
% 1.75/1.42 (![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.75/1.42 inference(quant_intro,[status(thm)],[1149])).
% 1.75/1.42 tff(1151,plain,
% 1.75/1.42 (![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.75/1.42 inference(rewrite,[status(thm)],[])).
% 1.75/1.42 tff(1152,plain,
% 1.75/1.42 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp0) <=> ((hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp0))), rewrite(((hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp0) <=> (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp0) <=> (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.75/1.42 inference(bind,[status(th)],[])).
% 1.75/1.42 tff(1153,plain,
% 1.75/1.42 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp0) <=> ![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.75/1.42 inference(quant_intro,[status(thm)],[1152])).
% 1.75/1.42 tff(1154,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.75/1.42 tff(1155,plain,
% 1.75/1.42 (![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.75/1.42 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 1.75/1.42 tff(1156,plain,
% 1.75/1.42 (![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.75/1.42 inference(modus_ponens,[status(thm)],[1155, 1151])).
% 1.75/1.42 tff(1157,plain,(
% 1.75/1.42 ![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.75/1.42 inference(skolemize,[status(sab)],[1156])).
% 1.75/1.42 tff(1158,plain,
% 1.75/1.42 (![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.75/1.42 inference(modus_ponens,[status(thm)],[1157, 1150])).
% 1.75/1.42 tff(1159,plain,
% 1.75/1.42 (((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c2_1(a4)))) <=> ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp0 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c2_1(a4)))),
% 1.75/1.42 inference(rewrite,[status(thm)],[])).
% 1.75/1.42 tff(1160,plain,
% 1.75/1.42 ((hskp5 | hskp0 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c2_1(a4))) <=> (hskp5 | hskp0 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c2_1(a4)))),
% 1.75/1.42 inference(rewrite,[status(thm)],[])).
% 1.75/1.42 tff(1161,plain,
% 1.75/1.42 (((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c2_1(a4)))) <=> ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c2_1(a4))))),
% 1.75/1.42 inference(monotonicity,[status(thm)],[1160])).
% 1.75/1.42 tff(1162,plain,
% 1.75/1.42 (((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c2_1(a4)))) <=> ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp0 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c2_1(a4)))),
% 1.75/1.42 inference(transitivity,[status(thm)],[1161, 1159])).
% 1.75/1.42 tff(1163,plain,
% 1.75/1.42 ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c2_1(a4)))),
% 1.75/1.42 inference(quant_inst,[status(thm)],[])).
% 1.75/1.42 tff(1164,plain,
% 1.75/1.42 ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp0 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c2_1(a4))),
% 1.75/1.42 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 1.75/1.42 tff(1165,plain,
% 1.75/1.42 (hskp5 | hskp0 | c0_1(a4) | (~c2_1(a4))),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1164, 84, 228, 1158])).
% 1.75/1.42 tff(1166,plain,
% 1.75/1.42 (hskp0),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1165, 315, 229, 1116])).
% 1.75/1.42 tff(1167,plain,
% 1.75/1.42 (c2_1(a1)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[736, 1166])).
% 1.75/1.42 tff(1168,plain,
% 1.75/1.42 (hskp9),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[926, 883, 214, 229, 228, 135, 134])).
% 1.75/1.42 tff(1169,plain,
% 1.75/1.42 (~c3_1(a12)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[576, 1168])).
% 1.75/1.42 tff(1170,plain,
% 1.75/1.42 (~c2_1(a12)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1058, 1168])).
% 1.75/1.42 tff(1171,plain,
% 1.75/1.42 (~c2_1(a4)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1045, 893, 1116])).
% 1.75/1.42 tff(1172,plain,
% 1.75/1.42 (hskp6),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1123, 893, 229, 1171, 228])).
% 1.75/1.42 tff(1173,plain,
% 1.75/1.42 (~c2_1(a8)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[873, 1172])).
% 1.75/1.42 tff(1174,plain,
% 1.75/1.42 (~c3_1(a8)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[879, 1172])).
% 1.75/1.42 tff(1175,plain,
% 1.75/1.42 ($false),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1091, 1174, 1173, 229, 883, 1170, 228, 1169, 214, 135, 134])).
% 1.75/1.42 tff(1176,plain,(c3_1(a5) | c0_1(a4) | c1_1(a4) | c1_1(a5) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.75/1.42 tff(1177,plain,
% 1.75/1.42 (c3_1(a5)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1176, 214, 228, 229, 135, 134])).
% 1.75/1.42 tff(1178,plain,
% 1.75/1.42 (c1_1(a1)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[725, 1166])).
% 1.75/1.42 tff(1179,plain,
% 1.75/1.42 (~c0_1(a1)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[714, 1166])).
% 1.75/1.42 tff(1180,plain,
% 1.75/1.42 ($false),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[785, 1179, 1178, 1177, 504, 1142, 1167, 214, 135, 134, 1148])).
% 1.75/1.42 tff(1181,plain,(c3_1(a4) | c1_1(a5) | hskp30 | hskp18 | c0_1(a4) | c1_1(a4)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.42 tff(1182,plain,
% 1.75/1.42 (c3_1(a4)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1181, 214, 135, 134, 229, 228])).
% 1.75/1.42 tff(1183,plain,
% 1.75/1.42 (~c2_1(a4)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1045, 1182, 1116])).
% 1.75/1.42 tff(1184,plain,
% 1.75/1.42 (hskp6),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1123, 1182, 229, 1183, 228])).
% 1.75/1.42 tff(1185,plain,
% 1.75/1.42 (~c3_1(a8)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[879, 1184])).
% 1.75/1.42 tff(1186,plain,
% 1.75/1.42 (~c2_1(a8)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[873, 1184])).
% 1.75/1.42 tff(1187,plain,
% 1.75/1.42 (~c1_1(a8)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1043, 1186, 1148, 229, 1183, 1185, 228, 1142, 214, 1182])).
% 1.75/1.42 tff(1188,plain,
% 1.75/1.42 (c0_1(a8)),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[976, 1184])).
% 1.75/1.42 tff(1189,plain,
% 1.75/1.42 ($false),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1139, 84, 1188, 1186, 1185, 229, 228, 959, 1183, 1187])).
% 1.75/1.42 tff(1190,plain,(c1_1(a5) | c0_1(a4) | c1_1(a4) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.75/1.42 tff(1191,plain,
% 1.75/1.42 ($false),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1190, 227, 221, 214, 135, 134])).
% 1.75/1.42 tff(1192,plain,((~hskp3) | c1_1(a5) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.75/1.42 tff(1193,plain,
% 1.75/1.42 (~hskp3),
% 1.75/1.42 inference(unit_resolution,[status(thm)],[1192, 162, 135, 134])).
% 1.75/1.42 tff(1194,plain,
% 1.75/1.42 (^[U: $i] : refl((hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))),
% 1.75/1.43 inference(bind,[status(th)],[])).
% 1.75/1.43 tff(1195,plain,
% 1.75/1.43 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.75/1.43 inference(quant_intro,[status(thm)],[1194])).
% 1.75/1.43 tff(1196,plain,
% 1.75/1.43 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.75/1.43 inference(rewrite,[status(thm)],[])).
% 1.75/1.43 tff(1197,plain,
% 1.75/1.43 (^[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) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp21) <=> ((hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp21))), rewrite(((hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp21) <=> (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp21) <=> (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))))),
% 1.75/1.43 inference(bind,[status(th)],[])).
% 1.75/1.43 tff(1198,plain,
% 1.75/1.43 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp21) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.75/1.43 inference(quant_intro,[status(thm)],[1197])).
% 1.75/1.43 tff(1199,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 1.75/1.43 tff(1200,plain,
% 1.75/1.43 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1199, 1198])).
% 1.75/1.43 tff(1201,plain,
% 1.75/1.43 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1200, 1196])).
% 1.75/1.43 tff(1202,plain,(
% 1.75/1.43 ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.75/1.43 inference(skolemize,[status(sab)],[1201])).
% 1.75/1.43 tff(1203,plain,
% 1.75/1.43 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1202, 1195])).
% 1.75/1.43 tff(1204,plain,
% 1.75/1.43 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)))),
% 1.75/1.43 inference(rewrite,[status(thm)],[])).
% 1.75/1.43 tff(1205,plain,
% 1.75/1.43 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2))) <=> (hskp21 | hskp0 | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)))),
% 1.75/1.43 inference(rewrite,[status(thm)],[])).
% 1.75/1.43 tff(1206,plain,
% 1.75/1.43 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2))))),
% 1.75/1.43 inference(monotonicity,[status(thm)],[1205])).
% 1.75/1.43 tff(1207,plain,
% 1.75/1.43 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)))),
% 1.75/1.43 inference(transitivity,[status(thm)],[1206, 1204])).
% 1.75/1.43 tff(1208,plain,
% 1.75/1.43 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)))),
% 1.75/1.43 inference(quant_inst,[status(thm)],[])).
% 1.75/1.43 tff(1209,plain,
% 1.75/1.43 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2))),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 1.75/1.43 tff(1210,plain,
% 1.75/1.43 (hskp21 | c1_1(a2)),
% 1.75/1.43 inference(unit_resolution,[status(thm)],[1209, 84, 588, 634, 612, 1203])).
% 1.75/1.43 tff(1211,plain,
% 1.75/1.43 (hskp21),
% 1.75/1.43 inference(unit_resolution,[status(thm)],[1210, 641])).
% 1.75/1.43 tff(1212,plain,
% 1.75/1.43 (((~hskp21) | (~c0_1(a42))) <=> ((~hskp21) | (~c0_1(a42)))),
% 1.75/1.43 inference(rewrite,[status(thm)],[])).
% 1.75/1.43 tff(1213,plain,
% 1.75/1.43 (((~c0_1(a42)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a42)))),
% 1.75/1.43 inference(rewrite,[status(thm)],[])).
% 1.75/1.43 tff(1214,axiom,((~c0_1(a42)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.75/1.43 tff(1215,plain,
% 1.75/1.43 ((~hskp21) | (~c0_1(a42))),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 1.75/1.43 tff(1216,plain,
% 1.75/1.43 ((~hskp21) | (~c0_1(a42))),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1215, 1212])).
% 1.75/1.43 tff(1217,plain,
% 1.75/1.43 (~c0_1(a42)),
% 1.75/1.43 inference(unit_resolution,[status(thm)],[1216, 1211])).
% 1.75/1.43 tff(1218,plain,
% 1.75/1.43 (((~hskp21) | c3_1(a42)) <=> ((~hskp21) | c3_1(a42))),
% 1.75/1.43 inference(rewrite,[status(thm)],[])).
% 1.75/1.43 tff(1219,axiom,((~hskp21) | c3_1(a42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.75/1.43 tff(1220,plain,
% 1.75/1.43 ((~hskp21) | c3_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 1.75/1.43 tff(1221,plain,
% 1.75/1.43 ((~hskp21) | c3_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1220, 1218])).
% 1.75/1.43 tff(1222,plain,
% 1.75/1.43 ((~hskp21) | c3_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1221, 1218])).
% 1.75/1.43 tff(1223,plain,
% 1.75/1.43 ((~hskp21) | c3_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1222, 1218])).
% 1.75/1.43 tff(1224,plain,
% 1.75/1.43 ((~hskp21) | c3_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1223, 1218])).
% 1.75/1.43 tff(1225,plain,
% 1.75/1.43 ((~hskp21) | c3_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1224, 1218])).
% 1.75/1.43 tff(1226,plain,
% 1.75/1.43 ((~hskp21) | c3_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1225, 1218])).
% 1.75/1.43 tff(1227,plain,
% 1.75/1.43 ((~hskp21) | c3_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1226, 1218])).
% 1.75/1.43 tff(1228,plain,
% 1.75/1.43 (c3_1(a42)),
% 1.75/1.43 inference(unit_resolution,[status(thm)],[1227, 1211])).
% 1.75/1.43 tff(1229,plain,
% 1.75/1.43 (((~hskp21) | c2_1(a42)) <=> ((~hskp21) | c2_1(a42))),
% 1.75/1.43 inference(rewrite,[status(thm)],[])).
% 1.75/1.43 tff(1230,axiom,((~hskp21) | c2_1(a42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 1.75/1.43 tff(1231,plain,
% 1.75/1.43 ((~hskp21) | c2_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1230, 1229])).
% 1.75/1.43 tff(1232,plain,
% 1.75/1.43 ((~hskp21) | c2_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1231, 1229])).
% 1.75/1.43 tff(1233,plain,
% 1.75/1.43 ((~hskp21) | c2_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1232, 1229])).
% 1.75/1.43 tff(1234,plain,
% 1.75/1.43 ((~hskp21) | c2_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1233, 1229])).
% 1.75/1.43 tff(1235,plain,
% 1.75/1.43 ((~hskp21) | c2_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1234, 1229])).
% 1.75/1.43 tff(1236,plain,
% 1.75/1.43 ((~hskp21) | c2_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1235, 1229])).
% 1.75/1.43 tff(1237,plain,
% 1.75/1.43 ((~hskp21) | c2_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1236, 1229])).
% 1.75/1.43 tff(1238,plain,
% 1.75/1.43 ((~hskp21) | c2_1(a42)),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1237, 1229])).
% 1.75/1.43 tff(1239,plain,
% 1.75/1.43 (c2_1(a42)),
% 1.75/1.43 inference(unit_resolution,[status(thm)],[1238, 1211])).
% 1.75/1.43 tff(1240,plain,
% 1.75/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.75/1.43 inference(rewrite,[status(thm)],[])).
% 1.75/1.43 tff(1241,plain,
% 1.75/1.43 (((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42))) <=> (c1_1(a43) | c3_1(a43) | c0_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.75/1.43 inference(rewrite,[status(thm)],[])).
% 1.75/1.43 tff(1242,plain,
% 1.75/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 1.75/1.43 inference(monotonicity,[status(thm)],[1241])).
% 1.75/1.43 tff(1243,plain,
% 1.75/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.75/1.43 inference(transitivity,[status(thm)],[1242, 1240])).
% 1.75/1.43 tff(1244,plain,
% 1.75/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.75/1.43 inference(quant_inst,[status(thm)],[])).
% 1.75/1.43 tff(1245,plain,
% 1.75/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a43)) | (~c0_1(a43))),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 1.75/1.43 tff(1246,plain,
% 1.75/1.43 (~c0_1(a43)),
% 1.75/1.43 inference(unit_resolution,[status(thm)],[1245, 84, 700, 1239, 1228, 689, 683, 1217, 103])).
% 1.75/1.43 tff(1247,plain,
% 1.75/1.43 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.75/1.43 inference(bind,[status(th)],[])).
% 1.75/1.43 tff(1248,plain,
% 1.75/1.43 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.75/1.43 inference(quant_intro,[status(thm)],[1247])).
% 1.75/1.43 tff(1249,plain,
% 1.75/1.43 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.75/1.43 inference(rewrite,[status(thm)],[])).
% 1.75/1.43 tff(1250,plain,
% 1.75/1.43 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.75/1.43 inference(bind,[status(th)],[])).
% 1.75/1.43 tff(1251,plain,
% 1.75/1.43 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.75/1.43 inference(quant_intro,[status(thm)],[1250])).
% 1.75/1.43 tff(1252,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.75/1.43 tff(1253,plain,
% 1.75/1.43 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 1.75/1.43 tff(1254,plain,
% 1.75/1.43 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1253, 1249])).
% 1.75/1.43 tff(1255,plain,(
% 1.75/1.43 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.75/1.43 inference(skolemize,[status(sab)],[1254])).
% 1.75/1.43 tff(1256,plain,
% 1.75/1.43 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.75/1.43 inference(modus_ponens,[status(thm)],[1255, 1248])).
% 1.75/1.43 tff(1257,assumption,(~hskp3), introduced(assumption)).
% 1.75/1.43 tff(1258,plain,
% 1.75/1.43 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c1_1(a43) | c3_1(a43) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a43))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a43) | c3_1(a43) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a43))),
% 1.75/1.43 inference(rewrite,[status(thm)],[])).
% 1.75/1.43 tff(1259,plain,
% 1.75/1.43 ((hskp3 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c0_1(a43) | c3_1(a43)) <=> (hskp3 | c1_1(a43) | c3_1(a43) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a43))),
% 1.75/1.43 inference(rewrite,[status(thm)],[])).
% 1.75/1.43 tff(1260,plain,
% 1.75/1.43 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c0_1(a43) | c3_1(a43))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c1_1(a43) | c3_1(a43) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a43)))),
% 1.75/1.44 inference(monotonicity,[status(thm)],[1259])).
% 1.75/1.44 tff(1261,plain,
% 1.75/1.44 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c0_1(a43) | c3_1(a43))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a43) | c3_1(a43) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a43))),
% 1.75/1.44 inference(transitivity,[status(thm)],[1260, 1258])).
% 1.75/1.44 tff(1262,plain,
% 1.75/1.44 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c0_1(a43) | c3_1(a43))),
% 1.75/1.44 inference(quant_inst,[status(thm)],[])).
% 1.75/1.44 tff(1263,plain,
% 1.75/1.44 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a43) | c3_1(a43) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a43)),
% 1.75/1.44 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 1.75/1.44 tff(1264,plain,
% 1.75/1.44 ($false),
% 1.75/1.44 inference(unit_resolution,[status(thm)],[1263, 84, 1257, 634, 623, 689, 683, 612, 1256, 1246])).
% 1.75/1.44 tff(1265,plain,(hskp0 | hskp3 | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.44 tff(1266,plain,
% 1.75/1.44 (hskp0),
% 1.75/1.44 inference(unit_resolution,[status(thm)],[1265, 1193, 213, 202, 162, 191, 180, 169])).
% 1.75/1.44 tff(1267,plain,
% 1.75/1.44 (c2_1(a1)),
% 1.75/1.44 inference(unit_resolution,[status(thm)],[736, 1266])).
% 1.75/1.44 tff(1268,plain,
% 1.75/1.44 (c1_1(a1)),
% 1.75/1.44 inference(unit_resolution,[status(thm)],[725, 1266])).
% 1.75/1.44 tff(1269,assumption,(hskp19), introduced(assumption)).
% 1.75/1.44 tff(1270,plain,
% 1.75/1.44 (((~hskp19) | (~c3_1(a36))) <=> ((~hskp19) | (~c3_1(a36)))),
% 1.75/1.44 inference(rewrite,[status(thm)],[])).
% 1.75/1.44 tff(1271,plain,
% 1.75/1.44 (((~c3_1(a36)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a36)))),
% 1.75/1.44 inference(rewrite,[status(thm)],[])).
% 1.75/1.44 tff(1272,axiom,((~c3_1(a36)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.75/1.44 tff(1273,plain,
% 1.75/1.44 ((~hskp19) | (~c3_1(a36))),
% 1.75/1.44 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 1.75/1.44 tff(1274,plain,
% 1.75/1.44 ((~hskp19) | (~c3_1(a36))),
% 1.75/1.44 inference(modus_ponens,[status(thm)],[1273, 1270])).
% 1.75/1.44 tff(1275,plain,
% 1.75/1.44 (~c3_1(a36)),
% 1.75/1.44 inference(unit_resolution,[status(thm)],[1274, 1269])).
% 1.75/1.44 tff(1276,plain,
% 1.75/1.44 (((~hskp19) | (~c2_1(a36))) <=> ((~hskp19) | (~c2_1(a36)))),
% 1.75/1.44 inference(rewrite,[status(thm)],[])).
% 1.75/1.44 tff(1277,plain,
% 1.75/1.44 (((~c2_1(a36)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a36)))),
% 1.75/1.44 inference(rewrite,[status(thm)],[])).
% 1.75/1.44 tff(1278,axiom,((~c2_1(a36)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.75/1.44 tff(1279,plain,
% 1.75/1.44 ((~hskp19) | (~c2_1(a36))),
% 1.75/1.44 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 1.75/1.44 tff(1280,plain,
% 1.75/1.44 ((~hskp19) | (~c2_1(a36))),
% 1.75/1.44 inference(modus_ponens,[status(thm)],[1279, 1276])).
% 1.75/1.44 tff(1281,plain,
% 1.75/1.44 (~c2_1(a36)),
% 1.75/1.44 inference(unit_resolution,[status(thm)],[1280, 1269])).
% 1.75/1.44 tff(1282,plain,
% 1.75/1.44 (((~hskp19) | (~c1_1(a36))) <=> ((~hskp19) | (~c1_1(a36)))),
% 1.75/1.44 inference(rewrite,[status(thm)],[])).
% 1.75/1.44 tff(1283,plain,
% 1.75/1.44 (((~c1_1(a36)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a36)))),
% 1.75/1.44 inference(rewrite,[status(thm)],[])).
% 1.75/1.44 tff(1284,axiom,((~c1_1(a36)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.75/1.44 tff(1285,plain,
% 1.75/1.44 ((~hskp19) | (~c1_1(a36))),
% 1.75/1.44 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 1.75/1.44 tff(1286,plain,
% 1.75/1.44 ((~hskp19) | (~c1_1(a36))),
% 1.75/1.44 inference(modus_ponens,[status(thm)],[1285, 1282])).
% 1.75/1.44 tff(1287,plain,
% 1.75/1.44 (~c1_1(a36)),
% 1.75/1.44 inference(unit_resolution,[status(thm)],[1286, 1269])).
% 1.75/1.44 tff(1288,plain,
% 1.75/1.44 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0))),
% 1.75/1.44 inference(rewrite,[status(thm)],[])).
% 1.75/1.44 tff(1289,plain,
% 1.75/1.44 ((hskp30 | hskp18 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c2_1(a36)) <=> (hskp30 | hskp18 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0))),
% 1.75/1.44 inference(rewrite,[status(thm)],[])).
% 1.75/1.44 tff(1290,plain,
% 1.75/1.44 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c2_1(a36))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0)))),
% 1.75/1.44 inference(monotonicity,[status(thm)],[1289])).
% 1.75/1.44 tff(1291,plain,
% 1.75/1.44 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c2_1(a36))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0))),
% 1.75/1.44 inference(transitivity,[status(thm)],[1290, 1288])).
% 1.75/1.44 tff(1292,plain,
% 1.75/1.44 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c2_1(a36))),
% 1.75/1.44 inference(quant_inst,[status(thm)],[])).
% 1.75/1.44 tff(1293,plain,
% 1.75/1.44 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0)),
% 1.75/1.44 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 1.75/1.44 tff(1294,plain,
% 1.75/1.44 ($false),
% 1.75/1.44 inference(unit_resolution,[status(thm)],[1293, 135, 84, 134, 1287, 1281, 1275, 306])).
% 1.75/1.44 tff(1295,plain,((~hskp19) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.75/1.44 tff(1296,plain,
% 1.75/1.44 (~hskp19),
% 1.75/1.44 inference(unit_resolution,[status(thm)],[1295, 135, 134])).
% 1.75/1.44 tff(1297,plain,
% 1.75/1.44 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a5) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a5) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.75/1.44 inference(rewrite,[status(thm)],[])).
% 1.75/1.44 tff(1298,plain,
% 1.75/1.44 ((hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5))) <=> (hskp19 | c1_1(a5) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.75/1.44 inference(rewrite,[status(thm)],[])).
% 1.75/1.44 tff(1299,plain,
% 1.75/1.44 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a5) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | (~c2_1(a5)) | (~c3_1(a5))))),
% 1.75/1.44 inference(monotonicity,[status(thm)],[1298])).
% 1.75/1.44 tff(1300,plain,
% 1.75/1.44 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a5) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.75/1.44 inference(transitivity,[status(thm)],[1299, 1297])).
% 1.75/1.44 tff(1301,plain,
% 1.75/1.44 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))),
% 1.82/1.44 inference(quant_inst,[status(thm)],[])).
% 1.82/1.44 tff(1302,plain,
% 1.82/1.44 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a5) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | (~c2_1(a5)) | (~c3_1(a5))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1301, 1300])).
% 1.82/1.44 tff(1303,plain,
% 1.82/1.44 (~c3_1(a1)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1302, 84, 1296, 213, 202, 1268, 1267, 162, 155])).
% 1.82/1.44 tff(1304,plain,
% 1.82/1.44 (~c0_1(a1)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[714, 1266])).
% 1.82/1.44 tff(1305,plain,
% 1.82/1.44 (c3_1(a6)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[295, 242, 257, 255, 254, 256, 253])).
% 1.82/1.44 tff(1306,plain,
% 1.82/1.44 (hskp5),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1147, 242, 257, 214, 255, 254, 253])).
% 1.82/1.44 tff(1307,plain,
% 1.82/1.44 ($false),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1115, 1306, 1305])).
% 1.82/1.44 tff(1308,plain,(c0_1(a5) | (~c2_1(a5)) | c1_1(a5) | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3) | (~c3_1(a5))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.44 tff(1309,plain,
% 1.82/1.44 (c0_1(a5)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1308, 202, 162, 191, 180, 169, 213])).
% 1.82/1.44 tff(1310,plain,
% 1.82/1.44 (~hskp14),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[785, 1267, 1309, 1304, 213, 202, 162, 135, 134, 1268])).
% 1.82/1.44 tff(1311,plain,
% 1.82/1.44 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1312,plain,
% 1.82/1.44 ((hskp29 | hskp14 | (~ndr1_0) | c3_1(a1) | c0_1(a1) | (~c2_1(a1))) <=> (hskp29 | hskp14 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1313,plain,
% 1.82/1.44 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1)))),
% 1.82/1.44 inference(monotonicity,[status(thm)],[1312])).
% 1.82/1.44 tff(1314,plain,
% 1.82/1.44 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1))),
% 1.82/1.44 inference(transitivity,[status(thm)],[1313, 1311])).
% 1.82/1.44 tff(1315,plain,
% 1.82/1.44 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)))),
% 1.82/1.44 inference(quant_inst,[status(thm)],[])).
% 1.82/1.44 tff(1316,plain,
% 1.82/1.44 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 1.82/1.44 tff(1317,plain,
% 1.82/1.44 (hskp29),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1316, 84, 1310, 1267, 1304, 336, 1303])).
% 1.82/1.44 tff(1318,plain,
% 1.82/1.44 (c0_1(a25)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[354, 1317])).
% 1.82/1.44 tff(1319,plain,
% 1.82/1.44 (c2_1(a25)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[365, 1317])).
% 1.82/1.44 tff(1320,plain,
% 1.82/1.44 (c1_1(a25)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[386, 1317])).
% 1.82/1.44 tff(1321,plain,
% 1.82/1.44 (~c3_1(a25)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[393, 84, 1318, 1320, 1319, 376])).
% 1.82/1.44 tff(1322,plain,
% 1.82/1.44 (~hskp27),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[446, 1321, 1319, 191, 180, 169, 1318])).
% 1.82/1.44 tff(1323,plain,
% 1.82/1.44 ((hskp30 | hskp27 | hskp7) <=> (hskp30 | hskp27 | hskp7)),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1324,plain,
% 1.82/1.44 (((hskp30 | hskp27) | hskp7) <=> (hskp30 | hskp27 | hskp7)),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1325,plain,
% 1.82/1.44 ((hskp30 | hskp27) <=> (hskp30 | hskp27)),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1326,plain,
% 1.82/1.44 (((hskp30 | hskp27) | hskp7) <=> ((hskp30 | hskp27) | hskp7)),
% 1.82/1.44 inference(monotonicity,[status(thm)],[1325])).
% 1.82/1.44 tff(1327,plain,
% 1.82/1.44 (((hskp30 | hskp27) | hskp7) <=> (hskp30 | hskp27 | hskp7)),
% 1.82/1.44 inference(transitivity,[status(thm)],[1326, 1324])).
% 1.82/1.44 tff(1328,axiom,((hskp30 | hskp27) | hskp7), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 1.82/1.44 tff(1329,plain,
% 1.82/1.44 (hskp30 | hskp27 | hskp7),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1328, 1327])).
% 1.82/1.44 tff(1330,plain,
% 1.82/1.44 (hskp30 | hskp27 | hskp7),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1329, 1323])).
% 1.82/1.44 tff(1331,plain,
% 1.82/1.44 (hskp30 | hskp27 | hskp7),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1330, 1323])).
% 1.82/1.44 tff(1332,plain,
% 1.82/1.44 (hskp30 | hskp27 | hskp7),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1331, 1323])).
% 1.82/1.44 tff(1333,plain,
% 1.82/1.44 (hskp30 | hskp27 | hskp7),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1332, 1323])).
% 1.82/1.44 tff(1334,plain,
% 1.82/1.44 (hskp30 | hskp27 | hskp7),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1333, 1323])).
% 1.82/1.44 tff(1335,plain,
% 1.82/1.44 (hskp30 | hskp27 | hskp7),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1334, 1323])).
% 1.82/1.44 tff(1336,plain,
% 1.82/1.44 (hskp30 | hskp27 | hskp7),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1335, 1323])).
% 1.82/1.44 tff(1337,plain,
% 1.82/1.44 (hskp7),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1336, 1322, 135])).
% 1.82/1.44 tff(1338,plain,
% 1.82/1.44 (~c2_1(a9)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[823, 1337])).
% 1.82/1.44 tff(1339,plain,
% 1.82/1.44 (~c0_1(a9)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[829, 1337])).
% 1.82/1.44 tff(1340,plain,
% 1.82/1.44 (c1_1(a9)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[840, 1337])).
% 1.82/1.44 tff(1341,assumption,(hskp28), introduced(assumption)).
% 1.82/1.44 tff(1342,plain,
% 1.82/1.44 (((~hskp28) | c3_1(a15)) <=> ((~hskp28) | c3_1(a15))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1343,axiom,((~hskp28) | c3_1(a15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 1.82/1.44 tff(1344,plain,
% 1.82/1.44 ((~hskp28) | c3_1(a15)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 1.82/1.44 tff(1345,plain,
% 1.82/1.44 ((~hskp28) | c3_1(a15)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1344, 1342])).
% 1.82/1.44 tff(1346,plain,
% 1.82/1.44 ((~hskp28) | c3_1(a15)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1345, 1342])).
% 1.82/1.44 tff(1347,plain,
% 1.82/1.44 ((~hskp28) | c3_1(a15)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1346, 1342])).
% 1.82/1.44 tff(1348,plain,
% 1.82/1.44 ((~hskp28) | c3_1(a15)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1347, 1342])).
% 1.82/1.44 tff(1349,plain,
% 1.82/1.44 ((~hskp28) | c3_1(a15)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1348, 1342])).
% 1.82/1.44 tff(1350,plain,
% 1.82/1.44 ((~hskp28) | c3_1(a15)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1349, 1342])).
% 1.82/1.44 tff(1351,plain,
% 1.82/1.44 ((~hskp28) | c3_1(a15)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1350, 1342])).
% 1.82/1.44 tff(1352,plain,
% 1.82/1.44 (c3_1(a15)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1351, 1341])).
% 1.82/1.44 tff(1353,plain,
% 1.82/1.44 (((~hskp28) | c1_1(a15)) <=> ((~hskp28) | c1_1(a15))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1354,axiom,((~hskp28) | c1_1(a15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 1.82/1.44 tff(1355,plain,
% 1.82/1.44 ((~hskp28) | c1_1(a15)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1354, 1353])).
% 1.82/1.44 tff(1356,plain,
% 1.82/1.44 ((~hskp28) | c1_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1355, 1353])).
% 1.82/1.45 tff(1357,plain,
% 1.82/1.45 ((~hskp28) | c1_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1356, 1353])).
% 1.82/1.45 tff(1358,plain,
% 1.82/1.45 ((~hskp28) | c1_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1357, 1353])).
% 1.82/1.45 tff(1359,plain,
% 1.82/1.45 ((~hskp28) | c1_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1358, 1353])).
