TSTP Solution File: SYN498-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN498-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 23:55:57 EDT 2022
% Result : Unsatisfiable 2.63s 1.92s
% Output : Proof 3.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN498-1 : TPTP v8.1.0. Released v2.1.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 04:40:58 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 2.63/1.92 % SZS status Unsatisfiable
% 2.63/1.92 % SZS output start Proof
% 2.63/1.92 tff(c0_1_type, type, (
% 2.63/1.92 c0_1: $i > $o)).
% 2.63/1.92 tff(a20_type, type, (
% 2.63/1.92 a20: $i)).
% 2.63/1.92 tff(c2_1_type, type, (
% 2.63/1.92 c2_1: $i > $o)).
% 2.63/1.92 tff(a16_type, type, (
% 2.63/1.92 a16: $i)).
% 2.63/1.92 tff(a3_type, type, (
% 2.63/1.92 a3: $i)).
% 2.63/1.92 tff(a37_type, type, (
% 2.63/1.92 a37: $i)).
% 2.63/1.92 tff(c1_1_type, type, (
% 2.63/1.92 c1_1: $i > $o)).
% 2.63/1.92 tff(c3_1_type, type, (
% 2.63/1.92 c3_1: $i > $o)).
% 2.63/1.92 tff(ndr1_0_type, type, (
% 2.63/1.92 ndr1_0: $o)).
% 2.63/1.92 tff(hskp3_type, type, (
% 2.63/1.92 hskp3: $o)).
% 2.63/1.92 tff(hskp24_type, type, (
% 2.63/1.92 hskp24: $o)).
% 2.63/1.92 tff(hskp20_type, type, (
% 2.63/1.92 hskp20: $o)).
% 2.63/1.92 tff(hskp28_type, type, (
% 2.63/1.92 hskp28: $o)).
% 2.63/1.92 tff(hskp0_type, type, (
% 2.63/1.92 hskp0: $o)).
% 2.63/1.92 tff(a21_type, type, (
% 2.63/1.92 a21: $i)).
% 2.63/1.92 tff(hskp13_type, type, (
% 2.63/1.92 hskp13: $o)).
% 2.63/1.92 tff(hskp21_type, type, (
% 2.63/1.92 hskp21: $o)).
% 2.63/1.92 tff(hskp6_type, type, (
% 2.63/1.92 hskp6: $o)).
% 2.63/1.92 tff(hskp1_type, type, (
% 2.63/1.92 hskp1: $o)).
% 2.63/1.92 tff(a2_type, type, (
% 2.63/1.92 a2: $i)).
% 2.63/1.92 tff(a13_type, type, (
% 2.63/1.92 a13: $i)).
% 2.63/1.92 tff(a58_type, type, (
% 2.63/1.92 a58: $i)).
% 2.63/1.92 tff(a7_type, type, (
% 2.63/1.92 a7: $i)).
% 2.63/1.92 tff(hskp2_type, type, (
% 2.63/1.92 hskp2: $o)).
% 2.63/1.92 tff(a1_type, type, (
% 2.63/1.92 a1: $i)).
% 2.63/1.92 tff(hskp14_type, type, (
% 2.63/1.92 hskp14: $o)).
% 2.63/1.92 tff(hskp29_type, type, (
% 2.63/1.92 hskp29: $o)).
% 2.63/1.92 tff(hskp26_type, type, (
% 2.63/1.92 hskp26: $o)).
% 2.63/1.92 tff(a11_type, type, (
% 2.63/1.92 a11: $i)).
% 2.63/1.92 tff(hskp5_type, type, (
% 2.63/1.92 hskp5: $o)).
% 2.63/1.92 tff(a31_type, type, (
% 2.63/1.92 a31: $i)).
% 2.63/1.92 tff(hskp18_type, type, (
% 2.63/1.92 hskp18: $o)).
% 2.63/1.92 tff(a38_type, type, (
% 2.63/1.92 a38: $i)).
% 2.63/1.92 tff(a15_type, type, (
% 2.63/1.92 a15: $i)).
% 2.63/1.92 tff(a18_type, type, (
% 2.63/1.92 a18: $i)).
% 2.63/1.92 tff(a25_type, type, (
% 2.63/1.92 a25: $i)).
% 2.63/1.92 tff(hskp27_type, type, (
% 2.63/1.92 hskp27: $o)).
% 2.63/1.92 tff(a12_type, type, (
% 2.63/1.92 a12: $i)).
% 2.63/1.92 tff(hskp10_type, type, (
% 2.63/1.92 hskp10: $o)).
% 2.63/1.92 tff(hskp9_type, type, (
% 2.63/1.92 hskp9: $o)).
% 2.63/1.92 tff(hskp12_type, type, (
% 2.63/1.92 hskp12: $o)).
% 2.63/1.92 tff(a14_type, type, (
% 2.63/1.92 a14: $i)).
% 2.63/1.92 tff(hskp7_type, type, (
% 2.63/1.92 hskp7: $o)).
% 2.63/1.92 tff(hskp8_type, type, (
% 2.63/1.92 hskp8: $o)).
% 2.63/1.92 tff(a42_type, type, (
% 2.63/1.92 a42: $i)).
% 2.63/1.92 tff(hskp22_type, type, (
% 2.63/1.92 hskp22: $o)).
% 2.63/1.92 tff(a28_type, type, (
% 2.63/1.92 a28: $i)).
% 2.63/1.92 tff(hskp17_type, type, (
% 2.63/1.92 hskp17: $o)).
% 2.63/1.92 tff(1,plain,
% 2.63/1.92 (^[U: $i] : refl((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 2.63/1.92 inference(bind,[status(th)],[])).
% 2.63/1.92 tff(2,plain,
% 2.63/1.92 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.92 inference(quant_intro,[status(thm)],[1])).
% 2.63/1.92 tff(3,plain,
% 2.63/1.92 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.92 inference(rewrite,[status(thm)],[])).
% 2.63/1.92 tff(4,plain,
% 2.63/1.92 (^[U: $i] : 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)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp3) | hskp24) <=> ((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp24))), rewrite(((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp24) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp3) | hskp24) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 2.63/1.92 inference(bind,[status(th)],[])).
% 2.63/1.92 tff(5,plain,
% 2.63/1.92 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp3) | hskp24) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.92 inference(quant_intro,[status(thm)],[4])).
% 2.63/1.92 tff(6,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp3) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 2.63/1.92 tff(7,plain,
% 2.63/1.92 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.92 inference(modus_ponens,[status(thm)],[6, 5])).
% 2.63/1.92 tff(8,plain,
% 2.63/1.92 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.92 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.63/1.92 tff(9,plain,(
% 2.63/1.92 ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.92 inference(skolemize,[status(sab)],[8])).
% 2.63/1.92 tff(10,plain,
% 2.63/1.92 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.92 inference(modus_ponens,[status(thm)],[9, 2])).
% 2.63/1.92 tff(11,assumption,(~hskp0), introduced(assumption)).
% 2.63/1.92 tff(12,assumption,(~c3_1(a2)), introduced(assumption)).
% 2.63/1.92 tff(13,assumption,(~c2_1(a2)), introduced(assumption)).
% 2.63/1.92 tff(14,assumption,(~c0_1(a2)), introduced(assumption)).
% 2.63/1.92 tff(15,plain,
% 2.63/1.92 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 2.63/1.92 inference(bind,[status(th)],[])).
% 2.63/1.92 tff(16,plain,
% 2.63/1.92 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.92 inference(quant_intro,[status(thm)],[15])).
% 2.63/1.92 tff(17,plain,
% 2.63/1.92 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.92 inference(rewrite,[status(thm)],[])).
% 2.63/1.92 tff(18,plain,
% 2.63/1.92 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_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))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_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)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 2.63/1.92 inference(bind,[status(th)],[])).
% 2.63/1.92 tff(19,plain,
% 2.63/1.92 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.92 inference(quant_intro,[status(thm)],[18])).
% 2.63/1.92 tff(20,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 2.63/1.92 tff(21,plain,
% 2.63/1.92 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.92 inference(modus_ponens,[status(thm)],[20, 19])).
% 2.63/1.92 tff(22,plain,
% 2.63/1.92 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.92 inference(modus_ponens,[status(thm)],[21, 17])).
% 2.63/1.92 tff(23,plain,(
% 2.63/1.92 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.92 inference(skolemize,[status(sab)],[22])).
% 2.63/1.92 tff(24,plain,
% 2.63/1.92 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.92 inference(modus_ponens,[status(thm)],[23, 16])).
% 2.63/1.92 tff(25,assumption,(~hskp6), introduced(assumption)).
% 2.63/1.92 tff(26,assumption,(~c1_1(a58)), introduced(assumption)).
% 2.63/1.92 tff(27,plain,
% 2.63/1.92 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 2.63/1.92 inference(bind,[status(th)],[])).
% 2.63/1.92 tff(28,plain,
% 2.63/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.92 inference(quant_intro,[status(thm)],[27])).
% 2.63/1.92 tff(29,plain,
% 2.63/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.92 inference(rewrite,[status(thm)],[])).
% 2.63/1.92 tff(30,plain,
% 2.63/1.92 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 2.63/1.92 inference(bind,[status(th)],[])).
% 2.63/1.92 tff(31,plain,
% 2.63/1.92 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.92 inference(quant_intro,[status(thm)],[30])).
% 2.63/1.92 tff(32,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 2.63/1.92 tff(33,plain,
% 2.63/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.92 inference(modus_ponens,[status(thm)],[32, 31])).
% 2.63/1.92 tff(34,plain,
% 2.63/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.92 inference(modus_ponens,[status(thm)],[33, 29])).
% 2.63/1.92 tff(35,plain,(
% 2.63/1.92 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.92 inference(skolemize,[status(sab)],[34])).
% 2.63/1.92 tff(36,plain,
% 2.63/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.92 inference(modus_ponens,[status(thm)],[35, 28])).
% 2.63/1.92 tff(37,assumption,(~c0_1(a58)), introduced(assumption)).
% 2.63/1.92 tff(38,plain,
% 2.63/1.92 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 2.63/1.92 inference(bind,[status(th)],[])).
% 2.63/1.92 tff(39,plain,
% 2.63/1.92 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.92 inference(quant_intro,[status(thm)],[38])).
% 2.63/1.92 tff(40,plain,
% 2.63/1.92 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.92 inference(rewrite,[status(thm)],[])).
% 2.63/1.92 tff(41,plain,
% 2.63/1.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp1) <=> ((hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 2.63/1.92 inference(bind,[status(th)],[])).
% 2.63/1.92 tff(42,plain,
% 2.63/1.92 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp1) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.92 inference(quant_intro,[status(thm)],[41])).
% 2.63/1.92 tff(43,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 2.63/1.92 tff(44,plain,
% 2.63/1.92 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.92 inference(modus_ponens,[status(thm)],[43, 42])).
% 2.63/1.92 tff(45,plain,
% 2.63/1.92 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.92 inference(modus_ponens,[status(thm)],[44, 40])).
% 2.63/1.92 tff(46,plain,(
% 2.63/1.92 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.92 inference(skolemize,[status(sab)],[45])).
% 2.63/1.92 tff(47,plain,
% 2.63/1.92 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.92 inference(modus_ponens,[status(thm)],[46, 39])).
% 2.63/1.92 tff(48,assumption,(~hskp3), introduced(assumption)).
% 2.63/1.92 tff(49,plain,
% 2.63/1.92 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 2.63/1.92 inference(bind,[status(th)],[])).
% 2.63/1.92 tff(50,plain,
% 2.63/1.92 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.63/1.92 inference(quant_intro,[status(thm)],[49])).
% 2.63/1.92 tff(51,plain,
% 2.63/1.92 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(52,plain,
% 2.63/1.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 2.63/1.93 inference(bind,[status(th)],[])).
% 2.63/1.93 tff(53,plain,
% 2.63/1.93 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.63/1.93 inference(quant_intro,[status(thm)],[52])).
% 2.63/1.93 tff(54,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 2.63/1.93 tff(55,plain,
% 2.63/1.93 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[54, 53])).
% 2.63/1.93 tff(56,plain,
% 2.63/1.93 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[55, 51])).
% 2.63/1.93 tff(57,plain,(
% 2.63/1.93 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.63/1.93 inference(skolemize,[status(sab)],[56])).
% 2.63/1.93 tff(58,plain,
% 2.63/1.93 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[57, 50])).
% 2.63/1.93 tff(59,assumption,(c2_1(a58)), introduced(assumption)).
% 2.63/1.93 tff(60,plain,
% 2.63/1.93 (^[U: $i] : refl((hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 2.63/1.93 inference(bind,[status(th)],[])).
% 2.63/1.93 tff(61,plain,
% 2.63/1.93 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.93 inference(quant_intro,[status(thm)],[60])).
% 2.63/1.93 tff(62,plain,
% 2.63/1.93 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(63,plain,
% 2.63/1.93 (^[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)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp0) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp0))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp0) <=> (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp0) <=> (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 2.63/1.93 inference(bind,[status(th)],[])).
% 2.63/1.93 tff(64,plain,
% 2.63/1.93 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp0) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.93 inference(quant_intro,[status(thm)],[63])).
% 2.63/1.93 tff(65,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 2.63/1.93 tff(66,plain,
% 2.63/1.93 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[65, 64])).
% 2.63/1.93 tff(67,plain,
% 2.63/1.93 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[66, 62])).
% 2.63/1.93 tff(68,plain,(
% 2.63/1.93 ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.93 inference(skolemize,[status(sab)],[67])).
% 2.63/1.93 tff(69,plain,
% 2.63/1.93 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[68, 61])).
% 2.63/1.93 tff(70,assumption,(~ndr1_0), introduced(assumption)).
% 2.63/1.93 tff(71,plain,
% 2.63/1.93 ((ndr1_0 | (~hskp14)) <=> (ndr1_0 | (~hskp14))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(72,plain,
% 2.63/1.93 (((~hskp14) | ndr1_0) <=> (ndr1_0 | (~hskp14))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(73,axiom,((~hskp14) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause17')).
% 2.63/1.93 tff(74,plain,
% 2.63/1.93 (ndr1_0 | (~hskp14)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[73, 72])).
% 2.63/1.93 tff(75,plain,
% 2.63/1.93 (ndr1_0 | (~hskp14)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[74, 71])).
% 2.63/1.93 tff(76,plain,
% 2.63/1.93 (~hskp14),
% 2.63/1.93 inference(unit_resolution,[status(thm)],[75, 70])).
% 2.63/1.93 tff(77,plain,
% 2.63/1.93 ((ndr1_0 | (~hskp29)) <=> (ndr1_0 | (~hskp29))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(78,plain,
% 2.63/1.93 (((~hskp29) | ndr1_0) <=> (ndr1_0 | (~hskp29))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(79,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 2.63/1.93 tff(80,plain,
% 2.63/1.93 (ndr1_0 | (~hskp29)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[79, 78])).
% 2.63/1.93 tff(81,plain,
% 2.63/1.93 (ndr1_0 | (~hskp29)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[80, 77])).
% 2.63/1.93 tff(82,plain,
% 2.63/1.93 (~hskp29),
% 2.63/1.93 inference(unit_resolution,[status(thm)],[81, 70])).
% 2.63/1.93 tff(83,plain,
% 2.63/1.93 ((ndr1_0 | (~hskp26)) <=> (ndr1_0 | (~hskp26))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(84,plain,
% 2.63/1.93 (((~hskp26) | ndr1_0) <=> (ndr1_0 | (~hskp26))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(85,axiom,((~hskp26) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause5')).
% 2.63/1.93 tff(86,plain,
% 2.63/1.93 (ndr1_0 | (~hskp26)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[85, 84])).
% 2.63/1.93 tff(87,plain,
% 2.63/1.93 (ndr1_0 | (~hskp26)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[86, 83])).
% 2.63/1.93 tff(88,plain,
% 2.63/1.93 (~hskp26),
% 2.63/1.93 inference(unit_resolution,[status(thm)],[87, 70])).
% 2.63/1.93 tff(89,plain,
% 2.63/1.93 ((hskp29 | hskp26 | hskp14) <=> (hskp29 | hskp26 | hskp14)),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(90,plain,
% 2.63/1.93 (((hskp29 | hskp26) | hskp14) <=> (hskp29 | hskp26 | hskp14)),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(91,plain,
% 2.63/1.93 ((hskp29 | hskp26) <=> (hskp29 | hskp26)),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(92,plain,
% 2.63/1.93 (((hskp29 | hskp26) | hskp14) <=> ((hskp29 | hskp26) | hskp14)),
% 2.63/1.93 inference(monotonicity,[status(thm)],[91])).
% 2.63/1.93 tff(93,plain,
% 2.63/1.93 (((hskp29 | hskp26) | hskp14) <=> (hskp29 | hskp26 | hskp14)),
% 2.63/1.93 inference(transitivity,[status(thm)],[92, 90])).
% 2.63/1.93 tff(94,axiom,((hskp29 | hskp26) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 2.63/1.93 tff(95,plain,
% 2.63/1.93 (hskp29 | hskp26 | hskp14),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[94, 93])).
% 2.63/1.93 tff(96,plain,
% 2.63/1.93 (hskp29 | hskp26 | hskp14),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[95, 89])).
% 2.63/1.93 tff(97,plain,
% 2.63/1.93 (hskp29 | hskp26 | hskp14),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[96, 89])).
% 2.63/1.93 tff(98,plain,
% 2.63/1.93 (hskp29 | hskp26 | hskp14),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[97, 89])).
% 2.63/1.93 tff(99,plain,
% 2.63/1.93 (hskp29 | hskp26 | hskp14),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[98, 89])).
% 2.63/1.93 tff(100,plain,
% 2.63/1.93 (hskp29 | hskp26 | hskp14),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[99, 89])).
% 2.63/1.93 tff(101,plain,
% 2.63/1.93 (hskp29 | hskp26 | hskp14),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[100, 89])).
% 2.63/1.93 tff(102,plain,
% 2.63/1.93 (hskp29 | hskp26 | hskp14),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[101, 89])).
% 2.63/1.93 tff(103,plain,
% 2.63/1.93 ($false),
% 2.63/1.93 inference(unit_resolution,[status(thm)],[102, 88, 82, 76])).
% 2.63/1.93 tff(104,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 2.63/1.93 tff(105,plain,
% 2.63/1.93 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(106,plain,
% 2.63/1.93 ((hskp3 | hskp0 | (~ndr1_0) | c1_1(a58) | c0_1(a58) | (~c2_1(a58))) <=> (hskp3 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(107,plain,
% 2.63/1.93 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a58) | c0_1(a58) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | (~c2_1(a58))))),
% 2.63/1.93 inference(monotonicity,[status(thm)],[106])).
% 2.63/1.93 tff(108,plain,
% 2.63/1.93 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a58) | c0_1(a58) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)))),
% 2.63/1.93 inference(transitivity,[status(thm)],[107, 105])).
% 2.63/1.93 tff(109,plain,
% 2.63/1.93 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a58) | c0_1(a58) | (~c2_1(a58)))),
% 2.63/1.93 inference(quant_inst,[status(thm)],[])).
% 2.63/1.93 tff(110,plain,
% 2.63/1.93 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | (~c2_1(a58))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[109, 108])).
% 2.63/1.93 tff(111,plain,
% 2.63/1.93 (hskp0 | c1_1(a58) | (~c2_1(a58))),
% 2.63/1.93 inference(unit_resolution,[status(thm)],[110, 104, 48, 37, 69])).
% 2.63/1.93 tff(112,plain,
% 2.63/1.93 (hskp0),
% 2.63/1.93 inference(unit_resolution,[status(thm)],[111, 59, 26])).
% 2.63/1.93 tff(113,plain,
% 2.63/1.93 (((~hskp0) | (~c3_1(a1))) <=> ((~hskp0) | (~c3_1(a1)))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(114,plain,
% 2.63/1.93 (((~c3_1(a1)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a1)))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(115,axiom,((~c3_1(a1)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 2.63/1.93 tff(116,plain,
% 2.63/1.93 ((~hskp0) | (~c3_1(a1))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[115, 114])).
% 2.63/1.93 tff(117,plain,
% 2.63/1.93 ((~hskp0) | (~c3_1(a1))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[116, 113])).
% 2.63/1.93 tff(118,plain,
% 2.63/1.93 (~c3_1(a1)),
% 2.63/1.93 inference(unit_resolution,[status(thm)],[117, 112])).
% 2.63/1.93 tff(119,plain,
% 2.63/1.93 (((~hskp0) | c2_1(a1)) <=> ((~hskp0) | c2_1(a1))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(120,axiom,((~hskp0) | c2_1(a1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 2.63/1.93 tff(121,plain,
% 2.63/1.93 ((~hskp0) | c2_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[120, 119])).
% 2.63/1.93 tff(122,plain,
% 2.63/1.93 ((~hskp0) | c2_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[121, 119])).
% 2.63/1.93 tff(123,plain,
% 2.63/1.93 ((~hskp0) | c2_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[122, 119])).
% 2.63/1.93 tff(124,plain,
% 2.63/1.93 ((~hskp0) | c2_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[123, 119])).
% 2.63/1.93 tff(125,plain,
% 2.63/1.93 ((~hskp0) | c2_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[124, 119])).
% 2.63/1.93 tff(126,plain,
% 2.63/1.93 ((~hskp0) | c2_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[125, 119])).
% 2.63/1.93 tff(127,plain,
% 2.63/1.93 ((~hskp0) | c2_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[126, 119])).
% 2.63/1.93 tff(128,plain,
% 2.63/1.93 ((~hskp0) | c2_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[127, 119])).
% 2.63/1.93 tff(129,plain,
% 2.63/1.93 (c2_1(a1)),
% 2.63/1.93 inference(unit_resolution,[status(thm)],[128, 112])).
% 2.63/1.93 tff(130,plain,
% 2.63/1.93 (((~hskp0) | c1_1(a1)) <=> ((~hskp0) | c1_1(a1))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(131,axiom,((~hskp0) | c1_1(a1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 2.63/1.93 tff(132,plain,
% 2.63/1.93 ((~hskp0) | c1_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[131, 130])).
% 2.63/1.93 tff(133,plain,
% 2.63/1.93 ((~hskp0) | c1_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[132, 130])).
% 2.63/1.93 tff(134,plain,
% 2.63/1.93 ((~hskp0) | c1_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[133, 130])).
% 2.63/1.93 tff(135,plain,
% 2.63/1.93 ((~hskp0) | c1_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[134, 130])).
% 2.63/1.93 tff(136,plain,
% 2.63/1.93 ((~hskp0) | c1_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[135, 130])).
% 2.63/1.93 tff(137,plain,
% 2.63/1.93 ((~hskp0) | c1_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[136, 130])).
% 2.63/1.93 tff(138,plain,
% 2.63/1.93 ((~hskp0) | c1_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[137, 130])).
% 2.63/1.93 tff(139,plain,
% 2.63/1.93 ((~hskp0) | c1_1(a1)),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[138, 130])).
% 2.63/1.93 tff(140,plain,
% 2.63/1.93 (c1_1(a1)),
% 2.63/1.93 inference(unit_resolution,[status(thm)],[139, 112])).
% 2.63/1.93 tff(141,plain,
% 2.63/1.93 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 2.63/1.93 inference(bind,[status(th)],[])).
% 2.63/1.93 tff(142,plain,
% 2.63/1.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.63/1.93 inference(quant_intro,[status(thm)],[141])).
% 2.63/1.93 tff(143,plain,
% 2.63/1.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(144,plain,
% 2.63/1.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | 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)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 2.63/1.93 inference(bind,[status(th)],[])).