% 1.82/1.45 tff(1360,plain,
% 1.82/1.45 ((~hskp28) | c1_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1359, 1353])).
% 1.82/1.45 tff(1361,plain,
% 1.82/1.45 ((~hskp28) | c1_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1360, 1353])).
% 1.82/1.45 tff(1362,plain,
% 1.82/1.45 ((~hskp28) | c1_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1361, 1353])).
% 1.82/1.45 tff(1363,plain,
% 1.82/1.45 (c1_1(a15)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1362, 1341])).
% 1.82/1.45 tff(1364,plain,
% 1.82/1.45 (((~hskp28) | c0_1(a15)) <=> ((~hskp28) | c0_1(a15))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1365,axiom,((~hskp28) | c0_1(a15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.82/1.45 tff(1366,plain,
% 1.82/1.45 ((~hskp28) | c0_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 1.82/1.45 tff(1367,plain,
% 1.82/1.45 ((~hskp28) | c0_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1366, 1364])).
% 1.82/1.45 tff(1368,plain,
% 1.82/1.45 ((~hskp28) | c0_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1367, 1364])).
% 1.82/1.45 tff(1369,plain,
% 1.82/1.45 ((~hskp28) | c0_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1368, 1364])).
% 1.82/1.45 tff(1370,plain,
% 1.82/1.45 ((~hskp28) | c0_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1369, 1364])).
% 1.82/1.45 tff(1371,plain,
% 1.82/1.45 ((~hskp28) | c0_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1370, 1364])).
% 1.82/1.45 tff(1372,plain,
% 1.82/1.45 ((~hskp28) | c0_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1371, 1364])).
% 1.82/1.45 tff(1373,plain,
% 1.82/1.45 ((~hskp28) | c0_1(a15)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1372, 1364])).
% 1.82/1.45 tff(1374,plain,
% 1.82/1.45 (c0_1(a15)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1373, 1341])).
% 1.82/1.45 tff(1375,assumption,(c2_1(a15)), introduced(assumption)).
% 1.82/1.45 tff(1376,assumption,(c3_1(a15)), introduced(assumption)).
% 1.82/1.45 tff(1377,assumption,(c1_1(a15)), introduced(assumption)).
% 1.82/1.45 tff(1378,assumption,(c0_1(a15)), introduced(assumption)).
% 1.82/1.45 tff(1379,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1380,plain,
% 1.82/1.45 (((~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a15)) | (~c2_1(a15)) | (~c0_1(a15))) <=> ((~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1381,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a15)) | (~c2_1(a15)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1380])).
% 1.82/1.45 tff(1382,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a15)) | (~c2_1(a15)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1381, 1379])).
% 1.82/1.45 tff(1383,plain,
% 1.82/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a15)) | (~c2_1(a15)) | (~c0_1(a15)))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1384,plain,
% 1.82/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 1.82/1.45 tff(1385,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1384, 84, 1378, 1377, 1376, 376, 1375])).
% 1.82/1.45 tff(1386,plain,((~c2_1(a15)) | (~c0_1(a15)) | (~c1_1(a15)) | (~c3_1(a15))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1387,plain,
% 1.82/1.45 (~c2_1(a15)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1386, 1374, 1363, 1352])).
% 1.82/1.45 tff(1388,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1389,plain,
% 1.82/1.45 (((~ndr1_0) | (~c3_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5))) <=> (c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1390,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1389])).
% 1.82/1.45 tff(1391,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1390, 1388])).
% 1.82/1.45 tff(1392,plain,
% 1.82/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1393,plain,
% 1.82/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 1.82/1.45 tff(1394,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1393, 84, 1374, 1363, 1352, 257, 214, 587, 739, 1387])).
% 1.82/1.45 tff(1395,plain,((~hskp28) | (~c2_1(a5)) | c1_1(a5) | (~c0_1(a5))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1396,plain,
% 1.82/1.45 (~hskp28),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1395, 1309, 162, 213])).
% 1.82/1.45 tff(1397,plain,
% 1.82/1.45 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp28 | hskp27 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a9)))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp28 | hskp27 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a9)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1398,plain,
% 1.82/1.45 ((hskp28 | hskp27 | (~ndr1_0) | c0_1(a9) | c2_1(a9) | (~c1_1(a9))) <=> (hskp28 | hskp27 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a9)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1399,plain,
% 1.82/1.45 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp28 | hskp27 | (~ndr1_0) | c0_1(a9) | c2_1(a9) | (~c1_1(a9)))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp28 | hskp27 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a9))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1398])).
% 1.82/1.45 tff(1400,plain,
% 1.82/1.45 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp28 | hskp27 | (~ndr1_0) | c0_1(a9) | c2_1(a9) | (~c1_1(a9)))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp28 | hskp27 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a9)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1399, 1397])).
% 1.82/1.45 tff(1401,plain,
% 1.82/1.45 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp28 | hskp27 | (~ndr1_0) | c0_1(a9) | c2_1(a9) | (~c1_1(a9)))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1402,plain,
% 1.82/1.45 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp28 | hskp27 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a9))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 1.82/1.45 tff(1403,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1402, 84, 1396, 1322, 1340, 1339, 1338, 145])).
% 1.82/1.45 tff(1404,plain,((~hskp4) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1405,plain,
% 1.82/1.45 (~hskp4),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1404, 135, 134])).
% 1.82/1.45 tff(1406,assumption,(~hskp24), introduced(assumption)).
% 1.82/1.45 tff(1407,assumption,(~hskp4), introduced(assumption)).
% 1.82/1.45 tff(1408,plain,
% 1.82/1.45 (^[U: $i] : refl((hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.82/1.45 inference(bind,[status(th)],[])).
% 1.82/1.45 tff(1409,plain,
% 1.82/1.45 (![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.45 inference(quant_intro,[status(thm)],[1408])).
% 1.82/1.45 tff(1410,plain,
% 1.82/1.45 (![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1411,plain,
% 1.82/1.45 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp19) <=> ((hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp19))), rewrite(((hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp19) <=> (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.82/1.45 inference(bind,[status(th)],[])).
% 1.82/1.45 tff(1412,plain,
% 1.82/1.45 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp19) <=> ![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.45 inference(quant_intro,[status(thm)],[1411])).
% 1.82/1.45 tff(1413,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.82/1.45 tff(1414,plain,
% 1.82/1.45 (![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 1.82/1.45 tff(1415,plain,
% 1.82/1.45 (![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1414, 1410])).
% 1.82/1.46 tff(1416,plain,(
% 1.82/1.46 ![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.46 inference(skolemize,[status(sab)],[1415])).
% 1.82/1.46 tff(1417,plain,
% 1.82/1.46 (![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1416, 1409])).
% 1.82/1.46 tff(1418,assumption,(~hskp19), introduced(assumption)).
% 1.82/1.46 tff(1419,plain,
% 1.82/1.46 (~c2_1(a15)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1386, 1352, 1363, 1374])).
% 1.82/1.46 tff(1420,plain,
% 1.82/1.46 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1421,plain,
% 1.82/1.46 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.82/1.46 inference(quant_inst,[status(thm)],[])).
% 1.82/1.46 tff(1422,plain,
% 1.82/1.46 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 1.82/1.46 tff(1423,plain,
% 1.82/1.46 ($false),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1422, 1, 84, 1418, 1374, 1352, 1417, 1419])).
% 1.82/1.46 tff(1424,plain,((~hskp28) | hskp22 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.82/1.46 tff(1425,plain,
% 1.82/1.46 (~hskp28),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1424, 1, 1418])).
% 1.82/1.46 tff(1426,assumption,(hskp24), introduced(assumption)).
% 1.82/1.46 tff(1427,plain,
% 1.82/1.46 (((~hskp24) | c3_1(a58)) <=> ((~hskp24) | c3_1(a58))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1428,axiom,((~hskp24) | c3_1(a58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.82/1.46 tff(1429,plain,
% 1.82/1.46 ((~hskp24) | c3_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 1.82/1.46 tff(1430,plain,
% 1.82/1.46 ((~hskp24) | c3_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1429, 1427])).
% 1.82/1.46 tff(1431,plain,
% 1.82/1.46 ((~hskp24) | c3_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1430, 1427])).
% 1.82/1.46 tff(1432,plain,
% 1.82/1.46 ((~hskp24) | c3_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1431, 1427])).
% 1.82/1.46 tff(1433,plain,
% 1.82/1.46 ((~hskp24) | c3_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1432, 1427])).
% 1.82/1.46 tff(1434,plain,
% 1.82/1.46 ((~hskp24) | c3_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1433, 1427])).
% 1.82/1.46 tff(1435,plain,
% 1.82/1.46 ((~hskp24) | c3_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1434, 1427])).
% 1.82/1.46 tff(1436,plain,
% 1.82/1.46 ((~hskp24) | c3_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1435, 1427])).
% 1.82/1.46 tff(1437,plain,
% 1.82/1.46 (c3_1(a58)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1436, 1426])).
% 1.82/1.46 tff(1438,plain,
% 1.82/1.46 (((~hskp24) | c0_1(a58)) <=> ((~hskp24) | c0_1(a58))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1439,axiom,((~hskp24) | c0_1(a58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.82/1.46 tff(1440,plain,
% 1.82/1.46 ((~hskp24) | c0_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 1.82/1.46 tff(1441,plain,
% 1.82/1.46 ((~hskp24) | c0_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1440, 1438])).
% 1.82/1.46 tff(1442,plain,
% 1.82/1.46 ((~hskp24) | c0_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1441, 1438])).
% 1.82/1.46 tff(1443,plain,
% 1.82/1.46 ((~hskp24) | c0_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1442, 1438])).
% 1.82/1.46 tff(1444,plain,
% 1.82/1.46 ((~hskp24) | c0_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1443, 1438])).
% 1.82/1.46 tff(1445,plain,
% 1.82/1.46 ((~hskp24) | c0_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1444, 1438])).
% 1.82/1.46 tff(1446,plain,
% 1.82/1.46 ((~hskp24) | c0_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1445, 1438])).
% 1.82/1.46 tff(1447,plain,
% 1.82/1.46 ((~hskp24) | c0_1(a58)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1446, 1438])).
% 1.82/1.46 tff(1448,plain,
% 1.82/1.46 (c0_1(a58)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1447, 1426])).
% 1.82/1.46 tff(1449,plain,
% 1.82/1.46 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1450,plain,
% 1.82/1.46 ((hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58))) <=> (hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1451,plain,
% 1.82/1.46 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58))))),
% 1.82/1.46 inference(monotonicity,[status(thm)],[1450])).
% 1.82/1.46 tff(1452,plain,
% 1.82/1.46 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))),
% 1.82/1.46 inference(transitivity,[status(thm)],[1451, 1449])).
% 1.82/1.46 tff(1453,plain,
% 1.82/1.46 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))),
% 1.82/1.46 inference(quant_inst,[status(thm)],[])).
% 1.82/1.46 tff(1454,plain,
% 1.82/1.46 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1453, 1452])).
% 1.82/1.46 tff(1455,plain,
% 1.82/1.46 (c2_1(a58)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1454, 1, 84, 1418, 1448, 1437, 1417])).
% 1.82/1.46 tff(1456,plain,
% 1.82/1.46 (((~hskp24) | (~c1_1(a58))) <=> ((~hskp24) | (~c1_1(a58)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1457,plain,
% 1.82/1.46 (((~c1_1(a58)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a58)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1458,axiom,((~c1_1(a58)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.82/1.46 tff(1459,plain,
% 1.82/1.46 ((~hskp24) | (~c1_1(a58))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1458, 1457])).
% 1.82/1.46 tff(1460,plain,
% 1.82/1.46 ((~hskp24) | (~c1_1(a58))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1459, 1456])).
% 1.82/1.46 tff(1461,plain,
% 1.82/1.46 (~c1_1(a58)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1460, 1426])).
% 1.82/1.46 tff(1462,assumption,(~hskp21), introduced(assumption)).
% 1.82/1.46 tff(1463,plain,
% 1.82/1.46 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | c1_1(a58) | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c1_1(a58) | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1464,plain,
% 1.82/1.46 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58))) <=> (hskp21 | hskp0 | c1_1(a58) | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1465,plain,
% 1.82/1.46 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | c1_1(a58) | (~ndr1_0) | c2_1(a58) | (~c0_1(a58))))),
% 1.82/1.46 inference(monotonicity,[status(thm)],[1464])).
% 1.82/1.46 tff(1466,plain,
% 1.82/1.46 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c1_1(a58) | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)))),
% 1.82/1.46 inference(transitivity,[status(thm)],[1465, 1463])).
% 1.82/1.46 tff(1467,plain,
% 1.82/1.46 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)))),
% 1.82/1.46 inference(quant_inst,[status(thm)],[])).
% 1.82/1.46 tff(1468,plain,
% 1.82/1.46 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c1_1(a58) | (~ndr1_0) | c2_1(a58) | (~c0_1(a58))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 1.82/1.46 tff(1469,plain,
% 1.82/1.46 (c2_1(a58)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1468, 84, 1462, 588, 1448, 1461, 1203])).
% 1.82/1.46 tff(1470,plain,
% 1.82/1.46 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1471,plain,
% 1.82/1.46 ((hskp1 | hskp0 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58))) <=> (hskp1 | hskp0 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1472,plain,
% 1.82/1.46 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58))))),
% 1.82/1.46 inference(monotonicity,[status(thm)],[1471])).
% 1.82/1.46 tff(1473,plain,
% 1.82/1.46 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.82/1.46 inference(transitivity,[status(thm)],[1472, 1470])).
% 1.82/1.46 tff(1474,plain,
% 1.82/1.46 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.82/1.46 inference(quant_inst,[status(thm)],[])).
% 1.82/1.46 tff(1475,plain,
% 1.82/1.46 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1474, 1473])).
% 1.82/1.46 tff(1476,plain,
% 1.82/1.46 (hskp1),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1475, 84, 588, 1437, 1461, 598, 1469])).
% 1.82/1.46 tff(1477,plain,
% 1.82/1.46 (~c2_1(a2)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[611, 1476])).
% 1.82/1.46 tff(1478,plain,
% 1.82/1.46 (c3_1(a2)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[622, 1476])).
% 1.82/1.46 tff(1479,plain,
% 1.82/1.46 (c0_1(a2)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[633, 1476])).
% 1.82/1.46 tff(1480,plain,
% 1.82/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a58) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a58)) | (~c0_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a58) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a58)) | (~c0_1(a58)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1481,plain,
% 1.82/1.46 (((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58))) <=> (c1_1(a58) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a58)) | (~c0_1(a58)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1482,plain,
% 1.82/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a58) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a58)) | (~c0_1(a58))))),
% 1.82/1.46 inference(monotonicity,[status(thm)],[1481])).
% 1.82/1.46 tff(1483,plain,
% 1.82/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a58) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a58)) | (~c0_1(a58)))),
% 1.82/1.47 inference(transitivity,[status(thm)],[1482, 1480])).
% 1.82/1.47 tff(1484,plain,
% 1.82/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)))),
% 1.82/1.47 inference(quant_inst,[status(thm)],[])).
% 1.82/1.47 tff(1485,plain,
% 1.82/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a58) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a58)) | (~c0_1(a58))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 1.82/1.47 tff(1486,plain,
% 1.82/1.47 (~c1_1(a2)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1485, 84, 1448, 1479, 1478, 1461, 1477, 587, 1469])).
% 1.82/1.47 tff(1487,plain,
% 1.82/1.47 ($false),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1209, 84, 1462, 588, 1479, 1477, 1203, 1486])).
% 1.82/1.47 tff(1488,plain,((~hskp24) | hskp21 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.82/1.47 tff(1489,plain,
% 1.82/1.47 (hskp21),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1488, 1426, 588])).
% 1.82/1.47 tff(1490,plain,
% 1.82/1.47 (~c0_1(a42)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1216, 1489])).
% 1.82/1.47 tff(1491,plain,
% 1.82/1.47 (c3_1(a42)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1227, 1489])).
% 1.82/1.47 tff(1492,plain,
% 1.82/1.47 (c2_1(a42)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1238, 1489])).
% 1.82/1.47 tff(1493,plain,
% 1.82/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a58) | c0_1(a42) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a58)) | (~c0_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a58) | c0_1(a42) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a58)) | (~c0_1(a58)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1494,plain,
% 1.82/1.47 (((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42))) <=> (c1_1(a58) | c0_1(a42) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a58)) | (~c0_1(a58)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1495,plain,
% 1.82/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a58) | c0_1(a42) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a58)) | (~c0_1(a58))))),
% 1.82/1.47 inference(monotonicity,[status(thm)],[1494])).
% 1.82/1.47 tff(1496,plain,
% 1.82/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a58) | c0_1(a42) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a58)) | (~c0_1(a58)))),
% 1.82/1.47 inference(transitivity,[status(thm)],[1495, 1493])).
% 1.82/1.47 tff(1497,plain,
% 1.82/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.82/1.47 inference(quant_inst,[status(thm)],[])).
% 1.82/1.47 tff(1498,plain,
% 1.82/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a58) | c0_1(a42) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a58)) | (~c0_1(a58))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1497, 1496])).
% 1.82/1.47 tff(1499,plain,
% 1.82/1.47 ($false),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1498, 84, 1448, 1492, 1491, 44, 1461, 1490, 22, 103, 93, 1455])).
% 1.82/1.47 tff(1500,plain,((~hskp24) | hskp22 | hskp19 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.82/1.47 tff(1501,plain,
% 1.82/1.47 (~hskp24),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1500, 1, 1418, 588])).
% 1.82/1.47 tff(1502,assumption,(~hskp1), introduced(assumption)).
% 1.82/1.47 tff(1503,assumption,(c2_1(a19)), introduced(assumption)).
% 1.82/1.47 tff(1504,assumption,(~c3_1(a19)), introduced(assumption)).
% 1.82/1.47 tff(1505,assumption,(c0_1(a19)), introduced(assumption)).
% 1.82/1.47 tff(1506,assumption,(~hskp28), introduced(assumption)).
% 1.82/1.47 tff(1507,plain,
% 1.82/1.47 ((hskp28 | hskp9 | hskp1) <=> (hskp28 | hskp9 | hskp1)),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1508,plain,
% 1.82/1.47 (((hskp28 | hskp1) | hskp9) <=> (hskp28 | hskp9 | hskp1)),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1509,plain,
% 1.82/1.47 ((hskp28 | hskp1) <=> (hskp28 | hskp1)),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1510,plain,
% 1.82/1.47 (((hskp28 | hskp1) | hskp9) <=> ((hskp28 | hskp1) | hskp9)),
% 1.82/1.47 inference(monotonicity,[status(thm)],[1509])).
% 1.82/1.47 tff(1511,plain,
% 1.82/1.47 (((hskp28 | hskp1) | hskp9) <=> (hskp28 | hskp9 | hskp1)),
% 1.82/1.47 inference(transitivity,[status(thm)],[1510, 1508])).
% 1.82/1.47 tff(1512,axiom,((hskp28 | hskp1) | hskp9), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 1.82/1.47 tff(1513,plain,
% 1.82/1.47 (hskp28 | hskp9 | hskp1),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 1.82/1.47 tff(1514,plain,
% 1.82/1.47 (hskp28 | hskp9 | hskp1),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1513, 1507])).
% 1.82/1.47 tff(1515,plain,
% 1.82/1.47 (hskp28 | hskp9 | hskp1),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1514, 1507])).
% 1.82/1.47 tff(1516,plain,
% 1.82/1.47 (hskp28 | hskp9 | hskp1),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1515, 1507])).
% 1.82/1.47 tff(1517,plain,
% 1.82/1.47 (hskp28 | hskp9 | hskp1),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1516, 1507])).
% 1.82/1.47 tff(1518,plain,
% 1.82/1.47 (hskp28 | hskp9 | hskp1),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1517, 1507])).
% 1.82/1.47 tff(1519,plain,
% 1.82/1.47 (hskp28 | hskp9 | hskp1),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1518, 1507])).
% 1.82/1.47 tff(1520,plain,
% 1.82/1.47 (hskp28 | hskp9 | hskp1),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1519, 1507])).
% 1.82/1.47 tff(1521,plain,
% 1.82/1.47 (hskp9),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1520, 1502, 1506])).
% 1.82/1.47 tff(1522,plain,
% 1.82/1.47 (~c2_1(a12)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1058, 1521])).
% 1.82/1.47 tff(1523,plain,
% 1.82/1.47 (~c3_1(a12)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[576, 1521])).
% 1.82/1.47 tff(1524,plain,
% 1.82/1.47 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.82/1.47 inference(bind,[status(th)],[])).
% 1.82/1.47 tff(1525,plain,
% 1.82/1.47 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.82/1.47 inference(quant_intro,[status(thm)],[1524])).
% 1.82/1.47 tff(1526,plain,
% 1.82/1.47 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1527,plain,
% 1.85/1.47 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_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))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_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))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp24) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp24))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp24) <=> (hskp24 | (~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))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.85/1.47 inference(bind,[status(th)],[])).
% 1.85/1.47 tff(1528,plain,
% 1.85/1.47 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.85/1.47 inference(quant_intro,[status(thm)],[1527])).
% 1.85/1.47 tff(1529,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 1.85/1.47 tff(1530,plain,
% 1.85/1.47 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1529, 1528])).
% 1.85/1.47 tff(1531,plain,
% 1.85/1.47 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1530, 1526])).
% 1.85/1.47 tff(1532,plain,(
% 1.85/1.47 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.85/1.47 inference(skolemize,[status(sab)],[1531])).
% 1.85/1.47 tff(1533,plain,
% 1.85/1.47 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1532, 1525])).
% 1.85/1.47 tff(1534,plain,
% 1.85/1.47 (^[U: $i] : refl((hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))),
% 1.85/1.47 inference(bind,[status(th)],[])).
% 1.85/1.47 tff(1535,plain,
% 1.85/1.47 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.85/1.47 inference(quant_intro,[status(thm)],[1534])).
% 1.85/1.47 tff(1536,plain,
% 1.85/1.47 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.85/1.47 inference(rewrite,[status(thm)],[])).
% 1.85/1.47 tff(1537,plain,
% 1.85/1.47 (^[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) | c1_1(U) | c2_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp19) <=> ((hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp19))), rewrite(((hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp19) <=> (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp19) <=> (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))))),
% 1.85/1.47 inference(bind,[status(th)],[])).
% 1.85/1.47 tff(1538,plain,
% 1.85/1.47 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp19) <=> ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.85/1.47 inference(quant_intro,[status(thm)],[1537])).
% 1.85/1.47 tff(1539,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.85/1.47 tff(1540,plain,
% 1.85/1.47 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1539, 1538])).
% 1.85/1.47 tff(1541,plain,
% 1.85/1.47 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1540, 1536])).
% 1.85/1.47 tff(1542,plain,(
% 1.85/1.47 ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.85/1.47 inference(skolemize,[status(sab)],[1541])).
% 1.85/1.47 tff(1543,plain,
% 1.85/1.47 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.85/1.47 inference(modus_ponens,[status(thm)],[1542, 1535])).
% 1.85/1.47 tff(1544,plain,
% 1.85/1.47 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp19 | hskp1 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(1545,plain,
% 1.85/1.48 ((hskp19 | hskp1 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12)) <=> (hskp19 | hskp1 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(1546,plain,
% 1.85/1.48 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0)))),
% 1.85/1.48 inference(monotonicity,[status(thm)],[1545])).
% 1.85/1.48 tff(1547,plain,
% 1.85/1.48 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp19 | hskp1 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))),
% 1.85/1.48 inference(transitivity,[status(thm)],[1546, 1544])).
% 1.85/1.48 tff(1548,plain,
% 1.85/1.48 ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12))),
% 1.85/1.48 inference(quant_inst,[status(thm)],[])).
% 1.85/1.48 tff(1549,plain,
% 1.85/1.48 ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp19 | hskp1 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0)),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[1548, 1547])).
% 1.85/1.48 tff(1550,plain,
% 1.85/1.48 (c1_1(a12) | c2_1(a12)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1549, 84, 1418, 1502, 652, 1543])).
% 1.85/1.48 tff(1551,plain,
% 1.85/1.48 (c1_1(a12)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1550, 1066])).
% 1.85/1.48 tff(1552,plain,
% 1.85/1.48 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a19) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a19)) | (~c0_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a19) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a19)) | (~c0_1(a19)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(1553,plain,
% 1.85/1.48 ((hskp24 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12))) <=> (hskp24 | c3_1(a19) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a19)) | (~c0_1(a19)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(1554,plain,
% 1.85/1.48 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a19) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a19)) | (~c0_1(a19))))),
% 1.85/1.48 inference(monotonicity,[status(thm)],[1553])).
% 1.85/1.48 tff(1555,plain,
% 1.85/1.48 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a19) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a19)) | (~c0_1(a19)))),
% 1.85/1.48 inference(transitivity,[status(thm)],[1554, 1552])).
% 1.85/1.48 tff(1556,plain,
% 1.85/1.48 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))),
% 1.85/1.48 inference(quant_inst,[status(thm)],[])).
% 1.85/1.48 tff(1557,plain,
% 1.85/1.48 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a19) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a19)) | (~c0_1(a19))),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 1.85/1.48 tff(1558,plain,
% 1.85/1.48 ($false),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1557, 84, 1406, 1505, 1551, 1504, 1066, 652, 1533, 1503])).
% 1.85/1.48 tff(1559,plain,(c2_1(a12) | hskp24 | (~c0_1(a19)) | c3_1(a19) | c3_1(a12) | (~c2_1(a19)) | hskp19 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.85/1.48 tff(1560,plain,
% 1.85/1.48 ($false),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1559, 1523, 1522, 1505, 1504, 1406, 1503, 1418, 1502])).
% 1.85/1.48 tff(1561,plain,(hskp1 | (~c0_1(a19)) | c3_1(a19) | hskp24 | (~c2_1(a19)) | hskp19 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.85/1.48 tff(1562,plain,
% 1.85/1.48 (hskp1),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1561, 44, 22, 1501, 93, 1418, 1425])).
% 1.85/1.48 tff(1563,plain,
% 1.85/1.48 (~c2_1(a2)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[611, 1562])).
% 1.85/1.48 tff(1564,plain,
% 1.85/1.48 (c3_1(a2)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[622, 1562])).
% 1.85/1.48 tff(1565,plain,
% 1.85/1.48 (c0_1(a2)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[633, 1562])).
% 1.85/1.48 tff(1566,plain,
% 1.85/1.48 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(1567,plain,
% 1.85/1.48 ((hskp22 | hskp19 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2))) <=> (hskp22 | hskp19 | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(1568,plain,
% 1.85/1.48 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2))))),
% 1.85/1.48 inference(monotonicity,[status(thm)],[1567])).
% 1.85/1.48 tff(1569,plain,
% 1.85/1.48 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)))),
% 1.85/1.48 inference(transitivity,[status(thm)],[1568, 1566])).
% 1.85/1.48 tff(1570,plain,
% 1.85/1.48 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)))),
% 1.85/1.48 inference(quant_inst,[status(thm)],[])).
% 1.85/1.48 tff(1571,plain,
% 1.85/1.48 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2))),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[1570, 1569])).
% 1.85/1.48 tff(1572,plain,
% 1.85/1.48 ($false),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1571, 1, 84, 1418, 1565, 1564, 1563, 1417])).
% 1.85/1.48 tff(1573,plain,(hskp22 | hskp19 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.85/1.48 tff(1574,plain,
% 1.85/1.48 (hskp22),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1573, 588, 1296])).
% 1.85/1.48 tff(1575,plain,
% 1.85/1.48 (~c3_1(a43)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[682, 1574])).
% 1.85/1.48 tff(1576,plain,
% 1.85/1.48 (~c1_1(a43)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[688, 1574])).
% 1.85/1.48 tff(1577,plain,
% 1.85/1.48 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c1_1(a43) | c3_1(a43) | (~ndr1_0) | c0_1(a43))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c1_1(a43) | c3_1(a43) | (~ndr1_0) | c0_1(a43))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(1578,plain,
% 1.85/1.48 ((hskp4 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | c0_1(a43)) <=> (hskp4 | c1_1(a43) | c3_1(a43) | (~ndr1_0) | c0_1(a43))),
% 1.85/1.48 inference(rewrite,[status(thm)],[])).
% 1.85/1.48 tff(1579,plain,
% 1.85/1.48 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | c0_1(a43))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c1_1(a43) | c3_1(a43) | (~ndr1_0) | c0_1(a43)))),
% 1.85/1.48 inference(monotonicity,[status(thm)],[1578])).
% 1.85/1.48 tff(1580,plain,
% 1.85/1.48 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | c0_1(a43))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c1_1(a43) | c3_1(a43) | (~ndr1_0) | c0_1(a43))),
% 1.85/1.48 inference(transitivity,[status(thm)],[1579, 1577])).
% 1.85/1.48 tff(1581,plain,
% 1.85/1.48 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | c0_1(a43))),
% 1.85/1.48 inference(quant_inst,[status(thm)],[])).
% 1.85/1.48 tff(1582,plain,
% 1.85/1.48 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c1_1(a43) | c3_1(a43) | (~ndr1_0) | c0_1(a43)),
% 1.85/1.48 inference(modus_ponens,[status(thm)],[1581, 1580])).
% 1.85/1.48 tff(1583,plain,
% 1.85/1.48 (c0_1(a43)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[1582, 84, 1407, 1576, 1575, 113])).
% 1.85/1.48 tff(1584,plain,
% 1.85/1.48 (c2_1(a43)),
% 1.85/1.48 inference(unit_resolution,[status(thm)],[699, 1574])).
% 1.85/1.49 tff(1585,assumption,(c0_1(a43)), introduced(assumption)).
% 1.85/1.49 tff(1586,assumption,(c2_1(a43)), introduced(assumption)).
% 1.85/1.49 tff(1587,assumption,(~c3_1(a43)), introduced(assumption)).
% 1.85/1.49 tff(1588,assumption,(hskp6), introduced(assumption)).
% 1.85/1.49 tff(1589,plain,
% 1.85/1.49 (~c2_1(a8)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[873, 1588])).
% 1.85/1.49 tff(1590,plain,
% 1.85/1.49 (~c3_1(a8)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[879, 1588])).
% 1.85/1.49 tff(1591,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a43) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(1592,plain,
% 1.85/1.49 ((hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a8) | c3_1(a8) | (~c1_1(a8))) <=> (hskp24 | c3_1(a43) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(1593,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a8) | c3_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a43) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 1.85/1.49 inference(monotonicity,[status(thm)],[1592])).
% 1.85/1.49 tff(1594,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a8) | c3_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.49 inference(transitivity,[status(thm)],[1593, 1591])).
% 1.85/1.49 tff(1595,plain,
% 1.85/1.49 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a8) | c3_1(a8) | (~c1_1(a8)))),
% 1.85/1.49 inference(quant_inst,[status(thm)],[])).
% 1.85/1.49 tff(1596,plain,
% 1.85/1.49 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c2_1(a43)) | (~c0_1(a43))),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 1.85/1.49 tff(1597,plain,
% 1.85/1.49 ($false),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[1596, 84, 1406, 1586, 1587, 882, 881, 1533, 935, 1585])).
% 1.85/1.49 tff(1598,plain,(c2_1(a8) | hskp24 | (~c2_1(a43)) | c3_1(a43) | c3_1(a8) | (~c0_1(a43)) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.85/1.49 tff(1599,plain,
% 1.85/1.49 ($false),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[1598, 1590, 1589, 134, 1587, 1586, 1585, 135, 1406])).
% 1.85/1.49 tff(1600,plain,((~hskp6) | hskp18 | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | hskp30 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.85/1.49 tff(1601,plain,
% 1.85/1.49 (~hskp6),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[1600, 1575, 134, 1584, 1583, 135, 1406])).
% 1.85/1.49 tff(1602,plain,
% 1.85/1.49 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | c3_1(a26))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | c3_1(a26))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(1603,plain,
% 1.85/1.49 ((hskp4 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c0_1(a26)) <=> (hskp4 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | c3_1(a26))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(1604,plain,
% 1.85/1.49 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c0_1(a26))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | c3_1(a26)))),
% 1.85/1.49 inference(monotonicity,[status(thm)],[1603])).
% 1.85/1.49 tff(1605,plain,
% 1.85/1.49 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c0_1(a26))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | c3_1(a26))),
% 1.85/1.49 inference(transitivity,[status(thm)],[1604, 1602])).
% 1.85/1.49 tff(1606,plain,
% 1.85/1.49 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c0_1(a26))),
% 1.85/1.49 inference(quant_inst,[status(thm)],[])).
% 1.85/1.49 tff(1607,plain,
% 1.85/1.49 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | c3_1(a26)),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[1606, 1605])).
% 1.85/1.49 tff(1608,plain,
% 1.85/1.49 (c3_1(a26)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[1607, 84, 1407, 753, 752, 113])).
% 1.85/1.49 tff(1609,plain,
% 1.85/1.49 (^[U: $i] : refl((hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))),
% 1.85/1.49 inference(bind,[status(th)],[])).
% 1.85/1.49 tff(1610,plain,
% 1.85/1.49 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.85/1.49 inference(quant_intro,[status(thm)],[1609])).
% 1.85/1.49 tff(1611,plain,
% 1.85/1.49 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(1612,plain,
% 1.85/1.49 (^[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) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp11))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) | hskp6) <=> ((hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp6))), rewrite(((hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp6) <=> (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) | hskp6) <=> (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))))),
% 1.85/1.49 inference(bind,[status(th)],[])).
% 1.85/1.49 tff(1613,plain,
% 1.85/1.49 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) | hskp6) <=> ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.85/1.49 inference(quant_intro,[status(thm)],[1612])).
% 1.85/1.49 tff(1614,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 1.85/1.49 tff(1615,plain,
% 1.85/1.49 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 1.85/1.49 tff(1616,plain,
% 1.85/1.49 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[1615, 1611])).
% 1.85/1.49 tff(1617,plain,(
% 1.85/1.49 ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.85/1.49 inference(skolemize,[status(sab)],[1616])).
% 1.85/1.49 tff(1618,plain,
% 1.85/1.49 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[1617, 1610])).
% 1.85/1.49 tff(1619,assumption,(~hskp11), introduced(assumption)).
% 1.85/1.49 tff(1620,plain,
% 1.85/1.49 (((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | c0_1(a26) | c2_1(a26) | (~ndr1_0) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp11 | hskp6 | c0_1(a26) | c2_1(a26) | (~ndr1_0) | (~c3_1(a26)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(1621,plain,
% 1.85/1.49 ((hskp11 | hskp6 | (~ndr1_0) | c0_1(a26) | c2_1(a26) | (~c3_1(a26))) <=> (hskp11 | hskp6 | c0_1(a26) | c2_1(a26) | (~ndr1_0) | (~c3_1(a26)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(1622,plain,
% 1.85/1.49 (((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | (~ndr1_0) | c0_1(a26) | c2_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | c0_1(a26) | c2_1(a26) | (~ndr1_0) | (~c3_1(a26))))),
% 1.85/1.49 inference(monotonicity,[status(thm)],[1621])).
% 1.85/1.49 tff(1623,plain,
% 1.85/1.49 (((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | (~ndr1_0) | c0_1(a26) | c2_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp11 | hskp6 | c0_1(a26) | c2_1(a26) | (~ndr1_0) | (~c3_1(a26)))),
% 1.85/1.49 inference(transitivity,[status(thm)],[1622, 1620])).
% 1.85/1.49 tff(1624,plain,
% 1.85/1.49 ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | (~ndr1_0) | c0_1(a26) | c2_1(a26) | (~c3_1(a26)))),
% 1.85/1.49 inference(quant_inst,[status(thm)],[])).
% 1.85/1.49 tff(1625,plain,
% 1.85/1.49 ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp11 | hskp6 | c0_1(a26) | c2_1(a26) | (~ndr1_0) | (~c3_1(a26))),
% 1.85/1.49 inference(modus_ponens,[status(thm)],[1624, 1623])).
% 1.85/1.49 tff(1626,plain,
% 1.85/1.49 (~c3_1(a26)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[1625, 1619, 84, 799, 753, 751, 1618])).
% 1.85/1.49 tff(1627,plain,
% 1.85/1.49 ($false),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[1607, 84, 1407, 753, 752, 113, 1626])).
% 1.85/1.49 tff(1628,plain,((~hskp14) | hskp4 | hskp11 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.85/1.49 tff(1629,plain,
% 1.85/1.49 (hskp11),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[1628, 750, 1407, 799])).
% 1.85/1.49 tff(1630,plain,
% 1.85/1.49 (~c3_1(a19)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[21, 1629])).
% 1.85/1.49 tff(1631,plain,
% 1.85/1.49 (c1_1(a19)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[32, 1629])).
% 1.85/1.49 tff(1632,plain,
% 1.85/1.49 (c0_1(a19)),
% 1.85/1.49 inference(unit_resolution,[status(thm)],[43, 1629])).
% 1.85/1.49 tff(1633,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a26) | c2_1(a26) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a26) | c2_1(a26) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a26)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(1634,plain,
% 1.85/1.49 ((hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26))) <=> (hskp0 | c1_1(a26) | c2_1(a26) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a26)))),
% 1.85/1.49 inference(rewrite,[status(thm)],[])).
% 1.85/1.49 tff(1635,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a26) | c2_1(a26) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a26))))),
% 1.85/1.49 inference(monotonicity,[status(thm)],[1634])).
% 1.85/1.49 tff(1636,plain,
% 1.85/1.49 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a26) | c2_1(a26) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a26)))),
% 1.85/1.50 inference(transitivity,[status(thm)],[1635, 1633])).
% 1.85/1.50 tff(1637,plain,
% 1.85/1.50 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26)))),
% 1.85/1.50 inference(quant_inst,[status(thm)],[])).
% 1.85/1.50 tff(1638,plain,
% 1.85/1.50 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a26) | c2_1(a26) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a26))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[1637, 1636])).
% 1.85/1.50 tff(1639,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1638, 84, 588, 1632, 1631, 752, 751, 1630, 651, 1608])).
% 1.85/1.50 tff(1640,plain,((~hskp14) | hskp0 | hskp4 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(1641,plain,
% 1.85/1.50 (~hskp14),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1640, 1601, 1407, 588])).
% 1.85/1.50 tff(1642,plain,
% 1.85/1.50 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | (~ndr1_0) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(1643,plain,
% 1.85/1.50 ((hskp18 | hskp14 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15))) <=> (hskp18 | hskp14 | (~ndr1_0) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(1644,plain,
% 1.85/1.50 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15))))),
% 1.85/1.50 inference(monotonicity,[status(thm)],[1643])).
% 1.85/1.50 tff(1645,plain,
% 1.85/1.50 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | (~ndr1_0) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)))),
% 1.85/1.50 inference(transitivity,[status(thm)],[1644, 1642])).
% 1.85/1.50 tff(1646,plain,
% 1.85/1.50 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))),
% 1.85/1.50 inference(quant_inst,[status(thm)],[])).
% 1.85/1.50 tff(1647,plain,
% 1.85/1.50 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | (~ndr1_0) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 1.85/1.50 tff(1648,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1647, 84, 134, 307, 1363, 1352, 325, 1419])).
% 1.85/1.50 tff(1649,plain,((~hskp28) | hskp18 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(1650,plain,
% 1.85/1.50 (~hskp28),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1649, 1641, 134])).
% 1.85/1.50 tff(1651,assumption,(hskp9), introduced(assumption)).
% 1.85/1.50 tff(1652,plain,
% 1.85/1.50 (~c2_1(a12)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1058, 1651])).
% 1.85/1.50 tff(1653,plain,
% 1.85/1.50 (~c3_1(a12)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[576, 1651])).
% 1.85/1.50 tff(1654,plain,
% 1.85/1.50 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a43) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(1655,plain,
% 1.85/1.50 ((hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12))) <=> (hskp24 | c3_1(a43) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(1656,plain,
% 1.85/1.50 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a43) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 1.85/1.50 inference(monotonicity,[status(thm)],[1655])).
% 1.85/1.50 tff(1657,plain,
% 1.85/1.50 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.50 inference(transitivity,[status(thm)],[1656, 1654])).
% 1.85/1.50 tff(1658,plain,
% 1.85/1.50 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))),
% 1.85/1.50 inference(quant_inst,[status(thm)],[])).
% 1.85/1.50 tff(1659,plain,
% 1.85/1.50 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a43)) | (~c0_1(a43))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 1.85/1.50 tff(1660,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1659, 84, 1406, 1586, 1551, 1587, 1066, 652, 1533, 1585])).
% 1.85/1.50 tff(1661,plain,(c2_1(a12) | hskp24 | (~c2_1(a43)) | c3_1(a43) | c3_1(a12) | (~c0_1(a43)) | hskp19 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(1662,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1661, 1653, 1652, 1586, 1587, 1502, 1585, 1418, 1406])).
% 1.85/1.50 tff(1663,plain,((~hskp9) | (~c2_1(a43)) | c3_1(a43) | hskp1 | (~c0_1(a43)) | hskp19 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(1664,plain,
% 1.85/1.50 (~hskp9),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1663, 1502, 1587, 1586, 1585, 1418, 1406])).
% 1.85/1.50 tff(1665,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1520, 1664, 1502, 1506])).
% 1.85/1.50 tff(1666,plain,(hskp1 | hskp28 | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | hskp19 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(1667,plain,
% 1.85/1.50 (hskp1),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1666, 1650, 1575, 1584, 1583, 1296, 1406])).
% 1.85/1.50 tff(1668,plain,
% 1.85/1.50 (~c2_1(a2)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[611, 1667])).
% 1.85/1.50 tff(1669,plain,
% 1.85/1.50 (c0_1(a2)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[633, 1667])).
% 1.85/1.50 tff(1670,assumption,(hskp21), introduced(assumption)).
% 1.85/1.50 tff(1671,plain,
% 1.85/1.50 (~c0_1(a42)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1216, 1670])).
% 1.85/1.50 tff(1672,assumption,(~c1_1(a43)), introduced(assumption)).
% 1.85/1.50 tff(1673,plain,
% 1.85/1.50 (c3_1(a42)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1227, 1670])).
% 1.85/1.50 tff(1674,plain,
% 1.85/1.50 (c2_1(a42)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1238, 1670])).
% 1.85/1.50 tff(1675,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1245, 84, 1586, 1674, 1673, 1672, 1587, 1671, 103, 1585])).
% 1.85/1.50 tff(1676,plain,((~hskp21) | (~c2_1(a43)) | c1_1(a43) | c3_1(a43) | (~c0_1(a43))), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(1677,plain,
% 1.85/1.50 (~hskp21),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1676, 1584, 1576, 1575, 1583])).
% 1.85/1.50 tff(1678,plain,
% 1.85/1.50 (c1_1(a2)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1209, 84, 1677, 588, 1669, 1668, 1203])).
% 1.85/1.50 tff(1679,plain,
% 1.85/1.50 (c3_1(a2)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[622, 1667])).
% 1.85/1.50 tff(1680,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a43) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a43) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(1681,plain,
% 1.85/1.50 (((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43))) <=> (c1_1(a43) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(1682,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a43) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 1.85/1.50 inference(monotonicity,[status(thm)],[1681])).
% 1.85/1.50 tff(1683,plain,
% 1.85/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a43) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.50 inference(transitivity,[status(thm)],[1682, 1680])).
% 1.85/1.50 tff(1684,plain,
% 1.85/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.50 inference(quant_inst,[status(thm)],[])).
% 1.85/1.50 tff(1685,plain,
% 1.85/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a43) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)) | (~c0_1(a43))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[1684, 1683])).
% 1.85/1.50 tff(1686,plain,
% 1.85/1.50 ($false),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1685, 84, 1584, 1669, 1679, 1576, 1668, 587, 1583, 1678])).
% 1.85/1.50 tff(1687,plain,(hskp0 | hskp24 | hskp18 | hskp4 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.85/1.50 tff(1688,plain,
% 1.85/1.50 (hskp0),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[1687, 1407, 134, 1406, 135])).
% 1.85/1.50 tff(1689,plain,
% 1.85/1.50 (~c0_1(a1)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[714, 1688])).
% 1.85/1.50 tff(1690,plain,
% 1.85/1.50 (^[U: $i] : refl((hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.85/1.50 inference(bind,[status(th)],[])).
% 1.85/1.50 tff(1691,plain,
% 1.85/1.50 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(quant_intro,[status(thm)],[1690])).
% 1.85/1.50 tff(1692,plain,
% 1.85/1.50 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(1693,plain,
% 1.85/1.50 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp4) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp4))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp4) <=> (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.85/1.50 inference(bind,[status(th)],[])).
% 1.85/1.50 tff(1694,plain,
% 1.85/1.50 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp4) <=> ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(quant_intro,[status(thm)],[1693])).
% 1.85/1.50 tff(1695,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.85/1.50 tff(1696,plain,
% 1.85/1.50 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[1695, 1694])).
% 1.85/1.50 tff(1697,plain,
% 1.85/1.50 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[1696, 1692])).
% 1.85/1.50 tff(1698,plain,(
% 1.85/1.50 ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(skolemize,[status(sab)],[1697])).
% 1.85/1.50 tff(1699,plain,
% 1.85/1.50 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.85/1.50 inference(modus_ponens,[status(thm)],[1698, 1691])).
% 1.85/1.50 tff(1700,plain,
% 1.85/1.50 (c2_1(a1)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[736, 1688])).
% 1.85/1.50 tff(1701,plain,
% 1.85/1.50 (c1_1(a1)),
% 1.85/1.50 inference(unit_resolution,[status(thm)],[725, 1688])).
% 1.85/1.50 tff(1702,plain,
% 1.85/1.50 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp4 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp4 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(1703,plain,
% 1.85/1.50 ((hskp15 | hskp4 | (~ndr1_0) | c0_1(a1) | (~c2_1(a1)) | (~c1_1(a1))) <=> (hskp15 | hskp4 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.85/1.50 inference(rewrite,[status(thm)],[])).
% 1.85/1.50 tff(1704,plain,
% 1.85/1.50 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c0_1(a1) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp4 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))))),
% 1.85/1.50 inference(monotonicity,[status(thm)],[1703])).
% 1.85/1.50 tff(1705,plain,
% 1.85/1.50 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c0_1(a1) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp4 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.85/1.50 inference(transitivity,[status(thm)],[1704, 1702])).
% 1.85/1.50 tff(1706,plain,
% 1.85/1.50 ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c0_1(a1) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.85/1.50 inference(quant_inst,[status(thm)],[])).
% 1.85/1.50 tff(1707,plain,
% 1.85/1.50 ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp4 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 1.85/1.51 tff(1708,plain,
% 1.85/1.51 (hskp15),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1707, 84, 1407, 1701, 1700, 1689, 1699])).
% 1.85/1.51 tff(1709,plain,
% 1.85/1.51 (((~hskp15) | (~c2_1(a27))) <=> ((~hskp15) | (~c2_1(a27)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(1710,plain,
% 1.85/1.51 (((~c2_1(a27)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a27)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(1711,axiom,((~c2_1(a27)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.85/1.51 tff(1712,plain,
% 1.85/1.51 ((~hskp15) | (~c2_1(a27))),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 1.85/1.51 tff(1713,plain,
% 1.85/1.51 ((~hskp15) | (~c2_1(a27))),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1712, 1709])).
% 1.85/1.51 tff(1714,plain,
% 1.85/1.51 (~c2_1(a27)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1713, 1708])).
% 1.85/1.51 tff(1715,plain,
% 1.85/1.51 (((~hskp15) | c0_1(a27)) <=> ((~hskp15) | c0_1(a27))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(1716,axiom,((~hskp15) | c0_1(a27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.85/1.51 tff(1717,plain,
% 1.85/1.51 ((~hskp15) | c0_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 1.85/1.51 tff(1718,plain,
% 1.85/1.51 ((~hskp15) | c0_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1717, 1715])).
% 1.85/1.51 tff(1719,plain,
% 1.85/1.51 ((~hskp15) | c0_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1718, 1715])).
% 1.85/1.51 tff(1720,plain,
% 1.85/1.51 ((~hskp15) | c0_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1719, 1715])).
% 1.85/1.51 tff(1721,plain,
% 1.85/1.51 ((~hskp15) | c0_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1720, 1715])).
% 1.85/1.51 tff(1722,plain,
% 1.85/1.51 ((~hskp15) | c0_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1721, 1715])).
% 1.85/1.51 tff(1723,plain,
% 1.85/1.51 ((~hskp15) | c0_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1722, 1715])).
% 1.85/1.51 tff(1724,plain,
% 1.85/1.51 ((~hskp15) | c0_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1723, 1715])).
% 1.85/1.51 tff(1725,plain,
% 1.85/1.51 (c0_1(a27)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1724, 1708])).
% 1.85/1.51 tff(1726,plain,
% 1.85/1.51 (((~hskp15) | c1_1(a27)) <=> ((~hskp15) | c1_1(a27))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(1727,axiom,((~hskp15) | c1_1(a27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.85/1.51 tff(1728,plain,
% 1.85/1.51 ((~hskp15) | c1_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1727, 1726])).
% 1.85/1.51 tff(1729,plain,
% 1.85/1.51 ((~hskp15) | c1_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1728, 1726])).
% 1.85/1.51 tff(1730,plain,
% 1.85/1.51 ((~hskp15) | c1_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1729, 1726])).
% 1.85/1.51 tff(1731,plain,
% 1.85/1.51 ((~hskp15) | c1_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1730, 1726])).
% 1.85/1.51 tff(1732,plain,
% 1.85/1.51 ((~hskp15) | c1_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1731, 1726])).
% 1.85/1.51 tff(1733,plain,
% 1.85/1.51 ((~hskp15) | c1_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1732, 1726])).
% 1.85/1.51 tff(1734,plain,
% 1.85/1.51 ((~hskp15) | c1_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1733, 1726])).
% 1.85/1.51 tff(1735,plain,
% 1.85/1.51 ((~hskp15) | c1_1(a27)),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1734, 1726])).
% 1.85/1.51 tff(1736,plain,
% 1.85/1.51 (c1_1(a27)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1735, 1708])).
% 1.85/1.51 tff(1737,assumption,(~c2_1(a27)), introduced(assumption)).
% 1.85/1.51 tff(1738,assumption,(c0_1(a27)), introduced(assumption)).
% 1.85/1.51 tff(1739,plain,
% 1.85/1.51 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | c2_1(a27) | (~ndr1_0) | (~c3_1(a27)) | (~c0_1(a27)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | c2_1(a27) | (~ndr1_0) | (~c3_1(a27)) | (~c0_1(a27)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(1740,plain,
% 1.85/1.51 ((hskp22 | hskp19 | (~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27))) <=> (hskp22 | hskp19 | c2_1(a27) | (~ndr1_0) | (~c3_1(a27)) | (~c0_1(a27)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(1741,plain,
% 1.85/1.51 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | c2_1(a27) | (~ndr1_0) | (~c3_1(a27)) | (~c0_1(a27))))),
% 1.85/1.51 inference(monotonicity,[status(thm)],[1740])).
% 1.85/1.51 tff(1742,plain,
% 1.85/1.51 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | c2_1(a27) | (~ndr1_0) | (~c3_1(a27)) | (~c0_1(a27)))),
% 1.85/1.51 inference(transitivity,[status(thm)],[1741, 1739])).
% 1.85/1.51 tff(1743,plain,
% 1.85/1.51 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)))),
% 1.85/1.51 inference(quant_inst,[status(thm)],[])).
% 1.85/1.51 tff(1744,plain,
% 1.85/1.51 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | c2_1(a27) | (~ndr1_0) | (~c3_1(a27)) | (~c0_1(a27))),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 1.85/1.51 tff(1745,plain,
% 1.85/1.51 (hskp22 | (~c3_1(a27))),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1744, 84, 1418, 1738, 1737, 1417])).
% 1.85/1.51 tff(1746,plain,
% 1.85/1.51 (~c3_1(a27)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1745, 1])).
% 1.85/1.51 tff(1747,assumption,(c1_1(a27)), introduced(assumption)).
% 1.85/1.51 tff(1748,plain,
% 1.85/1.51 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c0_1(a27)) | (~c1_1(a27)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c0_1(a27)) | (~c1_1(a27)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(1749,plain,
% 1.85/1.51 ((hskp22 | (~ndr1_0) | c3_1(a27) | c2_1(a27) | (~c1_1(a27)) | c2_1(a27) | c3_1(a27) | (~c0_1(a27))) <=> (hskp22 | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c0_1(a27)) | (~c1_1(a27)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(1750,plain,
% 1.85/1.51 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a27) | c2_1(a27) | (~c1_1(a27)) | c2_1(a27) | c3_1(a27) | (~c0_1(a27)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c0_1(a27)) | (~c1_1(a27))))),
% 1.85/1.51 inference(monotonicity,[status(thm)],[1749])).
% 1.85/1.51 tff(1751,plain,
% 1.85/1.51 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a27) | c2_1(a27) | (~c1_1(a27)) | c2_1(a27) | c3_1(a27) | (~c0_1(a27)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c0_1(a27)) | (~c1_1(a27)))),
% 1.85/1.51 inference(transitivity,[status(thm)],[1750, 1748])).
% 1.85/1.51 tff(1752,plain,
% 1.85/1.51 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a27) | c2_1(a27) | (~c1_1(a27)) | c2_1(a27) | c3_1(a27) | (~c0_1(a27)))),
% 1.85/1.51 inference(quant_inst,[status(thm)],[])).
% 1.85/1.51 tff(1753,plain,
% 1.85/1.51 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c0_1(a27)) | (~c1_1(a27))),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 1.85/1.51 tff(1754,plain,
% 1.85/1.51 ($false),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1753, 1, 84, 1738, 1747, 1737, 12, 1746])).
% 1.85/1.51 tff(1755,plain,(hskp22 | (~c0_1(a27)) | (~c1_1(a27)) | c2_1(a27) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.85/1.51 tff(1756,plain,
% 1.85/1.51 (hskp22),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1755, 1736, 1725, 1714, 1296])).
% 1.85/1.51 tff(1757,plain,
% 1.85/1.51 (~c3_1(a43)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[682, 1756])).
% 1.85/1.51 tff(1758,plain,
% 1.85/1.51 (~c1_1(a43)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[688, 1756])).
% 1.85/1.51 tff(1759,plain,
% 1.85/1.51 (c2_1(a43)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[699, 1756])).
% 1.85/1.51 tff(1760,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c2_1(a27) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a27)) | (~c0_1(a27)) | (~c2_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a27) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a27)) | (~c0_1(a27)) | (~c2_1(a43)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(1761,plain,
% 1.85/1.51 (((~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1))) <=> (c1_1(a43) | c3_1(a43) | c2_1(a27) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a27)) | (~c0_1(a27)) | (~c2_1(a43)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(1762,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c2_1(a27) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a27)) | (~c0_1(a27)) | (~c2_1(a43))))),
% 1.85/1.51 inference(monotonicity,[status(thm)],[1761])).
% 1.85/1.51 tff(1763,plain,
% 1.85/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a27) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a27)) | (~c0_1(a27)) | (~c2_1(a43)))),
% 1.85/1.51 inference(transitivity,[status(thm)],[1762, 1760])).
% 1.85/1.51 tff(1764,plain,
% 1.85/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))),
% 1.85/1.51 inference(quant_inst,[status(thm)],[])).
% 1.85/1.51 tff(1765,plain,
% 1.85/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a27) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a27)) | (~c0_1(a27)) | (~c2_1(a43))),
% 1.85/1.51 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 1.85/1.51 tff(1766,plain,
% 1.85/1.51 (~c3_1(a27)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1765, 84, 1759, 1725, 1701, 1700, 1758, 1757, 1714, 1689, 133])).
% 1.85/1.51 tff(1767,plain,
% 1.85/1.51 (c0_1(a43)),
% 1.85/1.51 inference(unit_resolution,[status(thm)],[1582, 84, 1407, 1758, 1757, 113])).
% 1.85/1.51 tff(1768,plain,
% 1.85/1.51 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a43) | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c1_1(a27)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c1_1(a27)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(1769,plain,
% 1.85/1.51 ((hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a27) | c3_1(a27) | (~c1_1(a27))) <=> (hskp24 | c3_1(a43) | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c1_1(a27)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.51 inference(rewrite,[status(thm)],[])).
% 1.85/1.51 tff(1770,plain,
% 1.85/1.51 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a27) | c3_1(a27) | (~c1_1(a27)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a43) | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c1_1(a27)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 1.85/1.52 inference(monotonicity,[status(thm)],[1769])).
% 1.85/1.52 tff(1771,plain,
% 1.85/1.52 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a27) | c3_1(a27) | (~c1_1(a27)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c1_1(a27)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.52 inference(transitivity,[status(thm)],[1770, 1768])).
% 1.85/1.52 tff(1772,plain,
% 1.85/1.52 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a27) | c3_1(a27) | (~c1_1(a27)))),
% 1.85/1.52 inference(quant_inst,[status(thm)],[])).
% 1.85/1.52 tff(1773,plain,
% 1.85/1.52 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c1_1(a27)) | (~c2_1(a43)) | (~c0_1(a43))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[1772, 1771])).
% 1.85/1.52 tff(1774,plain,
% 1.85/1.52 ($false),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1773, 84, 1406, 1759, 1736, 1757, 1714, 1533, 1767, 1766])).
% 1.85/1.52 tff(1775,plain,(hskp4 | hskp24 | hskp18 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.85/1.52 tff(1776,plain,
% 1.85/1.52 (hskp24),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1775, 1405, 134, 135])).
% 1.85/1.52 tff(1777,plain,
% 1.85/1.52 (hskp0),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1500, 1, 1418, 1426])).
% 1.85/1.52 tff(1778,plain,
% 1.85/1.52 (~c0_1(a1)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[714, 1777])).
% 1.85/1.52 tff(1779,plain,
% 1.85/1.52 (c2_1(a1)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[736, 1777])).
% 1.85/1.52 tff(1780,plain,
% 1.85/1.52 (c1_1(a1)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[725, 1777])).
% 1.85/1.52 tff(1781,plain,
% 1.85/1.52 (hskp15),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1707, 84, 1407, 1780, 1779, 1778, 1699])).
% 1.85/1.52 tff(1782,plain,
% 1.85/1.52 (~c2_1(a27)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1713, 1781])).
% 1.85/1.52 tff(1783,plain,
% 1.85/1.52 (c0_1(a27)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1724, 1781])).
% 1.85/1.52 tff(1784,plain,
% 1.85/1.52 (c1_1(a27)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1735, 1781])).
% 1.85/1.52 tff(1785,plain,
% 1.85/1.52 ($false),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1755, 1784, 1783, 1, 1782, 1418])).
% 1.85/1.52 tff(1786,plain,(hskp22 | hskp19 | hskp4 | (~hskp24)), inference(lemma,lemma(discharge,[]))).
% 1.85/1.52 tff(1787,plain,
% 1.85/1.52 (hskp22),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1786, 1296, 1405, 1776])).
% 1.85/1.52 tff(1788,plain,
% 1.85/1.52 (~c3_1(a43)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[682, 1787])).
% 1.85/1.52 tff(1789,plain,
% 1.85/1.52 (~c1_1(a43)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[688, 1787])).
% 1.85/1.52 tff(1790,plain,
% 1.85/1.52 (c0_1(a43)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1582, 84, 1405, 1789, 1788, 113])).
% 1.85/1.52 tff(1791,plain,
% 1.85/1.52 (c2_1(a43)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[699, 1787])).
% 1.85/1.52 tff(1792,plain,
% 1.85/1.52 (~hskp21),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1676, 1790, 1789, 1788, 1791])).
% 1.85/1.52 tff(1793,plain,
% 1.85/1.52 (hskp0),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1488, 1792, 1776])).
% 1.85/1.52 tff(1794,plain,
% 1.85/1.52 (~c0_1(a1)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[714, 1793])).
% 1.85/1.52 tff(1795,plain,
% 1.85/1.52 (c2_1(a1)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[736, 1793])).
% 1.85/1.52 tff(1796,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(1797,plain,
% 1.85/1.52 (((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a1) | (~c2_1(a1)) | (~c3_1(a1))) <=> (c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(1798,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a1) | (~c2_1(a1)) | (~c3_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 1.85/1.52 inference(monotonicity,[status(thm)],[1797])).
% 1.85/1.52 tff(1799,plain,
% 1.85/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a1) | (~c2_1(a1)) | (~c3_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.85/1.52 inference(transitivity,[status(thm)],[1798, 1796])).
% 1.85/1.52 tff(1800,plain,
% 1.85/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a1) | (~c2_1(a1)) | (~c3_1(a1)))),
% 1.85/1.52 inference(quant_inst,[status(thm)],[])).
% 1.85/1.52 tff(1801,plain,
% 1.85/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c2_1(a43)) | (~c0_1(a43))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.85/1.52 tff(1802,plain,
% 1.85/1.52 (~c3_1(a1)),
% 1.85/1.52 inference(unit_resolution,[status(thm)],[1801, 84, 1791, 1795, 1789, 1788, 1794, 103, 1790])).
% 1.85/1.52 tff(1803,plain,
% 1.85/1.52 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.85/1.52 inference(bind,[status(th)],[])).
% 1.85/1.52 tff(1804,plain,
% 1.85/1.52 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.52 inference(quant_intro,[status(thm)],[1803])).
% 1.85/1.52 tff(1805,plain,
% 1.85/1.52 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(1806,plain,
% 1.85/1.52 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_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))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_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))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.85/1.52 inference(bind,[status(th)],[])).
% 1.85/1.52 tff(1807,plain,
% 1.85/1.52 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.52 inference(quant_intro,[status(thm)],[1806])).
% 1.85/1.52 tff(1808,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 1.85/1.52 tff(1809,plain,
% 1.85/1.52 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[1808, 1807])).
% 1.85/1.52 tff(1810,plain,
% 1.85/1.52 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[1809, 1805])).
% 1.85/1.52 tff(1811,plain,(
% 1.85/1.52 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.52 inference(skolemize,[status(sab)],[1810])).
% 1.85/1.52 tff(1812,plain,
% 1.85/1.52 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.85/1.52 inference(modus_ponens,[status(thm)],[1811, 1804])).
% 1.85/1.52 tff(1813,plain,
% 1.85/1.52 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a43)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a43)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(1814,plain,
% 1.85/1.52 ((hskp3 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | c3_1(a1) | (~c2_1(a1))) <=> (hskp3 | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a43)))),
% 1.85/1.52 inference(rewrite,[status(thm)],[])).
% 1.85/1.52 tff(1815,plain,
% 1.85/1.52 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | c3_1(a1) | (~c2_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a43))))),
% 1.90/1.53 inference(monotonicity,[status(thm)],[1814])).
% 1.90/1.53 tff(1816,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | c3_1(a1) | (~c2_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a43)))),
% 1.90/1.53 inference(transitivity,[status(thm)],[1815, 1813])).