% 2.63/1.93 tff(145,plain,
% 2.63/1.93 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.63/1.93 inference(quant_intro,[status(thm)],[144])).
% 2.63/1.93 tff(146,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 2.63/1.93 tff(147,plain,
% 2.63/1.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[146, 145])).
% 2.63/1.93 tff(148,plain,
% 2.63/1.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[147, 143])).
% 2.63/1.93 tff(149,plain,(
% 2.63/1.93 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.63/1.93 inference(skolemize,[status(sab)],[148])).
% 2.63/1.93 tff(150,plain,
% 2.63/1.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[149, 142])).
% 2.63/1.93 tff(151,assumption,(~c3_1(a1)), introduced(assumption)).
% 2.63/1.93 tff(152,assumption,(c2_1(a1)), introduced(assumption)).
% 2.63/1.93 tff(153,assumption,(c1_1(a1)), introduced(assumption)).
% 2.63/1.93 tff(154,plain,
% 2.63/1.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(155,plain,
% 2.63/1.93 ((hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | (~c2_1(a1)) | (~c0_1(a1))) <=> (hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(156,plain,
% 2.63/1.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | (~c2_1(a1)) | (~c0_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1))))),
% 2.63/1.93 inference(monotonicity,[status(thm)],[155])).
% 2.63/1.93 tff(157,plain,
% 2.63/1.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | (~c2_1(a1)) | (~c0_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)))),
% 2.63/1.93 inference(transitivity,[status(thm)],[156, 154])).
% 2.63/1.93 tff(158,plain,
% 2.63/1.93 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | (~c2_1(a1)) | (~c0_1(a1)))),
% 2.63/1.93 inference(quant_inst,[status(thm)],[])).
% 2.63/1.93 tff(159,plain,
% 2.63/1.93 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[158, 157])).
% 2.63/1.93 tff(160,plain,
% 2.63/1.93 (hskp6 | (~c0_1(a1))),
% 2.63/1.93 inference(unit_resolution,[status(thm)],[159, 104, 153, 152, 151, 150])).
% 2.63/1.93 tff(161,plain,
% 2.63/1.93 (~c0_1(a1)),
% 2.63/1.93 inference(unit_resolution,[status(thm)],[160, 25])).
% 2.63/1.93 tff(162,plain,
% 2.63/1.93 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 2.63/1.93 inference(bind,[status(th)],[])).
% 2.63/1.93 tff(163,plain,
% 2.63/1.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.63/1.93 inference(quant_intro,[status(thm)],[162])).
% 2.63/1.93 tff(164,plain,
% 2.63/1.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(165,plain,
% 2.63/1.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 2.63/1.93 inference(bind,[status(th)],[])).
% 2.63/1.93 tff(166,plain,
% 2.63/1.93 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.63/1.93 inference(quant_intro,[status(thm)],[165])).
% 2.63/1.93 tff(167,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 2.63/1.93 tff(168,plain,
% 2.63/1.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[167, 166])).
% 2.63/1.93 tff(169,plain,
% 2.63/1.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[168, 164])).
% 2.63/1.93 tff(170,plain,(
% 2.63/1.93 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.63/1.93 inference(skolemize,[status(sab)],[169])).
% 2.63/1.93 tff(171,plain,
% 2.63/1.93 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.63/1.93 inference(modus_ponens,[status(thm)],[170, 163])).
% 2.63/1.93 tff(172,plain,
% 2.63/1.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a1))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a1))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(173,plain,
% 2.63/1.93 ((hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1))) <=> (hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a1))),
% 2.63/1.93 inference(rewrite,[status(thm)],[])).
% 2.63/1.93 tff(174,plain,
% 2.63/1.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a1)))),
% 2.63/1.93 inference(monotonicity,[status(thm)],[173])).
% 2.63/1.93 tff(175,plain,
% 2.63/1.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a1))),
% 2.63/1.94 inference(transitivity,[status(thm)],[174, 172])).
% 2.63/1.94 tff(176,plain,
% 2.63/1.94 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)))),
% 2.63/1.94 inference(quant_inst,[status(thm)],[])).
% 2.63/1.94 tff(177,plain,
% 2.63/1.94 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a1)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[176, 175])).
% 2.63/1.94 tff(178,plain,
% 2.63/1.94 (hskp6 | c0_1(a1)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[177, 104, 153, 152, 151, 171])).
% 2.63/1.94 tff(179,plain,
% 2.63/1.94 ($false),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[178, 161, 25])).
% 2.63/1.94 tff(180,plain,(hskp6 | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1)), inference(lemma,lemma(discharge,[]))).
% 2.63/1.94 tff(181,plain,
% 2.63/1.94 (hskp6),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[180, 140, 129, 118])).
% 2.63/1.94 tff(182,plain,
% 2.63/1.94 (((~hskp6) | (~c3_1(a13))) <=> ((~hskp6) | (~c3_1(a13)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(183,plain,
% 2.63/1.94 (((~c3_1(a13)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a13)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(184,axiom,((~c3_1(a13)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 2.63/1.94 tff(185,plain,
% 2.63/1.94 ((~hskp6) | (~c3_1(a13))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[184, 183])).
% 2.63/1.94 tff(186,plain,
% 2.63/1.94 ((~hskp6) | (~c3_1(a13))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[185, 182])).
% 2.63/1.94 tff(187,plain,
% 2.63/1.94 (~c3_1(a13)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[186, 181])).
% 2.63/1.94 tff(188,plain,
% 2.63/1.94 (((~hskp6) | (~c1_1(a13))) <=> ((~hskp6) | (~c1_1(a13)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(189,plain,
% 2.63/1.94 (((~c1_1(a13)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a13)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(190,axiom,((~c1_1(a13)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 2.63/1.94 tff(191,plain,
% 2.63/1.94 ((~hskp6) | (~c1_1(a13))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[190, 189])).
% 2.63/1.94 tff(192,plain,
% 2.63/1.94 ((~hskp6) | (~c1_1(a13))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[191, 188])).
% 2.63/1.94 tff(193,plain,
% 2.63/1.94 (~c1_1(a13)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[192, 181])).
% 2.63/1.94 tff(194,plain,
% 2.63/1.94 (((~hskp6) | (~c0_1(a13))) <=> ((~hskp6) | (~c0_1(a13)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(195,plain,
% 2.63/1.94 (((~c0_1(a13)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a13)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(196,axiom,((~c0_1(a13)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 2.63/1.94 tff(197,plain,
% 2.63/1.94 ((~hskp6) | (~c0_1(a13))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[196, 195])).
% 2.63/1.94 tff(198,plain,
% 2.63/1.94 ((~hskp6) | (~c0_1(a13))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[197, 194])).
% 2.63/1.94 tff(199,plain,
% 2.63/1.94 (~c0_1(a13)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[198, 181])).
% 2.63/1.94 tff(200,assumption,(~hskp1), introduced(assumption)).
% 2.63/1.94 tff(201,assumption,(hskp2), introduced(assumption)).
% 2.63/1.94 tff(202,plain,
% 2.63/1.94 (((~hskp2) | (~c2_1(a3))) <=> ((~hskp2) | (~c2_1(a3)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(203,plain,
% 2.63/1.94 (((~c2_1(a3)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a3)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(204,axiom,((~c2_1(a3)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 2.63/1.94 tff(205,plain,
% 2.63/1.94 ((~hskp2) | (~c2_1(a3))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[204, 203])).
% 2.63/1.94 tff(206,plain,
% 2.63/1.94 ((~hskp2) | (~c2_1(a3))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[205, 202])).
% 2.63/1.94 tff(207,plain,
% 2.63/1.94 (~c2_1(a3)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[206, 201])).
% 2.63/1.94 tff(208,plain,
% 2.63/1.94 (((~hskp2) | c3_1(a3)) <=> ((~hskp2) | c3_1(a3))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(209,axiom,((~hskp2) | c3_1(a3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 2.63/1.94 tff(210,plain,
% 2.63/1.94 ((~hskp2) | c3_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[209, 208])).
% 2.63/1.94 tff(211,plain,
% 2.63/1.94 ((~hskp2) | c3_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[210, 208])).
% 2.63/1.94 tff(212,plain,
% 2.63/1.94 ((~hskp2) | c3_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[211, 208])).
% 2.63/1.94 tff(213,plain,
% 2.63/1.94 ((~hskp2) | c3_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[212, 208])).
% 2.63/1.94 tff(214,plain,
% 2.63/1.94 ((~hskp2) | c3_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[213, 208])).
% 2.63/1.94 tff(215,plain,
% 2.63/1.94 ((~hskp2) | c3_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[214, 208])).
% 2.63/1.94 tff(216,plain,
% 2.63/1.94 ((~hskp2) | c3_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[215, 208])).
% 2.63/1.94 tff(217,plain,
% 2.63/1.94 ((~hskp2) | c3_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[216, 208])).
% 2.63/1.94 tff(218,plain,
% 2.63/1.94 (c3_1(a3)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[217, 201])).
% 2.63/1.94 tff(219,plain,
% 2.63/1.94 (((~hskp2) | c1_1(a3)) <=> ((~hskp2) | c1_1(a3))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(220,axiom,((~hskp2) | c1_1(a3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 2.63/1.94 tff(221,plain,
% 2.63/1.94 ((~hskp2) | c1_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[220, 219])).
% 2.63/1.94 tff(222,plain,
% 2.63/1.94 ((~hskp2) | c1_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[221, 219])).
% 2.63/1.94 tff(223,plain,
% 2.63/1.94 ((~hskp2) | c1_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[222, 219])).
% 2.63/1.94 tff(224,plain,
% 2.63/1.94 ((~hskp2) | c1_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[223, 219])).
% 2.63/1.94 tff(225,plain,
% 2.63/1.94 ((~hskp2) | c1_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[224, 219])).
% 2.63/1.94 tff(226,plain,
% 2.63/1.94 ((~hskp2) | c1_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[225, 219])).
% 2.63/1.94 tff(227,plain,
% 2.63/1.94 ((~hskp2) | c1_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[226, 219])).
% 2.63/1.94 tff(228,plain,
% 2.63/1.94 ((~hskp2) | c1_1(a3)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[227, 219])).
% 2.63/1.94 tff(229,plain,
% 2.63/1.94 (c1_1(a3)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[228, 201])).
% 2.63/1.94 tff(230,plain,
% 2.63/1.94 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a58)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(231,plain,
% 2.63/1.94 ((hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58))) <=> (hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a58)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(232,plain,
% 2.63/1.94 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a58))))),
% 2.63/1.94 inference(monotonicity,[status(thm)],[231])).
% 2.63/1.94 tff(233,plain,
% 2.63/1.94 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a58)))),
% 2.63/1.94 inference(transitivity,[status(thm)],[232, 230])).
% 2.63/1.94 tff(234,plain,
% 2.63/1.94 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))),
% 2.63/1.94 inference(quant_inst,[status(thm)],[])).
% 2.63/1.94 tff(235,plain,
% 2.63/1.94 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a58))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[234, 233])).
% 2.63/1.94 tff(236,plain,
% 2.63/1.94 ($false),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[235, 104, 200, 59, 229, 218, 37, 26, 207, 58])).
% 2.63/1.94 tff(237,plain,((~hskp2) | hskp1 | (~c2_1(a58)) | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.63/1.94 tff(238,plain,
% 2.63/1.94 (~hskp2),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[237, 200, 59, 37, 26])).
% 2.63/1.94 tff(239,assumption,(~c3_1(a13)), introduced(assumption)).
% 2.63/1.94 tff(240,assumption,(~c1_1(a13)), introduced(assumption)).
% 2.63/1.94 tff(241,assumption,(~c0_1(a13)), introduced(assumption)).
% 2.63/1.94 tff(242,plain,
% 2.63/1.94 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(243,plain,
% 2.63/1.94 ((hskp2 | hskp1 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13)) <=> (hskp2 | hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(244,plain,
% 2.63/1.94 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0)))),
% 2.63/1.94 inference(monotonicity,[status(thm)],[243])).
% 2.63/1.94 tff(245,plain,
% 2.63/1.94 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))),
% 2.63/1.94 inference(transitivity,[status(thm)],[244, 242])).
% 2.63/1.94 tff(246,plain,
% 2.63/1.94 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13))),
% 2.63/1.94 inference(quant_inst,[status(thm)],[])).
% 2.63/1.94 tff(247,plain,
% 2.63/1.94 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0)),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[246, 245])).
% 2.63/1.94 tff(248,plain,
% 2.63/1.94 (hskp2 | hskp1),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[247, 104, 241, 240, 239, 47])).
% 2.63/1.94 tff(249,plain,
% 2.63/1.94 ($false),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[248, 238, 200])).
% 2.63/1.94 tff(250,plain,(hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~c2_1(a58)) | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.63/1.94 tff(251,plain,
% 2.63/1.94 (hskp1),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[250, 199, 193, 187, 59, 37, 26])).
% 2.63/1.94 tff(252,plain,
% 2.63/1.94 (((~hskp1) | (~c3_1(a2))) <=> ((~hskp1) | (~c3_1(a2)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(253,plain,
% 2.63/1.94 (((~c3_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a2)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(254,axiom,((~c3_1(a2)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 2.63/1.94 tff(255,plain,
% 2.63/1.94 ((~hskp1) | (~c3_1(a2))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[254, 253])).
% 2.63/1.94 tff(256,plain,
% 2.63/1.94 ((~hskp1) | (~c3_1(a2))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[255, 252])).
% 2.63/1.94 tff(257,plain,
% 2.63/1.94 (~c3_1(a2)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[256, 251])).
% 2.63/1.94 tff(258,plain,
% 2.63/1.94 (((~hskp1) | (~c2_1(a2))) <=> ((~hskp1) | (~c2_1(a2)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(259,plain,
% 2.63/1.94 (((~c2_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a2)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(260,axiom,((~c2_1(a2)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 2.63/1.94 tff(261,plain,
% 2.63/1.94 ((~hskp1) | (~c2_1(a2))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[260, 259])).
% 2.63/1.94 tff(262,plain,
% 2.63/1.94 ((~hskp1) | (~c2_1(a2))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[261, 258])).
% 2.63/1.94 tff(263,plain,
% 2.63/1.94 (~c2_1(a2)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[262, 251])).
% 2.63/1.94 tff(264,plain,
% 2.63/1.94 (((~hskp1) | (~c0_1(a2))) <=> ((~hskp1) | (~c0_1(a2)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(265,plain,
% 2.63/1.94 (((~c0_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a2)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(266,axiom,((~c0_1(a2)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 2.63/1.94 tff(267,plain,
% 2.63/1.94 ((~hskp1) | (~c0_1(a2))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[266, 265])).
% 2.63/1.94 tff(268,plain,
% 2.63/1.94 ((~hskp1) | (~c0_1(a2))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[267, 264])).
% 2.63/1.94 tff(269,plain,
% 2.63/1.94 (~c0_1(a2)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[268, 251])).
% 2.63/1.94 tff(270,plain,
% 2.63/1.94 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 2.63/1.94 inference(bind,[status(th)],[])).
% 2.63/1.94 tff(271,plain,
% 2.63/1.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.63/1.94 inference(quant_intro,[status(thm)],[270])).
% 2.63/1.94 tff(272,plain,
% 2.63/1.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(273,plain,
% 2.63/1.94 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 2.63/1.94 inference(bind,[status(th)],[])).
% 2.63/1.94 tff(274,plain,
% 2.63/1.94 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.63/1.94 inference(quant_intro,[status(thm)],[273])).
% 2.63/1.94 tff(275,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause201')).
% 2.63/1.94 tff(276,plain,
% 2.63/1.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[275, 274])).
% 2.63/1.94 tff(277,plain,
% 2.63/1.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[276, 272])).
% 2.63/1.94 tff(278,plain,(
% 2.63/1.94 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.63/1.94 inference(skolemize,[status(sab)],[277])).
% 2.63/1.94 tff(279,plain,
% 2.63/1.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[278, 271])).
% 2.63/1.94 tff(280,assumption,(c2_1(a13)), introduced(assumption)).
% 2.63/1.94 tff(281,plain,
% 2.63/1.94 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 2.63/1.94 inference(bind,[status(th)],[])).
% 2.63/1.94 tff(282,plain,
% 2.63/1.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.94 inference(quant_intro,[status(thm)],[281])).
% 2.63/1.94 tff(283,plain,
% 2.63/1.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(284,plain,
% 2.63/1.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 2.63/1.94 inference(bind,[status(th)],[])).
% 2.63/1.94 tff(285,plain,
% 2.63/1.94 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.94 inference(quant_intro,[status(thm)],[284])).
% 2.63/1.94 tff(286,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 2.63/1.94 tff(287,plain,
% 2.63/1.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[286, 285])).
% 2.63/1.94 tff(288,plain,
% 2.63/1.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[287, 283])).
% 2.63/1.94 tff(289,plain,(
% 2.63/1.94 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.94 inference(skolemize,[status(sab)],[288])).
% 2.63/1.94 tff(290,plain,
% 2.63/1.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[289, 282])).
% 2.63/1.94 tff(291,plain,
% 2.63/1.94 (hskp6),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[180, 153, 152, 151])).
% 2.63/1.94 tff(292,plain,
% 2.63/1.94 (~c3_1(a13)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[186, 291])).
% 2.63/1.94 tff(293,plain,
% 2.63/1.94 (~c1_1(a13)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[192, 291])).
% 2.63/1.94 tff(294,plain,
% 2.63/1.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a13)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(295,plain,
% 2.63/1.94 ((hskp5 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp5 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a13)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(296,plain,
% 2.63/1.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a13))))),
% 2.63/1.94 inference(monotonicity,[status(thm)],[295])).
% 2.63/1.94 tff(297,plain,
% 2.63/1.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a13)))),
% 2.63/1.94 inference(transitivity,[status(thm)],[296, 294])).
% 2.63/1.94 tff(298,plain,
% 2.63/1.94 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 2.63/1.94 inference(quant_inst,[status(thm)],[])).
% 2.63/1.94 tff(299,plain,
% 2.63/1.94 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a13))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[298, 297])).
% 2.63/1.94 tff(300,plain,
% 2.63/1.94 (hskp5 | (~c2_1(a13))),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[299, 104, 293, 292, 14, 13, 12, 290])).
% 2.63/1.94 tff(301,plain,
% 2.63/1.94 (hskp5),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[300, 280])).
% 2.63/1.94 tff(302,plain,
% 2.63/1.94 (((~hskp5) | (~c2_1(a11))) <=> ((~hskp5) | (~c2_1(a11)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(303,plain,
% 2.63/1.94 (((~c2_1(a11)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a11)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(304,axiom,((~c2_1(a11)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 2.63/1.94 tff(305,plain,
% 2.63/1.94 ((~hskp5) | (~c2_1(a11))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[304, 303])).
% 2.63/1.94 tff(306,plain,
% 2.63/1.94 ((~hskp5) | (~c2_1(a11))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[305, 302])).
% 2.63/1.94 tff(307,plain,
% 2.63/1.94 (~c2_1(a11)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[306, 301])).
% 2.63/1.94 tff(308,plain,
% 2.63/1.94 (((~hskp5) | (~c1_1(a11))) <=> ((~hskp5) | (~c1_1(a11)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(309,plain,
% 2.63/1.94 (((~c1_1(a11)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a11)))),
% 2.63/1.94 inference(rewrite,[status(thm)],[])).
% 2.63/1.94 tff(310,axiom,((~c1_1(a11)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 2.63/1.94 tff(311,plain,
% 2.63/1.94 ((~hskp5) | (~c1_1(a11))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[310, 309])).
% 2.63/1.94 tff(312,plain,
% 2.63/1.94 ((~hskp5) | (~c1_1(a11))),
% 2.63/1.94 inference(modus_ponens,[status(thm)],[311, 308])).
% 2.63/1.94 tff(313,plain,
% 2.63/1.94 (~c1_1(a11)),
% 2.63/1.94 inference(unit_resolution,[status(thm)],[312, 301])).
% 2.63/1.95 tff(314,plain,
% 2.63/1.95 (((~hskp5) | c0_1(a11)) <=> ((~hskp5) | c0_1(a11))),
% 2.63/1.95 inference(rewrite,[status(thm)],[])).
% 2.63/1.95 tff(315,axiom,((~hskp5) | c0_1(a11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 2.63/1.95 tff(316,plain,
% 2.63/1.95 ((~hskp5) | c0_1(a11)),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[315, 314])).
% 2.63/1.95 tff(317,plain,
% 2.63/1.95 ((~hskp5) | c0_1(a11)),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[316, 314])).
% 2.63/1.95 tff(318,plain,
% 2.63/1.95 ((~hskp5) | c0_1(a11)),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[317, 314])).
% 2.63/1.95 tff(319,plain,
% 2.63/1.95 ((~hskp5) | c0_1(a11)),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[318, 314])).
% 2.63/1.95 tff(320,plain,
% 2.63/1.95 ((~hskp5) | c0_1(a11)),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[319, 314])).
% 2.63/1.95 tff(321,plain,
% 2.63/1.95 ((~hskp5) | c0_1(a11)),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[320, 314])).
% 2.63/1.95 tff(322,plain,
% 2.63/1.95 ((~hskp5) | c0_1(a11)),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[321, 314])).
% 2.63/1.95 tff(323,plain,
% 2.63/1.95 ((~hskp5) | c0_1(a11)),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[322, 314])).
% 2.63/1.95 tff(324,plain,
% 2.63/1.95 (c0_1(a11)),
% 2.63/1.95 inference(unit_resolution,[status(thm)],[323, 301])).
% 2.63/1.95 tff(325,plain,
% 2.63/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a11) | c2_1(a11) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a11)) | (~c0_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a11) | c2_1(a11) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a11)) | (~c0_1(a11)))),
% 2.63/1.95 inference(rewrite,[status(thm)],[])).
% 2.63/1.95 tff(326,plain,
% 2.63/1.95 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11))) <=> (c1_1(a11) | c2_1(a11) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a11)) | (~c0_1(a11)))),
% 2.63/1.95 inference(rewrite,[status(thm)],[])).
% 2.63/1.95 tff(327,plain,
% 2.63/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a11) | c2_1(a11) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a11)) | (~c0_1(a11))))),
% 2.63/1.95 inference(monotonicity,[status(thm)],[326])).
% 2.63/1.95 tff(328,plain,
% 2.63/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a11) | c2_1(a11) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a11)) | (~c0_1(a11)))),
% 2.63/1.95 inference(transitivity,[status(thm)],[327, 325])).
% 2.63/1.95 tff(329,plain,
% 2.63/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11)))),
% 2.63/1.95 inference(quant_inst,[status(thm)],[])).
% 2.63/1.95 tff(330,plain,
% 2.63/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a11) | c2_1(a11) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a11)) | (~c0_1(a11))),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[329, 328])).
% 2.63/1.95 tff(331,plain,
% 2.63/1.95 (~c3_1(a11)),
% 2.63/1.95 inference(unit_resolution,[status(thm)],[330, 104, 324, 153, 152, 313, 307, 151, 279])).
% 2.63/1.95 tff(332,plain,
% 2.63/1.95 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))),
% 2.63/1.95 inference(bind,[status(th)],[])).
% 2.63/1.95 tff(333,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 2.63/1.95 inference(quant_intro,[status(thm)],[332])).
% 2.63/1.95 tff(334,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 2.63/1.95 inference(rewrite,[status(thm)],[])).
% 2.63/1.95 tff(335,plain,
% 2.63/1.95 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~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)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c1_1(W))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))))),
% 2.63/1.95 inference(bind,[status(th)],[])).