% 1.90/1.53 tff(1817,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | c3_1(a1) | (~c2_1(a1)))),
% 1.90/1.53 inference(quant_inst,[status(thm)],[])).
% 1.90/1.53 tff(1818,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a43))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 1.90/1.53 tff(1819,plain,
% 1.90/1.53 (hskp3),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1818, 84, 1795, 1789, 1788, 1794, 1812, 1802, 1790])).
% 1.90/1.53 tff(1820,plain,
% 1.90/1.53 (~c0_1(a4)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[220, 1819])).
% 1.90/1.53 tff(1821,plain,
% 1.90/1.53 (~c1_1(a4)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[226, 1819])).
% 1.90/1.53 tff(1822,plain,
% 1.90/1.53 (c1_1(a5)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1190, 229, 228, 135, 134])).
% 1.90/1.53 tff(1823,plain,
% 1.90/1.53 (~hskp4),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[161, 1822])).
% 1.90/1.53 tff(1824,plain,
% 1.90/1.53 (c3_1(a4)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[238, 1823, 229])).
% 1.90/1.53 tff(1825,plain,
% 1.90/1.53 (hskp5),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[855, 326, 800])).
% 1.90/1.53 tff(1826,plain,
% 1.90/1.53 (~c3_1(a6)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1115, 1825])).
% 1.90/1.53 tff(1827,plain,
% 1.90/1.53 (c2_1(a6)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[285, 1825])).
% 1.90/1.53 tff(1828,plain,
% 1.90/1.53 (c0_1(a6)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[274, 1825])).
% 1.90/1.53 tff(1829,plain,
% 1.90/1.53 ($false),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[864, 84, 1828, 1827, 800, 255, 254, 1826, 229, 253, 103, 326])).
% 1.90/1.53 tff(1830,plain,((~c2_1(a4)) | (~c3_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | c0_1(a4) | c1_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.90/1.53 tff(1831,plain,
% 1.90/1.53 (~c2_1(a4)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1830, 1824, 191, 180, 229, 169])).
% 1.90/1.53 tff(1832,plain,
% 1.90/1.53 (hskp6),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1123, 1831, 229, 1824, 228])).
% 1.90/1.53 tff(1833,plain,
% 1.90/1.53 (~c3_1(a8)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[879, 1832])).
% 1.90/1.53 tff(1834,plain,
% 1.90/1.53 (~c2_1(a8)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[873, 1832])).
% 1.90/1.53 tff(1835,plain,
% 1.90/1.53 (c0_1(a8)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[976, 1832])).
% 1.90/1.53 tff(1836,plain,
% 1.90/1.53 (c1_1(a8)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1139, 84, 1835, 1834, 1833, 229, 228, 959, 1831])).
% 1.90/1.53 tff(1837,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c3_1(a8) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a8)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a8) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a8)) | (~c1_1(a8)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(1838,plain,
% 1.90/1.53 ((hskp0 | (~ndr1_0) | c3_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | (~c3_1(a4))) <=> (hskp0 | c3_1(a8) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a8)) | (~c1_1(a8)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(1839,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | (~c3_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c3_1(a8) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a8)) | (~c1_1(a8))))),
% 1.90/1.53 inference(monotonicity,[status(thm)],[1838])).
% 1.90/1.53 tff(1840,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | (~c3_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a8) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a8)) | (~c1_1(a8)))),
% 1.90/1.53 inference(transitivity,[status(thm)],[1839, 1837])).
% 1.90/1.53 tff(1841,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | (~c3_1(a4)))),
% 1.90/1.53 inference(quant_inst,[status(thm)],[])).
% 1.90/1.53 tff(1842,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a8) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a8)) | (~c1_1(a8))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[1841, 1840])).
% 1.90/1.53 tff(1843,plain,
% 1.90/1.53 (hskp0),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1842, 84, 1835, 1824, 1833, 228, 651, 1831, 1836])).
% 1.90/1.53 tff(1844,plain,
% 1.90/1.53 (~c0_1(a1)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[714, 1843])).
% 1.90/1.53 tff(1845,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a4) | c1_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a4) | c1_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(1846,plain,
% 1.90/1.53 ((hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4) | c1_1(a4) | c0_1(a4)) <=> (hskp1 | c0_1(a4) | c1_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(1847,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a4) | c1_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4)))),
% 1.90/1.53 inference(monotonicity,[status(thm)],[1846])).
% 1.90/1.53 tff(1848,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a4) | c1_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4))),
% 1.90/1.53 inference(transitivity,[status(thm)],[1847, 1845])).
% 1.90/1.53 tff(1849,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4) | c1_1(a4) | c0_1(a4))),
% 1.90/1.53 inference(quant_inst,[status(thm)],[])).
% 1.90/1.53 tff(1850,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a4) | c1_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4)),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 1.90/1.53 tff(1851,plain,
% 1.90/1.53 (hskp1),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1850, 84, 191, 180, 229, 228, 169, 749, 1831])).
% 1.90/1.53 tff(1852,plain,
% 1.90/1.53 (~c2_1(a2)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[611, 1851])).
% 1.90/1.53 tff(1853,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c1_1(a8)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(1854,plain,
% 1.90/1.53 ((hskp22 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (hskp22 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c1_1(a8)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(1855,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c1_1(a8))))),
% 1.90/1.53 inference(monotonicity,[status(thm)],[1854])).
% 1.90/1.53 tff(1856,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c1_1(a8)))),
% 1.90/1.53 inference(transitivity,[status(thm)],[1855, 1853])).
% 1.90/1.53 tff(1857,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.90/1.53 inference(quant_inst,[status(thm)],[])).
% 1.90/1.53 tff(1858,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c1_1(a8))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[1857, 1856])).
% 1.90/1.53 tff(1859,plain,
% 1.90/1.53 (hskp22),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1858, 84, 1835, 1834, 1833, 12, 1836])).
% 1.90/1.53 tff(1860,plain,
% 1.90/1.53 (~c3_1(a43)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[682, 1859])).
% 1.90/1.53 tff(1861,plain,
% 1.90/1.53 (~c1_1(a43)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[688, 1859])).
% 1.90/1.53 tff(1862,plain,
% 1.90/1.53 (c2_1(a1)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[736, 1843])).
% 1.90/1.53 tff(1863,plain,
% 1.90/1.53 (c1_1(a1)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[725, 1843])).
% 1.90/1.53 tff(1864,plain,
% 1.90/1.53 (c3_1(a2)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[622, 1851])).
% 1.90/1.53 tff(1865,plain,
% 1.90/1.53 (c0_1(a2)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[633, 1851])).
% 1.90/1.53 tff(1866,plain,
% 1.90/1.53 (c2_1(a43)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[699, 1859])).
% 1.90/1.53 tff(1867,plain,
% 1.90/1.53 ($false),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[783, 84, 1866, 1865, 1864, 1863, 1862, 1861, 1860, 1852, 1844, 133])).
% 1.90/1.53 tff(1868,plain,(c0_1(a4) | c1_1(a4) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.90/1.53 tff(1869,plain,
% 1.90/1.53 ($false),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1868, 1821, 1820, 135, 134])).
% 1.90/1.53 tff(1870,plain,(hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.90/1.53 tff(1871,plain,
% 1.90/1.53 (hskp30),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1870, 134])).
% 1.90/1.53 tff(1872,plain,
% 1.90/1.53 (((~hskp30) | c0_1(a33)) <=> ((~hskp30) | c0_1(a33))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(1873,axiom,((~hskp30) | c0_1(a33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.90/1.53 tff(1874,plain,
% 1.90/1.53 ((~hskp30) | c0_1(a33)),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[1873, 1872])).
% 1.90/1.53 tff(1875,plain,
% 1.90/1.53 ((~hskp30) | c0_1(a33)),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[1874, 1872])).
% 1.90/1.53 tff(1876,plain,
% 1.90/1.53 ((~hskp30) | c0_1(a33)),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[1875, 1872])).
% 1.90/1.53 tff(1877,plain,
% 1.90/1.53 ((~hskp30) | c0_1(a33)),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[1876, 1872])).
% 1.90/1.54 tff(1878,plain,
% 1.90/1.54 ((~hskp30) | c0_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1877, 1872])).
% 1.90/1.54 tff(1879,plain,
% 1.90/1.54 ((~hskp30) | c0_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1878, 1872])).
% 1.90/1.54 tff(1880,plain,
% 1.90/1.54 ((~hskp30) | c0_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1879, 1872])).
% 1.90/1.54 tff(1881,plain,
% 1.90/1.54 ((~hskp30) | c0_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1880, 1872])).
% 1.90/1.54 tff(1882,plain,
% 1.90/1.54 (c0_1(a33)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1881, 1871])).
% 1.90/1.54 tff(1883,plain,
% 1.90/1.54 (((~hskp30) | c3_1(a33)) <=> ((~hskp30) | c3_1(a33))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(1884,axiom,((~hskp30) | c3_1(a33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.90/1.54 tff(1885,plain,
% 1.90/1.54 ((~hskp30) | c3_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 1.90/1.54 tff(1886,plain,
% 1.90/1.54 ((~hskp30) | c3_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1885, 1883])).
% 1.90/1.54 tff(1887,plain,
% 1.90/1.54 ((~hskp30) | c3_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1886, 1883])).
% 1.90/1.54 tff(1888,plain,
% 1.90/1.54 ((~hskp30) | c3_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1887, 1883])).
% 1.90/1.54 tff(1889,plain,
% 1.90/1.54 ((~hskp30) | c3_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1888, 1883])).
% 1.90/1.54 tff(1890,plain,
% 1.90/1.54 ((~hskp30) | c3_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1889, 1883])).
% 1.90/1.54 tff(1891,plain,
% 1.90/1.54 ((~hskp30) | c3_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1890, 1883])).
% 1.90/1.54 tff(1892,plain,
% 1.90/1.54 ((~hskp30) | c3_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1891, 1883])).
% 1.90/1.54 tff(1893,plain,
% 1.90/1.54 (c3_1(a33)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1892, 1871])).
% 1.90/1.54 tff(1894,plain,
% 1.90/1.54 (((~hskp30) | c2_1(a33)) <=> ((~hskp30) | c2_1(a33))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(1895,axiom,((~hskp30) | c2_1(a33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.90/1.54 tff(1896,plain,
% 1.90/1.54 ((~hskp30) | c2_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 1.90/1.54 tff(1897,plain,
% 1.90/1.54 ((~hskp30) | c2_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1896, 1894])).
% 1.90/1.54 tff(1898,plain,
% 1.90/1.54 ((~hskp30) | c2_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1897, 1894])).
% 1.90/1.54 tff(1899,plain,
% 1.90/1.54 ((~hskp30) | c2_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1898, 1894])).
% 1.90/1.54 tff(1900,plain,
% 1.90/1.54 ((~hskp30) | c2_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1899, 1894])).
% 1.90/1.54 tff(1901,plain,
% 1.90/1.54 ((~hskp30) | c2_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1900, 1894])).
% 1.90/1.54 tff(1902,plain,
% 1.90/1.54 ((~hskp30) | c2_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1901, 1894])).
% 1.90/1.54 tff(1903,plain,
% 1.90/1.54 ((~hskp30) | c2_1(a33)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1902, 1894])).
% 1.90/1.54 tff(1904,plain,
% 1.90/1.54 (c2_1(a33)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1903, 1871])).
% 1.90/1.54 tff(1905,assumption,(c1_1(a33)), introduced(assumption)).
% 1.90/1.54 tff(1906,assumption,(c3_1(a33)), introduced(assumption)).
% 1.90/1.54 tff(1907,assumption,(c2_1(a33)), introduced(assumption)).
% 1.90/1.54 tff(1908,assumption,(c0_1(a33)), introduced(assumption)).
% 1.90/1.54 tff(1909,plain,
% 1.90/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(1910,plain,
% 1.90/1.54 (((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33))) <=> ((~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(1911,plain,
% 1.90/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33))))),
% 1.90/1.54 inference(monotonicity,[status(thm)],[1910])).
% 1.90/1.54 tff(1912,plain,
% 1.90/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)))),
% 1.90/1.54 inference(transitivity,[status(thm)],[1911, 1909])).
% 1.90/1.54 tff(1913,plain,
% 1.90/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.90/1.54 inference(quant_inst,[status(thm)],[])).
% 1.90/1.54 tff(1914,plain,
% 1.90/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 1.90/1.54 tff(1915,plain,
% 1.90/1.54 ($false),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1914, 84, 1908, 1907, 1906, 376, 1905])).
% 1.90/1.54 tff(1916,plain,((~c1_1(a33)) | (~c0_1(a33)) | (~c2_1(a33)) | (~c3_1(a33))), inference(lemma,lemma(discharge,[]))).
% 1.90/1.54 tff(1917,plain,
% 1.90/1.54 (~c1_1(a33)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1916, 1882, 1904, 1893])).
% 1.90/1.54 tff(1918,plain,
% 1.90/1.54 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(1919,plain,
% 1.90/1.54 ((hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33))) <=> (hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(1920,plain,
% 1.90/1.54 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33))))),
% 1.90/1.54 inference(monotonicity,[status(thm)],[1919])).
% 1.90/1.54 tff(1921,plain,
% 1.90/1.54 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.90/1.54 inference(transitivity,[status(thm)],[1920, 1918])).
% 1.90/1.54 tff(1922,plain,
% 1.90/1.54 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)))),
% 1.90/1.54 inference(quant_inst,[status(thm)],[])).
% 1.90/1.54 tff(1923,plain,
% 1.90/1.54 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1922, 1921])).
% 1.90/1.54 tff(1924,plain,
% 1.90/1.54 (hskp1 | hskp0 | c1_1(a33)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1923, 84, 1904, 1893, 598])).
% 1.90/1.54 tff(1925,plain,
% 1.90/1.54 (hskp0),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1924, 1502, 1917])).
% 1.90/1.54 tff(1926,plain,
% 1.90/1.54 (c2_1(a1)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[736, 1925])).
% 1.90/1.54 tff(1927,plain,
% 1.90/1.54 (c1_1(a1)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[725, 1925])).
% 1.90/1.54 tff(1928,assumption,(~c1_1(a33)), introduced(assumption)).
% 1.90/1.54 tff(1929,plain,
% 1.90/1.54 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(1930,plain,
% 1.90/1.54 ((hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a26) | c1_1(a26) | c0_1(a26)) <=> (hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(1931,plain,
% 1.90/1.54 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a26) | c1_1(a26) | c0_1(a26))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33))))),
% 1.90/1.54 inference(monotonicity,[status(thm)],[1930])).
% 1.90/1.54 tff(1932,plain,
% 1.90/1.54 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a26) | c1_1(a26) | c0_1(a26))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.90/1.54 inference(transitivity,[status(thm)],[1931, 1929])).
% 1.90/1.54 tff(1933,plain,
% 1.90/1.54 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a26) | c1_1(a26) | c0_1(a26))),
% 1.90/1.54 inference(quant_inst,[status(thm)],[])).
% 1.90/1.54 tff(1934,plain,
% 1.90/1.54 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[1933, 1932])).
% 1.90/1.54 tff(1935,plain,
% 1.90/1.54 ($false),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1934, 84, 1502, 1908, 1907, 753, 752, 751, 749, 1928])).
% 1.90/1.54 tff(1936,plain,((~hskp14) | hskp1 | (~c0_1(a33)) | (~c2_1(a33)) | c1_1(a33)), inference(lemma,lemma(discharge,[]))).
% 1.90/1.54 tff(1937,plain,
% 1.90/1.54 (~hskp14),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1936, 1502, 1882, 1904, 1917])).
% 1.90/1.54 tff(1938,assumption,(hskp25), introduced(assumption)).
% 1.90/1.54 tff(1939,plain,
% 1.90/1.54 (~c2_1(a64)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[470, 1938])).
% 1.90/1.54 tff(1940,plain,
% 1.90/1.54 (c3_1(a64)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[481, 1938])).
% 1.90/1.54 tff(1941,plain,
% 1.90/1.54 (c1_1(a64)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[492, 1938])).
% 1.90/1.54 tff(1942,plain,
% 1.90/1.54 ($false),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[499, 84, 134, 307, 1941, 1940, 1939, 325])).
% 1.90/1.54 tff(1943,plain,((~hskp25) | hskp18 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.90/1.54 tff(1944,plain,
% 1.90/1.54 (~hskp25),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1943, 1937, 134])).
% 1.90/1.54 tff(1945,assumption,(~hskp25), introduced(assumption)).
% 1.90/1.54 tff(1946,plain,
% 1.90/1.54 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a1)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(1947,plain,
% 1.90/1.54 ((hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a1)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(1948,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a1))))),
% 1.90/1.55 inference(monotonicity,[status(thm)],[1947])).
% 1.90/1.55 tff(1949,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a1)))),
% 1.90/1.55 inference(transitivity,[status(thm)],[1948, 1946])).
% 1.90/1.55 tff(1950,plain,
% 1.90/1.55 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.90/1.55 inference(quant_inst,[status(thm)],[])).
% 1.90/1.55 tff(1951,plain,
% 1.90/1.55 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a1))),
% 1.90/1.55 inference(modus_ponens,[status(thm)],[1950, 1949])).
% 1.90/1.55 tff(1952,plain,
% 1.90/1.55 (hskp19 | (~c3_1(a1))),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1951, 84, 1907, 1906, 774, 773, 155, 1928])).
% 1.90/1.55 tff(1953,plain,
% 1.90/1.55 (~c3_1(a1)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1952, 1418])).
% 1.90/1.55 tff(1954,plain,
% 1.90/1.55 (((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp25 | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(1955,plain,
% 1.90/1.55 ((hskp27 | hskp25 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1))) <=> (hskp27 | hskp25 | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(1956,plain,
% 1.90/1.55 (((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1))))),
% 1.90/1.55 inference(monotonicity,[status(thm)],[1955])).
% 1.90/1.55 tff(1957,plain,
% 1.90/1.55 (((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp25 | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1)))),
% 1.90/1.55 inference(transitivity,[status(thm)],[1956, 1954])).
% 1.90/1.55 tff(1958,plain,
% 1.90/1.55 ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.90/1.55 inference(quant_inst,[status(thm)],[])).
% 1.90/1.55 tff(1959,plain,
% 1.90/1.55 ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp25 | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1))),
% 1.90/1.55 inference(modus_ponens,[status(thm)],[1958, 1957])).
% 1.90/1.55 tff(1960,plain,
% 1.90/1.55 (hskp27 | hskp25 | c3_1(a1)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1959, 84, 774, 773, 457])).
% 1.90/1.55 tff(1961,plain,
% 1.90/1.55 (hskp27),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1960, 1953, 1945])).
% 1.90/1.55 tff(1962,plain,
% 1.90/1.55 (c3_1(a10)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[405, 1961])).
% 1.90/1.55 tff(1963,plain,
% 1.90/1.55 (c2_1(a10)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[416, 1961])).
% 1.90/1.55 tff(1964,plain,
% 1.90/1.55 (c1_1(a10)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[427, 1961])).
% 1.90/1.55 tff(1965,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(1966,plain,
% 1.90/1.55 ((hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp19 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(1967,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10))))),
% 1.90/1.55 inference(monotonicity,[status(thm)],[1966])).
% 1.90/1.55 tff(1968,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)))),
% 1.90/1.55 inference(transitivity,[status(thm)],[1967, 1965])).
% 1.90/1.55 tff(1969,plain,
% 1.90/1.55 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.90/1.55 inference(quant_inst,[status(thm)],[])).
% 1.90/1.55 tff(1970,plain,
% 1.90/1.55 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10))),
% 1.90/1.55 inference(modus_ponens,[status(thm)],[1969, 1968])).
% 1.90/1.55 tff(1971,plain,
% 1.90/1.55 ($false),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1970, 84, 1418, 1907, 1906, 1964, 1963, 1962, 155, 1928])).
% 1.90/1.55 tff(1972,plain,(hskp19 | (~c2_1(a33)) | (~c3_1(a33)) | c1_1(a33) | hskp25 | (~c1_1(a1)) | (~c2_1(a1))), inference(lemma,lemma(discharge,[]))).
% 1.90/1.55 tff(1973,plain,
% 1.90/1.55 (hskp19),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1972, 1944, 1893, 1917, 1904, 1927, 1926])).
% 1.90/1.55 tff(1974,plain,
% 1.90/1.55 (~c2_1(a36)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1280, 1973])).
% 1.90/1.55 tff(1975,plain,
% 1.90/1.55 (~c1_1(a36)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1286, 1973])).
% 1.90/1.55 tff(1976,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a36))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a36))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(1977,plain,
% 1.90/1.55 ((hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a36) | c1_1(a36) | c0_1(a36)) <=> (hskp1 | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a36))),
% 1.93/1.55 inference(rewrite,[status(thm)],[])).
% 1.93/1.55 tff(1978,plain,
% 1.93/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a36) | c1_1(a36) | c0_1(a36))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a36)))),
% 1.93/1.55 inference(monotonicity,[status(thm)],[1977])).
% 1.93/1.55 tff(1979,plain,
% 1.93/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a36) | c1_1(a36) | c0_1(a36))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a36))),
% 1.93/1.55 inference(transitivity,[status(thm)],[1978, 1976])).
% 1.93/1.55 tff(1980,plain,
% 1.93/1.55 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a36) | c1_1(a36) | c0_1(a36))),
% 1.93/1.55 inference(quant_inst,[status(thm)],[])).
% 1.93/1.55 tff(1981,plain,
% 1.93/1.55 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a36)),
% 1.93/1.55 inference(modus_ponens,[status(thm)],[1980, 1979])).
% 1.93/1.55 tff(1982,plain,
% 1.93/1.55 (c0_1(a36)),
% 1.93/1.55 inference(unit_resolution,[status(thm)],[1981, 84, 1502, 1882, 1904, 1975, 1974, 749, 1917])).
% 1.93/1.55 tff(1983,plain,
% 1.93/1.55 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.93/1.55 inference(bind,[status(th)],[])).
% 1.93/1.55 tff(1984,plain,
% 1.93/1.55 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.93/1.55 inference(quant_intro,[status(thm)],[1983])).
% 1.93/1.55 tff(1985,plain,
% 1.93/1.55 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.93/1.55 inference(rewrite,[status(thm)],[])).
% 1.93/1.55 tff(1986,plain,
% 1.93/1.55 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.93/1.55 inference(bind,[status(th)],[])).
% 1.93/1.55 tff(1987,plain,
% 1.93/1.55 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.93/1.55 inference(quant_intro,[status(thm)],[1986])).
% 1.93/1.55 tff(1988,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 1.93/1.55 tff(1989,plain,
% 1.93/1.55 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.93/1.55 inference(modus_ponens,[status(thm)],[1988, 1987])).
% 1.93/1.55 tff(1990,plain,
% 1.93/1.55 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.93/1.55 inference(modus_ponens,[status(thm)],[1989, 1985])).
% 1.93/1.55 tff(1991,plain,(
% 1.93/1.55 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.93/1.55 inference(skolemize,[status(sab)],[1990])).
% 1.93/1.55 tff(1992,plain,
% 1.93/1.55 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.93/1.55 inference(modus_ponens,[status(thm)],[1991, 1984])).
% 1.93/1.55 tff(1993,plain,
% 1.93/1.55 (~c3_1(a36)),
% 1.93/1.55 inference(unit_resolution,[status(thm)],[1274, 1973])).
% 1.93/1.55 tff(1994,plain,
% 1.93/1.55 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp17 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 1.93/1.55 inference(rewrite,[status(thm)],[])).
% 1.93/1.55 tff(1995,plain,
% 1.93/1.55 ((hskp17 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | c3_1(a36)) <=> (hskp17 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 1.93/1.55 inference(rewrite,[status(thm)],[])).
% 1.93/1.55 tff(1996,plain,
% 1.93/1.55 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | c3_1(a36))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36))))),
% 1.93/1.55 inference(monotonicity,[status(thm)],[1995])).
% 1.93/1.55 tff(1997,plain,
% 1.93/1.55 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | c3_1(a36))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp17 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 1.93/1.55 inference(transitivity,[status(thm)],[1996, 1994])).
% 1.93/1.55 tff(1998,plain,
% 1.93/1.55 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | c3_1(a36))),
% 1.93/1.56 inference(quant_inst,[status(thm)],[])).
% 1.93/1.56 tff(1999,plain,
% 1.93/1.56 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp17 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36))),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 1.93/1.56 tff(2000,plain,
% 1.93/1.56 (hskp17),
% 1.93/1.56 inference(unit_resolution,[status(thm)],[1999, 84, 1975, 1974, 1993, 1992, 1982])).
% 1.93/1.56 tff(2001,plain,
% 1.93/1.56 (((~hskp17) | (~c2_1(a32))) <=> ((~hskp17) | (~c2_1(a32)))),
% 1.93/1.56 inference(rewrite,[status(thm)],[])).
% 1.93/1.56 tff(2002,plain,
% 1.93/1.56 (((~c2_1(a32)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a32)))),
% 1.93/1.56 inference(rewrite,[status(thm)],[])).
% 1.93/1.56 tff(2003,axiom,((~c2_1(a32)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.93/1.56 tff(2004,plain,
% 1.93/1.56 ((~hskp17) | (~c2_1(a32))),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 1.93/1.56 tff(2005,plain,
% 1.93/1.56 ((~hskp17) | (~c2_1(a32))),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2004, 2001])).
% 1.93/1.56 tff(2006,plain,
% 1.93/1.56 (~c2_1(a32)),
% 1.93/1.56 inference(unit_resolution,[status(thm)],[2005, 2000])).
% 1.93/1.56 tff(2007,plain,
% 1.93/1.56 (((~hskp17) | c3_1(a32)) <=> ((~hskp17) | c3_1(a32))),
% 1.93/1.56 inference(rewrite,[status(thm)],[])).
% 1.93/1.56 tff(2008,axiom,((~hskp17) | c3_1(a32)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.93/1.56 tff(2009,plain,
% 1.93/1.56 ((~hskp17) | c3_1(a32)),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 1.93/1.56 tff(2010,plain,
% 1.93/1.56 ((~hskp17) | c3_1(a32)),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2009, 2007])).
% 1.93/1.56 tff(2011,plain,
% 1.93/1.56 ((~hskp17) | c3_1(a32)),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2010, 2007])).
% 1.93/1.56 tff(2012,plain,
% 1.93/1.56 ((~hskp17) | c3_1(a32)),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2011, 2007])).
% 1.93/1.56 tff(2013,plain,
% 1.93/1.56 ((~hskp17) | c3_1(a32)),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2012, 2007])).
% 1.93/1.56 tff(2014,plain,
% 1.93/1.56 ((~hskp17) | c3_1(a32)),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2013, 2007])).
% 1.93/1.56 tff(2015,plain,
% 1.93/1.56 ((~hskp17) | c3_1(a32)),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2014, 2007])).
% 1.93/1.56 tff(2016,plain,
% 1.93/1.56 ((~hskp17) | c3_1(a32)),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2015, 2007])).
% 1.93/1.56 tff(2017,plain,
% 1.93/1.56 (c3_1(a32)),
% 1.93/1.56 inference(unit_resolution,[status(thm)],[2016, 2000])).
% 1.93/1.56 tff(2018,plain,
% 1.93/1.56 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | c2_1(a32) | (~ndr1_0) | (~c3_1(a32)) | (~c1_1(a32)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c2_1(a32) | (~ndr1_0) | (~c3_1(a32)) | (~c1_1(a32)))),
% 1.93/1.56 inference(rewrite,[status(thm)],[])).
% 1.93/1.56 tff(2019,plain,
% 1.93/1.56 ((hskp18 | hskp14 | (~ndr1_0) | c2_1(a32) | (~c3_1(a32)) | (~c1_1(a32))) <=> (hskp18 | hskp14 | c2_1(a32) | (~ndr1_0) | (~c3_1(a32)) | (~c1_1(a32)))),
% 1.93/1.56 inference(rewrite,[status(thm)],[])).
% 1.93/1.56 tff(2020,plain,
% 1.93/1.56 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a32) | (~c3_1(a32)) | (~c1_1(a32)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | c2_1(a32) | (~ndr1_0) | (~c3_1(a32)) | (~c1_1(a32))))),
% 1.93/1.56 inference(monotonicity,[status(thm)],[2019])).
% 1.93/1.56 tff(2021,plain,
% 1.93/1.56 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a32) | (~c3_1(a32)) | (~c1_1(a32)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c2_1(a32) | (~ndr1_0) | (~c3_1(a32)) | (~c1_1(a32)))),
% 1.93/1.56 inference(transitivity,[status(thm)],[2020, 2018])).
% 1.93/1.56 tff(2022,plain,
% 1.93/1.56 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a32) | (~c3_1(a32)) | (~c1_1(a32)))),
% 1.93/1.56 inference(quant_inst,[status(thm)],[])).
% 1.93/1.56 tff(2023,plain,
% 1.93/1.56 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c2_1(a32) | (~ndr1_0) | (~c3_1(a32)) | (~c1_1(a32))),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2022, 2021])).
% 1.93/1.56 tff(2024,plain,
% 1.93/1.56 (~c1_1(a32)),
% 1.93/1.56 inference(unit_resolution,[status(thm)],[2023, 84, 134, 1937, 2017, 2006, 325])).
% 1.93/1.56 tff(2025,plain,
% 1.93/1.56 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.93/1.56 inference(bind,[status(th)],[])).
% 1.93/1.56 tff(2026,plain,
% 1.93/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.93/1.56 inference(quant_intro,[status(thm)],[2025])).
% 1.93/1.56 tff(2027,plain,
% 1.93/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.93/1.56 inference(rewrite,[status(thm)],[])).
% 1.93/1.56 tff(2028,plain,
% 1.93/1.56 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.93/1.56 inference(bind,[status(th)],[])).
% 1.93/1.56 tff(2029,plain,
% 1.93/1.56 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.93/1.56 inference(quant_intro,[status(thm)],[2028])).
% 1.93/1.56 tff(2030,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.93/1.56 tff(2031,plain,
% 1.93/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2030, 2029])).
% 1.93/1.56 tff(2032,plain,
% 1.93/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2031, 2027])).
% 1.93/1.56 tff(2033,plain,(
% 1.93/1.56 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.93/1.56 inference(skolemize,[status(sab)],[2032])).
% 1.93/1.56 tff(2034,plain,
% 1.93/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.93/1.56 inference(modus_ponens,[status(thm)],[2033, 2026])).
% 1.93/1.56 tff(2035,plain,
% 1.93/1.56 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.93/1.56 inference(bind,[status(th)],[])).
% 1.93/1.56 tff(2036,plain,
% 1.93/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.93/1.56 inference(quant_intro,[status(thm)],[2035])).
% 1.93/1.56 tff(2037,plain,
% 1.93/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.93/1.56 inference(rewrite,[status(thm)],[])).
% 1.93/1.56 tff(2038,plain,
% 1.93/1.56 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~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(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | 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)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | 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)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.93/1.57 inference(bind,[status(th)],[])).
% 1.93/1.57 tff(2039,plain,
% 1.93/1.57 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.93/1.57 inference(quant_intro,[status(thm)],[2038])).
% 1.93/1.57 tff(2040,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.93/1.57 tff(2041,plain,
% 1.93/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.93/1.57 inference(modus_ponens,[status(thm)],[2040, 2039])).
% 1.93/1.57 tff(2042,plain,
% 1.93/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.93/1.57 inference(modus_ponens,[status(thm)],[2041, 2037])).
% 1.93/1.57 tff(2043,plain,(
% 1.93/1.57 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.93/1.57 inference(skolemize,[status(sab)],[2042])).
% 1.93/1.57 tff(2044,plain,
% 1.93/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.93/1.57 inference(modus_ponens,[status(thm)],[2043, 2036])).
% 1.93/1.57 tff(2045,plain,
% 1.93/1.57 (~c0_1(a1)),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[714, 1925])).
% 1.93/1.57 tff(2046,plain,
% 1.93/1.57 (~hskp28),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[1649, 1937, 134])).
% 1.93/1.57 tff(2047,plain,
% 1.93/1.57 (hskp9),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[1520, 2046, 1502])).
% 1.93/1.57 tff(2048,plain,
% 1.93/1.57 (~c2_1(a12)),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[1058, 2047])).
% 1.93/1.57 tff(2049,plain,
% 1.93/1.57 (c1_1(a12)),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[570, 2047])).
% 1.93/1.57 tff(2050,plain,
% 1.93/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a36) | c3_1(a36) | c2_1(a12) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a12) | (~c1_1(a12)) | (~c0_1(a36)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a36) | c3_1(a36) | c2_1(a12) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a12) | (~c1_1(a12)) | (~c0_1(a36)))),
% 1.93/1.57 inference(rewrite,[status(thm)],[])).
% 1.93/1.57 tff(2051,plain,
% 1.93/1.57 (((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12))) <=> (c1_1(a36) | c3_1(a36) | c2_1(a12) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a12) | (~c1_1(a12)) | (~c0_1(a36)))),
% 1.93/1.57 inference(rewrite,[status(thm)],[])).
% 1.93/1.57 tff(2052,plain,
% 1.93/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a36) | c3_1(a36) | c2_1(a12) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a12) | (~c1_1(a12)) | (~c0_1(a36))))),
% 1.93/1.57 inference(monotonicity,[status(thm)],[2051])).
% 1.93/1.57 tff(2053,plain,
% 1.93/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a36) | c3_1(a36) | c2_1(a12) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a12) | (~c1_1(a12)) | (~c0_1(a36)))),
% 1.93/1.57 inference(transitivity,[status(thm)],[2052, 2050])).
% 1.93/1.57 tff(2054,plain,
% 1.93/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12)))),
% 1.93/1.57 inference(quant_inst,[status(thm)],[])).
% 1.93/1.57 tff(2055,plain,
% 1.93/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a36) | c3_1(a36) | c2_1(a12) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a12) | (~c1_1(a12)) | (~c0_1(a36))),
% 1.93/1.57 inference(modus_ponens,[status(thm)],[2054, 2053])).
% 1.93/1.57 tff(2056,plain,
% 1.93/1.57 (c0_1(a12)),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[2055, 84, 2049, 1927, 1926, 1975, 1993, 2048, 2045, 2044, 1982])).
% 1.93/1.57 tff(2057,plain,
% 1.93/1.57 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.93/1.57 inference(bind,[status(th)],[])).
% 1.93/1.57 tff(2058,plain,
% 1.93/1.57 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.93/1.57 inference(quant_intro,[status(thm)],[2057])).
% 1.93/1.57 tff(2059,plain,
% 1.93/1.57 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.93/1.57 inference(rewrite,[status(thm)],[])).
% 1.93/1.57 tff(2060,plain,
% 1.93/1.57 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.93/1.57 inference(bind,[status(th)],[])).
% 1.93/1.57 tff(2061,plain,
% 1.93/1.57 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.93/1.57 inference(quant_intro,[status(thm)],[2060])).
% 1.93/1.57 tff(2062,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 1.93/1.57 tff(2063,plain,
% 1.93/1.57 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.93/1.57 inference(modus_ponens,[status(thm)],[2062, 2061])).
% 1.93/1.57 tff(2064,plain,
% 1.93/1.57 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.93/1.57 inference(modus_ponens,[status(thm)],[2063, 2059])).
% 1.93/1.57 tff(2065,plain,(
% 1.93/1.57 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.93/1.57 inference(skolemize,[status(sab)],[2064])).
% 1.93/1.57 tff(2066,plain,
% 1.93/1.57 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.93/1.57 inference(modus_ponens,[status(thm)],[2065, 2058])).
% 1.93/1.57 tff(2067,plain,
% 1.93/1.57 (~c3_1(a12)),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[576, 2047])).
% 1.93/1.57 tff(2068,plain,
% 1.93/1.57 (hskp1 | hskp0 | c1_1(a33)),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[1923, 84, 1907, 1906, 598])).
% 1.93/1.57 tff(2069,plain,
% 1.93/1.57 (c1_1(a33)),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[2068, 1502, 588])).
% 1.93/1.57 tff(2070,plain,
% 1.93/1.57 (hskp22),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[1573, 588, 1418])).
% 1.93/1.57 tff(2071,plain,
% 1.93/1.57 (c2_1(a43)),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[699, 2070])).
% 1.93/1.57 tff(2072,plain,
% 1.93/1.57 (~c3_1(a43)),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[682, 2070])).
% 1.93/1.57 tff(2073,plain,
% 1.93/1.57 (hskp28),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[1666, 1502, 1585, 2072, 2071, 1418, 1406])).
% 1.93/1.57 tff(2074,plain,
% 1.93/1.57 (c3_1(a15)),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[1351, 2073])).
% 1.93/1.57 tff(2075,plain,
% 1.93/1.57 (c1_1(a15)),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[1362, 2073])).
% 1.93/1.57 tff(2076,plain,
% 1.93/1.57 (c0_1(a15)),
% 1.93/1.57 inference(unit_resolution,[status(thm)],[1373, 2073])).
% 1.93/1.57 tff(2077,plain,
% 1.93/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.93/1.57 inference(rewrite,[status(thm)],[])).
% 1.93/1.57 tff(2078,plain,
% 1.93/1.57 (((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33))) <=> ((~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.93/1.57 inference(rewrite,[status(thm)],[])).
% 1.93/1.57 tff(2079,plain,
% 1.93/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15))))),
% 1.93/1.58 inference(monotonicity,[status(thm)],[2078])).
% 1.93/1.58 tff(2080,plain,
% 1.93/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.93/1.58 inference(transitivity,[status(thm)],[2079, 2077])).
% 1.93/1.58 tff(2081,plain,
% 1.93/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.93/1.58 inference(quant_inst,[status(thm)],[])).
% 1.93/1.58 tff(2082,plain,
% 1.93/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15))),
% 1.93/1.58 inference(modus_ponens,[status(thm)],[2081, 2080])).
% 1.93/1.58 tff(2083,plain,
% 1.93/1.58 ($false),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[2082, 84, 1908, 1907, 1906, 2076, 2075, 2074, 376, 2069])).
% 1.93/1.58 tff(2084,plain,(hskp1 | (~c0_1(a33)) | (~c2_1(a33)) | (~c3_1(a33)) | hskp0 | (~c0_1(a43)) | hskp19 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.93/1.58 tff(2085,plain,
% 1.93/1.58 (hskp1),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[2084, 1585, 1907, 1906, 588, 1908, 1418, 1406])).
% 1.93/1.58 tff(2086,plain,
% 1.93/1.58 (~c2_1(a2)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[611, 2085])).
% 1.93/1.58 tff(2087,plain,
% 1.93/1.58 (c0_1(a2)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[633, 2085])).
% 1.93/1.58 tff(2088,plain,
% 1.93/1.58 (~c1_1(a43)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[688, 2070])).
% 1.93/1.58 tff(2089,plain,
% 1.93/1.58 (~hskp21),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[1676, 1585, 2088, 2072, 2071])).
% 1.93/1.58 tff(2090,plain,
% 1.93/1.58 (c1_1(a2)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[1209, 84, 2089, 588, 2087, 2086, 1203])).
% 1.93/1.58 tff(2091,plain,
% 1.93/1.58 (c3_1(a2)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[622, 2085])).
% 1.93/1.58 tff(2092,plain,
% 1.93/1.58 ($false),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[1685, 84, 2071, 2087, 2091, 2088, 2086, 587, 1585, 2090])).
% 1.93/1.58 tff(2093,plain,((~c0_1(a43)) | hskp0 | (~c2_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | hskp19 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.93/1.58 tff(2094,plain,
% 1.93/1.58 (~c0_1(a43)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[2093, 588, 1907, 1906, 1908, 1418, 1406])).
% 1.93/1.58 tff(2095,plain,
% 1.93/1.58 (hskp4 | c0_1(a43)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[1582, 84, 2088, 2072, 113])).
% 1.93/1.58 tff(2096,plain,
% 1.93/1.58 (hskp4),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[2095, 2094])).
% 1.93/1.58 tff(2097,plain,
% 1.93/1.58 (~c1_1(a5)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[161, 2096])).
% 1.93/1.58 tff(2098,plain,
% 1.93/1.58 (c3_1(a5)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[201, 2096])).
% 1.93/1.58 tff(2099,plain,
% 1.93/1.58 (c2_1(a5)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[212, 2096])).
% 1.93/1.58 tff(2100,plain,
% 1.93/1.58 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a5) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a5) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a33)))),
% 1.93/1.58 inference(rewrite,[status(thm)],[])).
% 1.93/1.58 tff(2101,plain,
% 1.93/1.58 ((hskp19 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5))) <=> (hskp19 | c1_1(a5) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a33)))),
% 1.93/1.58 inference(rewrite,[status(thm)],[])).
% 1.93/1.58 tff(2102,plain,
% 1.93/1.58 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a5) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a33))))),
% 1.93/1.58 inference(monotonicity,[status(thm)],[2101])).
% 1.93/1.58 tff(2103,plain,
% 1.93/1.58 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a5) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a33)))),
% 1.93/1.58 inference(transitivity,[status(thm)],[2102, 2100])).
% 1.93/1.58 tff(2104,plain,
% 1.93/1.58 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))),
% 1.93/1.58 inference(quant_inst,[status(thm)],[])).
% 1.93/1.58 tff(2105,plain,
% 1.93/1.58 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a5) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a33))),
% 1.93/1.58 inference(modus_ponens,[status(thm)],[2104, 2103])).
% 1.93/1.58 tff(2106,plain,
% 1.93/1.58 (~c1_1(a33)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[2105, 84, 1418, 1907, 1906, 2099, 2098, 2097, 155])).
% 1.93/1.58 tff(2107,plain,
% 1.93/1.58 (hskp1),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[604, 84, 588, 2099, 2098, 2097, 598])).
% 1.93/1.58 tff(2108,plain,
% 1.93/1.58 (~c2_1(a2)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[611, 2107])).
% 1.93/1.58 tff(2109,plain,
% 1.93/1.58 (c3_1(a2)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[622, 2107])).
% 1.93/1.58 tff(2110,plain,
% 1.93/1.58 (c0_1(a2)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[633, 2107])).
% 1.93/1.58 tff(2111,plain,
% 1.93/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c0_1(a33)))),
% 1.93/1.58 inference(rewrite,[status(thm)],[])).
% 1.93/1.58 tff(2112,plain,
% 1.93/1.58 (((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33))) <=> (c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c0_1(a33)))),
% 1.93/1.58 inference(rewrite,[status(thm)],[])).
% 1.93/1.58 tff(2113,plain,
% 1.93/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c0_1(a33))))),
% 1.93/1.58 inference(monotonicity,[status(thm)],[2112])).
% 1.93/1.58 tff(2114,plain,
% 1.93/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c0_1(a33)))),
% 1.93/1.58 inference(transitivity,[status(thm)],[2113, 2111])).
% 1.93/1.58 tff(2115,plain,
% 1.93/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.93/1.58 inference(quant_inst,[status(thm)],[])).
% 1.93/1.58 tff(2116,plain,
% 1.93/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c0_1(a33))),
% 1.93/1.58 inference(modus_ponens,[status(thm)],[2115, 2114])).
% 1.93/1.58 tff(2117,plain,
% 1.93/1.58 (~c1_1(a2)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[2116, 84, 1908, 1907, 2110, 2109, 2108, 587, 2106])).
% 1.93/1.58 tff(2118,plain,
% 1.93/1.58 (((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | c1_1(a43) | (~ndr1_0) | (~c2_1(a43)) | c0_1(a43))) <=> ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp0 | c1_1(a43) | (~ndr1_0) | (~c2_1(a43)) | c0_1(a43))),
% 1.93/1.58 inference(rewrite,[status(thm)],[])).
% 1.93/1.58 tff(2119,plain,
% 1.93/1.58 ((hskp5 | hskp0 | (~ndr1_0) | c1_1(a43) | c0_1(a43) | (~c2_1(a43))) <=> (hskp5 | hskp0 | c1_1(a43) | (~ndr1_0) | (~c2_1(a43)) | c0_1(a43))),
% 1.93/1.58 inference(rewrite,[status(thm)],[])).
% 1.93/1.58 tff(2120,plain,
% 1.93/1.58 (((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | (~ndr1_0) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)))) <=> ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | c1_1(a43) | (~ndr1_0) | (~c2_1(a43)) | c0_1(a43)))),
% 1.93/1.58 inference(monotonicity,[status(thm)],[2119])).
% 1.93/1.58 tff(2121,plain,
% 1.93/1.58 (((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | (~ndr1_0) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)))) <=> ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp0 | c1_1(a43) | (~ndr1_0) | (~c2_1(a43)) | c0_1(a43))),
% 1.93/1.58 inference(transitivity,[status(thm)],[2120, 2118])).
% 1.93/1.58 tff(2122,plain,
% 1.93/1.58 ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | (~ndr1_0) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)))),
% 1.93/1.58 inference(quant_inst,[status(thm)],[])).
% 1.93/1.58 tff(2123,plain,
% 1.93/1.58 ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp0 | c1_1(a43) | (~ndr1_0) | (~c2_1(a43)) | c0_1(a43)),
% 1.93/1.58 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 1.93/1.58 tff(2124,plain,
% 1.93/1.58 (hskp5 | c0_1(a43)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[2123, 84, 588, 2071, 2088, 1158])).
% 1.93/1.58 tff(2125,plain,
% 1.93/1.58 (hskp5),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[2124, 2094])).
% 1.93/1.58 tff(2126,plain,
% 1.93/1.58 (~c3_1(a6)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[1115, 2125])).
% 1.93/1.58 tff(2127,plain,
% 1.93/1.58 (c0_1(a6)),
% 1.93/1.58 inference(unit_resolution,[status(thm)],[274, 2125])).
% 1.93/1.58 tff(2128,plain,
% 1.93/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c3_1(a6) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a6) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a6)) | (~c1_1(a6)))),
% 1.93/1.58 inference(rewrite,[status(thm)],[])).
% 1.93/1.58 tff(2129,plain,
% 1.93/1.58 ((hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2))) <=> (hskp0 | c3_1(a6) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a6)) | (~c1_1(a6)))),
% 1.93/1.59 inference(rewrite,[status(thm)],[])).
% 1.93/1.59 tff(2130,plain,
% 1.93/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c3_1(a6) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a6)) | (~c1_1(a6))))),
% 1.93/1.59 inference(monotonicity,[status(thm)],[2129])).
% 1.93/1.59 tff(2131,plain,
% 1.93/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a6) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a6)) | (~c1_1(a6)))),
% 1.93/1.59 inference(transitivity,[status(thm)],[2130, 2128])).
% 1.93/1.59 tff(2132,plain,
% 1.93/1.59 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))),
% 1.93/1.59 inference(quant_inst,[status(thm)],[])).
% 1.93/1.59 tff(2133,plain,
% 1.93/1.59 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a6) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a6)) | (~c1_1(a6))),
% 1.93/1.59 inference(modus_ponens,[status(thm)],[2132, 2131])).
% 1.93/1.59 tff(2134,plain,
% 1.93/1.59 (~c1_1(a6)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2133, 84, 588, 2127, 2109, 2126, 2108, 651, 2117])).
% 1.93/1.59 tff(2135,plain,
% 1.93/1.59 (hskp21),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1209, 84, 588, 2110, 2108, 1203, 2117])).
% 1.93/1.59 tff(2136,plain,
% 1.93/1.59 (~c0_1(a42)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1216, 2135])).
% 1.93/1.59 tff(2137,plain,
% 1.93/1.59 (c2_1(a6)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[285, 2125])).
% 1.93/1.59 tff(2138,plain,
% 1.93/1.59 (c3_1(a42)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1227, 2135])).
% 1.93/1.59 tff(2139,plain,
% 1.93/1.59 (c2_1(a42)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1238, 2135])).
% 1.93/1.59 tff(2140,plain,
% 1.93/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a42) | c3_1(a6) | (~ndr1_0) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a42) | c3_1(a6) | (~ndr1_0) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.93/1.59 inference(rewrite,[status(thm)],[])).
% 1.93/1.59 tff(2141,plain,
% 1.93/1.59 (((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42))) <=> (c0_1(a42) | c3_1(a6) | (~ndr1_0) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.93/1.59 inference(rewrite,[status(thm)],[])).
% 1.93/1.59 tff(2142,plain,
% 1.93/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a42) | c3_1(a6) | (~ndr1_0) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a42)) | (~c3_1(a42))))),
% 1.93/1.59 inference(monotonicity,[status(thm)],[2141])).
% 1.93/1.59 tff(2143,plain,
% 1.93/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a42) | c3_1(a6) | (~ndr1_0) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.93/1.59 inference(transitivity,[status(thm)],[2142, 2140])).
% 1.93/1.59 tff(2144,plain,
% 1.93/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.93/1.59 inference(quant_inst,[status(thm)],[])).
% 1.93/1.59 tff(2145,plain,
% 1.93/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a42) | c3_1(a6) | (~ndr1_0) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a42)) | (~c3_1(a42))),
% 1.93/1.59 inference(modus_ponens,[status(thm)],[2144, 2143])).
% 1.93/1.59 tff(2146,plain,
% 1.93/1.59 ($false),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2145, 84, 2139, 2138, 2127, 2137, 2136, 2126, 103, 2134])).
% 1.93/1.59 tff(2147,plain,(hskp0 | (~c0_1(a33)) | (~c2_1(a33)) | hskp19 | (~c3_1(a33)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.93/1.59 tff(2148,plain,
% 1.93/1.59 (hskp0),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2147, 1418, 1904, 1882, 1893, 1406])).
% 1.93/1.59 tff(2149,plain,
% 1.93/1.59 (~c0_1(a1)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[714, 2148])).
% 1.93/1.59 tff(2150,plain,
% 1.93/1.59 (hskp1),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1561, 93, 1506, 1406, 22, 1418, 44])).
% 1.93/1.59 tff(2151,plain,
% 1.93/1.59 (~c2_1(a2)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[611, 2150])).
% 1.93/1.59 tff(2152,plain,
% 1.93/1.59 (c3_1(a2)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[622, 2150])).
% 1.93/1.59 tff(2153,plain,
% 1.93/1.59 (c0_1(a2)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[633, 2150])).
% 1.93/1.59 tff(2154,plain,
% 1.93/1.59 ($false),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1571, 1, 84, 1418, 2153, 2152, 2151, 1417])).
% 1.93/1.59 tff(2155,plain,(hskp22 | hskp19 | hskp28 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.93/1.59 tff(2156,plain,
% 1.93/1.59 ($false),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2155, 1425, 1, 1406, 1418])).
% 1.93/1.59 tff(2157,plain,(hskp22 | hskp24 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.93/1.59 tff(2158,plain,
% 1.93/1.59 (hskp22),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2157, 1418, 1406])).
% 1.93/1.59 tff(2159,plain,
% 1.93/1.59 (~c1_1(a43)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[688, 2158])).
% 1.93/1.59 tff(2160,plain,
% 1.93/1.59 (c2_1(a1)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[736, 2148])).
% 1.93/1.59 tff(2161,plain,
% 1.93/1.59 (c1_1(a1)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[725, 2148])).
% 1.93/1.59 tff(2162,plain,
% 1.93/1.59 (~c3_1(a43)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[682, 2158])).
% 1.93/1.59 tff(2163,plain,
% 1.93/1.59 (c2_1(a43)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[699, 2158])).
% 1.93/1.59 tff(2164,plain,
% 1.93/1.59 (hskp15 | hskp4),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1707, 84, 774, 773, 738, 1699])).
% 1.93/1.59 tff(2165,plain,
% 1.93/1.59 (hskp15),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2164, 1407])).
% 1.93/1.59 tff(2166,plain,
% 1.93/1.59 (~c2_1(a27)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1713, 2165])).
% 1.93/1.59 tff(2167,plain,
% 1.93/1.59 (c0_1(a27)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1724, 2165])).
% 1.93/1.59 tff(2168,plain,
% 1.93/1.59 (~c3_1(a27)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1765, 84, 1586, 2167, 774, 773, 1672, 1587, 2166, 738, 133])).
% 1.93/1.59 tff(2169,plain,
% 1.93/1.59 (hskp4 | c0_1(a43)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1582, 84, 1672, 1587, 113])).
% 1.93/1.59 tff(2170,plain,
% 1.93/1.59 (c0_1(a43)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2169, 1407])).
% 1.93/1.59 tff(2171,plain,
% 1.93/1.59 (c1_1(a27)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1735, 2165])).
% 1.93/1.59 tff(2172,plain,
% 1.93/1.59 ($false),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1773, 84, 1406, 1586, 2171, 1587, 2166, 1533, 2170, 2168])).
% 1.93/1.59 tff(2173,plain,(hskp4 | hskp24 | (~c2_1(a43)) | c3_1(a43) | (~c1_1(a1)) | (~c2_1(a1)) | c1_1(a43) | c0_1(a1)), inference(lemma,lemma(discharge,[]))).
% 1.93/1.59 tff(2174,plain,
% 1.93/1.59 (hskp4),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2173, 2163, 1406, 2162, 2161, 2160, 2159, 2149])).
% 1.93/1.59 tff(2175,plain,
% 1.93/1.59 (~c1_1(a5)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[161, 2174])).
% 1.93/1.59 tff(2176,plain,
% 1.93/1.59 (c3_1(a5)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[201, 2174])).
% 1.93/1.59 tff(2177,plain,
% 1.93/1.59 (c2_1(a5)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[212, 2174])).
% 1.93/1.59 tff(2178,plain,
% 1.93/1.59 (~c1_1(a33)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2105, 84, 1418, 1904, 1893, 2177, 2176, 2175, 155])).
% 1.93/1.59 tff(2179,plain,
% 1.93/1.59 (~c3_1(a1)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1302, 84, 1418, 2177, 2176, 2161, 2160, 2175, 155])).
% 1.93/1.59 tff(2180,plain,
% 1.93/1.59 (~hskp14),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1936, 1502, 1882, 1904, 1928])).
% 1.93/1.59 tff(2181,plain,
% 1.93/1.59 (~hskp28),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1649, 2180, 134])).
% 1.93/1.59 tff(2182,plain,
% 1.93/1.59 (hskp9),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1520, 2181, 1502])).
% 1.93/1.59 tff(2183,plain,
% 1.93/1.59 (~c3_1(a12)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[576, 2182])).
% 1.93/1.59 tff(2184,assumption,(~c3_1(a1)), introduced(assumption)).
% 1.93/1.59 tff(2185,plain,
% 1.93/1.59 (hskp29 | hskp14 | c3_1(a1)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1316, 84, 773, 738, 336])).
% 1.93/1.59 tff(2186,plain,
% 1.93/1.59 (hskp29),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2185, 2180, 2184])).
% 1.93/1.59 tff(2187,plain,
% 1.93/1.59 (c1_1(a12)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[570, 2182])).
% 1.93/1.59 tff(2188,plain,
% 1.93/1.59 (~c2_1(a12)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1058, 2182])).
% 1.93/1.59 tff(2189,assumption,(hskp29), introduced(assumption)).
% 1.93/1.59 tff(2190,plain,
% 1.93/1.59 (c2_1(a25)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[365, 2189])).
% 1.93/1.59 tff(2191,plain,
% 1.93/1.59 (c1_1(a25)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[386, 2189])).
% 1.93/1.59 tff(2192,plain,
% 1.93/1.59 (c0_1(a25)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[354, 2189])).
% 1.93/1.59 tff(2193,plain,
% 1.93/1.59 (~c3_1(a25)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[393, 84, 2192, 2191, 2190, 376])).
% 1.93/1.59 tff(2194,plain,
% 1.93/1.59 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25))),
% 1.93/1.59 inference(rewrite,[status(thm)],[])).
% 1.93/1.59 tff(2195,plain,
% 1.93/1.59 ((hskp24 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12))) <=> (hskp24 | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25))),
% 1.93/1.59 inference(rewrite,[status(thm)],[])).
% 1.93/1.59 tff(2196,plain,
% 1.93/1.59 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25)))),
% 1.93/1.59 inference(monotonicity,[status(thm)],[2195])).
% 1.93/1.59 tff(2197,plain,
% 1.93/1.59 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25))),
% 1.93/1.59 inference(transitivity,[status(thm)],[2196, 2194])).
% 1.93/1.59 tff(2198,plain,
% 1.93/1.59 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))),
% 1.93/1.59 inference(quant_inst,[status(thm)],[])).
% 1.93/1.59 tff(2199,plain,
% 1.93/1.59 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25)),
% 1.93/1.59 inference(modus_ponens,[status(thm)],[2198, 2197])).
% 1.93/1.59 tff(2200,plain,
% 1.93/1.59 ($false),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2199, 84, 1406, 2192, 2190, 653, 1066, 652, 1533, 2193])).
% 1.93/1.59 tff(2201,plain,((~hskp29) | hskp24 | (~c1_1(a12)) | c2_1(a12) | c3_1(a12)), inference(lemma,lemma(discharge,[]))).
% 1.93/1.59 tff(2202,plain,
% 1.93/1.59 ($false),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2201, 2188, 2187, 1406, 2186, 2183])).
% 1.93/1.59 tff(2203,plain,(hskp1 | hskp24 | c3_1(a1) | (~c2_1(a1)) | c0_1(a1) | hskp18 | c1_1(a33)), inference(lemma,lemma(discharge,[]))).
% 1.93/1.59 tff(2204,plain,
% 1.93/1.59 (hskp1),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2203, 2179, 1406, 2160, 2149, 134, 2178])).
% 1.93/1.59 tff(2205,plain,
% 1.93/1.59 (~c2_1(a2)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[611, 2204])).
% 1.93/1.59 tff(2206,plain,
% 1.93/1.59 (c3_1(a2)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[622, 2204])).
% 1.93/1.59 tff(2207,plain,
% 1.93/1.59 (c0_1(a2)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[633, 2204])).
% 1.93/1.59 tff(2208,plain,
% 1.93/1.59 ($false),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[783, 84, 2163, 2207, 2206, 2161, 2160, 2159, 2162, 2205, 2149, 133])).
% 1.93/1.59 tff(2209,plain,(hskp19 | hskp24 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.93/1.59 tff(2210,plain,
% 1.93/1.59 (hskp19),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2209, 1406, 134])).
% 1.93/1.59 tff(2211,plain,
% 1.93/1.59 (~c2_1(a36)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1280, 2210])).
% 1.93/1.59 tff(2212,plain,
% 1.93/1.59 (~c1_1(a36)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1286, 2210])).
% 1.93/1.59 tff(2213,plain,
% 1.93/1.59 (hskp1 | c0_1(a36)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[1981, 84, 1882, 1904, 2212, 2211, 749, 1917])).
% 1.93/1.59 tff(2214,plain,
% 1.93/1.59 (c0_1(a36)),
% 1.93/1.59 inference(unit_resolution,[status(thm)],[2213, 1502])).
% 1.93/1.59 tff(2215,plain,
% 1.93/1.59 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.93/1.59 inference(bind,[status(th)],[])).
% 1.93/1.59 tff(2216,plain,
% 1.93/1.59 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.93/1.59 inference(quant_intro,[status(thm)],[2215])).
% 1.93/1.59 tff(2217,plain,
% 1.93/1.59 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.93/1.59 inference(rewrite,[status(thm)],[])).
% 1.93/1.59 tff(2218,plain,
% 1.93/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp29) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp29))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.93/1.60 inference(bind,[status(th)],[])).
% 1.93/1.60 tff(2219,plain,
% 1.93/1.60 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.93/1.60 inference(quant_intro,[status(thm)],[2218])).
% 1.93/1.60 tff(2220,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 1.93/1.60 tff(2221,plain,
% 1.93/1.60 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2220, 2219])).
% 1.93/1.60 tff(2222,plain,
% 1.93/1.60 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2221, 2217])).
% 1.93/1.60 tff(2223,plain,(
% 1.93/1.60 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.93/1.60 inference(skolemize,[status(sab)],[2222])).
% 1.93/1.60 tff(2224,plain,
% 1.93/1.60 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2223, 2216])).
% 1.93/1.60 tff(2225,plain,
% 1.93/1.60 (~c3_1(a36)),
% 1.93/1.60 inference(unit_resolution,[status(thm)],[1274, 2210])).
% 1.93/1.60 tff(2226,plain,
% 1.93/1.60 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp29 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp29 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c0_1(a36)))),
% 1.93/1.60 inference(rewrite,[status(thm)],[])).
% 1.93/1.60 tff(2227,plain,
% 1.93/1.60 ((hskp29 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | c1_1(a36) | c3_1(a36) | (~c0_1(a36))) <=> (hskp29 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c0_1(a36)))),
% 1.93/1.60 inference(rewrite,[status(thm)],[])).
% 1.93/1.60 tff(2228,plain,
% 1.93/1.60 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | c1_1(a36) | c3_1(a36) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp29 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c0_1(a36))))),
% 1.93/1.60 inference(monotonicity,[status(thm)],[2227])).
% 1.93/1.60 tff(2229,plain,
% 1.93/1.60 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | c1_1(a36) | c3_1(a36) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp29 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c0_1(a36)))),
% 1.93/1.60 inference(transitivity,[status(thm)],[2228, 2226])).
% 1.93/1.60 tff(2230,plain,
% 1.93/1.60 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | c1_1(a36) | c3_1(a36) | (~c0_1(a36)))),
% 1.93/1.60 inference(quant_inst,[status(thm)],[])).
% 1.93/1.60 tff(2231,plain,
% 1.93/1.60 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp29 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c0_1(a36))),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 1.93/1.60 tff(2232,plain,
% 1.93/1.60 (hskp29 | (~c0_1(a36))),
% 1.93/1.60 inference(unit_resolution,[status(thm)],[2231, 84, 1882, 1904, 1893, 2212, 2225, 2224])).
% 1.93/1.60 tff(2233,plain,
% 1.93/1.60 (hskp29),
% 1.93/1.60 inference(unit_resolution,[status(thm)],[2232, 2214])).
% 1.93/1.60 tff(2234,plain,
% 1.93/1.60 ($false),
% 1.93/1.60 inference(unit_resolution,[status(thm)],[2201, 2048, 2049, 1406, 2233, 2067])).
% 1.93/1.60 tff(2235,plain,(hskp1 | hskp24 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.93/1.60 tff(2236,plain,
% 1.93/1.60 (hskp1),
% 1.93/1.60 inference(unit_resolution,[status(thm)],[2235, 1406, 134])).
% 1.93/1.60 tff(2237,plain,
% 1.93/1.60 (~c2_1(a2)),
% 1.93/1.60 inference(unit_resolution,[status(thm)],[611, 2236])).
% 1.93/1.60 tff(2238,plain,
% 1.93/1.60 (c0_1(a2)),
% 1.93/1.60 inference(unit_resolution,[status(thm)],[633, 2236])).
% 1.93/1.60 tff(2239,plain,
% 1.93/1.60 (c3_1(a2)),
% 1.93/1.60 inference(unit_resolution,[status(thm)],[622, 2236])).