% 2.63/1.95 tff(336,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 2.63/1.95 inference(quant_intro,[status(thm)],[335])).
% 2.63/1.95 tff(337,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 2.63/1.95 tff(338,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[337, 336])).
% 2.63/1.95 tff(339,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[338, 334])).
% 2.63/1.95 tff(340,plain,(
% 2.63/1.95 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 2.63/1.95 inference(skolemize,[status(sab)],[339])).
% 2.63/1.95 tff(341,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[340, 333])).
% 2.63/1.95 tff(342,plain,
% 2.63/1.95 (~c0_1(a13)),
% 2.63/1.95 inference(unit_resolution,[status(thm)],[198, 291])).
% 2.63/1.95 tff(343,plain,
% 2.63/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a13) | c3_1(a13) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a13) | c3_1(a13) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a13)))),
% 2.63/1.95 inference(rewrite,[status(thm)],[])).
% 2.63/1.95 tff(344,plain,
% 2.63/1.95 (((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a11) | c1_1(a11) | c3_1(a11)) <=> (c0_1(a13) | c3_1(a13) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a13)))),
% 2.63/1.95 inference(rewrite,[status(thm)],[])).
% 2.63/1.95 tff(345,plain,
% 2.63/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a11) | c1_1(a11) | c3_1(a11))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a13) | c3_1(a13) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a13))))),
% 2.63/1.95 inference(monotonicity,[status(thm)],[344])).
% 2.63/1.95 tff(346,plain,
% 2.63/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a11) | c1_1(a11) | c3_1(a11))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a13) | c3_1(a13) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a13)))),
% 2.63/1.95 inference(transitivity,[status(thm)],[345, 343])).
% 2.63/1.95 tff(347,plain,
% 2.63/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a11) | c1_1(a11) | c3_1(a11))),
% 2.63/1.95 inference(quant_inst,[status(thm)],[])).
% 2.63/1.95 tff(348,plain,
% 2.63/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a13) | c3_1(a13) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a13))),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[347, 346])).
% 2.63/1.95 tff(349,plain,
% 2.63/1.95 ($false),
% 2.63/1.95 inference(unit_resolution,[status(thm)],[348, 104, 324, 342, 292, 313, 307, 341, 280, 331])).
% 2.63/1.95 tff(350,plain,((~c2_1(a13)) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.63/1.95 tff(351,plain,
% 2.63/1.95 (~c2_1(a13)),
% 2.63/1.95 inference(unit_resolution,[status(thm)],[350, 269, 129, 118, 140, 263, 257])).
% 2.63/1.95 tff(352,assumption,(~c2_1(a13)), introduced(assumption)).
% 2.63/1.95 tff(353,plain,
% 2.63/1.95 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 2.63/1.95 inference(bind,[status(th)],[])).
% 2.63/1.95 tff(354,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.95 inference(quant_intro,[status(thm)],[353])).
% 2.63/1.95 tff(355,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.95 inference(rewrite,[status(thm)],[])).
% 2.63/1.95 tff(356,plain,
% 2.63/1.95 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~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)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_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))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 2.63/1.95 inference(bind,[status(th)],[])).
% 2.63/1.95 tff(357,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.95 inference(quant_intro,[status(thm)],[356])).
% 2.63/1.95 tff(358,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 2.63/1.95 tff(359,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[358, 357])).
% 2.63/1.95 tff(360,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[359, 355])).
% 2.63/1.95 tff(361,plain,(
% 2.63/1.95 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.95 inference(skolemize,[status(sab)],[360])).
% 2.63/1.95 tff(362,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[361, 354])).
% 2.63/1.95 tff(363,plain,
% 2.63/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.63/1.95 inference(rewrite,[status(thm)],[])).
% 2.63/1.95 tff(364,plain,
% 2.63/1.95 (((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a58) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.63/1.95 inference(rewrite,[status(thm)],[])).
% 2.63/1.95 tff(365,plain,
% 2.63/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58))))),
% 2.63/1.95 inference(monotonicity,[status(thm)],[364])).
% 2.63/1.95 tff(366,plain,
% 2.63/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.63/1.95 inference(transitivity,[status(thm)],[365, 363])).
% 2.63/1.95 tff(367,plain,
% 2.63/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 2.63/1.95 inference(quant_inst,[status(thm)],[])).
% 2.63/1.95 tff(368,plain,
% 2.63/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58))),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[367, 366])).
% 2.63/1.95 tff(369,plain,
% 2.63/1.95 (c0_1(a2) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58))),
% 2.63/1.95 inference(unit_resolution,[status(thm)],[368, 104, 26, 240, 239, 13, 12, 362])).
% 2.63/1.95 tff(370,plain,
% 2.63/1.95 (~c3_1(a58)),
% 2.63/1.95 inference(unit_resolution,[status(thm)],[369, 59, 352, 14])).
% 2.63/1.95 tff(371,plain,
% 2.63/1.95 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 2.63/1.95 inference(bind,[status(th)],[])).
% 2.63/1.95 tff(372,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.63/1.95 inference(quant_intro,[status(thm)],[371])).
% 2.63/1.95 tff(373,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.63/1.95 inference(rewrite,[status(thm)],[])).
% 2.63/1.95 tff(374,plain,
% 2.63/1.95 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 2.63/1.95 inference(bind,[status(th)],[])).
% 2.63/1.95 tff(375,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_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) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.63/1.95 inference(quant_intro,[status(thm)],[374])).
% 2.63/1.95 tff(376,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 2.63/1.95 tff(377,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[376, 375])).
% 2.63/1.95 tff(378,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[377, 373])).
% 2.63/1.95 tff(379,plain,(
% 2.63/1.95 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.63/1.95 inference(skolemize,[status(sab)],[378])).
% 2.63/1.95 tff(380,plain,
% 2.63/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.63/1.95 inference(modus_ponens,[status(thm)],[379, 372])).
% 2.63/1.95 tff(381,plain,
% 2.63/1.95 (^[U: $i] : refl((hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 2.63/1.95 inference(bind,[status(th)],[])).
% 2.63/1.95 tff(382,plain,
% 2.63/1.95 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.95 inference(quant_intro,[status(thm)],[381])).
% 2.63/1.95 tff(383,plain,
% 2.63/1.95 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.95 inference(rewrite,[status(thm)],[])).
% 2.63/1.95 tff(384,plain,
% 2.63/1.95 (^[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)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp3) | hskp18) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp18))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp18) <=> (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp3) | hskp18) <=> (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 2.63/1.96 inference(bind,[status(th)],[])).
% 2.63/1.96 tff(385,plain,
% 2.63/1.96 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp3) | hskp18) <=> ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.96 inference(quant_intro,[status(thm)],[384])).
% 2.63/1.96 tff(386,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp3) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 2.63/1.96 tff(387,plain,
% 2.63/1.96 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[386, 385])).
% 2.63/1.96 tff(388,plain,
% 2.63/1.96 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[387, 383])).
% 2.63/1.96 tff(389,plain,(
% 2.63/1.96 ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.96 inference(skolemize,[status(sab)],[388])).
% 2.63/1.96 tff(390,plain,
% 2.63/1.96 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[389, 382])).
% 2.63/1.96 tff(391,plain,
% 2.63/1.96 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(392,plain,
% 2.63/1.96 ((hskp18 | hskp3 | (~ndr1_0) | c3_1(a58) | c0_1(a58) | (~c2_1(a58))) <=> (hskp18 | hskp3 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(393,plain,
% 2.63/1.96 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)))),
% 2.63/1.96 inference(monotonicity,[status(thm)],[392])).
% 2.63/1.96 tff(394,plain,
% 2.63/1.96 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 2.63/1.96 inference(transitivity,[status(thm)],[393, 391])).
% 2.63/1.96 tff(395,plain,
% 2.63/1.96 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)))),
% 2.63/1.96 inference(quant_inst,[status(thm)],[])).
% 2.63/1.96 tff(396,plain,
% 2.63/1.96 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[395, 394])).
% 2.63/1.96 tff(397,plain,
% 2.63/1.96 (hskp18 | (~c2_1(a58)) | c3_1(a58)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[396, 104, 48, 37, 390])).
% 2.63/1.96 tff(398,plain,
% 2.63/1.96 (hskp18),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[397, 59, 370])).
% 2.63/1.96 tff(399,plain,
% 2.63/1.96 (((~hskp18) | (~c3_1(a31))) <=> ((~hskp18) | (~c3_1(a31)))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(400,plain,
% 2.63/1.96 (((~c3_1(a31)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a31)))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(401,axiom,((~c3_1(a31)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 2.63/1.96 tff(402,plain,
% 2.63/1.96 ((~hskp18) | (~c3_1(a31))),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[401, 400])).
% 2.63/1.96 tff(403,plain,
% 2.63/1.96 ((~hskp18) | (~c3_1(a31))),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[402, 399])).
% 2.63/1.96 tff(404,plain,
% 2.63/1.96 (~c3_1(a31)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[403, 398])).
% 2.63/1.96 tff(405,plain,
% 2.63/1.96 (((~hskp18) | c1_1(a31)) <=> ((~hskp18) | c1_1(a31))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(406,axiom,((~hskp18) | c1_1(a31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 2.63/1.96 tff(407,plain,
% 2.63/1.96 ((~hskp18) | c1_1(a31)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[406, 405])).
% 2.63/1.96 tff(408,plain,
% 2.63/1.96 ((~hskp18) | c1_1(a31)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[407, 405])).
% 2.63/1.96 tff(409,plain,
% 2.63/1.96 ((~hskp18) | c1_1(a31)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[408, 405])).
% 2.63/1.96 tff(410,plain,
% 2.63/1.96 ((~hskp18) | c1_1(a31)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[409, 405])).
% 2.63/1.96 tff(411,plain,
% 2.63/1.96 ((~hskp18) | c1_1(a31)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[410, 405])).
% 2.63/1.96 tff(412,plain,
% 2.63/1.96 ((~hskp18) | c1_1(a31)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[411, 405])).
% 2.63/1.96 tff(413,plain,
% 2.63/1.96 ((~hskp18) | c1_1(a31)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[412, 405])).
% 2.63/1.96 tff(414,plain,
% 2.63/1.96 ((~hskp18) | c1_1(a31)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[413, 405])).
% 2.63/1.96 tff(415,plain,
% 2.63/1.96 (c1_1(a31)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[414, 398])).
% 2.63/1.96 tff(416,plain,
% 2.63/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a58) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(417,plain,
% 2.63/1.96 (((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13)) <=> (c1_1(a58) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(418,plain,
% 2.63/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a58) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58)))),
% 2.63/1.96 inference(monotonicity,[status(thm)],[417])).
% 2.63/1.96 tff(419,plain,
% 2.63/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))),
% 2.63/1.96 inference(transitivity,[status(thm)],[418, 416])).
% 2.63/1.96 tff(420,plain,
% 2.63/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13))),
% 2.63/1.96 inference(quant_inst,[status(thm)],[])).
% 2.63/1.96 tff(421,plain,
% 2.63/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[420, 419])).
% 2.63/1.96 tff(422,plain,
% 2.63/1.96 (c2_1(a31)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[421, 104, 59, 415, 26, 404, 241, 240, 380, 352, 370])).
% 2.63/1.96 tff(423,plain,
% 2.63/1.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(424,plain,
% 2.63/1.96 ((hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a13) | c2_1(a13) | c0_1(a13)) <=> (hskp5 | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(425,plain,
% 2.63/1.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a13) | c2_1(a13) | c0_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58)))),
% 2.63/1.96 inference(monotonicity,[status(thm)],[424])).
% 2.63/1.96 tff(426,plain,
% 2.63/1.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a13) | c2_1(a13) | c0_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))),
% 2.63/1.96 inference(transitivity,[status(thm)],[425, 423])).
% 2.63/1.96 tff(427,plain,
% 2.63/1.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a13) | c2_1(a13) | c0_1(a13))),
% 2.63/1.96 inference(quant_inst,[status(thm)],[])).
% 2.63/1.96 tff(428,plain,
% 2.63/1.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[427, 426])).
% 2.63/1.96 tff(429,plain,
% 2.63/1.96 (hskp5),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[428, 104, 59, 26, 241, 239, 290, 352, 370])).
% 2.63/1.96 tff(430,plain,
% 2.63/1.96 (~c2_1(a11)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[306, 429])).
% 2.63/1.96 tff(431,plain,
% 2.63/1.96 (~c1_1(a11)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[312, 429])).
% 2.63/1.96 tff(432,plain,
% 2.63/1.96 (c0_1(a11)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[323, 429])).
% 2.63/1.96 tff(433,plain,
% 2.63/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c1_1(a31)) | (~c2_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(434,plain,
% 2.63/1.96 (((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11))) <=> (c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(435,plain,
% 2.63/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c1_1(a31)) | (~c2_1(a31))))),
% 2.63/1.96 inference(monotonicity,[status(thm)],[434])).
% 2.63/1.96 tff(436,plain,
% 2.63/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.63/1.96 inference(transitivity,[status(thm)],[435, 433])).
% 2.63/1.96 tff(437,plain,
% 2.63/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11)))),
% 2.63/1.96 inference(quant_inst,[status(thm)],[])).
% 2.63/1.96 tff(438,plain,
% 2.63/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c1_1(a31)) | (~c2_1(a31))),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[437, 436])).
% 2.63/1.96 tff(439,plain,
% 2.63/1.96 (~c3_1(a11)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[438, 104, 415, 432, 404, 431, 430, 279, 422])).
% 2.63/1.96 tff(440,plain,
% 2.63/1.96 (((~hskp18) | (~c0_1(a31))) <=> ((~hskp18) | (~c0_1(a31)))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(441,plain,
% 2.63/1.96 (((~c0_1(a31)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a31)))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(442,axiom,((~c0_1(a31)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 2.63/1.96 tff(443,plain,
% 2.63/1.96 ((~hskp18) | (~c0_1(a31))),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[442, 441])).
% 2.63/1.96 tff(444,plain,
% 2.63/1.96 ((~hskp18) | (~c0_1(a31))),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[443, 440])).
% 2.63/1.96 tff(445,plain,
% 2.63/1.96 (~c0_1(a31)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[444, 398])).
% 2.63/1.96 tff(446,plain,
% 2.63/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a31) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a31) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(447,plain,
% 2.63/1.96 (((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a11) | c1_1(a11) | c3_1(a11)) <=> (c0_1(a31) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(448,plain,
% 2.63/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a11) | c1_1(a11) | c3_1(a11))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a31) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31))))),
% 2.63/1.96 inference(monotonicity,[status(thm)],[447])).
% 2.63/1.96 tff(449,plain,
% 2.63/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a11) | c1_1(a11) | c3_1(a11))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a31) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))),
% 2.63/1.96 inference(transitivity,[status(thm)],[448, 446])).
% 2.63/1.96 tff(450,plain,
% 2.63/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a11) | c1_1(a11) | c3_1(a11))),
% 2.63/1.96 inference(quant_inst,[status(thm)],[])).
% 2.63/1.96 tff(451,plain,
% 2.63/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a31) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31))),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[450, 449])).
% 2.63/1.96 tff(452,plain,
% 2.63/1.96 ($false),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[451, 104, 432, 445, 404, 431, 430, 341, 422, 439])).
% 2.63/1.96 tff(453,plain,((~c2_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c2_1(a13) | c1_1(a13) | hskp3 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.63/1.96 tff(454,plain,
% 2.63/1.96 ($false),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[453, 351, 269, 59, 187, 26, 193, 48, 37, 199, 263, 257])).
% 2.63/1.96 tff(455,plain,((~c2_1(a58)) | c1_1(a58) | hskp3 | c0_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.63/1.96 tff(456,plain,
% 2.63/1.96 (~c2_1(a58)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[455, 48, 26, 37])).
% 2.63/1.96 tff(457,plain,
% 2.63/1.96 (((~hskp24) | c2_1(a58)) <=> ((~hskp24) | c2_1(a58))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(458,axiom,((~hskp24) | c2_1(a58)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 2.63/1.96 tff(459,plain,
% 2.63/1.96 ((~hskp24) | c2_1(a58)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[458, 457])).
% 2.63/1.96 tff(460,plain,
% 2.63/1.96 ((~hskp24) | c2_1(a58)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[459, 457])).
% 2.63/1.96 tff(461,plain,
% 2.63/1.96 ((~hskp24) | c2_1(a58)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[460, 457])).
% 2.63/1.96 tff(462,plain,
% 2.63/1.96 ((~hskp24) | c2_1(a58)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[461, 457])).
% 2.63/1.96 tff(463,plain,
% 2.63/1.96 ((~hskp24) | c2_1(a58)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[462, 457])).
% 2.63/1.96 tff(464,plain,
% 2.63/1.96 ((~hskp24) | c2_1(a58)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[463, 457])).
% 2.63/1.96 tff(465,plain,
% 2.63/1.96 ((~hskp24) | c2_1(a58)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[464, 457])).
% 2.63/1.96 tff(466,plain,
% 2.63/1.96 ((~hskp24) | c2_1(a58)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[465, 457])).
% 2.63/1.96 tff(467,plain,
% 2.63/1.96 (~hskp24),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[466, 456])).
% 2.63/1.96 tff(468,assumption,(~c3_1(a15)), introduced(assumption)).
% 2.63/1.96 tff(469,assumption,(hskp6), introduced(assumption)).
% 2.63/1.96 tff(470,plain,
% 2.63/1.96 (~c0_1(a13)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[198, 469])).
% 2.63/1.96 tff(471,plain,
% 2.63/1.96 (~c3_1(a13)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[186, 469])).
% 2.63/1.96 tff(472,plain,
% 2.63/1.96 (~c2_1(a58)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[455, 26, 48, 37])).
% 2.63/1.96 tff(473,plain,
% 2.63/1.96 (~hskp24),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[466, 472])).
% 2.63/1.96 tff(474,assumption,(~c2_1(a38)), introduced(assumption)).
% 2.63/1.96 tff(475,assumption,(~c1_1(a15)), introduced(assumption)).
% 2.63/1.96 tff(476,plain,
% 2.63/1.96 (~c2_1(a58)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[111, 11, 26])).
% 2.63/1.96 tff(477,assumption,(hskp28), introduced(assumption)).
% 2.63/1.96 tff(478,plain,
% 2.63/1.96 (((~hskp28) | c3_1(a25)) <=> ((~hskp28) | c3_1(a25))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(479,axiom,((~hskp28) | c3_1(a25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 2.63/1.96 tff(480,plain,
% 2.63/1.96 ((~hskp28) | c3_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[479, 478])).
% 2.63/1.96 tff(481,plain,
% 2.63/1.96 ((~hskp28) | c3_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[480, 478])).
% 2.63/1.96 tff(482,plain,
% 2.63/1.96 ((~hskp28) | c3_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[481, 478])).
% 2.63/1.96 tff(483,plain,
% 2.63/1.96 ((~hskp28) | c3_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[482, 478])).
% 2.63/1.96 tff(484,plain,
% 2.63/1.96 ((~hskp28) | c3_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[483, 478])).
% 2.63/1.96 tff(485,plain,
% 2.63/1.96 ((~hskp28) | c3_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[484, 478])).
% 2.63/1.96 tff(486,plain,
% 2.63/1.96 ((~hskp28) | c3_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[485, 478])).
% 2.63/1.96 tff(487,plain,
% 2.63/1.96 ((~hskp28) | c3_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[486, 478])).
% 2.63/1.96 tff(488,plain,
% 2.63/1.96 (c3_1(a25)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[487, 477])).
% 2.63/1.96 tff(489,plain,
% 2.63/1.96 (((~hskp28) | c1_1(a25)) <=> ((~hskp28) | c1_1(a25))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(490,axiom,((~hskp28) | c1_1(a25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 2.63/1.96 tff(491,plain,
% 2.63/1.96 ((~hskp28) | c1_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[490, 489])).
% 2.63/1.96 tff(492,plain,
% 2.63/1.96 ((~hskp28) | c1_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[491, 489])).
% 2.63/1.96 tff(493,plain,
% 2.63/1.96 ((~hskp28) | c1_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[492, 489])).
% 2.63/1.96 tff(494,plain,
% 2.63/1.96 ((~hskp28) | c1_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[493, 489])).
% 2.63/1.96 tff(495,plain,
% 2.63/1.96 ((~hskp28) | c1_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[494, 489])).
% 2.63/1.96 tff(496,plain,
% 2.63/1.96 ((~hskp28) | c1_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[495, 489])).
% 2.63/1.96 tff(497,plain,
% 2.63/1.96 ((~hskp28) | c1_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[496, 489])).
% 2.63/1.96 tff(498,plain,
% 2.63/1.96 ((~hskp28) | c1_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[497, 489])).
% 2.63/1.96 tff(499,plain,
% 2.63/1.96 (c1_1(a25)),
% 2.63/1.96 inference(unit_resolution,[status(thm)],[498, 477])).
% 2.63/1.96 tff(500,plain,
% 2.63/1.96 (((~hskp28) | c2_1(a25)) <=> ((~hskp28) | c2_1(a25))),
% 2.63/1.96 inference(rewrite,[status(thm)],[])).
% 2.63/1.96 tff(501,axiom,((~hskp28) | c2_1(a25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 2.63/1.96 tff(502,plain,
% 2.63/1.96 ((~hskp28) | c2_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[501, 500])).
% 2.63/1.96 tff(503,plain,
% 2.63/1.96 ((~hskp28) | c2_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[502, 500])).
% 2.63/1.96 tff(504,plain,
% 2.63/1.96 ((~hskp28) | c2_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[503, 500])).
% 2.63/1.96 tff(505,plain,
% 2.63/1.96 ((~hskp28) | c2_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[504, 500])).
% 2.63/1.96 tff(506,plain,
% 2.63/1.96 ((~hskp28) | c2_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[505, 500])).
% 2.63/1.96 tff(507,plain,
% 2.63/1.96 ((~hskp28) | c2_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[506, 500])).
% 2.63/1.96 tff(508,plain,
% 2.63/1.96 ((~hskp28) | c2_1(a25)),
% 2.63/1.96 inference(modus_ponens,[status(thm)],[507, 500])).
% 2.63/1.96 tff(509,plain,
% 2.63/1.96 ((~hskp28) | c2_1(a25)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[508, 500])).
% 2.63/1.97 tff(510,plain,
% 2.63/1.97 (c2_1(a25)),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[509, 477])).
% 2.63/1.97 tff(511,assumption,(ndr1_0), introduced(assumption)).
% 2.63/1.97 tff(512,plain,
% 2.63/1.97 (hskp3 | hskp0 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58))),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[110, 26, 69])).
% 2.63/1.97 tff(513,plain,
% 2.63/1.97 (~c2_1(a58)),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[512, 48, 11, 511, 37])).
% 2.63/1.97 tff(514,assumption,(c3_1(a25)), introduced(assumption)).
% 2.63/1.97 tff(515,assumption,(c2_1(a25)), introduced(assumption)).
% 2.63/1.97 tff(516,assumption,(c1_1(a25)), introduced(assumption)).
% 2.63/1.97 tff(517,plain,
% 2.63/1.97 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(518,plain,
% 2.63/1.97 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(519,plain,
% 2.63/1.97 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c2_1(a25))))),
% 2.63/1.97 inference(monotonicity,[status(thm)],[518])).
% 2.63/1.97 tff(520,plain,
% 2.63/1.97 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 2.63/1.97 inference(transitivity,[status(thm)],[519, 517])).
% 2.63/1.97 tff(521,plain,
% 2.63/1.97 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)))),
% 2.63/1.97 inference(quant_inst,[status(thm)],[])).
% 2.63/1.97 tff(522,plain,
% 2.63/1.97 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c2_1(a25))),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[521, 520])).
% 2.63/1.97 tff(523,plain,
% 2.63/1.97 (hskp24 | hskp3),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[522, 511, 516, 515, 514, 10])).
% 2.63/1.97 tff(524,plain,
% 2.63/1.97 (hskp24),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[523, 48])).
% 2.63/1.97 tff(525,plain,
% 2.63/1.97 ($false),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[466, 524, 513])).
% 2.63/1.97 tff(526,plain,(hskp3 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | (~c3_1(a25)) | hskp0 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.63/1.97 tff(527,plain,
% 2.63/1.97 (hskp3 | (~c1_1(a25)) | (~c2_1(a25)) | (~c3_1(a25)) | hskp0 | c0_1(a58) | c1_1(a58)),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[526, 104])).
% 2.63/1.97 tff(528,plain,
% 2.63/1.97 ($false),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[527, 510, 499, 48, 488, 11, 37, 26])).
% 2.63/1.97 tff(529,plain,((~hskp28) | hskp3 | hskp0 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.63/1.97 tff(530,plain,
% 2.63/1.97 (~hskp28),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[529, 11, 48, 37, 26])).
% 2.63/1.97 tff(531,plain,
% 2.63/1.97 ((hskp28 | hskp20 | hskp1) <=> (hskp28 | hskp20 | hskp1)),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(532,plain,
% 2.63/1.97 (((hskp28 | hskp20) | hskp1) <=> (hskp28 | hskp20 | hskp1)),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(533,plain,
% 2.63/1.97 ((hskp28 | hskp20) <=> (hskp28 | hskp20)),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(534,plain,
% 2.63/1.97 (((hskp28 | hskp20) | hskp1) <=> ((hskp28 | hskp20) | hskp1)),
% 2.63/1.97 inference(monotonicity,[status(thm)],[533])).
% 2.63/1.97 tff(535,plain,
% 2.63/1.97 (((hskp28 | hskp20) | hskp1) <=> (hskp28 | hskp20 | hskp1)),
% 2.63/1.97 inference(transitivity,[status(thm)],[534, 532])).
% 2.63/1.97 tff(536,axiom,((hskp28 | hskp20) | hskp1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 2.63/1.97 tff(537,plain,
% 2.63/1.97 (hskp28 | hskp20 | hskp1),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[536, 535])).
% 2.63/1.97 tff(538,plain,
% 2.63/1.97 (hskp28 | hskp20 | hskp1),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[537, 531])).
% 2.63/1.97 tff(539,plain,
% 2.63/1.97 (hskp28 | hskp20 | hskp1),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[538, 531])).
% 2.63/1.97 tff(540,plain,
% 2.63/1.97 (hskp28 | hskp20 | hskp1),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[539, 531])).
% 2.63/1.97 tff(541,plain,
% 2.63/1.97 (hskp28 | hskp20 | hskp1),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[540, 531])).
% 2.63/1.97 tff(542,plain,
% 2.63/1.97 (hskp28 | hskp20 | hskp1),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[541, 531])).
% 2.63/1.97 tff(543,plain,
% 2.63/1.97 (hskp28 | hskp20 | hskp1),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[542, 531])).
% 2.63/1.97 tff(544,plain,
% 2.63/1.97 (hskp28 | hskp20 | hskp1),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[543, 531])).
% 2.63/1.97 tff(545,plain,
% 2.63/1.97 (hskp20),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[544, 530, 200])).
% 2.63/1.97 tff(546,plain,
% 2.63/1.97 (((~hskp20) | c3_1(a37)) <=> ((~hskp20) | c3_1(a37))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(547,axiom,((~hskp20) | c3_1(a37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 2.63/1.97 tff(548,plain,
% 2.63/1.97 ((~hskp20) | c3_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[547, 546])).
% 2.63/1.97 tff(549,plain,
% 2.63/1.97 ((~hskp20) | c3_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[548, 546])).
% 2.63/1.97 tff(550,plain,
% 2.63/1.97 ((~hskp20) | c3_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[549, 546])).
% 2.63/1.97 tff(551,plain,
% 2.63/1.97 ((~hskp20) | c3_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[550, 546])).
% 2.63/1.97 tff(552,plain,
% 2.63/1.97 ((~hskp20) | c3_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[551, 546])).
% 2.63/1.97 tff(553,plain,
% 2.63/1.97 ((~hskp20) | c3_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[552, 546])).
% 2.63/1.97 tff(554,plain,
% 2.63/1.97 ((~hskp20) | c3_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[553, 546])).
% 2.63/1.97 tff(555,plain,
% 2.63/1.97 ((~hskp20) | c3_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[554, 546])).
% 2.63/1.97 tff(556,plain,
% 2.63/1.97 (c3_1(a37)),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[555, 545])).
% 2.63/1.97 tff(557,plain,
% 2.63/1.97 (((~hskp20) | c1_1(a37)) <=> ((~hskp20) | c1_1(a37))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(558,axiom,((~hskp20) | c1_1(a37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 2.63/1.97 tff(559,plain,
% 2.63/1.97 ((~hskp20) | c1_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[558, 557])).
% 2.63/1.97 tff(560,plain,
% 2.63/1.97 ((~hskp20) | c1_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[559, 557])).
% 2.63/1.97 tff(561,plain,
% 2.63/1.97 ((~hskp20) | c1_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[560, 557])).
% 2.63/1.97 tff(562,plain,
% 2.63/1.97 ((~hskp20) | c1_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[561, 557])).
% 2.63/1.97 tff(563,plain,
% 2.63/1.97 ((~hskp20) | c1_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[562, 557])).
% 2.63/1.97 tff(564,plain,
% 2.63/1.97 ((~hskp20) | c1_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[563, 557])).
% 2.63/1.97 tff(565,plain,
% 2.63/1.97 ((~hskp20) | c1_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[564, 557])).
% 2.63/1.97 tff(566,plain,
% 2.63/1.97 ((~hskp20) | c1_1(a37)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[565, 557])).
% 2.63/1.97 tff(567,plain,
% 2.63/1.97 (c1_1(a37)),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[566, 545])).
% 2.63/1.97 tff(568,assumption,(~hskp24), introduced(assumption)).
% 2.63/1.97 tff(569,plain,
% 2.63/1.97 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(570,plain,
% 2.63/1.97 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.63/1.97 inference(quant_inst,[status(thm)],[])).
% 2.63/1.97 tff(571,plain,
% 2.63/1.97 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)) | (~c1_1(a37))),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[570, 569])).
% 2.63/1.97 tff(572,plain,
% 2.63/1.97 (~c2_1(a37)),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[571, 104, 568, 48, 567, 556, 10])).
% 2.63/1.97 tff(573,plain,
% 2.63/1.97 (^[U: $i] : refl((hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 2.63/1.97 inference(bind,[status(th)],[])).
% 2.63/1.97 tff(574,plain,
% 2.63/1.97 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.97 inference(quant_intro,[status(thm)],[573])).
% 2.63/1.97 tff(575,plain,
% 2.63/1.97 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(576,plain,
% 2.63/1.97 (^[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)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp0) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0) <=> (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp0) <=> (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 2.63/1.97 inference(bind,[status(th)],[])).
% 2.63/1.97 tff(577,plain,
% 2.63/1.97 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp0) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.97 inference(quant_intro,[status(thm)],[576])).
% 2.63/1.97 tff(578,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 2.63/1.97 tff(579,plain,
% 2.63/1.97 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[578, 577])).
% 2.63/1.97 tff(580,plain,
% 2.63/1.97 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[579, 575])).
% 2.63/1.97 tff(581,plain,(
% 2.63/1.97 ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.97 inference(skolemize,[status(sab)],[580])).
% 2.63/1.97 tff(582,plain,
% 2.63/1.97 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[581, 574])).
% 2.63/1.97 tff(583,plain,
% 2.63/1.97 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(584,plain,
% 2.63/1.97 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.63/1.97 inference(quant_inst,[status(thm)],[])).
% 2.63/1.97 tff(585,plain,
% 2.63/1.97 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[584, 583])).
% 2.63/1.97 tff(586,plain,
% 2.63/1.97 ($false),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[585, 104, 530, 11, 567, 556, 582, 572])).
% 2.63/1.97 tff(587,plain,(hskp0 | hskp24 | hskp3 | hskp1 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.63/1.97 tff(588,plain,
% 2.63/1.97 (hskp24),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[587, 11, 48, 200, 37, 26])).
% 2.63/1.97 tff(589,plain,
% 2.63/1.97 ($false),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[466, 588, 476])).
% 2.63/1.97 tff(590,plain,(hskp0 | hskp3 | hskp1 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.63/1.97 tff(591,plain,
% 2.63/1.97 (hskp1),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[590, 11, 48, 37, 26])).
% 2.63/1.97 tff(592,plain,
% 2.63/1.97 (~c0_1(a2)),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[268, 591])).
% 2.63/1.97 tff(593,plain,
% 2.63/1.97 (~c2_1(a2)),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[262, 591])).
% 2.63/1.97 tff(594,plain,
% 2.63/1.97 (~hskp24),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[466, 476])).
% 2.63/1.97 tff(595,assumption,(hskp27), introduced(assumption)).
% 2.63/1.97 tff(596,plain,
% 2.63/1.97 (((~hskp27) | c3_1(a12)) <=> ((~hskp27) | c3_1(a12))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(597,axiom,((~hskp27) | c3_1(a12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 2.63/1.97 tff(598,plain,
% 2.63/1.97 ((~hskp27) | c3_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[597, 596])).
% 2.63/1.97 tff(599,plain,
% 2.63/1.97 ((~hskp27) | c3_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[598, 596])).
% 2.63/1.97 tff(600,plain,
% 2.63/1.97 ((~hskp27) | c3_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[599, 596])).
% 2.63/1.97 tff(601,plain,
% 2.63/1.97 ((~hskp27) | c3_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[600, 596])).
% 2.63/1.97 tff(602,plain,
% 2.63/1.97 ((~hskp27) | c3_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[601, 596])).
% 2.63/1.97 tff(603,plain,
% 2.63/1.97 ((~hskp27) | c3_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[602, 596])).
% 2.63/1.97 tff(604,plain,
% 2.63/1.97 ((~hskp27) | c3_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[603, 596])).
% 2.63/1.97 tff(605,plain,
% 2.63/1.97 ((~hskp27) | c3_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[604, 596])).
% 2.63/1.97 tff(606,plain,
% 2.63/1.97 (c3_1(a12)),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[605, 595])).
% 2.63/1.97 tff(607,plain,
% 2.63/1.97 (((~hskp27) | c1_1(a12)) <=> ((~hskp27) | c1_1(a12))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(608,axiom,((~hskp27) | c1_1(a12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 2.63/1.97 tff(609,plain,
% 2.63/1.97 ((~hskp27) | c1_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[608, 607])).
% 2.63/1.97 tff(610,plain,
% 2.63/1.97 ((~hskp27) | c1_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[609, 607])).
% 2.63/1.97 tff(611,plain,
% 2.63/1.97 ((~hskp27) | c1_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[610, 607])).
% 2.63/1.97 tff(612,plain,
% 2.63/1.97 ((~hskp27) | c1_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[611, 607])).
% 2.63/1.97 tff(613,plain,
% 2.63/1.97 ((~hskp27) | c1_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[612, 607])).
% 2.63/1.97 tff(614,plain,
% 2.63/1.97 ((~hskp27) | c1_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[613, 607])).
% 2.63/1.97 tff(615,plain,
% 2.63/1.97 ((~hskp27) | c1_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[614, 607])).
% 2.63/1.97 tff(616,plain,
% 2.63/1.97 ((~hskp27) | c1_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[615, 607])).
% 2.63/1.97 tff(617,plain,
% 2.63/1.97 (c1_1(a12)),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[616, 595])).
% 2.63/1.97 tff(618,plain,
% 2.63/1.97 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c2_1(a12)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c2_1(a12)))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(619,plain,
% 2.63/1.97 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a12)) | (~c3_1(a12)) | (~c1_1(a12))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c2_1(a12)))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(620,plain,
% 2.63/1.97 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a12)) | (~c3_1(a12)) | (~c1_1(a12)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c2_1(a12))))),
% 2.63/1.97 inference(monotonicity,[status(thm)],[619])).
% 2.63/1.97 tff(621,plain,
% 2.63/1.97 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a12)) | (~c3_1(a12)) | (~c1_1(a12)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c2_1(a12)))),
% 2.63/1.97 inference(transitivity,[status(thm)],[620, 618])).
% 2.63/1.97 tff(622,plain,
% 2.63/1.97 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a12)) | (~c3_1(a12)) | (~c1_1(a12)))),
% 2.63/1.97 inference(quant_inst,[status(thm)],[])).
% 2.63/1.97 tff(623,plain,
% 2.63/1.97 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c2_1(a12))),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[622, 621])).
% 2.63/1.97 tff(624,plain,
% 2.63/1.97 (~c2_1(a12)),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[623, 104, 568, 48, 617, 606, 10])).
% 2.63/1.97 tff(625,assumption,(~hskp28), introduced(assumption)).
% 2.63/1.97 tff(626,plain,
% 2.63/1.97 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | c2_1(a12))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | c2_1(a12))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(627,plain,
% 2.63/1.97 ((hskp28 | hskp0 | (~ndr1_0) | c2_1(a12) | (~c3_1(a12)) | (~c1_1(a12))) <=> (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | c2_1(a12))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(628,plain,
% 2.63/1.97 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a12) | (~c3_1(a12)) | (~c1_1(a12)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | c2_1(a12)))),
% 2.63/1.97 inference(monotonicity,[status(thm)],[627])).
% 2.63/1.97 tff(629,plain,
% 2.63/1.97 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a12) | (~c3_1(a12)) | (~c1_1(a12)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | c2_1(a12))),
% 2.63/1.97 inference(transitivity,[status(thm)],[628, 626])).
% 2.63/1.97 tff(630,plain,
% 2.63/1.97 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a12) | (~c3_1(a12)) | (~c1_1(a12)))),
% 2.63/1.97 inference(quant_inst,[status(thm)],[])).
% 2.63/1.97 tff(631,plain,
% 2.63/1.97 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | c2_1(a12)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[630, 629])).
% 2.63/1.97 tff(632,plain,
% 2.63/1.97 ($false),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[631, 104, 625, 11, 617, 606, 582, 624])).
% 2.63/1.97 tff(633,plain,((~hskp27) | hskp28 | hskp0 | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.63/1.97 tff(634,plain,
% 2.63/1.97 (~hskp27),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[633, 530, 594, 11, 48])).
% 2.63/1.97 tff(635,assumption,(~hskp27), introduced(assumption)).
% 2.63/1.97 tff(636,assumption,(hskp21), introduced(assumption)).
% 2.63/1.97 tff(637,plain,
% 2.63/1.97 (((~hskp21) | c0_1(a38)) <=> ((~hskp21) | c0_1(a38))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(638,axiom,((~hskp21) | c0_1(a38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 2.63/1.97 tff(639,plain,
% 2.63/1.97 ((~hskp21) | c0_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[638, 637])).
% 2.63/1.97 tff(640,plain,
% 2.63/1.97 ((~hskp21) | c0_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[639, 637])).
% 2.63/1.97 tff(641,plain,
% 2.63/1.97 ((~hskp21) | c0_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[640, 637])).
% 2.63/1.97 tff(642,plain,
% 2.63/1.97 ((~hskp21) | c0_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[641, 637])).
% 2.63/1.97 tff(643,plain,
% 2.63/1.97 ((~hskp21) | c0_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[642, 637])).
% 2.63/1.97 tff(644,plain,
% 2.63/1.97 ((~hskp21) | c0_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[643, 637])).
% 2.63/1.97 tff(645,plain,
% 2.63/1.97 ((~hskp21) | c0_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[644, 637])).
% 2.63/1.97 tff(646,plain,
% 2.63/1.97 ((~hskp21) | c0_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[645, 637])).
% 2.63/1.97 tff(647,plain,
% 2.63/1.97 (c0_1(a38)),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[646, 636])).
% 2.63/1.97 tff(648,plain,
% 2.63/1.97 (((~hskp21) | c1_1(a38)) <=> ((~hskp21) | c1_1(a38))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(649,axiom,((~hskp21) | c1_1(a38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 2.63/1.97 tff(650,plain,
% 2.63/1.97 ((~hskp21) | c1_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[649, 648])).
% 2.63/1.97 tff(651,plain,
% 2.63/1.97 ((~hskp21) | c1_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[650, 648])).
% 2.63/1.97 tff(652,plain,
% 2.63/1.97 ((~hskp21) | c1_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[651, 648])).
% 2.63/1.97 tff(653,plain,
% 2.63/1.97 ((~hskp21) | c1_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[652, 648])).
% 2.63/1.97 tff(654,plain,
% 2.63/1.97 ((~hskp21) | c1_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[653, 648])).
% 2.63/1.97 tff(655,plain,
% 2.63/1.97 ((~hskp21) | c1_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[654, 648])).
% 2.63/1.97 tff(656,plain,
% 2.63/1.97 ((~hskp21) | c1_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[655, 648])).
% 2.63/1.97 tff(657,plain,
% 2.63/1.97 ((~hskp21) | c1_1(a38)),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[656, 648])).
% 2.63/1.97 tff(658,plain,
% 2.63/1.97 (c1_1(a38)),
% 2.63/1.97 inference(unit_resolution,[status(thm)],[657, 636])).
% 2.63/1.97 tff(659,plain,
% 2.63/1.97 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 2.63/1.97 inference(bind,[status(th)],[])).
% 2.63/1.97 tff(660,plain,
% 2.63/1.97 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.97 inference(quant_intro,[status(thm)],[659])).
% 2.63/1.97 tff(661,plain,
% 2.63/1.97 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(662,plain,
% 2.63/1.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 2.63/1.97 inference(bind,[status(th)],[])).
% 2.63/1.97 tff(663,plain,
% 2.63/1.97 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.97 inference(quant_intro,[status(thm)],[662])).
% 2.63/1.97 tff(664,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 2.63/1.97 tff(665,plain,
% 2.63/1.97 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[664, 663])).
% 2.63/1.97 tff(666,plain,
% 2.63/1.97 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[665, 661])).
% 2.63/1.97 tff(667,plain,(
% 2.63/1.97 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.97 inference(skolemize,[status(sab)],[666])).
% 2.63/1.97 tff(668,plain,
% 2.63/1.97 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.63/1.97 inference(modus_ponens,[status(thm)],[667, 660])).
% 2.63/1.97 tff(669,plain,
% 2.63/1.97 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(670,plain,
% 2.63/1.97 ((hskp27 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.63/1.97 inference(rewrite,[status(thm)],[])).
% 2.63/1.97 tff(671,plain,
% 2.63/1.97 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38))))),
% 2.63/1.97 inference(monotonicity,[status(thm)],[670])).
% 2.63/1.97 tff(672,plain,
% 2.63/1.97 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.63/1.98 inference(transitivity,[status(thm)],[671, 669])).
% 2.63/1.98 tff(673,plain,
% 2.63/1.98 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 2.63/1.98 inference(quant_inst,[status(thm)],[])).
% 2.63/1.98 tff(674,plain,
% 2.63/1.98 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38))),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[673, 672])).
% 2.63/1.98 tff(675,plain,
% 2.63/1.98 (hskp27 | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38))),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[674, 474, 14, 13, 12, 668])).
% 2.63/1.98 tff(676,plain,
% 2.63/1.98 ($false),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[675, 658, 647, 511, 635])).
% 2.63/1.98 tff(677,plain,((~hskp21) | (~ndr1_0) | hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.63/1.98 tff(678,plain,
% 2.63/1.98 ((~hskp21) | hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2)),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[677, 104])).
% 2.63/1.98 tff(679,plain,
% 2.63/1.98 (~hskp21),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[678, 634, 474, 593, 12, 592])).
% 2.63/1.98 tff(680,assumption,(hskp20), introduced(assumption)).
% 2.63/1.98 tff(681,plain,
% 2.63/1.98 (((~hskp20) | (~c0_1(a37))) <=> ((~hskp20) | (~c0_1(a37)))),
% 2.63/1.98 inference(rewrite,[status(thm)],[])).
% 2.63/1.98 tff(682,plain,
% 2.63/1.98 (((~c0_1(a37)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a37)))),
% 2.63/1.98 inference(rewrite,[status(thm)],[])).
% 2.63/1.98 tff(683,axiom,((~c0_1(a37)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 2.63/1.98 tff(684,plain,
% 2.63/1.98 ((~hskp20) | (~c0_1(a37))),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[683, 682])).
% 2.63/1.98 tff(685,plain,
% 2.63/1.98 ((~hskp20) | (~c0_1(a37))),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[684, 681])).
% 2.63/1.98 tff(686,plain,
% 2.63/1.98 (~c0_1(a37)),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[685, 680])).
% 2.63/1.98 tff(687,plain,
% 2.63/1.98 (c3_1(a37)),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[555, 680])).
% 2.63/1.98 tff(688,plain,
% 2.63/1.98 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)))),
% 2.63/1.98 inference(rewrite,[status(thm)],[])).
% 2.63/1.98 tff(689,plain,
% 2.63/1.98 ((hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp0 | c0_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)))),
% 2.63/1.98 inference(rewrite,[status(thm)],[])).
% 2.63/1.98 tff(690,plain,
% 2.63/1.98 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37))))),
% 2.63/1.98 inference(monotonicity,[status(thm)],[689])).
% 2.63/1.98 tff(691,plain,
% 2.63/1.98 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)))),
% 2.63/1.98 inference(transitivity,[status(thm)],[690, 688])).
% 2.63/1.98 tff(692,plain,
% 2.63/1.98 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 2.63/1.98 inference(quant_inst,[status(thm)],[])).
% 2.63/1.98 tff(693,plain,
% 2.63/1.98 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37))),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[692, 691])).
% 2.63/1.98 tff(694,plain,
% 2.63/1.98 (~c2_1(a37)),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[693, 104, 11, 687, 686, 14, 13, 12, 24])).
% 2.63/1.98 tff(695,plain,
% 2.63/1.98 (c1_1(a37)),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[566, 680])).
% 2.63/1.98 tff(696,plain,
% 2.63/1.98 ($false),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[585, 104, 625, 11, 695, 687, 582, 694])).
% 2.63/1.98 tff(697,plain,((~hskp20) | hskp28 | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.63/1.98 tff(698,plain,
% 2.63/1.98 (~hskp20),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[697, 593, 12, 11, 592, 530])).
% 2.63/1.98 tff(699,plain,
% 2.63/1.98 (^[U: $i] : refl((hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))),
% 2.63/1.98 inference(bind,[status(th)],[])).
% 2.63/1.98 tff(700,plain,
% 2.63/1.98 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.63/1.98 inference(quant_intro,[status(thm)],[699])).
% 2.63/1.98 tff(701,plain,
% 2.63/1.98 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.63/1.98 inference(rewrite,[status(thm)],[])).
% 2.63/1.98 tff(702,plain,
% 2.63/1.98 (^[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)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp20) <=> ((hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp20))), rewrite(((hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp20) <=> (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp20) <=> (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))))),
% 2.63/1.98 inference(bind,[status(th)],[])).
% 2.63/1.98 tff(703,plain,
% 2.63/1.98 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp20) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.63/1.98 inference(quant_intro,[status(thm)],[702])).
% 2.63/1.98 tff(704,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 2.63/1.98 tff(705,plain,
% 2.63/1.98 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[704, 703])).
% 2.63/1.98 tff(706,plain,
% 2.63/1.98 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[705, 701])).