% 1.93/1.60 tff(2240,plain,
% 1.93/1.60 (~c1_1(a2)),
% 1.93/1.60 inference(unit_resolution,[status(thm)],[2116, 84, 1882, 1904, 2238, 2239, 2237, 587, 1917])).
% 1.93/1.60 tff(2241,plain,
% 1.93/1.60 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)) | (~c0_1(a19)) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)) | (~c0_1(a19)) | (~c1_1(a19)))),
% 1.93/1.60 inference(rewrite,[status(thm)],[])).
% 1.93/1.60 tff(2242,plain,
% 1.93/1.60 ((hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33))) <=> (hskp16 | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)) | (~c0_1(a19)) | (~c1_1(a19)))),
% 1.93/1.60 inference(rewrite,[status(thm)],[])).
% 1.93/1.60 tff(2243,plain,
% 1.93/1.60 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)) | (~c0_1(a19)) | (~c1_1(a19))))),
% 1.93/1.60 inference(monotonicity,[status(thm)],[2242])).
% 1.93/1.60 tff(2244,plain,
% 1.93/1.60 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)) | (~c0_1(a19)) | (~c1_1(a19)))),
% 1.93/1.60 inference(transitivity,[status(thm)],[2243, 2241])).
% 1.93/1.60 tff(2245,plain,
% 1.93/1.60 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)))),
% 1.93/1.60 inference(quant_inst,[status(thm)],[])).
% 1.93/1.60 tff(2246,plain,
% 1.93/1.60 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)) | (~c0_1(a19)) | (~c1_1(a19))),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2245, 2244])).
% 1.93/1.60 tff(2247,plain,
% 1.93/1.60 (hskp16),
% 1.93/1.60 inference(unit_resolution,[status(thm)],[2246, 84, 1882, 1893, 44, 33, 22, 2066, 1917])).
% 1.93/1.60 tff(2248,plain,
% 1.93/1.60 (((~hskp16) | (~c0_1(a31))) <=> ((~hskp16) | (~c0_1(a31)))),
% 1.93/1.60 inference(rewrite,[status(thm)],[])).
% 1.93/1.60 tff(2249,plain,
% 1.93/1.60 (((~c0_1(a31)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a31)))),
% 1.93/1.60 inference(rewrite,[status(thm)],[])).
% 1.93/1.60 tff(2250,axiom,((~c0_1(a31)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.93/1.60 tff(2251,plain,
% 1.93/1.60 ((~hskp16) | (~c0_1(a31))),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2250, 2249])).
% 1.93/1.60 tff(2252,plain,
% 1.93/1.60 ((~hskp16) | (~c0_1(a31))),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2251, 2248])).
% 1.93/1.60 tff(2253,plain,
% 1.93/1.60 (~c0_1(a31)),
% 1.93/1.60 inference(unit_resolution,[status(thm)],[2252, 2247])).
% 1.93/1.60 tff(2254,plain,
% 1.93/1.60 (((~hskp16) | c2_1(a31)) <=> ((~hskp16) | c2_1(a31))),
% 1.93/1.60 inference(rewrite,[status(thm)],[])).
% 1.93/1.60 tff(2255,axiom,((~hskp16) | c2_1(a31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.93/1.60 tff(2256,plain,
% 1.93/1.60 ((~hskp16) | c2_1(a31)),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2255, 2254])).
% 1.93/1.60 tff(2257,plain,
% 1.93/1.60 ((~hskp16) | c2_1(a31)),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2256, 2254])).
% 1.93/1.60 tff(2258,plain,
% 1.93/1.60 ((~hskp16) | c2_1(a31)),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2257, 2254])).
% 1.93/1.60 tff(2259,plain,
% 1.93/1.60 ((~hskp16) | c2_1(a31)),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2258, 2254])).
% 1.93/1.60 tff(2260,plain,
% 1.93/1.60 ((~hskp16) | c2_1(a31)),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2259, 2254])).
% 1.93/1.60 tff(2261,plain,
% 1.93/1.60 ((~hskp16) | c2_1(a31)),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2260, 2254])).
% 1.93/1.60 tff(2262,plain,
% 1.93/1.60 ((~hskp16) | c2_1(a31)),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2261, 2254])).
% 1.93/1.60 tff(2263,plain,
% 1.93/1.60 ((~hskp16) | c2_1(a31)),
% 1.93/1.60 inference(modus_ponens,[status(thm)],[2262, 2254])).
% 1.93/1.60 tff(2264,plain,
% 1.93/1.60 (c2_1(a31)),
% 1.93/1.60 inference(unit_resolution,[status(thm)],[2263, 2247])).
% 1.93/1.60 tff(2265,plain,
% 1.93/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a31) | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a31) | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.93/1.60 inference(rewrite,[status(thm)],[])).
% 1.93/1.60 tff(2266,plain,
% 1.93/1.60 (((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31))) <=> (c0_1(a31) | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.93/1.60 inference(rewrite,[status(thm)],[])).
% 1.93/1.60 tff(2267,plain,
% 1.93/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a31) | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.93/1.60 inference(monotonicity,[status(thm)],[2266])).
% 1.93/1.60 tff(2268,plain,
% 1.93/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a31) | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.93/1.61 inference(transitivity,[status(thm)],[2267, 2265])).
% 1.93/1.61 tff(2269,plain,
% 1.93/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.93/1.61 inference(quant_inst,[status(thm)],[])).
% 1.93/1.61 tff(2270,plain,
% 1.93/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a31) | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.93/1.61 inference(modus_ponens,[status(thm)],[2269, 2268])).
% 1.93/1.61 tff(2271,plain,
% 1.93/1.61 (~c3_1(a31)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2270, 84, 1882, 1904, 2264, 44, 2253, 22, 103, 93, 1917])).
% 1.93/1.61 tff(2272,assumption,(~c3_1(a31)), introduced(assumption)).
% 1.93/1.61 tff(2273,assumption,(~c0_1(a31)), introduced(assumption)).
% 1.93/1.61 tff(2274,assumption,(c2_1(a31)), introduced(assumption)).
% 1.93/1.61 tff(2275,plain,
% 1.93/1.61 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | c0_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c0_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 1.93/1.61 inference(rewrite,[status(thm)],[])).
% 1.93/1.61 tff(2276,plain,
% 1.93/1.61 ((hskp29 | hskp14 | (~ndr1_0) | c3_1(a31) | c0_1(a31) | (~c2_1(a31))) <=> (hskp29 | hskp14 | c0_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 1.93/1.61 inference(rewrite,[status(thm)],[])).
% 1.93/1.61 tff(2277,plain,
% 1.93/1.61 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | c0_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31)))),
% 1.93/1.61 inference(monotonicity,[status(thm)],[2276])).
% 1.93/1.61 tff(2278,plain,
% 1.93/1.61 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c0_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 1.93/1.61 inference(transitivity,[status(thm)],[2277, 2275])).
% 1.93/1.61 tff(2279,plain,
% 1.93/1.61 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)))),
% 1.93/1.61 inference(quant_inst,[status(thm)],[])).
% 1.93/1.61 tff(2280,plain,
% 1.93/1.61 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c0_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31)),
% 1.93/1.61 inference(modus_ponens,[status(thm)],[2279, 2278])).
% 1.93/1.61 tff(2281,plain,
% 1.93/1.61 (hskp29 | hskp14 | c3_1(a31)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2280, 84, 2274, 2273, 336])).
% 1.93/1.61 tff(2282,plain,
% 1.93/1.61 (hskp29),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2281, 1937, 2272])).
% 1.93/1.61 tff(2283,plain,
% 1.93/1.61 ($false),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2201, 2048, 2049, 1406, 2282, 2067])).
% 1.93/1.61 tff(2284,plain,(hskp1 | hskp24 | c3_1(a31) | (~c2_1(a31)) | c0_1(a31) | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.93/1.61 tff(2285,plain,
% 1.93/1.61 (hskp1),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2284, 2271, 1406, 2264, 2253, 134])).
% 1.93/1.61 tff(2286,plain,
% 1.93/1.61 (~c2_1(a2)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[611, 2285])).
% 1.93/1.61 tff(2287,plain,
% 1.93/1.61 (c3_1(a2)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[622, 2285])).
% 1.93/1.61 tff(2288,plain,
% 1.93/1.61 (c0_1(a2)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[633, 2285])).
% 1.93/1.61 tff(2289,plain,
% 1.93/1.61 (~c1_1(a2)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2116, 84, 1882, 1904, 2288, 2287, 2286, 587, 1917])).
% 1.93/1.61 tff(2290,plain,
% 1.93/1.61 (((~hskp16) | (~c1_1(a31))) <=> ((~hskp16) | (~c1_1(a31)))),
% 1.93/1.61 inference(rewrite,[status(thm)],[])).
% 1.93/1.61 tff(2291,plain,
% 1.93/1.61 (((~c1_1(a31)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a31)))),
% 1.93/1.61 inference(rewrite,[status(thm)],[])).
% 1.93/1.61 tff(2292,axiom,((~c1_1(a31)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.93/1.61 tff(2293,plain,
% 1.93/1.61 ((~hskp16) | (~c1_1(a31))),
% 1.93/1.61 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 1.93/1.61 tff(2294,plain,
% 1.93/1.61 ((~hskp16) | (~c1_1(a31))),
% 1.93/1.61 inference(modus_ponens,[status(thm)],[2293, 2290])).
% 1.93/1.61 tff(2295,plain,
% 1.93/1.61 (~c1_1(a31)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2294, 2247])).
% 1.93/1.61 tff(2296,plain,
% 1.93/1.61 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c0_1(a31) | c1_1(a31) | (~ndr1_0) | c3_1(a31))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c0_1(a31) | c1_1(a31) | (~ndr1_0) | c3_1(a31))),
% 1.93/1.61 inference(rewrite,[status(thm)],[])).
% 1.93/1.61 tff(2297,plain,
% 1.93/1.61 ((hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | c0_1(a31)) <=> (hskp4 | c0_1(a31) | c1_1(a31) | (~ndr1_0) | c3_1(a31))),
% 1.93/1.61 inference(rewrite,[status(thm)],[])).
% 1.93/1.61 tff(2298,plain,
% 1.93/1.61 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | c0_1(a31))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c0_1(a31) | c1_1(a31) | (~ndr1_0) | c3_1(a31)))),
% 1.93/1.61 inference(monotonicity,[status(thm)],[2297])).
% 1.93/1.61 tff(2299,plain,
% 1.93/1.61 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | c0_1(a31))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c0_1(a31) | c1_1(a31) | (~ndr1_0) | c3_1(a31))),
% 1.93/1.61 inference(transitivity,[status(thm)],[2298, 2296])).
% 1.93/1.61 tff(2300,plain,
% 1.93/1.61 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | c0_1(a31))),
% 1.93/1.61 inference(quant_inst,[status(thm)],[])).
% 1.93/1.61 tff(2301,plain,
% 1.93/1.61 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c0_1(a31) | c1_1(a31) | (~ndr1_0) | c3_1(a31)),
% 1.93/1.61 inference(modus_ponens,[status(thm)],[2300, 2299])).
% 1.93/1.61 tff(2302,plain,
% 1.93/1.61 (hskp4 | c3_1(a31)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2301, 84, 2253, 2295, 113])).
% 1.93/1.61 tff(2303,plain,
% 1.93/1.61 (hskp4),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2302, 2271])).
% 1.93/1.61 tff(2304,plain,
% 1.93/1.61 (~c1_1(a5)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[161, 2303])).
% 1.93/1.61 tff(2305,plain,
% 1.93/1.61 (c3_1(a5)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[201, 2303])).
% 1.93/1.61 tff(2306,plain,
% 1.93/1.61 (c2_1(a5)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[212, 2303])).
% 1.93/1.61 tff(2307,plain,
% 1.93/1.61 ($false),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[676, 1, 84, 2306, 2305, 2287, 2304, 2286, 123, 2289])).
% 1.93/1.61 tff(2308,plain,(hskp22 | hskp24 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.93/1.61 tff(2309,plain,
% 1.93/1.61 (hskp22),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2308, 1406, 134])).
% 1.93/1.61 tff(2310,plain,
% 1.93/1.61 (~c3_1(a43)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[682, 2309])).
% 1.93/1.61 tff(2311,plain,
% 1.93/1.61 (~c1_1(a43)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[688, 2309])).
% 1.93/1.61 tff(2312,plain,
% 1.93/1.61 (c2_1(a43)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[699, 2309])).
% 1.93/1.61 tff(2313,assumption,(~c1_1(a2)), introduced(assumption)).
% 1.93/1.61 tff(2314,assumption,(~c2_1(a2)), introduced(assumption)).
% 1.93/1.61 tff(2315,assumption,(c0_1(a2)), introduced(assumption)).
% 1.93/1.61 tff(2316,plain,
% 1.93/1.61 (hskp21 | hskp0 | c1_1(a2)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[1209, 84, 2315, 2314, 1203])).
% 1.93/1.61 tff(2317,plain,
% 1.93/1.61 (hskp21),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2316, 588, 2313])).
% 1.93/1.61 tff(2318,plain,
% 1.93/1.61 (~c0_1(a43)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[1676, 2317, 1672, 1587, 1586])).
% 1.93/1.61 tff(2319,plain,
% 1.93/1.61 (hskp5 | hskp0 | c0_1(a43)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2123, 84, 1586, 1672, 1158])).
% 1.93/1.61 tff(2320,plain,
% 1.93/1.61 (hskp5),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2319, 2318, 588])).
% 1.93/1.61 tff(2321,plain,
% 1.93/1.61 (~c3_1(a6)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[1115, 2320])).
% 1.93/1.61 tff(2322,plain,
% 1.93/1.61 (~c0_1(a42)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[1216, 2317])).
% 1.93/1.61 tff(2323,plain,
% 1.93/1.61 (c2_1(a6)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[285, 2320])).
% 1.93/1.61 tff(2324,plain,
% 1.93/1.61 (c0_1(a6)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[274, 2320])).
% 1.93/1.61 tff(2325,plain,
% 1.93/1.61 (c3_1(a42)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[1227, 2317])).
% 1.93/1.61 tff(2326,plain,
% 1.93/1.61 (c2_1(a42)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[1238, 2317])).
% 1.93/1.61 tff(2327,plain,
% 1.93/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a42) | c3_1(a6) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a6)) | (~c0_1(a6)) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a42) | c3_1(a6) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a6)) | (~c0_1(a6)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.93/1.61 inference(rewrite,[status(thm)],[])).
% 1.93/1.61 tff(2328,plain,
% 1.93/1.61 (((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42))) <=> (c0_1(a42) | c3_1(a6) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a6)) | (~c0_1(a6)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.93/1.61 inference(rewrite,[status(thm)],[])).
% 1.93/1.61 tff(2329,plain,
% 1.93/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a42) | c3_1(a6) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a6)) | (~c0_1(a6)) | (~c2_1(a42)) | (~c3_1(a42))))),
% 1.93/1.61 inference(monotonicity,[status(thm)],[2328])).
% 1.93/1.61 tff(2330,plain,
% 1.93/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a42) | c3_1(a6) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a6)) | (~c0_1(a6)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.93/1.61 inference(transitivity,[status(thm)],[2329, 2327])).
% 1.93/1.61 tff(2331,plain,
% 1.93/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.93/1.61 inference(quant_inst,[status(thm)],[])).
% 1.93/1.61 tff(2332,plain,
% 1.93/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a42) | c3_1(a6) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a6)) | (~c0_1(a6)) | (~c2_1(a42)) | (~c3_1(a42))),
% 1.93/1.61 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 1.93/1.61 tff(2333,plain,
% 1.93/1.61 ($false),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2332, 84, 1908, 1907, 2326, 2325, 2324, 2323, 2322, 2321, 103, 1928])).
% 1.93/1.61 tff(2334,plain,(hskp0 | (~c0_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c2_1(a43)) | c1_1(a43) | c3_1(a43) | c1_1(a2) | (~c0_1(a2)) | c2_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.93/1.61 tff(2335,plain,
% 1.93/1.61 (hskp0),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2334, 2312, 1904, 1917, 1882, 2311, 2310, 2240, 2238, 2237])).
% 1.93/1.61 tff(2336,plain,
% 1.93/1.61 (~c0_1(a1)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[714, 2335])).
% 1.93/1.61 tff(2337,plain,
% 1.93/1.61 (c2_1(a1)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[736, 2335])).
% 1.93/1.61 tff(2338,plain,
% 1.93/1.61 (c1_1(a1)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[725, 2335])).
% 1.93/1.61 tff(2339,plain,
% 1.93/1.61 ($false),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[783, 84, 2312, 2238, 2239, 2338, 2337, 2311, 2310, 2237, 2336, 133])).
% 1.93/1.61 tff(2340,plain,(hskp24 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.93/1.61 tff(2341,plain,
% 1.93/1.61 (hskp24),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2340, 134])).
% 1.93/1.61 tff(2342,plain,
% 1.93/1.61 (~c1_1(a58)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[1460, 2341])).
% 1.93/1.61 tff(2343,plain,
% 1.93/1.61 (c3_1(a58)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[1436, 2341])).
% 1.93/1.61 tff(2344,plain,
% 1.93/1.61 (c0_1(a58)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[1447, 2341])).
% 1.93/1.61 tff(2345,plain,
% 1.93/1.61 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a58) | c3_1(a12) | (~ndr1_0) | (~c0_1(a12)) | (~c1_1(a12)) | (~c0_1(a58)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a58) | c3_1(a12) | (~ndr1_0) | (~c0_1(a12)) | (~c1_1(a12)) | (~c0_1(a58)) | (~c3_1(a58)))),
% 1.93/1.61 inference(rewrite,[status(thm)],[])).
% 1.93/1.61 tff(2346,plain,
% 1.93/1.61 ((hskp16 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58))) <=> (hskp16 | c1_1(a58) | c3_1(a12) | (~ndr1_0) | (~c0_1(a12)) | (~c1_1(a12)) | (~c0_1(a58)) | (~c3_1(a58)))),
% 1.93/1.61 inference(rewrite,[status(thm)],[])).
% 1.93/1.61 tff(2347,plain,
% 1.93/1.61 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a58) | c3_1(a12) | (~ndr1_0) | (~c0_1(a12)) | (~c1_1(a12)) | (~c0_1(a58)) | (~c3_1(a58))))),
% 1.93/1.61 inference(monotonicity,[status(thm)],[2346])).
% 1.93/1.61 tff(2348,plain,
% 1.93/1.61 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a58) | c3_1(a12) | (~ndr1_0) | (~c0_1(a12)) | (~c1_1(a12)) | (~c0_1(a58)) | (~c3_1(a58)))),
% 1.93/1.61 inference(transitivity,[status(thm)],[2347, 2345])).
% 1.93/1.61 tff(2349,plain,
% 1.93/1.61 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))),
% 1.93/1.61 inference(quant_inst,[status(thm)],[])).
% 1.93/1.61 tff(2350,plain,
% 1.93/1.61 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a58) | c3_1(a12) | (~ndr1_0) | (~c0_1(a12)) | (~c1_1(a12)) | (~c0_1(a58)) | (~c3_1(a58))),
% 1.93/1.61 inference(modus_ponens,[status(thm)],[2349, 2348])).
% 1.93/1.61 tff(2351,plain,
% 1.93/1.61 (hskp16 | (~c0_1(a12))),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2350, 84, 2344, 2343, 2049, 2342, 2067, 2066])).
% 1.93/1.61 tff(2352,plain,
% 1.93/1.61 (hskp16),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2351, 2056])).
% 1.93/1.61 tff(2353,plain,
% 1.93/1.61 (~c1_1(a31)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2294, 2352])).
% 1.93/1.61 tff(2354,plain,
% 1.93/1.61 (~c0_1(a31)),
% 1.93/1.61 inference(unit_resolution,[status(thm)],[2252, 2352])).
% 1.93/1.61 tff(2355,plain,
% 1.93/1.61 (((~hskp17) | (~c0_1(a32))) <=> ((~hskp17) | (~c0_1(a32)))),
% 1.93/1.61 inference(rewrite,[status(thm)],[])).
% 1.93/1.61 tff(2356,plain,
% 1.93/1.61 (((~c0_1(a32)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a32)))),
% 1.93/1.61 inference(rewrite,[status(thm)],[])).
% 1.93/1.61 tff(2357,axiom,((~c0_1(a32)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.93/1.61 tff(2358,plain,
% 1.93/1.61 ((~hskp17) | (~c0_1(a32))),
% 1.93/1.61 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 1.93/1.61 tff(2359,plain,
% 1.93/1.61 ((~hskp17) | (~c0_1(a32))),
% 1.93/1.61 inference(modus_ponens,[status(thm)],[2358, 2355])).
% 1.93/1.62 tff(2360,plain,
% 1.93/1.62 (~c0_1(a32)),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[2359, 2000])).
% 1.93/1.62 tff(2361,plain,
% 1.93/1.62 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a36) | c3_1(a36) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a36) | c3_1(a36) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a36)))),
% 1.93/1.62 inference(rewrite,[status(thm)],[])).
% 1.93/1.62 tff(2362,plain,
% 1.93/1.62 ((hskp22 | (~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c1_1(a12)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36))) <=> (hskp22 | c2_1(a36) | c3_1(a36) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a36)))),
% 1.93/1.62 inference(rewrite,[status(thm)],[])).
% 1.93/1.62 tff(2363,plain,
% 1.93/1.62 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c1_1(a12)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a36) | c3_1(a36) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a36))))),
% 1.93/1.62 inference(monotonicity,[status(thm)],[2362])).
% 1.93/1.62 tff(2364,plain,
% 1.93/1.62 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c1_1(a12)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a36) | c3_1(a36) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a36)))),
% 1.93/1.62 inference(transitivity,[status(thm)],[2363, 2361])).
% 1.93/1.62 tff(2365,plain,
% 1.93/1.62 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c1_1(a12)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36)))),
% 1.93/1.62 inference(quant_inst,[status(thm)],[])).
% 1.93/1.62 tff(2366,plain,
% 1.93/1.62 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a36) | c3_1(a36) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a36))),
% 1.93/1.62 inference(modus_ponens,[status(thm)],[2365, 2364])).
% 1.93/1.62 tff(2367,plain,
% 1.93/1.62 (hskp22 | (~c0_1(a36))),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[2366, 84, 2049, 1974, 1993, 2048, 2067, 12])).
% 1.93/1.62 tff(2368,plain,
% 1.93/1.62 (hskp22),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[2367, 1982])).
% 1.93/1.62 tff(2369,plain,
% 1.93/1.62 (~c3_1(a43)),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[682, 2368])).
% 1.93/1.62 tff(2370,plain,
% 1.93/1.62 (~c1_1(a43)),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[688, 2368])).
% 1.93/1.62 tff(2371,plain,
% 1.93/1.62 (c2_1(a31)),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[2263, 2352])).
% 1.93/1.62 tff(2372,plain,
% 1.93/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a31) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c1_1(a32) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a31) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c1_1(a32) | (~c0_1(a43)))),
% 1.93/1.62 inference(rewrite,[status(thm)],[])).
% 1.93/1.62 tff(2373,plain,
% 1.93/1.62 (((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c1_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a31) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c1_1(a32) | (~c0_1(a43)))),
% 1.93/1.62 inference(rewrite,[status(thm)],[])).
% 1.93/1.62 tff(2374,plain,
% 1.93/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c1_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a31) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c1_1(a32) | (~c0_1(a43))))),
% 1.93/1.62 inference(monotonicity,[status(thm)],[2373])).
% 1.93/1.62 tff(2375,plain,
% 1.93/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c1_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a31) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c1_1(a32) | (~c0_1(a43)))),
% 1.93/1.62 inference(transitivity,[status(thm)],[2374, 2372])).
% 1.93/1.62 tff(2376,plain,
% 1.93/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c1_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a32) | c1_1(a32) | c0_1(a32))),
% 1.93/1.62 inference(quant_inst,[status(thm)],[])).
% 1.93/1.62 tff(2377,plain,
% 1.93/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a31) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c1_1(a32) | (~c0_1(a43))),
% 1.93/1.62 inference(modus_ponens,[status(thm)],[2376, 2375])).
% 1.93/1.62 tff(2378,plain,
% 1.93/1.62 (~c0_1(a43)),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[2377, 84, 2371, 2370, 2369, 2360, 2006, 2354, 2353, 2034, 2024])).
% 1.93/1.62 tff(2379,plain,
% 1.93/1.62 (c2_1(a43)),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[699, 2368])).
% 1.93/1.62 tff(2380,plain,
% 1.93/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a43) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)) | (~c2_1(a43)) | c0_1(a43))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)) | (~c2_1(a43)) | c0_1(a43))),
% 1.93/1.62 inference(rewrite,[status(thm)],[])).
% 1.93/1.62 tff(2381,plain,
% 1.93/1.62 (((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c1_1(a43) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)) | (~c2_1(a43)) | c0_1(a43))),
% 1.93/1.62 inference(rewrite,[status(thm)],[])).
% 1.93/1.62 tff(2382,plain,
% 1.93/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a43) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)) | (~c2_1(a43)) | c0_1(a43)))),
% 1.93/1.62 inference(monotonicity,[status(thm)],[2381])).
% 1.93/1.62 tff(2383,plain,
% 1.93/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)) | (~c2_1(a43)) | c0_1(a43))),
% 1.93/1.62 inference(transitivity,[status(thm)],[2382, 2380])).
% 1.93/1.62 tff(2384,plain,
% 1.93/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32))),
% 1.93/1.62 inference(quant_inst,[status(thm)],[])).
% 1.93/1.62 tff(2385,plain,
% 1.93/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)) | (~c2_1(a43)) | c0_1(a43)),
% 1.93/1.62 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 1.93/1.62 tff(2386,plain,
% 1.93/1.62 ($false),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[2385, 84, 2379, 2370, 1975, 1993, 2360, 2006, 2034, 2378, 1982, 2024])).
% 1.93/1.62 tff(2387,plain,(hskp1 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.93/1.62 tff(2388,plain,
% 1.93/1.62 (hskp1),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[2387, 134])).
% 1.93/1.62 tff(2389,plain,
% 1.93/1.62 (c0_1(a2)),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[633, 2388])).
% 1.93/1.62 tff(2390,plain,
% 1.93/1.62 (~c2_1(a2)),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[611, 2388])).
% 1.93/1.62 tff(2391,plain,
% 1.93/1.62 (c3_1(a2)),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[622, 2388])).
% 1.93/1.62 tff(2392,plain,
% 1.93/1.62 (~c1_1(a2)),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[2116, 84, 1882, 1904, 2389, 2391, 2390, 587, 1917])).
% 1.93/1.62 tff(2393,plain,
% 1.93/1.62 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a2) | (~c3_1(a2)))),
% 1.93/1.62 inference(rewrite,[status(thm)],[])).
% 1.93/1.62 tff(2394,plain,
% 1.93/1.62 ((hskp22 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2))) <=> (hskp22 | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a2) | (~c3_1(a2)))),
% 1.93/1.62 inference(rewrite,[status(thm)],[])).
% 1.93/1.62 tff(2395,plain,
% 1.93/1.62 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a2) | (~c3_1(a2))))),
% 1.93/1.62 inference(monotonicity,[status(thm)],[2394])).
% 1.93/1.62 tff(2396,plain,
% 1.93/1.62 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a2) | (~c3_1(a2)))),
% 1.93/1.62 inference(transitivity,[status(thm)],[2395, 2393])).
% 1.93/1.62 tff(2397,plain,
% 1.93/1.62 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))),
% 1.93/1.62 inference(quant_inst,[status(thm)],[])).
% 1.93/1.62 tff(2398,plain,
% 1.93/1.62 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a2) | (~c3_1(a2))),
% 1.93/1.62 inference(modus_ponens,[status(thm)],[2397, 2396])).
% 1.93/1.62 tff(2399,plain,
% 1.93/1.62 (hskp22),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[2398, 84, 1904, 1893, 2391, 2390, 123, 1917, 2392])).
% 1.93/1.62 tff(2400,plain,
% 1.93/1.62 (~c3_1(a43)),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[682, 2399])).
% 1.93/1.62 tff(2401,plain,
% 1.93/1.62 (~c1_1(a43)),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[688, 2399])).
% 1.93/1.62 tff(2402,plain,
% 1.93/1.62 (c2_1(a43)),
% 1.93/1.62 inference(unit_resolution,[status(thm)],[699, 2399])).
% 1.93/1.62 tff(2403,plain,
% 1.93/1.62 (hskp0),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[2334, 2402, 1904, 1917, 2390, 2401, 2400, 2392, 2389, 1882])).
% 1.93/1.63 tff(2404,plain,
% 1.93/1.63 (~c0_1(a1)),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[714, 2403])).
% 1.93/1.63 tff(2405,plain,
% 1.93/1.63 (c2_1(a1)),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[736, 2403])).
% 1.93/1.63 tff(2406,plain,
% 1.93/1.63 (c1_1(a1)),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[725, 2403])).
% 1.93/1.63 tff(2407,plain,
% 1.93/1.63 ($false),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[783, 84, 2402, 2389, 2391, 2406, 2405, 2401, 2400, 2390, 2404, 133])).
% 1.93/1.63 tff(2408,plain,(hskp18), inference(lemma,lemma(discharge,[]))).
% 1.93/1.63 tff(2409,plain,
% 1.93/1.63 (((~hskp18) | (~c2_1(a34))) <=> ((~hskp18) | (~c2_1(a34)))),
% 1.93/1.63 inference(rewrite,[status(thm)],[])).
% 1.93/1.63 tff(2410,plain,
% 1.93/1.63 (((~c2_1(a34)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a34)))),
% 1.93/1.63 inference(rewrite,[status(thm)],[])).
% 1.93/1.63 tff(2411,axiom,((~c2_1(a34)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.93/1.63 tff(2412,plain,
% 1.93/1.63 ((~hskp18) | (~c2_1(a34))),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2411, 2410])).
% 1.93/1.63 tff(2413,plain,
% 1.93/1.63 ((~hskp18) | (~c2_1(a34))),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2412, 2409])).
% 1.93/1.63 tff(2414,plain,
% 1.93/1.63 (~c2_1(a34)),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[2413, 2408])).
% 1.93/1.63 tff(2415,plain,
% 1.93/1.63 (((~hskp18) | (~c1_1(a34))) <=> ((~hskp18) | (~c1_1(a34)))),
% 1.93/1.63 inference(rewrite,[status(thm)],[])).
% 1.93/1.63 tff(2416,plain,
% 1.93/1.63 (((~c1_1(a34)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a34)))),
% 1.93/1.63 inference(rewrite,[status(thm)],[])).
% 1.93/1.63 tff(2417,axiom,((~c1_1(a34)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.93/1.63 tff(2418,plain,
% 1.93/1.63 ((~hskp18) | (~c1_1(a34))),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2417, 2416])).
% 1.93/1.63 tff(2419,plain,
% 1.93/1.63 ((~hskp18) | (~c1_1(a34))),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2418, 2415])).
% 1.93/1.63 tff(2420,plain,
% 1.93/1.63 (~c1_1(a34)),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[2419, 2408])).
% 1.93/1.63 tff(2421,plain,
% 1.93/1.63 (hskp19),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[2157, 1, 1406])).
% 1.93/1.63 tff(2422,plain,
% 1.93/1.63 (~c3_1(a36)),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[1274, 2421])).
% 1.93/1.63 tff(2423,plain,
% 1.93/1.63 (~c1_1(a36)),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[1286, 2421])).
% 1.93/1.63 tff(2424,plain,
% 1.93/1.63 (((~hskp18) | c3_1(a34)) <=> ((~hskp18) | c3_1(a34))),
% 1.93/1.63 inference(rewrite,[status(thm)],[])).