% 2.63/1.98 tff(707,plain,(
% 2.63/1.98 ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.63/1.98 inference(skolemize,[status(sab)],[706])).
% 2.63/1.98 tff(708,plain,
% 2.63/1.98 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[707, 700])).
% 2.63/1.98 tff(709,plain,
% 2.63/1.98 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 2.63/1.98 inference(rewrite,[status(thm)],[])).
% 2.63/1.98 tff(710,plain,
% 2.63/1.98 ((hskp21 | hskp20 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c2_1(a2)) <=> (hskp21 | hskp20 | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 2.63/1.98 inference(rewrite,[status(thm)],[])).
% 2.63/1.98 tff(711,plain,
% 2.63/1.98 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c2_1(a2))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2)))),
% 2.63/1.98 inference(monotonicity,[status(thm)],[710])).
% 2.63/1.98 tff(712,plain,
% 2.63/1.98 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c2_1(a2))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 2.63/1.98 inference(transitivity,[status(thm)],[711, 709])).
% 2.63/1.98 tff(713,plain,
% 2.63/1.98 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c2_1(a2))),
% 2.63/1.98 inference(quant_inst,[status(thm)],[])).
% 2.63/1.98 tff(714,plain,
% 2.63/1.98 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2)),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[713, 712])).
% 2.63/1.98 tff(715,plain,
% 2.63/1.98 (hskp21 | hskp20 | c2_1(a2) | c1_1(a2)),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[714, 104, 12, 708])).
% 2.63/1.98 tff(716,plain,
% 2.63/1.98 (c1_1(a2)),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[715, 698, 593, 679])).
% 2.63/1.98 tff(717,plain,
% 2.63/1.98 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))),
% 2.63/1.98 inference(rewrite,[status(thm)],[])).
% 2.63/1.98 tff(718,plain,
% 2.63/1.98 ((hskp21 | hskp20 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c2_1(a58)) <=> (hskp21 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))),
% 2.63/1.98 inference(rewrite,[status(thm)],[])).
% 2.63/1.98 tff(719,plain,
% 2.63/1.98 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c2_1(a58))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58)))),
% 2.63/1.98 inference(monotonicity,[status(thm)],[718])).
% 2.63/1.98 tff(720,plain,
% 2.63/1.98 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c2_1(a58))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))),
% 2.63/1.98 inference(transitivity,[status(thm)],[719, 717])).
% 2.63/1.98 tff(721,plain,
% 2.63/1.98 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c2_1(a58))),
% 2.63/1.98 inference(quant_inst,[status(thm)],[])).
% 2.63/1.98 tff(722,plain,
% 2.63/1.98 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58)),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[721, 720])).
% 2.63/1.98 tff(723,plain,
% 2.63/1.98 (hskp21 | hskp20 | c2_1(a58) | c3_1(a58)),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[722, 104, 26, 708])).
% 2.63/1.98 tff(724,plain,
% 2.63/1.98 (c3_1(a58)),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[723, 679, 476, 698])).
% 2.63/1.98 tff(725,plain,
% 2.63/1.98 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 2.63/1.98 inference(bind,[status(th)],[])).
% 2.63/1.98 tff(726,plain,
% 2.63/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(quant_intro,[status(thm)],[725])).
% 2.63/1.98 tff(727,plain,
% 2.63/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(rewrite,[status(thm)],[])).
% 2.63/1.98 tff(728,plain,
% 2.63/1.98 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 2.63/1.98 inference(bind,[status(th)],[])).
% 2.63/1.98 tff(729,plain,
% 2.63/1.98 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(quant_intro,[status(thm)],[728])).
% 2.63/1.98 tff(730,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 2.63/1.98 tff(731,plain,
% 2.63/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[730, 729])).
% 2.63/1.98 tff(732,plain,
% 2.63/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[731, 727])).
% 2.63/1.98 tff(733,plain,(
% 2.63/1.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(skolemize,[status(sab)],[732])).
% 2.63/1.98 tff(734,plain,
% 2.63/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[733, 726])).
% 2.63/1.98 tff(735,plain,
% 2.63/1.98 (hskp1),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[587, 594, 48, 11, 37, 26])).
% 2.63/1.98 tff(736,plain,
% 2.63/1.98 (~c0_1(a2)),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[268, 735])).
% 2.63/1.98 tff(737,plain,
% 2.63/1.98 (~c2_1(a2)),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[262, 735])).
% 2.63/1.98 tff(738,plain,
% 2.63/1.98 (~hskp20),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[697, 737, 11, 12, 736, 530])).
% 2.63/1.98 tff(739,plain,
% 2.63/1.98 (~hskp27),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[633, 594, 530, 11, 48])).
% 2.63/1.98 tff(740,plain,
% 2.63/1.98 (~hskp21),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[678, 737, 474, 739, 12, 736])).
% 2.63/1.98 tff(741,plain,
% 2.63/1.98 (c3_1(a58)),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[723, 740, 476, 738])).
% 2.63/1.98 tff(742,plain,
% 2.63/1.98 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 2.63/1.98 inference(bind,[status(th)],[])).
% 2.63/1.98 tff(743,plain,
% 2.63/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(quant_intro,[status(thm)],[742])).
% 2.63/1.98 tff(744,plain,
% 2.63/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(rewrite,[status(thm)],[])).
% 2.63/1.98 tff(745,plain,
% 2.63/1.98 (^[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)) | (~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))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 2.63/1.98 inference(bind,[status(th)],[])).
% 2.63/1.98 tff(746,plain,
% 2.63/1.98 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(quant_intro,[status(thm)],[745])).
% 2.63/1.98 tff(747,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 2.63/1.98 tff(748,plain,
% 2.63/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[747, 746])).
% 2.63/1.98 tff(749,plain,
% 2.63/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[748, 744])).
% 2.63/1.98 tff(750,plain,(
% 2.63/1.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(skolemize,[status(sab)],[749])).
% 2.63/1.98 tff(751,plain,
% 2.63/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.63/1.98 inference(modus_ponens,[status(thm)],[750, 743])).
% 2.63/1.98 tff(752,assumption,(~c2_1(a15)), introduced(assumption)).
% 2.63/1.98 tff(753,plain,
% 2.63/1.98 (~hskp27),
% 2.63/1.98 inference(unit_resolution,[status(thm)],[633, 530, 11, 594, 48])).
% 2.63/1.98 tff(754,plain,
% 2.63/1.98 (^[U: $i] : refl((hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 2.63/1.98 inference(bind,[status(th)],[])).
% 2.63/1.98 tff(755,plain,
% 2.63/1.98 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.98 inference(quant_intro,[status(thm)],[754])).
% 2.63/1.98 tff(756,plain,
% 2.63/1.98 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.98 inference(rewrite,[status(thm)],[])).
% 2.63/1.98 tff(757,plain,
% 2.63/1.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1) <=> ((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 2.63/1.98 inference(bind,[status(th)],[])).
% 2.63/1.98 tff(758,plain,
% 2.63/1.98 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.99 inference(quant_intro,[status(thm)],[757])).
% 2.63/1.99 tff(759,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 2.63/1.99 tff(760,plain,
% 2.63/1.99 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[759, 758])).
% 2.63/1.99 tff(761,plain,
% 2.63/1.99 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[760, 756])).
% 2.63/1.99 tff(762,plain,(
% 2.63/1.99 ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.99 inference(skolemize,[status(sab)],[761])).
% 2.63/1.99 tff(763,plain,
% 2.63/1.99 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[762, 755])).
% 2.63/1.99 tff(764,plain,
% 2.63/1.99 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(765,plain,
% 2.63/1.99 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c0_1(a58)) <=> (hskp1 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(766,plain,
% 2.63/1.99 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58)))),
% 2.63/1.99 inference(monotonicity,[status(thm)],[765])).
% 2.63/1.99 tff(767,plain,
% 2.63/1.99 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))),
% 2.63/1.99 inference(transitivity,[status(thm)],[766, 764])).
% 2.63/1.99 tff(768,plain,
% 2.63/1.99 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c0_1(a58))),
% 2.63/1.99 inference(quant_inst,[status(thm)],[])).
% 2.63/1.99 tff(769,plain,
% 2.63/1.99 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[768, 767])).
% 2.63/1.99 tff(770,plain,
% 2.63/1.99 (hskp1 | hskp0 | c1_1(a58) | c3_1(a58)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[769, 104, 37, 763])).
% 2.63/1.99 tff(771,plain,
% 2.63/1.99 (c3_1(a58)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[770, 200, 26, 11])).
% 2.63/1.99 tff(772,plain,
% 2.63/1.99 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(773,plain,
% 2.63/1.99 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15)) <=> (hskp1 | hskp0 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(774,plain,
% 2.63/1.99 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15)))),
% 2.63/1.99 inference(monotonicity,[status(thm)],[773])).
% 2.63/1.99 tff(775,plain,
% 2.63/1.99 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))),
% 2.63/1.99 inference(transitivity,[status(thm)],[774, 772])).
% 2.63/1.99 tff(776,plain,
% 2.63/1.99 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))),
% 2.63/1.99 inference(quant_inst,[status(thm)],[])).
% 2.63/1.99 tff(777,plain,
% 2.63/1.99 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[776, 775])).
% 2.63/1.99 tff(778,plain,
% 2.63/1.99 (hskp1 | hskp0 | c3_1(a15) | c0_1(a15)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[777, 104, 475, 763])).
% 2.63/1.99 tff(779,plain,
% 2.63/1.99 (c0_1(a15)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[778, 200, 468, 11])).
% 2.63/1.99 tff(780,assumption,(~c2_1(a58)), introduced(assumption)).
% 2.63/1.99 tff(781,plain,
% 2.63/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a58)))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(782,plain,
% 2.63/1.99 (((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a58)))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(783,plain,
% 2.63/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a58))))),
% 2.63/1.99 inference(monotonicity,[status(thm)],[782])).
% 2.63/1.99 tff(784,plain,
% 2.63/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a58)))),
% 2.63/1.99 inference(transitivity,[status(thm)],[783, 781])).
% 2.63/1.99 tff(785,plain,
% 2.63/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 2.63/1.99 inference(quant_inst,[status(thm)],[])).
% 2.63/1.99 tff(786,plain,
% 2.63/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a58))),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[785, 784])).
% 2.63/1.99 tff(787,plain,
% 2.63/1.99 ((~c0_1(a15)) | (~c3_1(a58))),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[786, 104, 780, 37, 26, 475, 752, 751])).
% 2.63/1.99 tff(788,plain,
% 2.63/1.99 ($false),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[787, 779, 771])).
% 2.63/1.99 tff(789,plain,(hskp1 | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.63/1.99 tff(790,plain,
% 2.63/1.99 (hskp1),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[789, 476, 37, 26, 475, 752, 468, 11])).
% 2.63/1.99 tff(791,plain,
% 2.63/1.99 (~c3_1(a2)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[256, 790])).
% 2.63/1.99 tff(792,plain,
% 2.63/1.99 (~c0_1(a2)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[268, 790])).
% 2.63/1.99 tff(793,plain,
% 2.63/1.99 (~c2_1(a2)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[262, 790])).
% 2.63/1.99 tff(794,plain,
% 2.63/1.99 (~hskp21),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[678, 13, 474, 635, 14, 12])).
% 2.63/1.99 tff(795,plain,
% 2.63/1.99 (~hskp20),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[697, 13, 11, 12, 14, 625])).
% 2.63/1.99 tff(796,plain,
% 2.63/1.99 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(797,plain,
% 2.63/1.99 ((hskp21 | hskp20 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c2_1(a15)) <=> (hskp21 | hskp20 | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(798,plain,
% 2.63/1.99 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0)))),
% 2.63/1.99 inference(monotonicity,[status(thm)],[797])).
% 2.63/1.99 tff(799,plain,
% 2.63/1.99 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0))),
% 2.63/1.99 inference(transitivity,[status(thm)],[798, 796])).
% 2.63/1.99 tff(800,plain,
% 2.63/1.99 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c2_1(a15))),
% 2.63/1.99 inference(quant_inst,[status(thm)],[])).
% 2.63/1.99 tff(801,plain,
% 2.63/1.99 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[800, 799])).
% 2.63/1.99 tff(802,plain,
% 2.63/1.99 (hskp21 | hskp20 | c2_1(a15) | c3_1(a15)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[801, 104, 475, 708])).
% 2.63/1.99 tff(803,plain,
% 2.63/1.99 ($false),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[802, 795, 794, 752, 468])).
% 2.63/1.99 tff(804,plain,(c2_1(a2) | c2_1(a15) | c3_1(a15) | c1_1(a15) | hskp0 | c3_1(a2) | c0_1(a2) | hskp28 | c2_1(a38) | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.63/1.99 tff(805,plain,
% 2.63/1.99 ($false),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[804, 793, 792, 468, 475, 11, 791, 752, 530, 474, 753])).
% 2.63/1.99 tff(806,plain,(hskp0 | c3_1(a15) | c1_1(a15) | c2_1(a15) | c2_1(a38) | c0_1(a58) | c1_1(a58) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.63/1.99 tff(807,plain,
% 2.63/1.99 (hskp0),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[806, 468, 475, 752, 474, 37, 26, 48])).
% 2.63/1.99 tff(808,plain,
% 2.63/1.99 (c1_1(a1)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[139, 807])).
% 2.63/1.99 tff(809,plain,
% 2.63/1.99 (~c3_1(a1)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[117, 807])).
% 2.63/1.99 tff(810,plain,
% 2.63/1.99 (c2_1(a1)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[128, 807])).
% 2.63/1.99 tff(811,assumption,(~hskp21), introduced(assumption)).
% 2.63/1.99 tff(812,plain,
% 2.63/1.99 ((hskp24 | hskp21 | hskp13) <=> (hskp24 | hskp21 | hskp13)),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(813,plain,
% 2.63/1.99 (((hskp21 | hskp13) | hskp24) <=> (hskp24 | hskp21 | hskp13)),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(814,plain,
% 2.63/1.99 ((hskp21 | hskp13) <=> (hskp21 | hskp13)),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(815,plain,
% 2.63/1.99 (((hskp21 | hskp13) | hskp24) <=> ((hskp21 | hskp13) | hskp24)),
% 2.63/1.99 inference(monotonicity,[status(thm)],[814])).
% 2.63/1.99 tff(816,plain,
% 2.63/1.99 (((hskp21 | hskp13) | hskp24) <=> (hskp24 | hskp21 | hskp13)),
% 2.63/1.99 inference(transitivity,[status(thm)],[815, 813])).
% 2.63/1.99 tff(817,axiom,((hskp21 | hskp13) | hskp24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 2.63/1.99 tff(818,plain,
% 2.63/1.99 (hskp24 | hskp21 | hskp13),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[817, 816])).
% 2.63/1.99 tff(819,plain,
% 2.63/1.99 (hskp24 | hskp21 | hskp13),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[818, 812])).
% 2.63/1.99 tff(820,plain,
% 2.63/1.99 (hskp24 | hskp21 | hskp13),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[819, 812])).
% 2.63/1.99 tff(821,plain,
% 2.63/1.99 (hskp24 | hskp21 | hskp13),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[820, 812])).
% 2.63/1.99 tff(822,plain,
% 2.63/1.99 (hskp24 | hskp21 | hskp13),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[821, 812])).
% 2.63/1.99 tff(823,plain,
% 2.63/1.99 (hskp24 | hskp21 | hskp13),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[822, 812])).
% 2.63/1.99 tff(824,plain,
% 2.63/1.99 (hskp24 | hskp21 | hskp13),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[823, 812])).
% 2.63/1.99 tff(825,plain,
% 2.63/1.99 (hskp24 | hskp21 | hskp13),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[824, 812])).
% 2.63/1.99 tff(826,plain,
% 2.63/1.99 (hskp13),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[825, 811, 568])).
% 2.63/1.99 tff(827,plain,
% 2.63/1.99 (((~hskp13) | (~c3_1(a21))) <=> ((~hskp13) | (~c3_1(a21)))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(828,plain,
% 2.63/1.99 (((~c3_1(a21)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a21)))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(829,axiom,((~c3_1(a21)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 2.63/1.99 tff(830,plain,
% 2.63/1.99 ((~hskp13) | (~c3_1(a21))),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[829, 828])).
% 2.63/1.99 tff(831,plain,
% 2.63/1.99 ((~hskp13) | (~c3_1(a21))),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[830, 827])).
% 2.63/1.99 tff(832,plain,
% 2.63/1.99 (~c3_1(a21)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[831, 826])).
% 2.63/1.99 tff(833,plain,
% 2.63/1.99 (((~hskp13) | c2_1(a21)) <=> ((~hskp13) | c2_1(a21))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(834,axiom,((~hskp13) | c2_1(a21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 2.63/1.99 tff(835,plain,
% 2.63/1.99 ((~hskp13) | c2_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[834, 833])).
% 2.63/1.99 tff(836,plain,
% 2.63/1.99 ((~hskp13) | c2_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[835, 833])).
% 2.63/1.99 tff(837,plain,
% 2.63/1.99 ((~hskp13) | c2_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[836, 833])).
% 2.63/1.99 tff(838,plain,
% 2.63/1.99 ((~hskp13) | c2_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[837, 833])).
% 2.63/1.99 tff(839,plain,
% 2.63/1.99 ((~hskp13) | c2_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[838, 833])).
% 2.63/1.99 tff(840,plain,
% 2.63/1.99 ((~hskp13) | c2_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[839, 833])).
% 2.63/1.99 tff(841,plain,
% 2.63/1.99 ((~hskp13) | c2_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[840, 833])).
% 2.63/1.99 tff(842,plain,
% 2.63/1.99 ((~hskp13) | c2_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[841, 833])).
% 2.63/1.99 tff(843,plain,
% 2.63/1.99 (c2_1(a21)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[842, 826])).
% 2.63/1.99 tff(844,plain,
% 2.63/1.99 (((~hskp13) | c0_1(a21)) <=> ((~hskp13) | c0_1(a21))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(845,axiom,((~hskp13) | c0_1(a21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 2.63/1.99 tff(846,plain,
% 2.63/1.99 ((~hskp13) | c0_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[845, 844])).
% 2.63/1.99 tff(847,plain,
% 2.63/1.99 ((~hskp13) | c0_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[846, 844])).
% 2.63/1.99 tff(848,plain,
% 2.63/1.99 ((~hskp13) | c0_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[847, 844])).
% 2.63/1.99 tff(849,plain,
% 2.63/1.99 ((~hskp13) | c0_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[848, 844])).
% 2.63/1.99 tff(850,plain,
% 2.63/1.99 ((~hskp13) | c0_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[849, 844])).
% 2.63/1.99 tff(851,plain,
% 2.63/1.99 ((~hskp13) | c0_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[850, 844])).
% 2.63/1.99 tff(852,plain,
% 2.63/1.99 ((~hskp13) | c0_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[851, 844])).
% 2.63/1.99 tff(853,plain,
% 2.63/1.99 ((~hskp13) | c0_1(a21)),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[852, 844])).
% 2.63/1.99 tff(854,plain,
% 2.63/1.99 (c0_1(a21)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[853, 826])).
% 2.63/1.99 tff(855,plain,
% 2.63/1.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a21) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a21)) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a21) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(856,plain,
% 2.63/1.99 ((hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21))) <=> (hskp6 | c3_1(a21) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(857,plain,
% 2.63/1.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a21) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a21)) | (~c2_1(a21))))),
% 2.63/1.99 inference(monotonicity,[status(thm)],[856])).
% 2.63/1.99 tff(858,plain,
% 2.63/1.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a21) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.63/1.99 inference(transitivity,[status(thm)],[857, 855])).
% 2.63/1.99 tff(859,plain,
% 2.63/1.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))),
% 2.63/1.99 inference(quant_inst,[status(thm)],[])).
% 2.63/1.99 tff(860,plain,
% 2.63/1.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a21) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a21)) | (~c2_1(a21))),
% 2.63/1.99 inference(modus_ponens,[status(thm)],[859, 858])).
% 2.63/1.99 tff(861,plain,
% 2.63/1.99 (hskp6),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[860, 104, 854, 843, 153, 152, 832, 151, 150])).
% 2.63/1.99 tff(862,plain,
% 2.63/1.99 (~c3_1(a13)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[186, 861])).
% 2.63/1.99 tff(863,plain,
% 2.63/1.99 (~c1_1(a13)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[192, 861])).
% 2.63/1.99 tff(864,plain,
% 2.63/1.99 (~c0_1(a13)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[198, 861])).
% 2.63/1.99 tff(865,plain,
% 2.63/1.99 (hskp2),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[247, 104, 200, 864, 863, 862, 47])).
% 2.63/1.99 tff(866,plain,
% 2.63/1.99 (~c2_1(a3)),
% 2.63/1.99 inference(unit_resolution,[status(thm)],[206, 865])).
% 2.63/1.99 tff(867,plain,
% 2.63/1.99 (^[U: $i] : refl((hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 2.63/1.99 inference(bind,[status(th)],[])).
% 2.63/1.99 tff(868,plain,
% 2.63/1.99 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.63/1.99 inference(quant_intro,[status(thm)],[867])).
% 2.63/1.99 tff(869,plain,
% 2.63/1.99 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.63/1.99 inference(rewrite,[status(thm)],[])).
% 2.63/1.99 tff(870,plain,
% 2.63/1.99 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp10) <=> ((hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp10) <=> (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 2.71/1.99 inference(bind,[status(th)],[])).
% 2.71/1.99 tff(871,plain,
% 2.71/1.99 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp10) <=> ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/1.99 inference(quant_intro,[status(thm)],[870])).
% 2.71/1.99 tff(872,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 2.71/1.99 tff(873,plain,
% 2.71/1.99 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/1.99 inference(modus_ponens,[status(thm)],[872, 871])).
% 2.71/1.99 tff(874,plain,
% 2.71/1.99 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/1.99 inference(modus_ponens,[status(thm)],[873, 869])).
% 2.71/1.99 tff(875,plain,(
% 2.71/1.99 ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/1.99 inference(skolemize,[status(sab)],[874])).
% 2.71/1.99 tff(876,plain,
% 2.71/1.99 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/1.99 inference(modus_ponens,[status(thm)],[875, 868])).
% 2.71/1.99 tff(877,plain,
% 2.71/1.99 (hskp20),
% 2.71/1.99 inference(unit_resolution,[status(thm)],[802, 811, 752, 468])).
% 2.71/1.99 tff(878,plain,
% 2.71/1.99 (c3_1(a37)),
% 2.71/1.99 inference(unit_resolution,[status(thm)],[555, 877])).
% 2.71/1.99 tff(879,plain,
% 2.71/1.99 (c1_1(a37)),
% 2.71/1.99 inference(unit_resolution,[status(thm)],[566, 877])).
% 2.71/1.99 tff(880,plain,
% 2.71/1.99 (~c2_1(a37)),
% 2.71/1.99 inference(unit_resolution,[status(thm)],[571, 104, 568, 48, 879, 878, 10])).
% 2.71/1.99 tff(881,plain,
% 2.71/1.99 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 2.71/1.99 inference(bind,[status(th)],[])).
% 2.71/1.99 tff(882,plain,
% 2.71/1.99 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.71/1.99 inference(quant_intro,[status(thm)],[881])).
% 2.71/1.99 tff(883,plain,
% 2.71/1.99 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.71/1.99 inference(rewrite,[status(thm)],[])).
% 2.71/1.99 tff(884,plain,
% 2.71/1.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 2.71/1.99 inference(bind,[status(th)],[])).
% 2.71/1.99 tff(885,plain,
% 2.71/1.99 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.71/1.99 inference(quant_intro,[status(thm)],[884])).