% 1.93/1.63 tff(2425,axiom,((~hskp18) | c3_1(a34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.93/1.63 tff(2426,plain,
% 1.93/1.63 ((~hskp18) | c3_1(a34)),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2425, 2424])).
% 1.93/1.63 tff(2427,plain,
% 1.93/1.63 ((~hskp18) | c3_1(a34)),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2426, 2424])).
% 1.93/1.63 tff(2428,plain,
% 1.93/1.63 ((~hskp18) | c3_1(a34)),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2427, 2424])).
% 1.93/1.63 tff(2429,plain,
% 1.93/1.63 ((~hskp18) | c3_1(a34)),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2428, 2424])).
% 1.93/1.63 tff(2430,plain,
% 1.93/1.63 ((~hskp18) | c3_1(a34)),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2429, 2424])).
% 1.93/1.63 tff(2431,plain,
% 1.93/1.63 ((~hskp18) | c3_1(a34)),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2430, 2424])).
% 1.93/1.63 tff(2432,plain,
% 1.93/1.63 ((~hskp18) | c3_1(a34)),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2431, 2424])).
% 1.93/1.63 tff(2433,plain,
% 1.93/1.63 ((~hskp18) | c3_1(a34)),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2432, 2424])).
% 1.93/1.63 tff(2434,plain,
% 1.93/1.63 (c3_1(a34)),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[2433, 2408])).
% 1.93/1.63 tff(2435,plain,
% 1.93/1.63 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a34)))),
% 1.93/1.63 inference(rewrite,[status(thm)],[])).
% 1.93/1.63 tff(2436,plain,
% 1.93/1.63 ((hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34))) <=> (hskp22 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a34)))),
% 1.93/1.63 inference(rewrite,[status(thm)],[])).
% 1.93/1.63 tff(2437,plain,
% 1.93/1.63 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a34))))),
% 1.93/1.63 inference(monotonicity,[status(thm)],[2436])).
% 1.93/1.63 tff(2438,plain,
% 1.93/1.63 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a34)))),
% 1.93/1.63 inference(transitivity,[status(thm)],[2437, 2435])).
% 1.93/1.63 tff(2439,plain,
% 1.93/1.63 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))),
% 1.93/1.63 inference(quant_inst,[status(thm)],[])).
% 1.93/1.63 tff(2440,plain,
% 1.93/1.63 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a34))),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2439, 2438])).
% 1.93/1.63 tff(2441,plain,
% 1.93/1.63 ($false),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[2440, 1, 84, 2434, 213, 202, 2420, 2414, 162, 123])).
% 1.93/1.63 tff(2442,plain,((~hskp4) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.93/1.63 tff(2443,plain,
% 1.93/1.63 (~hskp4),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[2442, 1])).
% 1.93/1.63 tff(2444,plain,
% 1.93/1.63 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | c0_1(a36))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | c0_1(a36))),
% 1.93/1.63 inference(rewrite,[status(thm)],[])).
% 1.93/1.63 tff(2445,plain,
% 1.93/1.63 ((hskp4 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c0_1(a36)) <=> (hskp4 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | c0_1(a36))),
% 1.93/1.63 inference(rewrite,[status(thm)],[])).
% 1.93/1.63 tff(2446,plain,
% 1.93/1.63 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c0_1(a36))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | c0_1(a36)))),
% 1.93/1.63 inference(monotonicity,[status(thm)],[2445])).
% 1.93/1.63 tff(2447,plain,
% 1.93/1.63 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c0_1(a36))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | c0_1(a36))),
% 1.93/1.63 inference(transitivity,[status(thm)],[2446, 2444])).
% 1.93/1.63 tff(2448,plain,
% 1.93/1.63 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c0_1(a36))),
% 1.93/1.63 inference(quant_inst,[status(thm)],[])).
% 1.93/1.63 tff(2449,plain,
% 1.93/1.63 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | c0_1(a36)),
% 1.93/1.63 inference(modus_ponens,[status(thm)],[2448, 2447])).
% 1.93/1.63 tff(2450,plain,
% 1.93/1.63 (c0_1(a36)),
% 1.93/1.63 inference(unit_resolution,[status(thm)],[2449, 84, 2443, 2423, 2422, 113])).
% 1.93/1.63 tff(2451,plain,
% 1.93/1.63 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a34)))),
% 1.93/1.63 inference(rewrite,[status(thm)],[])).
% 1.93/1.63 tff(2452,plain,
% 1.93/1.63 ((hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34))) <=> (hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a34)))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(2453,plain,
% 2.01/1.63 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a34))))),
% 2.01/1.63 inference(monotonicity,[status(thm)],[2452])).
% 2.01/1.63 tff(2454,plain,
% 2.01/1.63 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a34)))),
% 2.01/1.63 inference(transitivity,[status(thm)],[2453, 2451])).
% 2.01/1.63 tff(2455,plain,
% 2.01/1.63 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))),
% 2.01/1.63 inference(quant_inst,[status(thm)],[])).
% 2.01/1.63 tff(2456,plain,
% 2.01/1.63 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a34))),
% 2.01/1.63 inference(modus_ponens,[status(thm)],[2455, 2454])).
% 2.01/1.63 tff(2457,plain,
% 2.01/1.63 (hskp0),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[2456, 84, 2434, 44, 33, 2420, 2414, 22, 651])).
% 2.01/1.63 tff(2458,plain,
% 2.01/1.63 (~c0_1(a1)),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[714, 2457])).
% 2.01/1.63 tff(2459,plain,
% 2.01/1.63 (~c2_1(a36)),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[1280, 2421])).
% 2.01/1.63 tff(2460,plain,
% 2.01/1.63 (hskp17),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[1999, 84, 2423, 2459, 2422, 1992, 2450])).
% 2.01/1.63 tff(2461,plain,
% 2.01/1.63 (~c2_1(a32)),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[2005, 2460])).
% 2.01/1.63 tff(2462,plain,
% 2.01/1.63 (~c0_1(a32)),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[2359, 2460])).
% 2.01/1.63 tff(2463,plain,
% 2.01/1.63 (c2_1(a1)),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[736, 2457])).
% 2.01/1.63 tff(2464,plain,
% 2.01/1.63 (c1_1(a1)),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[725, 2457])).
% 2.01/1.63 tff(2465,plain,
% 2.01/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a36)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a36)))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(2466,plain,
% 2.01/1.63 (((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32))) <=> (c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a36)))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(2467,plain,
% 2.01/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a36))))),
% 2.01/1.64 inference(monotonicity,[status(thm)],[2466])).
% 2.01/1.64 tff(2468,plain,
% 2.01/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a36)))),
% 2.01/1.64 inference(transitivity,[status(thm)],[2467, 2465])).
% 2.01/1.64 tff(2469,plain,
% 2.01/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32)))),
% 2.01/1.64 inference(quant_inst,[status(thm)],[])).
% 2.01/1.64 tff(2470,plain,
% 2.01/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a36))),
% 2.01/1.64 inference(modus_ponens,[status(thm)],[2469, 2468])).
% 2.01/1.64 tff(2471,plain,
% 2.01/1.64 (~c1_1(a32)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[2470, 84, 2464, 2463, 2423, 2422, 2462, 2461, 2458, 2044, 2450])).
% 2.01/1.64 tff(2472,plain,
% 2.01/1.64 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a36) | c2_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a36) | c2_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(2473,plain,
% 2.01/1.64 (((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c1_1(a36) | c2_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(2474,plain,
% 2.01/1.64 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a36) | c2_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36))))),
% 2.01/1.64 inference(monotonicity,[status(thm)],[2473])).
% 2.01/1.64 tff(2475,plain,
% 2.01/1.64 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a36) | c2_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)))),
% 2.01/1.64 inference(transitivity,[status(thm)],[2474, 2472])).
% 2.01/1.64 tff(2476,plain,
% 2.01/1.64 ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a32) | c1_1(a32) | c0_1(a32))),
% 2.01/1.64 inference(quant_inst,[status(thm)],[])).
% 2.01/1.64 tff(2477,plain,
% 2.01/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a36) | c2_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36))),
% 2.01/1.64 inference(modus_ponens,[status(thm)],[2476, 2475])).
% 2.01/1.64 tff(2478,plain,
% 2.01/1.64 ($false),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[2477, 84, 2423, 2459, 2422, 2462, 2461, 959, 2450, 2471])).
% 2.01/1.64 tff(2479,plain,(hskp22 | hskp24), inference(lemma,lemma(discharge,[]))).
% 2.01/1.64 tff(2480,plain,
% 2.01/1.64 (hskp22),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[2479, 1406])).
% 2.01/1.64 tff(2481,plain,
% 2.01/1.64 (c2_1(a43)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[699, 2480])).
% 2.01/1.64 tff(2482,plain,
% 2.01/1.64 (~c3_1(a43)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[682, 2480])).
% 2.01/1.64 tff(2483,plain,
% 2.01/1.64 (~c1_1(a43)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[688, 2480])).
% 2.01/1.64 tff(2484,assumption,(hskp1), introduced(assumption)).
% 2.01/1.64 tff(2485,plain,
% 2.01/1.64 (c3_1(a2)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[622, 2484])).
% 2.01/1.64 tff(2486,plain,
% 2.01/1.64 (~c2_1(a2)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[611, 2484])).
% 2.01/1.64 tff(2487,plain,
% 2.01/1.64 (c0_1(a2)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[633, 2484])).
% 2.01/1.64 tff(2488,assumption,(c3_1(a2)), introduced(assumption)).
% 2.01/1.64 tff(2489,plain,
% 2.01/1.64 (~hskp21),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1676, 1585, 1586, 1587, 1672])).
% 2.01/1.64 tff(2490,plain,
% 2.01/1.64 ((~c1_1(a2)) | (~c0_1(a43))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1685, 84, 1586, 2315, 2488, 1672, 2314, 587])).
% 2.01/1.64 tff(2491,plain,
% 2.01/1.64 (~c1_1(a2)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[2490, 1585])).
% 2.01/1.64 tff(2492,plain,
% 2.01/1.64 ($false),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[2316, 2491, 2489, 588])).
% 2.01/1.64 tff(2493,plain,((~c0_1(a43)) | hskp0 | (~c0_1(a2)) | c2_1(a2) | (~c2_1(a43)) | (~c3_1(a2)) | c1_1(a43) | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.64 tff(2494,plain,
% 2.01/1.64 (~c0_1(a43)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[2493, 588, 2315, 2314, 1586, 2488, 1672, 1587])).
% 2.01/1.64 tff(2495,plain,
% 2.01/1.64 (hskp5),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[2319, 2494, 588])).
% 2.01/1.64 tff(2496,plain,
% 2.01/1.64 (~c3_1(a6)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1115, 2495])).
% 2.01/1.64 tff(2497,plain,
% 2.01/1.64 (c0_1(a6)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[274, 2495])).
% 2.01/1.64 tff(2498,plain,
% 2.01/1.64 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | (~c1_1(a6)) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | (~c1_1(a6)) | (~c3_1(a34)))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(2499,plain,
% 2.01/1.64 ((hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34))) <=> (hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | (~c1_1(a6)) | (~c3_1(a34)))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(2500,plain,
% 2.01/1.64 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | (~c1_1(a6)) | (~c3_1(a34))))),
% 2.01/1.64 inference(monotonicity,[status(thm)],[2499])).
% 2.01/1.64 tff(2501,plain,
% 2.01/1.64 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | (~c1_1(a6)) | (~c3_1(a34)))),
% 2.01/1.64 inference(transitivity,[status(thm)],[2500, 2498])).
% 2.01/1.64 tff(2502,plain,
% 2.01/1.64 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))),
% 2.01/1.64 inference(quant_inst,[status(thm)],[])).
% 2.01/1.64 tff(2503,plain,
% 2.01/1.64 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | (~c1_1(a6)) | (~c3_1(a34))),
% 2.01/1.64 inference(modus_ponens,[status(thm)],[2502, 2501])).
% 2.01/1.64 tff(2504,plain,
% 2.01/1.64 (~c1_1(a6)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[2503, 84, 588, 2434, 2497, 2420, 2414, 2496, 651])).
% 2.01/1.64 tff(2505,plain,
% 2.01/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a43) | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | c1_1(a6) | c0_1(a34) | (~c2_1(a43)) | c0_1(a43))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | c1_1(a6) | c0_1(a34) | (~c2_1(a43)) | c0_1(a43))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(2506,plain,
% 2.01/1.64 (((~ndr1_0) | c3_1(a6) | c1_1(a6) | (~c0_1(a6)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34)) <=> (c1_1(a43) | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | c1_1(a6) | c0_1(a34) | (~c2_1(a43)) | c0_1(a43))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(2507,plain,
% 2.01/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a6) | c1_1(a6) | (~c0_1(a6)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a43) | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | c1_1(a6) | c0_1(a34) | (~c2_1(a43)) | c0_1(a43)))),
% 2.01/1.64 inference(monotonicity,[status(thm)],[2506])).
% 2.01/1.64 tff(2508,plain,
% 2.01/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a6) | c1_1(a6) | (~c0_1(a6)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | c1_1(a6) | c0_1(a34) | (~c2_1(a43)) | c0_1(a43))),
% 2.01/1.64 inference(transitivity,[status(thm)],[2507, 2505])).
% 2.01/1.64 tff(2509,plain,
% 2.01/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a6) | c1_1(a6) | (~c0_1(a6)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34))),
% 2.01/1.64 inference(quant_inst,[status(thm)],[])).
% 2.01/1.64 tff(2510,plain,
% 2.01/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | c1_1(a6) | c0_1(a34) | (~c2_1(a43)) | c0_1(a43)),
% 2.01/1.64 inference(modus_ponens,[status(thm)],[2509, 2508])).
% 2.01/1.64 tff(2511,plain,
% 2.01/1.64 (c1_1(a6) | c0_1(a34)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[2510, 84, 1586, 2497, 1672, 2420, 2414, 2496, 2034, 2494])).
% 2.01/1.64 tff(2512,plain,
% 2.01/1.64 (c0_1(a34)),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[2511, 2504])).
% 2.01/1.64 tff(2513,plain,
% 2.01/1.64 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c0_1(a34)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c0_1(a34)))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(2514,plain,
% 2.01/1.64 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a34) | c2_1(a34) | (~c0_1(a34))) <=> (hskp21 | hskp0 | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c0_1(a34)))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(2515,plain,
% 2.01/1.64 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a34) | c2_1(a34) | (~c0_1(a34)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c0_1(a34))))),
% 2.01/1.65 inference(monotonicity,[status(thm)],[2514])).
% 2.01/1.65 tff(2516,plain,
% 2.01/1.65 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a34) | c2_1(a34) | (~c0_1(a34)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c0_1(a34)))),
% 2.01/1.65 inference(transitivity,[status(thm)],[2515, 2513])).
% 2.01/1.65 tff(2517,plain,
% 2.01/1.65 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a34) | c2_1(a34) | (~c0_1(a34)))),
% 2.01/1.65 inference(quant_inst,[status(thm)],[])).
% 2.01/1.65 tff(2518,plain,
% 2.01/1.65 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c0_1(a34))),
% 2.01/1.65 inference(modus_ponens,[status(thm)],[2517, 2516])).
% 2.01/1.65 tff(2519,plain,
% 2.01/1.65 (hskp21 | hskp0 | (~c0_1(a34))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[2518, 84, 2420, 2414, 1203])).
% 2.01/1.65 tff(2520,plain,
% 2.01/1.65 (hskp21),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[2519, 2512, 588])).
% 2.01/1.65 tff(2521,plain,
% 2.01/1.65 (~c0_1(a42)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1216, 2520])).
% 2.01/1.65 tff(2522,plain,
% 2.01/1.65 (c2_1(a6)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[285, 2495])).
% 2.01/1.65 tff(2523,plain,
% 2.01/1.65 (c3_1(a42)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1227, 2520])).
% 2.01/1.65 tff(2524,plain,
% 2.01/1.65 (c2_1(a42)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1238, 2520])).
% 2.01/1.65 tff(2525,plain,
% 2.01/1.65 ($false),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[2145, 84, 2524, 2523, 2497, 2522, 2521, 2496, 103, 2504])).
% 2.01/1.65 tff(2526,plain,(hskp0 | (~c2_1(a43)) | c1_1(a43) | (~c0_1(a2)) | c2_1(a2) | (~c3_1(a2)) | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.65 tff(2527,plain,
% 2.01/1.65 (hskp0),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[2526, 2487, 1672, 1586, 2486, 2485, 1587])).
% 2.01/1.65 tff(2528,plain,
% 2.01/1.65 (~c0_1(a1)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[714, 2527])).
% 2.01/1.65 tff(2529,plain,
% 2.01/1.65 (c2_1(a1)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[736, 2527])).
% 2.01/1.65 tff(2530,plain,
% 2.01/1.65 (c1_1(a1)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[725, 2527])).
% 2.01/1.65 tff(2531,plain,
% 2.01/1.65 ($false),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[783, 84, 1586, 2487, 2485, 2530, 2529, 1672, 1587, 2486, 2528, 133])).
% 2.01/1.65 tff(2532,plain,((~hskp1) | (~c2_1(a43)) | c1_1(a43) | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.65 tff(2533,plain,
% 2.01/1.65 (~hskp1),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[2532, 2481, 2483, 2482])).
% 2.01/1.65 tff(2534,plain,
% 2.01/1.65 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a43) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a43) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a43)) | (~c0_1(a43)))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(2535,plain,
% 2.01/1.65 ((hskp1 | (~ndr1_0) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34)) <=> (hskp1 | c1_1(a43) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a43)) | (~c0_1(a43)))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(2536,plain,
% 2.01/1.65 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a43) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a43)) | (~c0_1(a43))))),
% 2.01/1.65 inference(monotonicity,[status(thm)],[2535])).
% 2.01/1.65 tff(2537,plain,
% 2.01/1.65 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a43) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a43)) | (~c0_1(a43)))),
% 2.01/1.65 inference(transitivity,[status(thm)],[2536, 2534])).
% 2.01/1.65 tff(2538,plain,
% 2.01/1.65 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34))),
% 2.01/1.65 inference(quant_inst,[status(thm)],[])).
% 2.01/1.65 tff(2539,plain,
% 2.01/1.65 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a43) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a43)) | (~c0_1(a43))),
% 2.01/1.65 inference(modus_ponens,[status(thm)],[2538, 2537])).
% 2.01/1.65 tff(2540,plain,
% 2.01/1.65 (hskp1 | c0_1(a34) | (~c0_1(a43))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[2539, 84, 1586, 1672, 2420, 2414, 749])).
% 2.01/1.65 tff(2541,plain,
% 2.01/1.65 (c0_1(a34)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[2540, 1585, 1502])).
% 2.01/1.65 tff(2542,plain,
% 2.01/1.65 ($false),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[2519, 2541, 2489, 588])).
% 2.01/1.65 tff(2543,plain,((~c0_1(a43)) | hskp0 | hskp1 | (~c2_1(a43)) | c1_1(a43) | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.65 tff(2544,plain,
% 2.01/1.65 (~c0_1(a43)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[2543, 588, 1502, 1586, 1672, 1587])).
% 2.01/1.65 tff(2545,plain,
% 2.01/1.65 (hskp4),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[2169, 2544])).
% 2.01/1.65 tff(2546,plain,
% 2.01/1.65 (~c1_1(a5)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[161, 2545])).
% 2.01/1.65 tff(2547,plain,
% 2.01/1.65 (c3_1(a5)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[201, 2545])).
% 2.01/1.65 tff(2548,plain,
% 2.01/1.65 (c2_1(a5)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[212, 2545])).
% 2.01/1.65 tff(2549,plain,
% 2.01/1.65 ($false),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[604, 84, 1502, 588, 2548, 2547, 2546, 598])).
% 2.01/1.65 tff(2550,plain,(hskp0 | hskp1 | c1_1(a43) | c3_1(a43) | (~c2_1(a43))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.65 tff(2551,plain,
% 2.01/1.65 (hskp0),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[2550, 2533, 2483, 2482, 2481])).
% 2.01/1.65 tff(2552,plain,
% 2.01/1.65 (~c0_1(a1)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[714, 2551])).
% 2.01/1.65 tff(2553,plain,
% 2.01/1.65 (c1_1(a1)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[725, 2551])).
% 2.01/1.65 tff(2554,plain,
% 2.01/1.65 (c2_1(a1)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[736, 2551])).
% 2.01/1.65 tff(2555,plain,
% 2.01/1.65 (hskp4),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[2173, 2554, 1406, 2482, 2481, 2483, 2553, 2552])).
% 2.01/1.65 tff(2556,plain,
% 2.01/1.65 (c2_1(a5)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[212, 2555])).
% 2.01/1.65 tff(2557,plain,
% 2.01/1.65 (c3_1(a5)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[201, 2555])).
% 2.01/1.65 tff(2558,plain,
% 2.01/1.65 (~c1_1(a5)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[161, 2555])).
% 2.01/1.65 tff(2559,plain,
% 2.01/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c2_1(a34) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a34)) | (~c0_1(a34)) | (~c2_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a34) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a34)) | (~c0_1(a34)) | (~c2_1(a43)))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(2560,plain,
% 2.01/1.65 (((~ndr1_0) | c2_1(a34) | (~c3_1(a34)) | (~c0_1(a34)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1))) <=> (c1_1(a43) | c3_1(a43) | c2_1(a34) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a34)) | (~c0_1(a34)) | (~c2_1(a43)))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(2561,plain,
% 2.01/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a34) | (~c3_1(a34)) | (~c0_1(a34)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c2_1(a34) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a34)) | (~c0_1(a34)) | (~c2_1(a43))))),
% 2.01/1.65 inference(monotonicity,[status(thm)],[2560])).
% 2.01/1.65 tff(2562,plain,
% 2.01/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a34) | (~c3_1(a34)) | (~c0_1(a34)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a34) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a34)) | (~c0_1(a34)) | (~c2_1(a43)))),
% 2.01/1.65 inference(transitivity,[status(thm)],[2561, 2559])).
% 2.01/1.65 tff(2563,plain,
% 2.01/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a34) | (~c3_1(a34)) | (~c0_1(a34)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))),
% 2.01/1.65 inference(quant_inst,[status(thm)],[])).
% 2.01/1.65 tff(2564,plain,
% 2.01/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a34) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a34)) | (~c0_1(a34)) | (~c2_1(a43))),
% 2.01/1.65 inference(modus_ponens,[status(thm)],[2563, 2562])).
% 2.01/1.65 tff(2565,plain,
% 2.01/1.65 (~c0_1(a34)),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[2564, 84, 2481, 2434, 2553, 2554, 2483, 2482, 2414, 2552, 133])).
% 2.01/1.65 tff(2566,plain,
% 2.01/1.65 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a34))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(2567,plain,
% 2.01/1.65 ((hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a34) | c1_1(a34) | c0_1(a34)) <=> (hskp1 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a34))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(2568,plain,
% 2.01/1.65 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a34)))),
% 2.01/1.65 inference(monotonicity,[status(thm)],[2567])).
% 2.01/1.65 tff(2569,plain,
% 2.01/1.65 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a34))),
% 2.01/1.65 inference(transitivity,[status(thm)],[2568, 2566])).
% 2.01/1.65 tff(2570,plain,
% 2.01/1.65 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a34) | c1_1(a34) | c0_1(a34))),
% 2.01/1.65 inference(quant_inst,[status(thm)],[])).
% 2.01/1.65 tff(2571,plain,
% 2.01/1.65 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a34)),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2570, 2569])).
% 2.01/1.66 tff(2572,plain,
% 2.01/1.66 ((~c0_1(a5)) | c0_1(a34)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2571, 84, 2533, 2556, 2420, 2414, 2558, 749])).
% 2.01/1.66 tff(2573,plain,
% 2.01/1.66 (~c0_1(a5)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2572, 2565])).
% 2.01/1.66 tff(2574,assumption,(hskp2), introduced(assumption)).
% 2.01/1.66 tff(2575,plain,
% 2.01/1.66 (~c1_1(a3)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[168, 2574])).
% 2.01/1.66 tff(2576,plain,
% 2.01/1.66 (c0_1(a3)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[190, 2574])).
% 2.01/1.66 tff(2577,plain,
% 2.01/1.66 (c2_1(a3)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[179, 2574])).
% 2.01/1.66 tff(2578,plain,
% 2.01/1.66 ($false),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[1308, 2577, 2576, 256, 214, 242, 2575, 257])).
% 2.01/1.66 tff(2579,plain,((~hskp2) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.66 tff(2580,plain,
% 2.01/1.66 (~hskp2),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2579, 2573, 2558, 2557, 2556])).
% 2.01/1.66 tff(2581,plain,
% 2.01/1.66 ((hskp24 | hskp23 | hskp2) <=> (hskp24 | hskp23 | hskp2)),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(2582,plain,
% 2.01/1.66 (((hskp2 | hskp24) | hskp23) <=> (hskp24 | hskp23 | hskp2)),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(2583,axiom,((hskp2 | hskp24) | hskp23), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 2.01/1.66 tff(2584,plain,
% 2.01/1.66 (hskp24 | hskp23 | hskp2),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2583, 2582])).
% 2.01/1.66 tff(2585,plain,
% 2.01/1.66 (hskp24 | hskp23 | hskp2),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2584, 2581])).
% 2.01/1.66 tff(2586,plain,
% 2.01/1.66 (hskp24 | hskp23 | hskp2),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2585, 2581])).
% 2.01/1.66 tff(2587,plain,
% 2.01/1.66 (hskp24 | hskp23 | hskp2),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2586, 2581])).
% 2.01/1.66 tff(2588,plain,
% 2.01/1.66 (hskp24 | hskp23 | hskp2),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2587, 2581])).
% 2.01/1.66 tff(2589,plain,
% 2.01/1.66 (hskp24 | hskp23 | hskp2),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2588, 2581])).
% 2.01/1.66 tff(2590,plain,
% 2.01/1.66 (hskp24 | hskp23 | hskp2),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2589, 2581])).
% 2.01/1.66 tff(2591,plain,
% 2.01/1.66 (hskp24 | hskp23 | hskp2),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2590, 2581])).
% 2.01/1.66 tff(2592,plain,
% 2.01/1.66 (hskp23),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2591, 2580, 1406])).
% 2.01/1.66 tff(2593,plain,
% 2.01/1.66 (((~hskp23) | (~c2_1(a52))) <=> ((~hskp23) | (~c2_1(a52)))),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(2594,plain,
% 2.01/1.66 (((~c2_1(a52)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a52)))),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(2595,axiom,((~c2_1(a52)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 2.01/1.66 tff(2596,plain,
% 2.01/1.66 ((~hskp23) | (~c2_1(a52))),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2595, 2594])).
% 2.01/1.66 tff(2597,plain,
% 2.01/1.66 ((~hskp23) | (~c2_1(a52))),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2596, 2593])).
% 2.01/1.66 tff(2598,plain,
% 2.01/1.66 (~c2_1(a52)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2597, 2592])).
% 2.01/1.66 tff(2599,plain,
% 2.01/1.66 (((~hskp23) | c0_1(a52)) <=> ((~hskp23) | c0_1(a52))),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(2600,axiom,((~hskp23) | c0_1(a52)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 2.01/1.66 tff(2601,plain,
% 2.01/1.66 ((~hskp23) | c0_1(a52)),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2600, 2599])).
% 2.01/1.66 tff(2602,plain,
% 2.01/1.66 ((~hskp23) | c0_1(a52)),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2601, 2599])).
% 2.01/1.66 tff(2603,plain,
% 2.01/1.66 ((~hskp23) | c0_1(a52)),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2602, 2599])).
% 2.01/1.66 tff(2604,plain,
% 2.01/1.66 ((~hskp23) | c0_1(a52)),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2603, 2599])).
% 2.01/1.66 tff(2605,plain,
% 2.01/1.66 ((~hskp23) | c0_1(a52)),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2604, 2599])).
% 2.01/1.66 tff(2606,plain,
% 2.01/1.66 ((~hskp23) | c0_1(a52)),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2605, 2599])).
% 2.01/1.66 tff(2607,plain,
% 2.01/1.66 ((~hskp23) | c0_1(a52)),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2606, 2599])).
% 2.01/1.66 tff(2608,plain,
% 2.01/1.66 ((~hskp23) | c0_1(a52)),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2607, 2599])).
% 2.01/1.66 tff(2609,plain,
% 2.01/1.66 (c0_1(a52)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2608, 2592])).
% 2.01/1.66 tff(2610,plain,
% 2.01/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a52) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | (~c3_1(a52)) | (~c0_1(a52)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a52) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | (~c3_1(a52)) | (~c0_1(a52)))),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(2611,plain,
% 2.01/1.66 (((~ndr1_0) | c2_1(a52) | (~c3_1(a52)) | (~c0_1(a52)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1))) <=> (c2_1(a52) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | (~c3_1(a52)) | (~c0_1(a52)))),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(2612,plain,
% 2.01/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a52) | (~c3_1(a52)) | (~c0_1(a52)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a52) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | (~c3_1(a52)) | (~c0_1(a52))))),
% 2.01/1.66 inference(monotonicity,[status(thm)],[2611])).
% 2.01/1.66 tff(2613,plain,
% 2.01/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a52) | (~c3_1(a52)) | (~c0_1(a52)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a52) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | (~c3_1(a52)) | (~c0_1(a52)))),
% 2.01/1.66 inference(transitivity,[status(thm)],[2612, 2610])).
% 2.01/1.66 tff(2614,plain,
% 2.01/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a52) | (~c3_1(a52)) | (~c0_1(a52)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))),
% 2.01/1.66 inference(quant_inst,[status(thm)],[])).
% 2.01/1.66 tff(2615,plain,
% 2.01/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a52) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | (~c3_1(a52)) | (~c0_1(a52))),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2614, 2613])).
% 2.01/1.66 tff(2616,plain,
% 2.01/1.66 (~c3_1(a52)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2615, 84, 2609, 2481, 2553, 2554, 2598, 2483, 2482, 2552, 133])).
% 2.01/1.66 tff(2617,plain,
% 2.01/1.66 (hskp0),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2550, 1502, 2483, 2482, 2481])).
% 2.01/1.66 tff(2618,plain,
% 2.01/1.66 (~c0_1(a1)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[714, 2617])).
% 2.01/1.66 tff(2619,plain,
% 2.01/1.66 (c1_1(a1)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[725, 2617])).
% 2.01/1.66 tff(2620,plain,
% 2.01/1.66 (c2_1(a1)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[736, 2617])).
% 2.01/1.66 tff(2621,plain,
% 2.01/1.66 (hskp4),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2173, 2620, 1406, 2482, 2481, 2483, 2619, 2618])).
% 2.01/1.66 tff(2622,plain,
% 2.01/1.66 (c2_1(a5)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[212, 2621])).
% 2.01/1.66 tff(2623,plain,
% 2.01/1.66 (~c0_1(a34)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2564, 84, 2481, 2434, 2619, 2620, 2483, 2482, 2414, 2618, 133])).
% 2.01/1.66 tff(2624,plain,
% 2.01/1.66 (~c1_1(a5)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[161, 2621])).
% 2.01/1.66 tff(2625,plain,
% 2.01/1.66 ((~c0_1(a5)) | c0_1(a34)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2571, 84, 1502, 2622, 2420, 2414, 2624, 749])).
% 2.01/1.66 tff(2626,plain,
% 2.01/1.66 (~c0_1(a5)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2625, 2623])).
% 2.01/1.66 tff(2627,plain,
% 2.01/1.66 (c3_1(a5)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[201, 2621])).