% 2.71/1.99 tff(886,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 2.71/1.99 tff(887,plain,
% 2.71/1.99 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.71/1.99 inference(modus_ponens,[status(thm)],[886, 885])).
% 2.71/1.99 tff(888,plain,
% 2.71/1.99 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.71/1.99 inference(modus_ponens,[status(thm)],[887, 883])).
% 2.71/1.99 tff(889,plain,(
% 2.71/1.99 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.71/1.99 inference(skolemize,[status(sab)],[888])).
% 2.71/1.99 tff(890,plain,
% 2.71/1.99 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.71/1.99 inference(modus_ponens,[status(thm)],[889, 882])).
% 2.71/1.99 tff(891,plain,
% 2.71/1.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.71/1.99 inference(rewrite,[status(thm)],[])).
% 2.71/1.99 tff(892,plain,
% 2.71/1.99 ((hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))) <=> (hskp9 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.71/1.99 inference(rewrite,[status(thm)],[])).
% 2.71/1.99 tff(893,plain,
% 2.71/1.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))))),
% 2.71/1.99 inference(monotonicity,[status(thm)],[892])).
% 2.71/1.99 tff(894,plain,
% 2.71/1.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.71/2.00 inference(transitivity,[status(thm)],[893, 891])).
% 2.71/2.00 tff(895,plain,
% 2.71/2.00 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.71/2.00 inference(quant_inst,[status(thm)],[])).
% 2.71/2.00 tff(896,plain,
% 2.71/2.00 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[895, 894])).
% 2.71/2.00 tff(897,plain,
% 2.71/2.00 (hskp9),
% 2.71/2.00 inference(unit_resolution,[status(thm)],[896, 104, 879, 878, 153, 152, 151, 890, 880])).
% 2.71/2.00 tff(898,plain,
% 2.71/2.00 (((~hskp9) | (~c3_1(a16))) <=> ((~hskp9) | (~c3_1(a16)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(899,plain,
% 2.71/2.00 (((~c3_1(a16)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a16)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(900,axiom,((~c3_1(a16)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 2.71/2.00 tff(901,plain,
% 2.71/2.00 ((~hskp9) | (~c3_1(a16))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[900, 899])).
% 2.71/2.00 tff(902,plain,
% 2.71/2.00 ((~hskp9) | (~c3_1(a16))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[901, 898])).
% 2.71/2.00 tff(903,plain,
% 2.71/2.00 (~c3_1(a16)),
% 2.71/2.00 inference(unit_resolution,[status(thm)],[902, 897])).
% 2.71/2.00 tff(904,plain,
% 2.71/2.00 (((~hskp9) | c1_1(a16)) <=> ((~hskp9) | c1_1(a16))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(905,axiom,((~hskp9) | c1_1(a16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 2.71/2.00 tff(906,plain,
% 2.71/2.00 ((~hskp9) | c1_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[905, 904])).
% 2.71/2.00 tff(907,plain,
% 2.71/2.00 ((~hskp9) | c1_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[906, 904])).
% 2.71/2.00 tff(908,plain,
% 2.71/2.00 ((~hskp9) | c1_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[907, 904])).
% 2.71/2.00 tff(909,plain,
% 2.71/2.00 ((~hskp9) | c1_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[908, 904])).
% 2.71/2.00 tff(910,plain,
% 2.71/2.00 ((~hskp9) | c1_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[909, 904])).
% 2.71/2.00 tff(911,plain,
% 2.71/2.00 ((~hskp9) | c1_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[910, 904])).
% 2.71/2.00 tff(912,plain,
% 2.71/2.00 ((~hskp9) | c1_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[911, 904])).
% 2.71/2.00 tff(913,plain,
% 2.71/2.00 ((~hskp9) | c1_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[912, 904])).
% 2.71/2.00 tff(914,plain,
% 2.71/2.00 (c1_1(a16)),
% 2.71/2.00 inference(unit_resolution,[status(thm)],[913, 897])).
% 2.71/2.00 tff(915,plain,
% 2.71/2.00 (((~hskp9) | c0_1(a16)) <=> ((~hskp9) | c0_1(a16))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(916,axiom,((~hskp9) | c0_1(a16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 2.71/2.00 tff(917,plain,
% 2.71/2.00 ((~hskp9) | c0_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[916, 915])).
% 2.71/2.00 tff(918,plain,
% 2.71/2.00 ((~hskp9) | c0_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[917, 915])).
% 2.71/2.00 tff(919,plain,
% 2.71/2.00 ((~hskp9) | c0_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[918, 915])).
% 2.71/2.00 tff(920,plain,
% 2.71/2.00 ((~hskp9) | c0_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[919, 915])).
% 2.71/2.00 tff(921,plain,
% 2.71/2.00 ((~hskp9) | c0_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[920, 915])).
% 2.71/2.00 tff(922,plain,
% 2.71/2.00 ((~hskp9) | c0_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[921, 915])).
% 2.71/2.00 tff(923,plain,
% 2.71/2.00 ((~hskp9) | c0_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[922, 915])).
% 2.71/2.00 tff(924,plain,
% 2.71/2.00 ((~hskp9) | c0_1(a16)),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[923, 915])).
% 2.71/2.00 tff(925,plain,
% 2.71/2.00 (c0_1(a16)),
% 2.71/2.00 inference(unit_resolution,[status(thm)],[924, 897])).
% 2.71/2.00 tff(926,plain,
% 2.71/2.00 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp10 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(927,plain,
% 2.71/2.00 ((hskp21 | hskp10 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16))) <=> (hskp21 | hskp10 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(928,plain,
% 2.71/2.00 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16))))),
% 2.71/2.00 inference(monotonicity,[status(thm)],[927])).
% 2.71/2.00 tff(929,plain,
% 2.71/2.00 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp10 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)))),
% 2.71/2.00 inference(transitivity,[status(thm)],[928, 926])).
% 2.71/2.00 tff(930,plain,
% 2.71/2.00 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)))),
% 2.71/2.00 inference(quant_inst,[status(thm)],[])).
% 2.71/2.00 tff(931,plain,
% 2.71/2.00 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp10 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[930, 929])).
% 2.71/2.00 tff(932,plain,
% 2.71/2.00 (hskp10),
% 2.71/2.00 inference(unit_resolution,[status(thm)],[931, 104, 811, 925, 914, 903, 876])).
% 2.71/2.00 tff(933,plain,
% 2.71/2.00 (((~hskp10) | (~c1_1(a18))) <=> ((~hskp10) | (~c1_1(a18)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(934,plain,
% 2.71/2.00 (((~c1_1(a18)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a18)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(935,axiom,((~c1_1(a18)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 2.71/2.00 tff(936,plain,
% 2.71/2.00 ((~hskp10) | (~c1_1(a18))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[935, 934])).
% 2.71/2.00 tff(937,plain,
% 2.71/2.00 ((~hskp10) | (~c1_1(a18))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[936, 933])).
% 2.71/2.00 tff(938,plain,
% 2.71/2.00 (~c1_1(a18)),
% 2.71/2.00 inference(unit_resolution,[status(thm)],[937, 932])).
% 2.71/2.00 tff(939,plain,
% 2.71/2.00 (((~hskp10) | (~c0_1(a18))) <=> ((~hskp10) | (~c0_1(a18)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(940,plain,
% 2.71/2.00 (((~c0_1(a18)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a18)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(941,axiom,((~c0_1(a18)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 2.71/2.00 tff(942,plain,
% 2.71/2.00 ((~hskp10) | (~c0_1(a18))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[941, 940])).
% 2.71/2.00 tff(943,plain,
% 2.71/2.00 ((~hskp10) | (~c0_1(a18))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[942, 939])).
% 2.71/2.00 tff(944,plain,
% 2.71/2.00 (~c0_1(a18)),
% 2.71/2.00 inference(unit_resolution,[status(thm)],[943, 932])).
% 2.71/2.00 tff(945,plain,
% 2.71/2.00 (c3_1(a3)),
% 2.71/2.00 inference(unit_resolution,[status(thm)],[217, 865])).
% 2.71/2.00 tff(946,plain,
% 2.71/2.00 (c1_1(a3)),
% 2.71/2.00 inference(unit_resolution,[status(thm)],[228, 865])).
% 2.71/2.00 tff(947,plain,
% 2.71/2.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a18) | c1_1(a18) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a18) | c1_1(a18) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a18)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(948,plain,
% 2.71/2.00 ((hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (hskp1 | c0_1(a18) | c1_1(a18) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a18)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(949,plain,
% 2.71/2.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a18) | c1_1(a18) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a18))))),
% 2.71/2.00 inference(monotonicity,[status(thm)],[948])).
% 2.71/2.00 tff(950,plain,
% 2.71/2.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a18) | c1_1(a18) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a18)))),
% 2.71/2.00 inference(transitivity,[status(thm)],[949, 947])).
% 2.71/2.00 tff(951,plain,
% 2.71/2.00 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 2.71/2.00 inference(quant_inst,[status(thm)],[])).
% 2.71/2.00 tff(952,plain,
% 2.71/2.00 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a18) | c1_1(a18) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a18))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[951, 950])).
% 2.71/2.00 tff(953,plain,
% 2.71/2.00 (~c2_1(a18)),
% 2.71/2.00 inference(unit_resolution,[status(thm)],[952, 104, 200, 946, 945, 944, 938, 866, 58])).
% 2.71/2.00 tff(954,plain,
% 2.71/2.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(955,plain,
% 2.71/2.00 ((hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13))) <=> (hskp1 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(956,plain,
% 2.71/2.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))))),
% 2.71/2.00 inference(monotonicity,[status(thm)],[955])).
% 2.71/2.00 tff(957,plain,
% 2.71/2.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.71/2.00 inference(transitivity,[status(thm)],[956, 954])).
% 2.71/2.00 tff(958,plain,
% 2.71/2.00 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))),
% 2.71/2.00 inference(quant_inst,[status(thm)],[])).
% 2.71/2.00 tff(959,plain,
% 2.71/2.00 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[958, 957])).
% 2.71/2.00 tff(960,plain,
% 2.71/2.00 (~c2_1(a13)),
% 2.71/2.00 inference(unit_resolution,[status(thm)],[959, 104, 200, 879, 878, 864, 863, 58, 880])).
% 2.71/2.00 tff(961,plain,
% 2.71/2.00 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W))))),
% 2.71/2.00 inference(bind,[status(th)],[])).
% 2.71/2.00 tff(962,plain,
% 2.71/2.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 2.71/2.00 inference(quant_intro,[status(thm)],[961])).
% 2.71/2.00 tff(963,plain,
% 2.71/2.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(964,plain,
% 2.71/2.00 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~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))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))))),
% 2.71/2.00 inference(bind,[status(th)],[])).
% 2.71/2.00 tff(965,plain,
% 2.71/2.00 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 2.71/2.00 inference(quant_intro,[status(thm)],[964])).
% 2.71/2.00 tff(966,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause203')).
% 2.71/2.00 tff(967,plain,
% 2.71/2.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[966, 965])).
% 2.71/2.00 tff(968,plain,
% 2.71/2.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[967, 963])).
% 2.71/2.00 tff(969,plain,(
% 2.71/2.00 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 2.71/2.00 inference(skolemize,[status(sab)],[968])).
% 2.71/2.00 tff(970,plain,
% 2.71/2.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[969, 962])).
% 2.71/2.00 tff(971,plain,
% 2.71/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c0_1(a16)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(972,plain,
% 2.71/2.00 (((~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_1(a3)) | (~c0_1(a3))) <=> (c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c0_1(a16)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(973,plain,
% 2.71/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_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) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c0_1(a16))))),
% 2.71/2.00 inference(monotonicity,[status(thm)],[972])).
% 2.71/2.00 tff(974,plain,
% 2.71/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_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) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c0_1(a16)))),
% 2.71/2.00 inference(transitivity,[status(thm)],[973, 971])).
% 2.71/2.00 tff(975,plain,
% 2.71/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_1(a3)) | (~c0_1(a3)))),
% 2.71/2.00 inference(quant_inst,[status(thm)],[])).
% 2.71/2.00 tff(976,plain,
% 2.71/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c0_1(a16))),
% 2.71/2.00 inference(modus_ponens,[status(thm)],[975, 974])).
% 2.71/2.00 tff(977,plain,
% 2.71/2.00 (~c0_1(a3)),
% 2.71/2.00 inference(unit_resolution,[status(thm)],[976, 104, 925, 914, 946, 945, 903, 866, 970])).
% 2.71/2.00 tff(978,plain,
% 2.71/2.00 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 2.71/2.00 inference(bind,[status(th)],[])).
% 2.71/2.00 tff(979,plain,
% 2.71/2.00 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.00 inference(quant_intro,[status(thm)],[978])).
% 2.71/2.00 tff(980,plain,
% 2.71/2.00 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.00 inference(rewrite,[status(thm)],[])).
% 2.71/2.00 tff(981,plain,
% 2.71/2.00 (^[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)) | 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)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 2.71/2.01 inference(bind,[status(th)],[])).
% 2.71/2.01 tff(982,plain,
% 2.71/2.01 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.01 inference(quant_intro,[status(thm)],[981])).
% 2.71/2.01 tff(983,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 2.71/2.01 tff(984,plain,
% 2.71/2.01 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[983, 982])).
% 2.71/2.01 tff(985,plain,
% 2.71/2.01 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[984, 980])).
% 2.71/2.01 tff(986,plain,(
% 2.71/2.01 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.01 inference(skolemize,[status(sab)],[985])).
% 2.71/2.01 tff(987,plain,
% 2.71/2.01 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[986, 979])).
% 2.71/2.01 tff(988,plain,
% 2.71/2.01 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | (~c0_1(a16)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(989,plain,
% 2.71/2.01 ((hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (hskp12 | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | (~c0_1(a16)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(990,plain,
% 2.71/2.01 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | (~c0_1(a16))))),
% 2.71/2.01 inference(monotonicity,[status(thm)],[989])).
% 2.71/2.01 tff(991,plain,
% 2.71/2.01 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | (~c0_1(a16)))),
% 2.71/2.01 inference(transitivity,[status(thm)],[990, 988])).
% 2.71/2.01 tff(992,plain,
% 2.71/2.01 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 2.71/2.01 inference(quant_inst,[status(thm)],[])).
% 2.71/2.01 tff(993,plain,
% 2.71/2.01 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | (~c0_1(a16))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[992, 991])).
% 2.71/2.01 tff(994,plain,
% 2.71/2.01 (hskp12),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[993, 104, 925, 914, 945, 903, 866, 987, 977])).
% 2.71/2.01 tff(995,plain,
% 2.71/2.01 (((~hskp12) | (~c3_1(a20))) <=> ((~hskp12) | (~c3_1(a20)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(996,plain,
% 2.71/2.01 (((~c3_1(a20)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a20)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(997,axiom,((~c3_1(a20)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 2.71/2.01 tff(998,plain,
% 2.71/2.01 ((~hskp12) | (~c3_1(a20))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[997, 996])).
% 2.71/2.01 tff(999,plain,
% 2.71/2.01 ((~hskp12) | (~c3_1(a20))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[998, 995])).
% 2.71/2.01 tff(1000,plain,
% 2.71/2.01 (~c3_1(a20)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[999, 994])).
% 2.71/2.01 tff(1001,plain,
% 2.71/2.01 (((~hskp12) | (~c1_1(a20))) <=> ((~hskp12) | (~c1_1(a20)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1002,plain,
% 2.71/2.01 (((~c1_1(a20)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a20)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1003,axiom,((~c1_1(a20)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 2.71/2.01 tff(1004,plain,
% 2.71/2.01 ((~hskp12) | (~c1_1(a20))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 2.71/2.01 tff(1005,plain,
% 2.71/2.01 ((~hskp12) | (~c1_1(a20))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1004, 1001])).
% 2.71/2.01 tff(1006,plain,
% 2.71/2.01 (~c1_1(a20)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1005, 994])).
% 2.71/2.01 tff(1007,plain,
% 2.71/2.01 (((~hskp12) | c2_1(a20)) <=> ((~hskp12) | c2_1(a20))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1008,axiom,((~hskp12) | c2_1(a20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 2.71/2.01 tff(1009,plain,
% 2.71/2.01 ((~hskp12) | c2_1(a20)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 2.71/2.01 tff(1010,plain,
% 2.71/2.01 ((~hskp12) | c2_1(a20)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1009, 1007])).
% 2.71/2.01 tff(1011,plain,
% 2.71/2.01 ((~hskp12) | c2_1(a20)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1010, 1007])).
% 2.71/2.01 tff(1012,plain,
% 2.71/2.01 ((~hskp12) | c2_1(a20)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1011, 1007])).
% 2.71/2.01 tff(1013,plain,
% 2.71/2.01 ((~hskp12) | c2_1(a20)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1012, 1007])).
% 2.71/2.01 tff(1014,plain,
% 2.71/2.01 ((~hskp12) | c2_1(a20)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1013, 1007])).
% 2.71/2.01 tff(1015,plain,
% 2.71/2.01 ((~hskp12) | c2_1(a20)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1014, 1007])).
% 2.71/2.01 tff(1016,plain,
% 2.71/2.01 ((~hskp12) | c2_1(a20)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1015, 1007])).
% 2.71/2.01 tff(1017,plain,
% 2.71/2.01 (c2_1(a20)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1016, 994])).
% 2.71/2.01 tff(1018,plain,
% 2.71/2.01 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1019,plain,
% 2.71/2.01 ((hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a13) | c2_1(a13) | c0_1(a13)) <=> (hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1020,plain,
% 2.71/2.01 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a13) | c2_1(a13) | c0_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20))))),
% 2.71/2.01 inference(monotonicity,[status(thm)],[1019])).
% 2.71/2.01 tff(1021,plain,
% 2.71/2.01 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a13) | c2_1(a13) | c0_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)))),
% 2.71/2.01 inference(transitivity,[status(thm)],[1020, 1018])).
% 2.71/2.01 tff(1022,plain,
% 2.71/2.01 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a13) | c2_1(a13) | c0_1(a13))),
% 2.71/2.01 inference(quant_inst,[status(thm)],[])).
% 2.71/2.01 tff(1023,plain,
% 2.71/2.01 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 2.71/2.01 tff(1024,plain,
% 2.71/2.01 (hskp5),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1023, 104, 1017, 1006, 1000, 864, 862, 290, 960])).
% 2.71/2.01 tff(1025,plain,
% 2.71/2.01 (~c2_1(a11)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[306, 1024])).
% 2.71/2.01 tff(1026,plain,
% 2.71/2.01 (~c1_1(a11)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[312, 1024])).
% 2.71/2.01 tff(1027,plain,
% 2.71/2.01 (c0_1(a11)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[323, 1024])).
% 2.71/2.01 tff(1028,plain,
% 2.71/2.01 (((~hskp10) | c3_1(a18)) <=> ((~hskp10) | c3_1(a18))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1029,axiom,((~hskp10) | c3_1(a18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 2.71/2.01 tff(1030,plain,
% 2.71/2.01 ((~hskp10) | c3_1(a18)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 2.71/2.01 tff(1031,plain,
% 2.71/2.01 ((~hskp10) | c3_1(a18)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1030, 1028])).
% 2.71/2.01 tff(1032,plain,
% 2.71/2.01 ((~hskp10) | c3_1(a18)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1031, 1028])).
% 2.71/2.01 tff(1033,plain,
% 2.71/2.01 ((~hskp10) | c3_1(a18)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1032, 1028])).
% 2.71/2.01 tff(1034,plain,
% 2.71/2.01 ((~hskp10) | c3_1(a18)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1033, 1028])).
% 2.71/2.01 tff(1035,plain,
% 2.71/2.01 ((~hskp10) | c3_1(a18)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1034, 1028])).
% 2.71/2.01 tff(1036,plain,
% 2.71/2.01 ((~hskp10) | c3_1(a18)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1035, 1028])).
% 2.71/2.01 tff(1037,plain,
% 2.71/2.01 ((~hskp10) | c3_1(a18)),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1036, 1028])).
% 2.71/2.01 tff(1038,plain,
% 2.71/2.01 (c3_1(a18)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1037, 932])).
% 2.71/2.01 tff(1039,plain,
% 2.71/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1040,plain,
% 2.71/2.01 (((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18))) <=> (c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1041,plain,
% 2.71/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18))))),
% 2.71/2.01 inference(monotonicity,[status(thm)],[1040])).
% 2.71/2.01 tff(1042,plain,
% 2.71/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)))),
% 2.71/2.01 inference(transitivity,[status(thm)],[1041, 1039])).
% 2.71/2.01 tff(1043,plain,
% 2.71/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))),
% 2.71/2.01 inference(quant_inst,[status(thm)],[])).
% 2.71/2.01 tff(1044,plain,
% 2.71/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 2.71/2.01 tff(1045,plain,
% 2.71/2.01 ($false),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1044, 104, 1038, 1027, 944, 938, 1026, 1025, 751, 953])).
% 2.71/2.01 tff(1046,plain,(hskp21 | hskp1 | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | hskp24 | hskp3 | c2_1(a15) | c3_1(a15) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.01 tff(1047,plain,
% 2.71/2.01 (hskp21),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1046, 568, 153, 152, 151, 200, 48, 752, 468, 475])).
% 2.71/2.01 tff(1048,plain,
% 2.71/2.01 (c1_1(a38)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[657, 1047])).
% 2.71/2.01 tff(1049,plain,
% 2.71/2.01 (c0_1(a38)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[646, 1047])).
% 2.71/2.01 tff(1050,plain,
% 2.71/2.01 (^[U: $i] : refl((hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 2.71/2.01 inference(bind,[status(th)],[])).
% 2.71/2.01 tff(1051,plain,
% 2.71/2.01 (![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.01 inference(quant_intro,[status(thm)],[1050])).
% 2.71/2.01 tff(1052,plain,
% 2.71/2.01 (![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1053,plain,
% 2.71/2.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp24))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) | hskp6) <=> ((hskp24 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp6))), rewrite(((hskp24 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) | hskp6) <=> (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 2.71/2.01 inference(bind,[status(th)],[])).
% 2.71/2.01 tff(1054,plain,
% 2.71/2.01 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) | hskp6) <=> ![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.01 inference(quant_intro,[status(thm)],[1053])).
% 2.71/2.01 tff(1055,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 2.71/2.01 tff(1056,plain,
% 2.71/2.01 (![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1055, 1054])).
% 2.71/2.01 tff(1057,plain,
% 2.71/2.01 (![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1056, 1052])).
% 2.71/2.01 tff(1058,plain,(
% 2.71/2.01 ![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.01 inference(skolemize,[status(sab)],[1057])).
% 2.71/2.01 tff(1059,plain,
% 2.71/2.01 (![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1058, 1051])).
% 2.71/2.01 tff(1060,plain,
% 2.71/2.01 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | c2_1(a38) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a38) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1061,plain,
% 2.71/2.01 ((hskp24 | hskp6 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38))) <=> (hskp24 | hskp6 | c2_1(a38) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1062,plain,
% 2.71/2.01 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | c2_1(a38) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38))))),
% 2.71/2.01 inference(monotonicity,[status(thm)],[1061])).
% 2.71/2.01 tff(1063,plain,
% 2.71/2.01 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a38) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.71/2.01 inference(transitivity,[status(thm)],[1062, 1060])).
% 2.71/2.01 tff(1064,plain,
% 2.71/2.01 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))),
% 2.71/2.01 inference(quant_inst,[status(thm)],[])).
% 2.71/2.01 tff(1065,plain,
% 2.71/2.01 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a38) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 2.71/2.01 tff(1066,plain,
% 2.71/2.01 (hskp24 | hskp6 | (~c0_1(a38)) | (~c1_1(a38))),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1065, 104, 474, 1059])).
% 2.71/2.01 tff(1067,plain,
% 2.71/2.01 (hskp6),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1066, 1049, 568, 1048])).
% 2.71/2.01 tff(1068,plain,
% 2.71/2.01 (~c3_1(a13)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[186, 1067])).
% 2.71/2.01 tff(1069,plain,
% 2.71/2.01 (~c1_1(a13)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[192, 1067])).
% 2.71/2.01 tff(1070,plain,
% 2.71/2.01 (~c0_1(a13)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[198, 1067])).
% 2.71/2.01 tff(1071,plain,
% 2.71/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1072,plain,
% 2.71/2.01 (((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1073,plain,
% 2.71/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38))))),
% 2.71/2.01 inference(monotonicity,[status(thm)],[1072])).
% 2.71/2.01 tff(1074,plain,
% 2.71/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.71/2.01 inference(transitivity,[status(thm)],[1073, 1071])).
% 2.71/2.01 tff(1075,plain,
% 2.71/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 2.71/2.01 inference(quant_inst,[status(thm)],[])).
% 2.71/2.01 tff(1076,plain,
% 2.71/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 2.71/2.01 tff(1077,plain,
% 2.71/2.01 (~c3_1(a38)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1076, 104, 1049, 1048, 474, 1070, 1069, 1068, 36])).
% 2.71/2.01 tff(1078,plain,
% 2.71/2.01 (hskp2),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[247, 104, 200, 1070, 1069, 1068, 47])).
% 2.71/2.01 tff(1079,plain,
% 2.71/2.01 (~c2_1(a3)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[206, 1078])).
% 2.71/2.01 tff(1080,plain,
% 2.71/2.01 (c3_1(a3)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[217, 1078])).
% 2.71/2.01 tff(1081,plain,
% 2.71/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a38) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a38) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1082,plain,
% 2.71/2.01 (((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38))) <=> (c2_1(a38) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1083,plain,
% 2.71/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a38) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38))))),
% 2.71/2.01 inference(monotonicity,[status(thm)],[1082])).
% 2.71/2.01 tff(1084,plain,
% 2.71/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a38) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1083, 1081])).
% 2.71/2.02 tff(1085,plain,
% 2.71/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1086,plain,
% 2.71/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a38) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38))),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 2.71/2.02 tff(1087,plain,
% 2.71/2.02 (~c0_1(a3)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1086, 104, 1049, 1048, 1080, 474, 1079, 970, 1077])).
% 2.71/2.02 tff(1088,plain,
% 2.71/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a38) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | c3_1(a38) | (~c1_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a38) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | c3_1(a38) | (~c1_1(a38)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1089,plain,
% 2.71/2.02 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a38) | c2_1(a38) | (~c1_1(a38)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c2_1(a38) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | c3_1(a38) | (~c1_1(a38)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1090,plain,
% 2.71/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a38) | c2_1(a38) | (~c1_1(a38)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a38) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | c3_1(a38) | (~c1_1(a38))))),
% 2.71/2.02 inference(monotonicity,[status(thm)],[1089])).
% 2.71/2.02 tff(1091,plain,
% 2.71/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a38) | c2_1(a38) | (~c1_1(a38)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a38) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | c3_1(a38) | (~c1_1(a38)))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1090, 1088])).
% 2.71/2.02 tff(1092,plain,
% 2.71/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a38) | c2_1(a38) | (~c1_1(a38)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1093,plain,
% 2.71/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a38) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | c3_1(a38) | (~c1_1(a38))),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 2.71/2.02 tff(1094,plain,
% 2.71/2.02 ($false),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1093, 104, 1048, 1080, 153, 152, 474, 1079, 151, 734, 1077, 1087])).
% 2.71/2.02 tff(1095,plain,(hskp24 | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a38) | c3_1(a1) | hskp1 | hskp3 | c2_1(a15) | c3_1(a15) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.02 tff(1096,plain,
% 2.71/2.02 (hskp24),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1095, 200, 810, 474, 809, 808, 48, 752, 468, 475])).
% 2.71/2.02 tff(1097,plain,
% 2.71/2.02 (c2_1(a58)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[466, 1096])).
% 2.71/2.02 tff(1098,plain,
% 2.71/2.02 (~hskp2),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[237, 200, 1097, 37, 26])).
% 2.71/2.02 tff(1099,plain,
% 2.71/2.02 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1100,plain,
% 2.71/2.02 ((hskp2 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15)) <=> (hskp2 | hskp1 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1101,plain,
% 2.71/2.02 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15)))),
% 2.71/2.02 inference(monotonicity,[status(thm)],[1100])).
% 2.71/2.02 tff(1102,plain,
% 2.71/2.02 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1101, 1099])).
% 2.71/2.02 tff(1103,plain,
% 2.71/2.02 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1104,plain,
% 2.71/2.02 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15)),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 2.71/2.02 tff(1105,plain,
% 2.71/2.02 (hskp2 | hskp1 | c3_1(a15) | c0_1(a15)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1104, 104, 475, 47])).
% 2.71/2.02 tff(1106,plain,
% 2.71/2.02 (c0_1(a15)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1105, 1098, 468, 200])).
% 2.71/2.02 tff(1107,plain,
% 2.71/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a15) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | (~c0_1(a15)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1108,plain,
% 2.71/2.02 (((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a15) | c1_1(a15) | c3_1(a15)) <=> (c1_1(a15) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | (~c0_1(a15)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1109,plain,
% 2.71/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a15) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | (~c0_1(a15))))),
% 2.71/2.02 inference(monotonicity,[status(thm)],[1108])).
% 2.71/2.02 tff(1110,plain,
% 2.71/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | (~c0_1(a15)))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1109, 1107])).
% 2.71/2.02 tff(1111,plain,
% 2.71/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a15) | c1_1(a15) | c3_1(a15))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1112,plain,
% 2.71/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | (~c0_1(a15))),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 2.71/2.02 tff(1113,plain,
% 2.71/2.02 (c0_1(a1) | (~c0_1(a15))),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1112, 104, 810, 475, 752, 468, 809, 341])).
% 2.71/2.02 tff(1114,plain,
% 2.71/2.02 (c0_1(a1)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1113, 1106])).
% 2.71/2.02 tff(1115,plain,
% 2.71/2.02 (hskp6 | (~c0_1(a1))),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[159, 104, 808, 810, 809, 150])).
% 2.71/2.02 tff(1116,plain,
% 2.71/2.02 (hskp6),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1115, 1114])).
% 2.71/2.02 tff(1117,plain,
% 2.71/2.02 (~c0_1(a13)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[198, 1116])).
% 2.71/2.02 tff(1118,plain,
% 2.71/2.02 (~c3_1(a13)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[186, 1116])).
% 2.71/2.02 tff(1119,assumption,(~hskp2), introduced(assumption)).
% 2.71/2.02 tff(1120,plain,
% 2.71/2.02 (c0_1(a15)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1105, 1119, 468, 200])).
% 2.71/2.02 tff(1121,plain,
% 2.71/2.02 (c0_1(a1) | (~c0_1(a15))),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1112, 104, 152, 475, 752, 468, 151, 341])).
% 2.71/2.02 tff(1122,plain,
% 2.71/2.02 (c0_1(a1)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1121, 1120])).
% 2.71/2.02 tff(1123,plain,
% 2.71/2.02 (hskp2 | c0_1(a13) | c1_1(a13)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[247, 104, 200, 239, 47])).
% 2.71/2.02 tff(1124,plain,
% 2.71/2.02 (c1_1(a13)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1123, 1119, 241])).
% 2.71/2.02 tff(1125,plain,
% 2.71/2.02 (~hskp6),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[192, 1124])).
% 2.71/2.02 tff(1126,plain,
% 2.71/2.02 ($false),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[160, 1125, 1122])).
% 2.71/2.02 tff(1127,plain,(hskp2 | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | hskp1 | c3_1(a13)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.02 tff(1128,plain,
% 2.71/2.02 ($false),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1127, 1118, 1117, 810, 809, 475, 752, 468, 808, 200, 1098])).
% 2.71/2.02 tff(1129,plain,(hskp1 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a58) | c1_1(a58) | c2_1(a38) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.71/2.02 tff(1130,plain,
% 2.71/2.02 (hskp1),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1129, 468, 752, 475, 37, 26, 474, 48])).
% 2.71/2.02 tff(1131,plain,
% 2.71/2.02 (~c2_1(a2)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[262, 1130])).
% 2.71/2.02 tff(1132,plain,
% 2.71/2.02 (~c0_1(a2)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[268, 1130])).
% 2.71/2.02 tff(1133,plain,
% 2.71/2.02 (~c3_1(a2)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[256, 1130])).
% 2.71/2.02 tff(1134,plain,
% 2.71/2.02 (~c0_1(a37)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[685, 877])).
% 2.71/2.02 tff(1135,plain,
% 2.71/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c0_1(a18) | c1_1(a18) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c0_1(a18) | c1_1(a18) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1136,plain,
% 2.71/2.02 (((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18))) <=> (c0_1(a37) | c0_1(a18) | c1_1(a18) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1137,plain,
% 2.71/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c0_1(a18) | c1_1(a18) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37))))),
% 2.71/2.02 inference(monotonicity,[status(thm)],[1136])).
% 2.71/2.02 tff(1138,plain,
% 2.71/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c0_1(a18) | c1_1(a18) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1137, 1135])).
% 2.71/2.02 tff(1139,plain,
% 2.71/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1140,plain,
% 2.71/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c0_1(a18) | c1_1(a18) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37))),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 2.71/2.02 tff(1141,plain,
% 2.71/2.02 (~c0_1(a15)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1140, 104, 878, 1038, 1134, 944, 938, 475, 752, 751, 880])).
% 2.71/2.02 tff(1142,plain,
% 2.71/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a18) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a18)) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a18) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a18)) | (~c3_1(a18)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1143,plain,
% 2.71/2.02 (((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a15) | c0_1(a15) | c3_1(a15)) <=> (c1_1(a18) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a18)) | (~c3_1(a18)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1144,plain,
% 2.71/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a15) | c0_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a18) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a18)) | (~c3_1(a18))))),
% 2.71/2.02 inference(monotonicity,[status(thm)],[1143])).
% 2.71/2.02 tff(1145,plain,
% 2.71/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a15) | c0_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a18) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a18)) | (~c3_1(a18)))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1144, 1142])).
% 2.71/2.02 tff(1146,plain,
% 2.71/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a15) | c0_1(a15) | c3_1(a15))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1147,plain,
% 2.71/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a18) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a18)) | (~c3_1(a18))),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 2.71/2.02 tff(1148,plain,
% 2.71/2.02 (~c2_1(a18)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1147, 104, 1038, 938, 475, 752, 468, 362, 1141])).
% 2.71/2.02 tff(1149,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a37) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a37) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | (~c3_1(a37)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1150,plain,
% 2.71/2.02 ((hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37))) <=> (hskp12 | c0_1(a37) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | (~c3_1(a37)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1151,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a37) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | (~c3_1(a37))))),
% 2.71/2.02 inference(monotonicity,[status(thm)],[1150])).
% 2.71/2.02 tff(1152,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a37) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | (~c3_1(a37)))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1151, 1149])).
% 2.71/2.02 tff(1153,plain,
% 2.71/2.02 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1154,plain,
% 2.71/2.02 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a37) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | (~c3_1(a37))),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 2.71/2.02 tff(1155,plain,
% 2.71/2.02 (hskp12),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1154, 104, 878, 925, 914, 1134, 903, 987, 880])).
% 2.71/2.02 tff(1156,plain,
% 2.71/2.02 (~c3_1(a20)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[999, 1155])).
% 2.71/2.02 tff(1157,plain,
% 2.71/2.02 (~c1_1(a20)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1005, 1155])).
% 2.71/2.02 tff(1158,plain,
% 2.71/2.02 (c2_1(a20)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1016, 1155])).
% 2.71/2.02 tff(1159,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a20)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1160,plain,
% 2.71/2.03 ((hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a20)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1161,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a20))))),
% 2.71/2.03 inference(monotonicity,[status(thm)],[1160])).
% 2.71/2.03 tff(1162,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a20)))),
% 2.71/2.03 inference(transitivity,[status(thm)],[1161, 1159])).
% 2.71/2.03 tff(1163,plain,
% 2.71/2.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 2.71/2.03 inference(quant_inst,[status(thm)],[])).
% 2.71/2.03 tff(1164,plain,
% 2.71/2.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a20))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 2.71/2.03 tff(1165,plain,
% 2.71/2.03 (hskp5),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1164, 104, 1158, 1157, 1156, 14, 13, 12, 290])).
% 2.71/2.03 tff(1166,plain,
% 2.71/2.03 (~c2_1(a11)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[306, 1165])).
% 2.71/2.03 tff(1167,plain,
% 2.71/2.03 (~c1_1(a11)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[312, 1165])).
% 2.71/2.03 tff(1168,plain,
% 2.71/2.03 (c0_1(a11)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[323, 1165])).
% 2.71/2.03 tff(1169,plain,
% 2.71/2.03 ($false),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1044, 104, 1038, 1168, 944, 938, 1167, 1166, 751, 1148])).
% 2.71/2.03 tff(1170,plain,(hskp21 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.71/2.03 tff(1171,plain,
% 2.71/2.03 (hskp21),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1170, 568, 752, 468, 14, 13, 12, 153, 152, 151, 475, 48])).
% 2.71/2.03 tff(1172,plain,
% 2.71/2.03 (hskp27),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[678, 1171, 474, 13, 14, 12])).
% 2.71/2.03 tff(1173,plain,
% 2.71/2.03 (c3_1(a12)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[605, 1172])).
% 2.71/2.03 tff(1174,plain,
% 2.71/2.03 (c1_1(a12)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[616, 1172])).
% 2.71/2.03 tff(1175,plain,
% 2.71/2.03 (~c2_1(a12)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[623, 104, 568, 48, 1174, 1173, 10])).
% 2.71/2.03 tff(1176,plain,
% 2.71/2.03 (c1_1(a38)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[657, 1171])).
% 2.71/2.03 tff(1177,plain,
% 2.71/2.03 (c0_1(a38)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[646, 1171])).
% 2.71/2.03 tff(1178,plain,
% 2.71/2.03 (hskp6),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1066, 1177, 568, 1176])).
% 2.71/2.03 tff(1179,plain,
% 2.71/2.03 (~c3_1(a13)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[186, 1178])).
% 2.71/2.03 tff(1180,plain,
% 2.71/2.03 (~c1_1(a13)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[192, 1178])).
% 2.71/2.03 tff(1181,plain,
% 2.71/2.03 (~c0_1(a13)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[198, 1178])).
% 2.71/2.03 tff(1182,plain,
% 2.71/2.03 (~c3_1(a38)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1076, 104, 1177, 1176, 474, 1181, 1180, 1179, 36])).
% 2.71/2.03 tff(1183,plain,
% 2.71/2.03 (((~hskp27) | c0_1(a12)) <=> ((~hskp27) | c0_1(a12))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1184,axiom,((~hskp27) | c0_1(a12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 2.71/2.03 tff(1185,plain,
% 2.71/2.03 ((~hskp27) | c0_1(a12)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 2.71/2.03 tff(1186,plain,
% 2.71/2.03 ((~hskp27) | c0_1(a12)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1185, 1183])).
% 2.71/2.03 tff(1187,plain,
% 2.71/2.03 ((~hskp27) | c0_1(a12)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1186, 1183])).
% 2.71/2.03 tff(1188,plain,
% 2.71/2.03 ((~hskp27) | c0_1(a12)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1187, 1183])).
% 2.71/2.03 tff(1189,plain,
% 2.71/2.03 ((~hskp27) | c0_1(a12)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1188, 1183])).
% 2.71/2.03 tff(1190,plain,
% 2.71/2.03 ((~hskp27) | c0_1(a12)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1189, 1183])).
% 2.71/2.03 tff(1191,plain,
% 2.71/2.03 ((~hskp27) | c0_1(a12)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1190, 1183])).
% 2.71/2.03 tff(1192,plain,
% 2.71/2.03 ((~hskp27) | c0_1(a12)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1191, 1183])).
% 2.71/2.03 tff(1193,plain,
% 2.71/2.03 (c0_1(a12)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1192, 1172])).
% 2.71/2.03 tff(1194,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a12))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a12))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1195,plain,
% 2.71/2.03 (((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a12) | (~c3_1(a12)) | (~c0_1(a12)) | c2_1(a12) | (~c1_1(a12)) | (~c0_1(a12))) <=> ((~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a12))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1196,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a12) | (~c3_1(a12)) | (~c0_1(a12)) | c2_1(a12) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a12)))),
% 2.71/2.03 inference(monotonicity,[status(thm)],[1195])).
% 2.71/2.03 tff(1197,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a12) | (~c3_1(a12)) | (~c0_1(a12)) | c2_1(a12) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a12))),
% 2.71/2.03 inference(transitivity,[status(thm)],[1196, 1194])).
% 2.71/2.03 tff(1198,plain,
% 2.71/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a12) | (~c3_1(a12)) | (~c0_1(a12)) | c2_1(a12) | (~c1_1(a12)) | (~c0_1(a12)))),
% 2.71/2.03 inference(quant_inst,[status(thm)],[])).
% 2.71/2.03 tff(1199,plain,
% 2.71/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a12)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 2.71/2.03 tff(1200,plain,
% 2.71/2.03 ($false),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1199, 104, 1193, 1174, 1173, 1177, 1176, 970, 1182, 1175])).
% 2.71/2.03 tff(1201,plain,(hskp24 | c2_1(a38) | hskp3 | c2_1(a2) | c0_1(a2) | c3_1(a2) | c2_1(a15) | c3_1(a15) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.03 tff(1202,plain,
% 2.71/2.03 (hskp24),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1201, 12, 48, 13, 14, 474, 752, 468, 808, 810, 809, 475])).
% 2.71/2.03 tff(1203,plain,
% 2.71/2.03 (c2_1(a58)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[466, 1202])).
% 2.71/2.03 tff(1204,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1205,plain,
% 2.71/2.03 (((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1206,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58))))),
% 2.71/2.03 inference(monotonicity,[status(thm)],[1205])).
% 2.71/2.03 tff(1207,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.71/2.03 inference(transitivity,[status(thm)],[1206, 1204])).
% 2.71/2.03 tff(1208,plain,
% 2.71/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 2.71/2.03 inference(quant_inst,[status(thm)],[])).
% 2.71/2.03 tff(1209,plain,
% 2.71/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 2.71/2.03 tff(1210,plain,
% 2.71/2.03 (c0_1(a2) | c3_1(a2) | (~c2_1(a58)) | (~c3_1(a58))),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1209, 104, 26, 475, 752, 468, 13, 362])).
% 2.71/2.03 tff(1211,plain,
% 2.71/2.03 (~c3_1(a58)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1210, 1203, 14, 12])).
% 2.71/2.03 tff(1212,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a58)) | c3_1(a58))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1213,plain,
% 2.71/2.03 (((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c3_1(a15)) <=> (c0_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a58)) | c3_1(a58))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1214,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a58)) | c3_1(a58)))),
% 2.71/2.03 inference(monotonicity,[status(thm)],[1213])).
% 2.71/2.03 tff(1215,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a58)) | c3_1(a58))),
% 2.71/2.03 inference(transitivity,[status(thm)],[1214, 1212])).
% 2.71/2.03 tff(1216,plain,
% 2.71/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c3_1(a15))),
% 2.71/2.03 inference(quant_inst,[status(thm)],[])).
% 2.71/2.03 tff(1217,plain,
% 2.71/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a58)) | c3_1(a58)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 2.71/2.03 tff(1218,plain,
% 2.71/2.03 (~c0_1(a15)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1217, 104, 1203, 37, 475, 752, 468, 341, 1211])).
% 2.71/2.03 tff(1219,plain,
% 2.71/2.03 (hskp18),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[397, 1211, 1203])).
% 2.71/2.03 tff(1220,plain,
% 2.71/2.03 (~c3_1(a31)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[403, 1219])).
% 2.71/2.03 tff(1221,plain,
% 2.71/2.03 (c1_1(a31)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[414, 1219])).
% 2.71/2.03 tff(1222,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a58) | c3_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | c3_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1223,plain,
% 2.71/2.03 (((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c0_1(a15)) <=> (c1_1(a58) | c3_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1224,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a58) | c3_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58)))),
% 2.71/2.03 inference(monotonicity,[status(thm)],[1223])).
% 2.71/2.03 tff(1225,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | c3_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))),
% 2.71/2.03 inference(transitivity,[status(thm)],[1224, 1222])).
% 2.71/2.03 tff(1226,plain,
% 2.71/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c0_1(a15))),
% 2.71/2.03 inference(quant_inst,[status(thm)],[])).
% 2.71/2.03 tff(1227,plain,
% 2.71/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | c3_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 2.71/2.03 tff(1228,plain,
% 2.71/2.03 (c2_1(a31)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1227, 104, 1203, 1221, 26, 1220, 475, 752, 380, 1211, 1218])).
% 2.71/2.03 tff(1229,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a58) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a58)) | c3_1(a58))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1230,plain,
% 2.71/2.03 ((hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a15) | c2_1(a15) | c0_1(a15)) <=> (hskp5 | c1_1(a58) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a58)) | c3_1(a58))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1231,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a15) | c2_1(a15) | c0_1(a15))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a58) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a58)) | c3_1(a58)))),
% 2.71/2.03 inference(monotonicity,[status(thm)],[1230])).
% 2.71/2.03 tff(1232,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a15) | c2_1(a15) | c0_1(a15))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a58)) | c3_1(a58))),
% 2.71/2.03 inference(transitivity,[status(thm)],[1231, 1229])).
% 2.71/2.03 tff(1233,plain,
% 2.71/2.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a15) | c2_1(a15) | c0_1(a15))),
% 2.71/2.03 inference(quant_inst,[status(thm)],[])).
% 2.71/2.03 tff(1234,plain,
% 2.71/2.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a58)) | c3_1(a58)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 2.71/2.03 tff(1235,plain,
% 2.71/2.03 (hskp5),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1234, 104, 1203, 26, 752, 468, 290, 1211, 1218])).
% 2.71/2.03 tff(1236,plain,
% 2.71/2.03 (~c2_1(a11)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[306, 1235])).
% 2.71/2.03 tff(1237,plain,
% 2.71/2.03 (~c1_1(a11)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[312, 1235])).
% 2.71/2.03 tff(1238,plain,
% 2.71/2.03 (c0_1(a11)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[323, 1235])).
% 2.71/2.03 tff(1239,plain,
% 2.71/2.03 (~c3_1(a11)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[438, 104, 1221, 1238, 1220, 1237, 1236, 279, 1228])).
% 2.71/2.03 tff(1240,plain,
% 2.71/2.03 (~c0_1(a31)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[444, 1219])).
% 2.71/2.03 tff(1241,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1242,plain,
% 2.71/2.04 (((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15)) <=> (c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1243,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31))))),
% 2.71/2.04 inference(monotonicity,[status(thm)],[1242])).
% 2.71/2.04 tff(1244,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))),
% 2.71/2.04 inference(transitivity,[status(thm)],[1243, 1241])).
% 2.71/2.04 tff(1245,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15))),
% 2.71/2.04 inference(quant_inst,[status(thm)],[])).
% 2.71/2.04 tff(1246,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 2.71/2.04 tff(1247,plain,
% 2.71/2.04 ($false),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1246, 104, 1238, 1240, 1220, 475, 752, 468, 1237, 341, 1228, 1239])).