% 2.01/1.66 tff(2628,plain,
% 2.01/1.66 (~hskp2),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2579, 2627, 2624, 2626, 2622])).
% 2.01/1.66 tff(2629,plain,
% 2.01/1.66 (hskp23),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2591, 2628, 1406])).
% 2.01/1.66 tff(2630,plain,
% 2.01/1.66 (~c2_1(a52)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2597, 2629])).
% 2.01/1.66 tff(2631,plain,
% 2.01/1.66 (((~hskp23) | (~c1_1(a52))) <=> ((~hskp23) | (~c1_1(a52)))),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(2632,plain,
% 2.01/1.66 (((~c1_1(a52)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a52)))),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(2633,axiom,((~c1_1(a52)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 2.01/1.66 tff(2634,plain,
% 2.01/1.66 ((~hskp23) | (~c1_1(a52))),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2633, 2632])).
% 2.01/1.66 tff(2635,plain,
% 2.01/1.66 ((~hskp23) | (~c1_1(a52))),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2634, 2631])).
% 2.01/1.66 tff(2636,plain,
% 2.01/1.66 (~c1_1(a52)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2635, 2629])).
% 2.01/1.66 tff(2637,plain,
% 2.01/1.66 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | c1_1(a52) | c2_1(a52) | (~ndr1_0) | c3_1(a52))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp19 | hskp1 | c1_1(a52) | c2_1(a52) | (~ndr1_0) | c3_1(a52))),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(2638,plain,
% 2.01/1.66 ((hskp19 | hskp1 | (~ndr1_0) | c3_1(a52) | c1_1(a52) | c2_1(a52)) <=> (hskp19 | hskp1 | c1_1(a52) | c2_1(a52) | (~ndr1_0) | c3_1(a52))),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(2639,plain,
% 2.01/1.66 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | (~ndr1_0) | c3_1(a52) | c1_1(a52) | c2_1(a52))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | c1_1(a52) | c2_1(a52) | (~ndr1_0) | c3_1(a52)))),
% 2.01/1.66 inference(monotonicity,[status(thm)],[2638])).
% 2.01/1.66 tff(2640,plain,
% 2.01/1.66 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | (~ndr1_0) | c3_1(a52) | c1_1(a52) | c2_1(a52))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp19 | hskp1 | c1_1(a52) | c2_1(a52) | (~ndr1_0) | c3_1(a52))),
% 2.01/1.66 inference(transitivity,[status(thm)],[2639, 2637])).
% 2.01/1.66 tff(2641,plain,
% 2.01/1.66 ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | (~ndr1_0) | c3_1(a52) | c1_1(a52) | c2_1(a52))),
% 2.01/1.66 inference(quant_inst,[status(thm)],[])).
% 2.01/1.66 tff(2642,plain,
% 2.01/1.66 ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp19 | hskp1 | c1_1(a52) | c2_1(a52) | (~ndr1_0) | c3_1(a52)),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[2641, 2640])).
% 2.01/1.66 tff(2643,plain,
% 2.01/1.66 (c3_1(a52)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2642, 84, 1418, 1502, 2636, 2630, 1543])).
% 2.01/1.66 tff(2644,plain,
% 2.01/1.66 (c0_1(a52)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2608, 2629])).
% 2.01/1.66 tff(2645,plain,
% 2.01/1.66 ($false),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2615, 84, 2644, 2481, 2619, 2620, 2630, 2483, 2482, 2618, 133, 2643])).
% 2.01/1.66 tff(2646,plain,(hskp1 | hskp19 | hskp24), inference(lemma,lemma(discharge,[]))).
% 2.01/1.66 tff(2647,plain,
% 2.01/1.66 (hskp19),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[2646, 2533, 1406])).
% 2.01/1.66 tff(2648,plain,
% 2.01/1.66 (~c3_1(a36)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[1274, 2647])).
% 2.01/1.66 tff(2649,plain,
% 2.01/1.66 (~c2_1(a36)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[1280, 2647])).
% 2.01/1.66 tff(2650,plain,
% 2.01/1.66 (~c1_1(a36)),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[1286, 2647])).
% 2.01/1.66 tff(2651,plain,
% 2.01/1.66 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a36) | c2_1(a36) | c3_1(a36) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c0_1(a36)))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a36) | c2_1(a36) | c3_1(a36) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c0_1(a36)))),
% 2.01/1.67 inference(rewrite,[status(thm)],[])).
% 2.01/1.67 tff(2652,plain,
% 2.01/1.67 (((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a34) | c1_1(a34) | c0_1(a34)) <=> (c1_1(a36) | c2_1(a36) | c3_1(a36) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c0_1(a36)))),
% 2.01/1.67 inference(rewrite,[status(thm)],[])).
% 2.01/1.67 tff(2653,plain,
% 2.01/1.67 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a36) | c2_1(a36) | c3_1(a36) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c0_1(a36))))),
% 2.01/1.67 inference(monotonicity,[status(thm)],[2652])).
% 2.01/1.67 tff(2654,plain,
% 2.01/1.67 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a36) | c2_1(a36) | c3_1(a36) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c0_1(a36)))),
% 2.01/1.67 inference(transitivity,[status(thm)],[2653, 2651])).
% 2.01/1.67 tff(2655,plain,
% 2.01/1.67 ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a34) | c1_1(a34) | c0_1(a34))),
% 2.01/1.67 inference(quant_inst,[status(thm)],[])).
% 2.01/1.67 tff(2656,plain,
% 2.01/1.67 ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a36) | c2_1(a36) | c3_1(a36) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c0_1(a36))),
% 2.01/1.67 inference(modus_ponens,[status(thm)],[2655, 2654])).
% 2.01/1.67 tff(2657,plain,
% 2.01/1.67 (c0_1(a34) | (~c0_1(a36))),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[2656, 84, 2650, 2649, 2648, 2420, 2414, 959])).
% 2.01/1.67 tff(2658,plain,
% 2.01/1.67 (~c0_1(a36)),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[2657, 2565])).
% 2.01/1.67 tff(2659,plain,
% 2.01/1.67 (~c1_1(a52)),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[2635, 2592])).
% 2.01/1.67 tff(2660,plain,
% 2.01/1.67 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a52) | c2_1(a52) | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c0_1(a36) | c3_1(a52) | (~c0_1(a52)))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a52) | c2_1(a52) | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c0_1(a36) | c3_1(a52) | (~c0_1(a52)))),
% 2.01/1.67 inference(rewrite,[status(thm)],[])).
% 2.01/1.67 tff(2661,plain,
% 2.01/1.67 (((~ndr1_0) | c3_1(a52) | c2_1(a52) | (~c0_1(a52)) | c2_1(a52) | c1_1(a52) | (~c0_1(a52)) | c2_1(a36) | c1_1(a36) | c0_1(a36)) <=> (c1_1(a52) | c2_1(a52) | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c0_1(a36) | c3_1(a52) | (~c0_1(a52)))),
% 2.01/1.67 inference(rewrite,[status(thm)],[])).
% 2.01/1.67 tff(2662,plain,
% 2.01/1.67 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a52) | c2_1(a52) | (~c0_1(a52)) | c2_1(a52) | c1_1(a52) | (~c0_1(a52)) | c2_1(a36) | c1_1(a36) | c0_1(a36))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a52) | c2_1(a52) | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c0_1(a36) | c3_1(a52) | (~c0_1(a52))))),
% 2.01/1.67 inference(monotonicity,[status(thm)],[2661])).
% 2.01/1.67 tff(2663,plain,
% 2.01/1.67 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a52) | c2_1(a52) | (~c0_1(a52)) | c2_1(a52) | c1_1(a52) | (~c0_1(a52)) | c2_1(a36) | c1_1(a36) | c0_1(a36))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a52) | c2_1(a52) | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c0_1(a36) | c3_1(a52) | (~c0_1(a52)))),
% 2.01/1.67 inference(transitivity,[status(thm)],[2662, 2660])).
% 2.01/1.67 tff(2664,plain,
% 2.01/1.67 ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a52) | c2_1(a52) | (~c0_1(a52)) | c2_1(a52) | c1_1(a52) | (~c0_1(a52)) | c2_1(a36) | c1_1(a36) | c0_1(a36))),
% 2.01/1.67 inference(quant_inst,[status(thm)],[])).
% 2.01/1.67 tff(2665,plain,
% 2.01/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a52) | c2_1(a52) | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c0_1(a36) | c3_1(a52) | (~c0_1(a52))),
% 2.01/1.67 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 2.01/1.67 tff(2666,plain,
% 2.01/1.67 ($false),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[2665, 84, 2609, 2659, 2598, 2650, 2649, 959, 2658, 2616])).
% 2.01/1.67 tff(2667,plain,(hskp24), inference(lemma,lemma(discharge,[]))).
% 2.01/1.67 tff(2668,plain,
% 2.01/1.67 (~c1_1(a58)),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[1460, 2667])).
% 2.01/1.67 tff(2669,plain,
% 2.01/1.67 (c3_1(a58)),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[1436, 2667])).
% 2.01/1.67 tff(2670,plain,
% 2.01/1.67 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c3_1(a34)) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c3_1(a34)) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.01/1.67 inference(rewrite,[status(thm)],[])).
% 2.01/1.67 tff(2671,plain,
% 2.01/1.67 ((hskp22 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34))) <=> (hskp22 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c3_1(a34)) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.01/1.67 inference(rewrite,[status(thm)],[])).
% 2.01/1.67 tff(2672,plain,
% 2.01/1.67 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c3_1(a34)) | (~c2_1(a58)) | (~c3_1(a58))))),
% 2.01/1.67 inference(monotonicity,[status(thm)],[2671])).
% 2.01/1.67 tff(2673,plain,
% 2.01/1.67 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c3_1(a34)) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.01/1.67 inference(transitivity,[status(thm)],[2672, 2670])).
% 2.01/1.67 tff(2674,plain,
% 2.01/1.67 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))),
% 2.01/1.67 inference(quant_inst,[status(thm)],[])).
% 2.01/1.67 tff(2675,plain,
% 2.01/1.67 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c3_1(a34)) | (~c2_1(a58)) | (~c3_1(a58))),
% 2.01/1.67 inference(modus_ponens,[status(thm)],[2674, 2673])).
% 2.01/1.67 tff(2676,plain,
% 2.01/1.67 (hskp22 | (~c2_1(a58))),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[2675, 84, 2669, 2434, 2668, 2420, 2414, 123])).
% 2.01/1.67 tff(2677,plain,
% 2.01/1.67 (~c2_1(a58)),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[2676, 1])).
% 2.01/1.67 tff(2678,plain,
% 2.01/1.67 (c0_1(a58)),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[1447, 2667])).
% 2.01/1.67 tff(2679,plain,
% 2.01/1.67 (hskp22 | hskp19 | c2_1(a58)),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[1454, 84, 2678, 2669, 1417])).
% 2.01/1.67 tff(2680,plain,
% 2.01/1.67 (hskp19),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[2679, 1, 2677])).
% 2.01/1.67 tff(2681,plain,
% 2.01/1.67 (~c3_1(a36)),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[1274, 2680])).
% 2.01/1.67 tff(2682,plain,
% 2.01/1.67 (~c1_1(a36)),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[1286, 2680])).
% 2.01/1.67 tff(2683,plain,
% 2.01/1.67 (c0_1(a36)),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[2449, 84, 2443, 2682, 2681, 113])).
% 2.01/1.67 tff(2684,plain,
% 2.01/1.67 (^[U: $i] : refl((hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 2.01/1.67 inference(bind,[status(th)],[])).
% 2.01/1.67 tff(2685,plain,
% 2.01/1.67 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.01/1.67 inference(quant_intro,[status(thm)],[2684])).
% 2.01/1.67 tff(2686,plain,
% 2.01/1.67 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.01/1.67 inference(rewrite,[status(thm)],[])).
% 2.01/1.67 tff(2687,plain,
% 2.01/1.67 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp4) <=> ((hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp4))), rewrite(((hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp4) <=> (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp4) <=> (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 2.01/1.67 inference(bind,[status(th)],[])).
% 2.01/1.67 tff(2688,plain,
% 2.01/1.67 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp4) <=> ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.01/1.67 inference(quant_intro,[status(thm)],[2687])).
% 2.01/1.67 tff(2689,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 2.01/1.67 tff(2690,plain,
% 2.01/1.67 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.01/1.67 inference(modus_ponens,[status(thm)],[2689, 2688])).
% 2.01/1.67 tff(2691,plain,
% 2.01/1.67 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.01/1.67 inference(modus_ponens,[status(thm)],[2690, 2686])).
% 2.01/1.67 tff(2692,plain,(
% 2.01/1.67 ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.01/1.67 inference(skolemize,[status(sab)],[2691])).
% 2.01/1.67 tff(2693,plain,
% 2.01/1.67 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.01/1.67 inference(modus_ponens,[status(thm)],[2692, 2685])).
% 2.01/1.67 tff(2694,plain,
% 2.01/1.67 (~c2_1(a36)),
% 2.01/1.67 inference(unit_resolution,[status(thm)],[1280, 2680])).
% 2.01/1.67 tff(2695,plain,
% 2.01/1.67 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp4 | hskp2 | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp4 | hskp2 | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(2696,plain,
% 2.01/1.68 ((hskp4 | hskp2 | (~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36))) <=> (hskp4 | hskp2 | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(2697,plain,
% 2.01/1.68 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp4 | hskp2 | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36))))),
% 2.01/1.68 inference(monotonicity,[status(thm)],[2696])).
% 2.01/1.68 tff(2698,plain,
% 2.01/1.68 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp4 | hskp2 | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 2.01/1.68 inference(transitivity,[status(thm)],[2697, 2695])).
% 2.01/1.68 tff(2699,plain,
% 2.01/1.68 ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)))),
% 2.01/1.68 inference(quant_inst,[status(thm)],[])).
% 2.01/1.68 tff(2700,plain,
% 2.01/1.68 ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp4 | hskp2 | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36))),
% 2.01/1.68 inference(modus_ponens,[status(thm)],[2699, 2698])).
% 2.01/1.68 tff(2701,plain,
% 2.01/1.68 (hskp2),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2700, 84, 2443, 2694, 2681, 2693, 2683])).
% 2.01/1.68 tff(2702,plain,
% 2.01/1.68 (~c1_1(a3)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[168, 2701])).
% 2.01/1.68 tff(2703,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c0_1(a58)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c0_1(a58)) | (~c3_1(a58)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(2704,plain,
% 2.01/1.68 ((hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58))) <=> (hskp16 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c0_1(a58)) | (~c3_1(a58)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(2705,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c0_1(a58)) | (~c3_1(a58))))),
% 2.01/1.68 inference(monotonicity,[status(thm)],[2704])).
% 2.01/1.68 tff(2706,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c0_1(a58)) | (~c3_1(a58)))),
% 2.01/1.68 inference(transitivity,[status(thm)],[2705, 2703])).
% 2.01/1.68 tff(2707,plain,
% 2.01/1.68 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))),
% 2.01/1.68 inference(quant_inst,[status(thm)],[])).
% 2.01/1.68 tff(2708,plain,
% 2.01/1.68 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c0_1(a58)) | (~c3_1(a58))),
% 2.01/1.68 inference(modus_ponens,[status(thm)],[2707, 2706])).
% 2.01/1.68 tff(2709,plain,
% 2.01/1.68 (hskp16),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2708, 84, 2678, 2669, 44, 33, 2668, 22, 2066])).
% 2.01/1.68 tff(2710,plain,
% 2.01/1.68 (~c0_1(a31)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2252, 2709])).
% 2.01/1.68 tff(2711,plain,
% 2.01/1.68 (c2_1(a3)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[179, 2701])).
% 2.01/1.68 tff(2712,plain,
% 2.01/1.68 (c0_1(a3)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[190, 2701])).
% 2.01/1.68 tff(2713,plain,
% 2.01/1.68 (c2_1(a31)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2263, 2709])).
% 2.01/1.68 tff(2714,plain,
% 2.01/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a31) | c3_1(a19) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a31) | c3_1(a19) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(2715,plain,
% 2.01/1.68 (((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31))) <=> (c0_1(a31) | c3_1(a19) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(2716,plain,
% 2.01/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a31) | c3_1(a19) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31))))),
% 2.01/1.68 inference(monotonicity,[status(thm)],[2715])).
% 2.01/1.68 tff(2717,plain,
% 2.01/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a31) | c3_1(a19) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 2.01/1.68 inference(transitivity,[status(thm)],[2716, 2714])).
% 2.01/1.68 tff(2718,plain,
% 2.01/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31)))),
% 2.01/1.68 inference(quant_inst,[status(thm)],[])).
% 2.01/1.68 tff(2719,plain,
% 2.01/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a31) | c3_1(a19) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31))),
% 2.01/1.68 inference(modus_ponens,[status(thm)],[2718, 2717])).
% 2.01/1.68 tff(2720,plain,
% 2.01/1.68 (~c3_1(a31)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2719, 84, 2713, 44, 2712, 2711, 2710, 22, 2702, 103, 93])).
% 2.01/1.68 tff(2721,plain,
% 2.01/1.68 (~c1_1(a31)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2294, 2709])).
% 2.01/1.68 tff(2722,plain,
% 2.01/1.68 ($false),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2301, 84, 2443, 2710, 2721, 113, 2720])).
% 2.01/1.68 tff(2723,plain,(hskp22), inference(lemma,lemma(discharge,[]))).
% 2.01/1.68 tff(2724,plain,
% 2.01/1.68 (~c1_1(a43)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[688, 2723])).
% 2.01/1.68 tff(2725,plain,
% 2.06/1.68 (~c3_1(a43)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[682, 2723])).
% 2.06/1.68 tff(2726,assumption,(~c2_1(a43)), introduced(assumption)).
% 2.06/1.68 tff(2727,plain,
% 2.06/1.68 (~hskp22),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[699, 2726])).
% 2.06/1.68 tff(2728,plain,
% 2.06/1.68 (~hskp4),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[2442, 2727])).
% 2.06/1.68 tff(2729,plain,
% 2.06/1.68 (hskp19),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[1786, 2728, 2667, 2727])).
% 2.06/1.68 tff(2730,plain,
% 2.06/1.68 (~c3_1(a36)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[1274, 2729])).
% 2.06/1.68 tff(2731,plain,
% 2.06/1.68 (~c1_1(a36)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[1286, 2729])).
% 2.06/1.68 tff(2732,plain,
% 2.06/1.68 (c0_1(a36)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[2449, 84, 2728, 2731, 2730, 113])).
% 2.06/1.68 tff(2733,plain,
% 2.06/1.68 (~c2_1(a36)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[1280, 2729])).
% 2.06/1.68 tff(2734,plain,
% 2.06/1.68 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a43) | (~c1_1(a43)) | c3_1(a43) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a43) | (~c1_1(a43)) | c3_1(a43) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 2.06/1.68 inference(rewrite,[status(thm)],[])).
% 2.06/1.68 tff(2735,plain,
% 2.06/1.68 ((hskp22 | (~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36))) <=> (hskp22 | c2_1(a43) | (~c1_1(a43)) | c3_1(a43) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 2.06/1.68 inference(rewrite,[status(thm)],[])).
% 2.06/1.68 tff(2736,plain,
% 2.06/1.68 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a43) | (~c1_1(a43)) | c3_1(a43) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36))))),
% 2.06/1.68 inference(monotonicity,[status(thm)],[2735])).
% 2.06/1.68 tff(2737,plain,
% 2.06/1.68 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a43) | (~c1_1(a43)) | c3_1(a43) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 2.06/1.68 inference(transitivity,[status(thm)],[2736, 2734])).
% 2.06/1.68 tff(2738,plain,
% 2.06/1.68 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36)))),
% 2.06/1.68 inference(quant_inst,[status(thm)],[])).
% 2.06/1.68 tff(2739,plain,
% 2.06/1.68 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a43) | (~c1_1(a43)) | c3_1(a43) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36))),
% 2.06/1.68 inference(modus_ponens,[status(thm)],[2738, 2737])).
% 2.06/1.68 tff(2740,plain,
% 2.06/1.68 (~c1_1(a43)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[2739, 2727, 84, 2726, 1587, 2733, 2730, 12, 2732])).
% 2.06/1.68 tff(2741,plain,
% 2.06/1.68 (hskp4 | c1_1(a43) | c0_1(a43)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[1582, 84, 1587, 113])).
% 2.06/1.68 tff(2742,plain,
% 2.06/1.68 (c0_1(a43)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[2741, 2740, 2728])).
% 2.06/1.68 tff(2743,plain,
% 2.06/1.68 (~c2_1(a58)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[2676, 2727])).
% 2.06/1.68 tff(2744,plain,
% 2.06/1.68 (hskp11),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[15, 2727])).
% 2.06/1.68 tff(2745,plain,
% 2.06/1.68 (~c3_1(a19)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[21, 2744])).
% 2.06/1.68 tff(2746,plain,
% 2.06/1.68 (c1_1(a19)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[32, 2744])).
% 2.06/1.68 tff(2747,plain,
% 2.06/1.68 (c0_1(a19)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[43, 2744])).
% 2.06/1.68 tff(2748,plain,
% 2.06/1.68 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | c2_1(a58) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | c2_1(a58) | (~c3_1(a58)))),
% 2.06/1.69 inference(rewrite,[status(thm)],[])).
% 2.06/1.69 tff(2749,plain,
% 2.06/1.69 ((hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58))) <=> (hskp0 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | c2_1(a58) | (~c3_1(a58)))),
% 2.06/1.69 inference(rewrite,[status(thm)],[])).
% 2.06/1.69 tff(2750,plain,
% 2.06/1.69 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | c2_1(a58) | (~c3_1(a58))))),
% 2.06/1.69 inference(monotonicity,[status(thm)],[2749])).
% 2.06/1.69 tff(2751,plain,
% 2.06/1.69 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | c2_1(a58) | (~c3_1(a58)))),
% 2.06/1.69 inference(transitivity,[status(thm)],[2750, 2748])).
% 2.06/1.69 tff(2752,plain,
% 2.06/1.69 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))),
% 2.06/1.69 inference(quant_inst,[status(thm)],[])).
% 2.06/1.69 tff(2753,plain,
% 2.06/1.69 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | c2_1(a58) | (~c3_1(a58))),
% 2.06/1.69 inference(modus_ponens,[status(thm)],[2752, 2751])).
% 2.06/1.69 tff(2754,plain,
% 2.06/1.69 (hskp0),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[2753, 84, 2669, 2747, 2746, 2668, 2745, 651, 2743])).
% 2.06/1.69 tff(2755,plain,
% 2.06/1.69 (~c0_1(a1)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[714, 2754])).
% 2.06/1.69 tff(2756,plain,
% 2.06/1.69 (hskp17),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[1999, 84, 2731, 2733, 2730, 1992, 2732])).
% 2.06/1.69 tff(2757,plain,
% 2.06/1.69 (~c2_1(a32)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[2005, 2756])).
% 2.06/1.69 tff(2758,plain,
% 2.06/1.69 (~c0_1(a32)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[2359, 2756])).
% 2.06/1.69 tff(2759,plain,
% 2.06/1.69 (c2_1(a1)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[736, 2754])).
% 2.06/1.69 tff(2760,plain,
% 2.06/1.69 (c1_1(a1)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[725, 2754])).
% 2.06/1.69 tff(2761,plain,
% 2.06/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a43)))),
% 2.06/1.69 inference(rewrite,[status(thm)],[])).
% 2.06/1.69 tff(2762,plain,
% 2.06/1.69 (((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32))) <=> (c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a43)))),
% 2.06/1.69 inference(rewrite,[status(thm)],[])).
% 2.06/1.69 tff(2763,plain,
% 2.06/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a43))))),
% 2.06/1.69 inference(monotonicity,[status(thm)],[2762])).
% 2.06/1.69 tff(2764,plain,
% 2.06/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a43)))),
% 2.06/1.69 inference(transitivity,[status(thm)],[2763, 2761])).
% 2.06/1.69 tff(2765,plain,
% 2.06/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32)))),
% 2.06/1.69 inference(quant_inst,[status(thm)],[])).
% 2.06/1.69 tff(2766,plain,
% 2.06/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a43))),
% 2.06/1.69 inference(modus_ponens,[status(thm)],[2765, 2764])).
% 2.06/1.69 tff(2767,plain,
% 2.06/1.69 (~c1_1(a32)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[2766, 84, 2760, 2759, 2740, 1587, 2758, 2757, 2755, 2044, 2742])).
% 2.06/1.69 tff(2768,plain,
% 2.06/1.69 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a43) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a43)))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a43) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a43)))),
% 2.06/1.69 inference(rewrite,[status(thm)],[])).
% 2.06/1.69 tff(2769,plain,
% 2.06/1.69 (((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c2_1(a43) | c1_1(a43) | (~c0_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c2_1(a43) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a43)))),
% 2.06/1.69 inference(rewrite,[status(thm)],[])).
% 2.06/1.69 tff(2770,plain,
% 2.06/1.69 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c2_1(a43) | c1_1(a43) | (~c0_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a43) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a43))))),
% 2.06/1.69 inference(monotonicity,[status(thm)],[2769])).
% 2.06/1.69 tff(2771,plain,
% 2.06/1.69 (((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c2_1(a43) | c1_1(a43) | (~c0_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a43) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a43)))),
% 2.06/1.69 inference(transitivity,[status(thm)],[2770, 2768])).
% 2.06/1.69 tff(2772,plain,
% 2.06/1.69 ((~![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)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c2_1(a43) | c1_1(a43) | (~c0_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32))),
% 2.06/1.69 inference(quant_inst,[status(thm)],[])).
% 2.06/1.69 tff(2773,plain,
% 2.06/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a43) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a43))),
% 2.06/1.69 inference(modus_ponens,[status(thm)],[2772, 2771])).
% 2.06/1.69 tff(2774,plain,
% 2.06/1.69 ($false),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[2773, 84, 2726, 2740, 1587, 2758, 2757, 959, 2742, 2767])).
% 2.06/1.69 tff(2775,plain,(c2_1(a43) | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.69 tff(2776,plain,
% 2.06/1.69 (c2_1(a43)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[2775, 1587])).
% 2.06/1.69 tff(2777,plain,
% 2.06/1.69 (~hskp1),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[2532, 1672, 2776, 1587])).
% 2.06/1.69 tff(2778,plain,
% 2.06/1.69 ($false),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[2550, 2777, 1672, 588, 1587, 2776])).
% 2.06/1.69 tff(2779,plain,(c1_1(a43) | hskp0 | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.69 tff(2780,plain,
% 2.06/1.69 (c1_1(a43)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[2779, 588, 1587])).
% 2.06/1.69 tff(2781,plain,
% 2.06/1.69 (~hskp22),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[688, 2780])).
% 2.06/1.69 tff(2782,plain,
% 2.06/1.69 (~c2_1(a58)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[2676, 2781])).
% 2.06/1.69 tff(2783,plain,
% 2.06/1.69 (hskp11),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[15, 2781])).
% 2.06/1.69 tff(2784,plain,
% 2.06/1.69 (~c3_1(a19)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[21, 2783])).
% 2.06/1.69 tff(2785,plain,
% 2.06/1.69 (c1_1(a19)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[32, 2783])).
% 2.06/1.69 tff(2786,plain,
% 2.06/1.69 (c0_1(a19)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[43, 2783])).
% 2.06/1.69 tff(2787,plain,
% 2.06/1.69 ($false),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[2753, 84, 588, 2669, 2786, 2785, 2668, 2784, 651, 2782])).
% 2.06/1.69 tff(2788,plain,(hskp0 | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.69 tff(2789,plain,
% 2.06/1.69 (hskp0),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[2788, 1587])).
% 2.06/1.69 tff(2790,plain,
% 2.06/1.69 (~c0_1(a1)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[714, 2789])).
% 2.06/1.69 tff(2791,plain,
% 2.06/1.69 (c2_1(a1)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[736, 2789])).
% 2.06/1.69 tff(2792,plain,
% 2.06/1.69 (c1_1(a1)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[725, 2789])).
% 2.06/1.69 tff(2793,plain,
% 2.06/1.69 (~c0_1(a34)),
% 2.06/1.69 inference(unit_resolution,[status(thm)],[2564, 84, 2776, 2434, 2792, 2791, 1672, 1587, 2414, 2790, 133])).
% 2.06/1.69 tff(2794,plain,
% 2.06/1.69 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a58)) | (~c0_1(a58)))),
% 2.06/1.69 inference(rewrite,[status(thm)],[])).
% 2.06/1.69 tff(2795,plain,
% 2.06/1.69 ((hskp1 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a34) | c1_1(a34) | c0_1(a34)) <=> (hskp1 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a58)) | (~c0_1(a58)))),
% 2.06/1.69 inference(rewrite,[status(thm)],[])).
% 2.06/1.69 tff(2796,plain,
% 2.06/1.69 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a58)) | (~c0_1(a58))))),
% 2.06/1.69 inference(monotonicity,[status(thm)],[2795])).
% 2.06/1.69 tff(2797,plain,
% 2.06/1.69 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a58)) | (~c0_1(a58)))),
% 2.06/1.69 inference(transitivity,[status(thm)],[2796, 2794])).
% 2.06/1.70 tff(2798,plain,
% 2.06/1.70 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a34) | c1_1(a34) | c0_1(a34))),
% 2.06/1.70 inference(quant_inst,[status(thm)],[])).
% 2.06/1.70 tff(2799,plain,
% 2.06/1.70 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a58)) | (~c0_1(a58))),
% 2.06/1.70 inference(modus_ponens,[status(thm)],[2798, 2797])).
% 2.06/1.70 tff(2800,plain,
% 2.06/1.70 (hskp1 | c0_1(a34) | (~c2_1(a58))),
% 2.06/1.70 inference(unit_resolution,[status(thm)],[2799, 84, 2678, 2668, 2420, 2414, 749])).
% 2.06/1.70 tff(2801,plain,
% 2.06/1.70 (~c2_1(a58)),
% 2.06/1.70 inference(unit_resolution,[status(thm)],[2800, 2793, 2777])).
% 2.06/1.70 tff(2802,plain,
% 2.06/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))),
% 2.06/1.70 inference(rewrite,[status(thm)],[])).
% 2.06/1.70 tff(2803,plain,
% 2.06/1.70 (((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1))) <=> (c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))),
% 2.06/1.70 inference(rewrite,[status(thm)],[])).
% 2.06/1.70 tff(2804,plain,
% 2.06/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58))))),
% 2.06/1.70 inference(monotonicity,[status(thm)],[2803])).
% 2.06/1.70 tff(2805,plain,
% 2.06/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))),
% 2.06/1.70 inference(transitivity,[status(thm)],[2804, 2802])).
% 2.06/1.70 tff(2806,plain,
% 2.06/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))),
% 2.06/1.70 inference(quant_inst,[status(thm)],[])).
% 2.06/1.70 tff(2807,plain,
% 2.06/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58))),
% 2.06/1.70 inference(modus_ponens,[status(thm)],[2806, 2805])).
% 2.06/1.70 tff(2808,plain,
% 2.06/1.70 ($false),
% 2.06/1.70 inference(unit_resolution,[status(thm)],[2807, 84, 2678, 2669, 2776, 2792, 2791, 1672, 1587, 2790, 133, 2801])).
% 2.06/1.70 tff(2809,plain,(c1_1(a43) | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.70 tff(2810,plain,
% 2.06/1.70 ($false),
% 2.06/1.70 inference(unit_resolution,[status(thm)],[2809, 2725, 2724])).
% 2.06/1.71 % SZS output end Proof
%------------------------------------------------------------------------------