% 2.71/2.04 tff(1248,plain,(c3_1(a2) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a58) | c0_1(a58) | hskp3 | c0_1(a2) | c2_1(a2) | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.04 tff(1249,plain,
% 2.71/2.04 ($false),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1248, 1133, 1132, 752, 468, 26, 37, 48, 475, 1131, 474])).
% 2.71/2.04 tff(1250,plain,(c3_1(a15) | c2_1(a15) | c1_1(a58) | c0_1(a58) | hskp3 | c1_1(a15) | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.04 tff(1251,plain,
% 2.71/2.04 (c3_1(a15)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1250, 752, 26, 37, 48, 475, 474])).
% 2.71/2.04 tff(1252,assumption,(c3_1(a15)), introduced(assumption)).
% 2.71/2.04 tff(1253,plain,
% 2.71/2.04 (hskp0),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[587, 200, 48, 568, 37, 26])).
% 2.71/2.04 tff(1254,plain,
% 2.71/2.04 (~c3_1(a1)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[117, 1253])).
% 2.71/2.04 tff(1255,plain,
% 2.71/2.04 (c2_1(a1)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[128, 1253])).
% 2.71/2.04 tff(1256,plain,
% 2.71/2.04 (c1_1(a1)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[139, 1253])).
% 2.71/2.04 tff(1257,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1258,plain,
% 2.71/2.04 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15))) <=> (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1259,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15))))),
% 2.71/2.04 inference(monotonicity,[status(thm)],[1258])).
% 2.71/2.04 tff(1260,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))),
% 2.71/2.04 inference(transitivity,[status(thm)],[1259, 1257])).
% 2.71/2.04 tff(1261,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15)))),
% 2.71/2.04 inference(quant_inst,[status(thm)],[])).
% 2.71/2.04 tff(1262,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 2.71/2.04 tff(1263,plain,
% 2.71/2.04 (~c0_1(a15)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1262, 104, 1256, 1255, 475, 752, 1252, 1254, 279])).
% 2.71/2.04 tff(1264,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | c0_1(a15))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1265,plain,
% 2.71/2.04 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | c0_1(a15))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1266,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | c0_1(a15)))),
% 2.71/2.04 inference(monotonicity,[status(thm)],[1265])).
% 2.71/2.04 tff(1267,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | c0_1(a15))),
% 2.71/2.04 inference(transitivity,[status(thm)],[1266, 1264])).
% 2.71/2.04 tff(1268,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 2.71/2.04 inference(quant_inst,[status(thm)],[])).
% 2.71/2.04 tff(1269,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | c0_1(a15)),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 2.71/2.04 tff(1270,plain,
% 2.71/2.04 (~c1_1(a2)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1269, 104, 1256, 1255, 752, 1252, 13, 12, 1254, 734, 1263])).
% 2.71/2.04 tff(1271,plain,
% 2.71/2.04 (~hskp20),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[697, 11, 13, 12, 14, 530])).
% 2.71/2.04 tff(1272,plain,
% 2.71/2.04 ($false),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[544, 1271, 530, 200])).
% 2.71/2.04 tff(1273,plain,(hskp0 | hskp1 | c2_1(a2) | c3_1(a2) | c0_1(a2) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.04 tff(1274,plain,
% 2.71/2.04 (hskp0),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1273, 14, 13, 12, 200, 48, 37, 26])).
% 2.71/2.04 tff(1275,plain,
% 2.71/2.04 (~c3_1(a1)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[117, 1274])).
% 2.71/2.04 tff(1276,plain,
% 2.71/2.04 (c2_1(a1)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[128, 1274])).
% 2.71/2.04 tff(1277,plain,
% 2.71/2.04 (c1_1(a1)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[139, 1274])).
% 2.71/2.04 tff(1278,plain,
% 2.71/2.04 (~c0_1(a15)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1262, 104, 1277, 1276, 475, 752, 1252, 1275, 279])).
% 2.71/2.04 tff(1279,plain,
% 2.71/2.04 (~c1_1(a2)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1269, 104, 1277, 1276, 752, 1252, 13, 12, 1275, 734, 1278])).
% 2.71/2.04 tff(1280,plain,
% 2.71/2.04 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1281,plain,
% 2.71/2.04 ((hskp2 | hskp1 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c0_1(a2)) <=> (hskp2 | hskp1 | c0_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1282,plain,
% 2.71/2.04 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c0_1(a2))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2)))),
% 2.71/2.04 inference(monotonicity,[status(thm)],[1281])).
% 2.71/2.04 tff(1283,plain,
% 2.71/2.04 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c0_1(a2))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 2.71/2.04 inference(transitivity,[status(thm)],[1282, 1280])).
% 2.71/2.04 tff(1284,plain,
% 2.71/2.04 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c0_1(a2))),
% 2.71/2.04 inference(quant_inst,[status(thm)],[])).
% 2.71/2.04 tff(1285,plain,
% 2.71/2.04 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2)),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 2.71/2.04 tff(1286,plain,
% 2.71/2.04 (hskp2 | hskp1 | c0_1(a2) | c1_1(a2)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1285, 104, 12, 47])).
% 2.71/2.04 tff(1287,plain,
% 2.71/2.04 (hskp2),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1286, 1279, 200, 14])).
% 2.71/2.04 tff(1288,plain,
% 2.71/2.04 (~c2_1(a3)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[206, 1287])).
% 2.71/2.04 tff(1289,plain,
% 2.71/2.04 (c3_1(a3)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[217, 1287])).
% 2.71/2.04 tff(1290,plain,
% 2.71/2.04 (c1_1(a3)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[228, 1287])).
% 2.71/2.04 tff(1291,plain,
% 2.71/2.04 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1292,plain,
% 2.71/2.04 ((hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp9 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1293,plain,
% 2.71/2.04 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | (~c1_1(a3))))),
% 2.71/2.04 inference(monotonicity,[status(thm)],[1292])).
% 2.71/2.04 tff(1294,plain,
% 2.71/2.04 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.71/2.04 inference(transitivity,[status(thm)],[1293, 1291])).
% 2.71/2.04 tff(1295,plain,
% 2.71/2.04 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.71/2.04 inference(quant_inst,[status(thm)],[])).
% 2.71/2.04 tff(1296,plain,
% 2.71/2.04 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | (~c1_1(a3))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 2.71/2.04 tff(1297,plain,
% 2.71/2.04 (hskp9),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1296, 104, 1290, 1289, 1277, 1276, 1288, 1275, 890])).
% 2.71/2.04 tff(1298,plain,
% 2.71/2.04 (~c3_1(a16)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[902, 1297])).
% 2.71/2.04 tff(1299,plain,
% 2.71/2.04 (c1_1(a16)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[913, 1297])).
% 2.71/2.04 tff(1300,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a16)) | c2_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a16)) | c2_1(a16))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1301,plain,
% 2.71/2.04 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a16)) | c2_1(a16))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1302,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a16)) | c2_1(a16)))),
% 2.71/2.04 inference(monotonicity,[status(thm)],[1301])).
% 2.71/2.04 tff(1303,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a16)) | c2_1(a16))),
% 2.71/2.04 inference(transitivity,[status(thm)],[1302, 1300])).
% 2.71/2.04 tff(1304,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 2.71/2.04 inference(quant_inst,[status(thm)],[])).
% 2.71/2.04 tff(1305,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a16)) | c2_1(a16)),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 2.71/2.04 tff(1306,plain,
% 2.71/2.04 (c2_1(a16)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1305, 104, 1299, 1277, 1276, 1298, 752, 1252, 1275, 734, 1278])).
% 2.71/2.04 tff(1307,plain,
% 2.71/2.04 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 2.71/2.04 inference(bind,[status(th)],[])).
% 2.71/2.04 tff(1308,plain,
% 2.71/2.04 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.71/2.04 inference(quant_intro,[status(thm)],[1307])).
% 2.71/2.04 tff(1309,plain,
% 2.71/2.04 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1310,plain,
% 2.71/2.04 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~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)) | 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)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 2.71/2.04 inference(bind,[status(th)],[])).
% 2.71/2.04 tff(1311,plain,
% 2.71/2.04 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.71/2.04 inference(quant_intro,[status(thm)],[1310])).
% 2.71/2.04 tff(1312,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 2.71/2.04 tff(1313,plain,
% 2.71/2.04 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[1312, 1311])).
% 2.71/2.04 tff(1314,plain,
% 2.71/2.04 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[1313, 1309])).
% 2.71/2.04 tff(1315,plain,(
% 2.71/2.04 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.71/2.04 inference(skolemize,[status(sab)],[1314])).
% 2.71/2.04 tff(1316,plain,
% 2.71/2.04 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[1315, 1308])).
% 2.71/2.04 tff(1317,plain,
% 2.71/2.04 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a3) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a3) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1318,plain,
% 2.71/2.04 ((hskp6 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp6 | c2_1(a3) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(1319,plain,
% 2.71/2.04 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a3) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3))))),
% 2.71/2.04 inference(monotonicity,[status(thm)],[1318])).
% 2.71/2.04 tff(1320,plain,
% 2.71/2.04 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a3) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.71/2.05 inference(transitivity,[status(thm)],[1319, 1317])).
% 2.71/2.05 tff(1321,plain,
% 2.71/2.05 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 2.71/2.05 inference(quant_inst,[status(thm)],[])).
% 2.71/2.05 tff(1322,plain,
% 2.71/2.05 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a3) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 2.71/2.05 tff(1323,plain,
% 2.71/2.05 (hskp6),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1322, 104, 1290, 1289, 1288, 14, 13, 12, 1316])).
% 2.71/2.05 tff(1324,plain,
% 2.71/2.05 (~c1_1(a13)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[192, 1323])).
% 2.71/2.05 tff(1325,plain,
% 2.71/2.05 (~c0_1(a13)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[198, 1323])).
% 2.71/2.05 tff(1326,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a13) | c1_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a13) | c1_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a13)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(1327,plain,
% 2.71/2.05 ((hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13))) <=> (hskp1 | c0_1(a13) | c1_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a13)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(1328,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a13) | c1_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a13))))),
% 2.71/2.05 inference(monotonicity,[status(thm)],[1327])).
% 2.71/2.05 tff(1329,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a13) | c1_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a13)))),
% 2.71/2.05 inference(transitivity,[status(thm)],[1328, 1326])).
% 2.71/2.05 tff(1330,plain,
% 2.71/2.05 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))),
% 2.71/2.05 inference(quant_inst,[status(thm)],[])).
% 2.71/2.05 tff(1331,plain,
% 2.71/2.05 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a13) | c1_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a13))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 2.71/2.05 tff(1332,plain,
% 2.71/2.05 (~c2_1(a13)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1331, 104, 200, 1290, 1289, 1325, 1324, 1288, 58])).
% 2.71/2.05 tff(1333,plain,
% 2.71/2.05 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 2.71/2.05 inference(bind,[status(th)],[])).
% 2.71/2.05 tff(1334,plain,
% 2.71/2.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.05 inference(quant_intro,[status(thm)],[1333])).
% 2.71/2.05 tff(1335,plain,
% 2.71/2.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(1336,plain,
% 2.71/2.05 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 2.71/2.05 inference(bind,[status(th)],[])).
% 2.71/2.05 tff(1337,plain,
% 2.71/2.05 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_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)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.05 inference(quant_intro,[status(thm)],[1336])).
% 2.71/2.05 tff(1338,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 2.71/2.05 tff(1339,plain,
% 2.71/2.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 2.71/2.05 tff(1340,plain,
% 2.71/2.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[1339, 1335])).
% 2.71/2.05 tff(1341,plain,(
% 2.71/2.05 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.05 inference(skolemize,[status(sab)],[1340])).
% 2.71/2.05 tff(1342,plain,
% 2.71/2.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[1341, 1334])).
% 2.71/2.05 tff(1343,plain,
% 2.71/2.05 (~c3_1(a13)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[186, 1323])).
% 2.71/2.05 tff(1344,plain,
% 2.71/2.05 (c0_1(a16)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[924, 1297])).
% 2.71/2.05 tff(1345,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c1_1(a16)) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c1_1(a16)) | (~c0_1(a16)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(1346,plain,
% 2.71/2.05 ((hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (hskp12 | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c1_1(a16)) | (~c0_1(a16)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(1347,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c1_1(a16)) | (~c0_1(a16))))),
% 2.71/2.05 inference(monotonicity,[status(thm)],[1346])).
% 2.71/2.05 tff(1348,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c1_1(a16)) | (~c0_1(a16)))),
% 2.71/2.05 inference(transitivity,[status(thm)],[1347, 1345])).
% 2.71/2.05 tff(1349,plain,
% 2.71/2.05 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 2.71/2.05 inference(quant_inst,[status(thm)],[])).
% 2.71/2.05 tff(1350,plain,
% 2.71/2.05 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c1_1(a16)) | (~c0_1(a16))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 2.71/2.05 tff(1351,plain,
% 2.71/2.05 (hskp12),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1350, 104, 1344, 1299, 1298, 752, 1252, 987, 1278])).
% 2.71/2.05 tff(1352,plain,
% 2.71/2.05 (~c1_1(a20)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1005, 1351])).
% 2.71/2.05 tff(1353,plain,
% 2.71/2.05 (c2_1(a20)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1016, 1351])).
% 2.71/2.05 tff(1354,plain,
% 2.71/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a20) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a20) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(1355,plain,
% 2.71/2.05 (((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c1_1(a20) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(1356,plain,
% 2.71/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a20) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20))))),
% 2.71/2.05 inference(monotonicity,[status(thm)],[1355])).
% 2.71/2.05 tff(1357,plain,
% 2.71/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a20) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))),
% 2.71/2.05 inference(transitivity,[status(thm)],[1356, 1354])).
% 2.71/2.05 tff(1358,plain,
% 2.71/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13))),
% 2.71/2.05 inference(quant_inst,[status(thm)],[])).
% 2.71/2.05 tff(1359,plain,
% 2.71/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a20) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 2.71/2.05 tff(1360,plain,
% 2.71/2.05 (~c0_1(a20)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1359, 104, 1353, 1299, 1352, 1298, 1325, 1343, 1342, 1332, 1306])).
% 2.71/2.05 tff(1361,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a20) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a20) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | (~c2_1(a20)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(1362,plain,
% 2.71/2.05 ((hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20))) <=> (hskp1 | c1_1(a20) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | (~c2_1(a20)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(1363,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a20) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | (~c2_1(a20))))),
% 2.71/2.05 inference(monotonicity,[status(thm)],[1362])).
% 2.71/2.05 tff(1364,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a20) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | (~c2_1(a20)))),
% 2.71/2.05 inference(transitivity,[status(thm)],[1363, 1361])).
% 2.71/2.05 tff(1365,plain,
% 2.71/2.05 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20)))),
% 2.71/2.05 inference(quant_inst,[status(thm)],[])).
% 2.71/2.05 tff(1366,plain,
% 2.71/2.05 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a20) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | (~c2_1(a20))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 2.71/2.05 tff(1367,plain,
% 2.71/2.05 ($false),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1366, 104, 200, 1353, 1290, 1289, 1352, 1288, 58, 1360])).
% 2.71/2.05 tff(1368,plain,(c0_1(a2) | hskp1 | c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c1_1(a15) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.05 tff(1369,plain,
% 2.71/2.05 (c0_1(a2)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1368, 200, 752, 1252, 13, 12, 475, 48, 37, 26])).
% 2.71/2.05 tff(1370,plain,
% 2.71/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(1371,plain,
% 2.71/2.05 (((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(1372,plain,
% 2.71/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15)))),
% 2.71/2.05 inference(monotonicity,[status(thm)],[1371])).
% 2.71/2.05 tff(1373,plain,
% 2.71/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))),
% 2.71/2.05 inference(transitivity,[status(thm)],[1372, 1370])).
% 2.71/2.05 tff(1374,plain,
% 2.71/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 2.71/2.05 inference(quant_inst,[status(thm)],[])).
% 2.71/2.05 tff(1375,plain,
% 2.71/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15)),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 2.71/2.05 tff(1376,plain,
% 2.71/2.05 ($false),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1375, 104, 475, 752, 1252, 1369, 13, 751, 1263, 1270])).
% 2.71/2.05 tff(1377,plain,(hskp1 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | hskp3 | hskp24 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.05 tff(1378,plain,
% 2.71/2.05 (hskp1),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1377, 13, 752, 1252, 475, 12, 48, 568, 37, 26])).
% 2.71/2.05 tff(1379,plain,
% 2.71/2.05 (~c0_1(a2)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[268, 1378])).
% 2.71/2.05 tff(1380,plain,
% 2.71/2.05 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 2.71/2.05 inference(bind,[status(th)],[])).
% 2.71/2.05 tff(1381,plain,
% 2.71/2.05 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.71/2.05 inference(quant_intro,[status(thm)],[1380])).
% 2.71/2.05 tff(1382,plain,
% 2.71/2.05 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(1383,plain,
% 2.71/2.05 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp8))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 2.71/2.05 inference(bind,[status(th)],[])).
% 2.71/2.05 tff(1384,plain,
% 2.71/2.05 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.71/2.05 inference(quant_intro,[status(thm)],[1383])).
% 2.71/2.05 tff(1385,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 2.71/2.06 tff(1386,plain,
% 2.71/2.06 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 2.71/2.06 tff(1387,plain,
% 2.71/2.06 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1386, 1382])).
% 2.71/2.06 tff(1388,plain,(
% 2.71/2.06 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.71/2.06 inference(skolemize,[status(sab)],[1387])).
% 2.71/2.06 tff(1389,plain,
% 2.71/2.06 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1388, 1381])).
% 2.71/2.06 tff(1390,plain,
% 2.71/2.06 (((~hskp8) | (~c3_1(a15))) <=> ((~hskp8) | (~c3_1(a15)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1391,plain,
% 2.71/2.06 (((~c3_1(a15)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a15)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1392,axiom,((~c3_1(a15)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 2.71/2.06 tff(1393,plain,
% 2.71/2.06 ((~hskp8) | (~c3_1(a15))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 2.71/2.06 tff(1394,plain,
% 2.71/2.06 ((~hskp8) | (~c3_1(a15))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1393, 1390])).
% 2.71/2.06 tff(1395,plain,
% 2.71/2.06 (~hskp8),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1394, 1252])).
% 2.71/2.06 tff(1396,plain,
% 2.71/2.06 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp7 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp7 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1397,plain,
% 2.71/2.06 ((hskp8 | hskp7 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | c2_1(a2)) <=> (hskp8 | hskp7 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1398,plain,
% 2.71/2.06 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | c2_1(a2))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp7 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0)))),
% 2.71/2.06 inference(monotonicity,[status(thm)],[1397])).
% 2.71/2.06 tff(1399,plain,
% 2.71/2.06 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | c2_1(a2))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp7 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 2.71/2.06 inference(transitivity,[status(thm)],[1398, 1396])).
% 2.71/2.06 tff(1400,plain,
% 2.71/2.06 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | c2_1(a2))),
% 2.71/2.06 inference(quant_inst,[status(thm)],[])).
% 2.71/2.06 tff(1401,plain,
% 2.71/2.06 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp7 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 2.71/2.06 tff(1402,plain,
% 2.71/2.06 (hskp7 | c0_1(a2) | c2_1(a2)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1401, 104, 1395, 12, 1389])).
% 2.71/2.06 tff(1403,plain,
% 2.71/2.06 (hskp7),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1402, 1379, 13])).
% 2.71/2.06 tff(1404,plain,
% 2.71/2.06 (((~hskp7) | (~c2_1(a14))) <=> ((~hskp7) | (~c2_1(a14)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1405,plain,
% 2.71/2.06 (((~c2_1(a14)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a14)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1406,axiom,((~c2_1(a14)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 2.71/2.06 tff(1407,plain,
% 2.71/2.06 ((~hskp7) | (~c2_1(a14))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 2.71/2.06 tff(1408,plain,
% 2.71/2.06 ((~hskp7) | (~c2_1(a14))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1407, 1404])).
% 2.71/2.06 tff(1409,plain,
% 2.71/2.06 (~c2_1(a14)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1408, 1403])).
% 2.71/2.06 tff(1410,plain,
% 2.71/2.06 (((~hskp7) | c1_1(a14)) <=> ((~hskp7) | c1_1(a14))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1411,axiom,((~hskp7) | c1_1(a14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 2.71/2.06 tff(1412,plain,
% 2.71/2.06 ((~hskp7) | c1_1(a14)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 2.71/2.06 tff(1413,plain,
% 2.71/2.06 ((~hskp7) | c1_1(a14)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1412, 1410])).
% 2.71/2.06 tff(1414,plain,
% 2.71/2.06 ((~hskp7) | c1_1(a14)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1413, 1410])).
% 2.71/2.06 tff(1415,plain,
% 2.71/2.06 ((~hskp7) | c1_1(a14)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1414, 1410])).
% 2.71/2.06 tff(1416,plain,
% 2.71/2.06 ((~hskp7) | c1_1(a14)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1415, 1410])).
% 2.71/2.06 tff(1417,plain,
% 2.71/2.06 ((~hskp7) | c1_1(a14)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1416, 1410])).
% 2.71/2.06 tff(1418,plain,
% 2.71/2.06 ((~hskp7) | c1_1(a14)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1417, 1410])).
% 2.71/2.06 tff(1419,plain,
% 2.71/2.06 ((~hskp7) | c1_1(a14)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1418, 1410])).
% 2.71/2.06 tff(1420,plain,
% 2.71/2.06 (c1_1(a14)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1419, 1403])).
% 2.71/2.06 tff(1421,plain,
% 2.71/2.06 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c1_1(a14)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1422,plain,
% 2.71/2.06 ((hskp28 | hskp0 | (~ndr1_0) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14))) <=> (hskp28 | hskp0 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c1_1(a14)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1423,plain,
% 2.71/2.06 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c1_1(a14))))),
% 2.71/2.06 inference(monotonicity,[status(thm)],[1422])).
% 2.71/2.06 tff(1424,plain,
% 2.71/2.06 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c1_1(a14)))),
% 2.71/2.06 inference(transitivity,[status(thm)],[1423, 1421])).
% 2.71/2.06 tff(1425,plain,
% 2.71/2.06 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))),
% 2.71/2.06 inference(quant_inst,[status(thm)],[])).
% 2.71/2.06 tff(1426,plain,
% 2.71/2.06 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c1_1(a14))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1425, 1424])).
% 2.71/2.06 tff(1427,plain,
% 2.71/2.06 (hskp28 | hskp0 | (~c3_1(a14))),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1426, 104, 1420, 1409, 582])).
% 2.71/2.06 tff(1428,plain,
% 2.71/2.06 (~c3_1(a14)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1427, 530, 11])).
% 2.71/2.06 tff(1429,plain,
% 2.71/2.06 (((~hskp7) | (~c0_1(a14))) <=> ((~hskp7) | (~c0_1(a14)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1430,plain,
% 2.71/2.06 (((~c0_1(a14)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a14)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1431,axiom,((~c0_1(a14)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 2.71/2.06 tff(1432,plain,
% 2.71/2.06 ((~hskp7) | (~c0_1(a14))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 2.71/2.06 tff(1433,plain,
% 2.71/2.06 ((~hskp7) | (~c0_1(a14))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1432, 1429])).
% 2.71/2.06 tff(1434,plain,
% 2.71/2.06 (~c0_1(a14)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1433, 1403])).
% 2.71/2.06 tff(1435,plain,
% 2.71/2.06 (~hskp27),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[633, 11, 530, 568, 48])).
% 2.71/2.06 tff(1436,plain,
% 2.71/2.06 ((hskp27 | hskp13 | hskp8) <=> (hskp27 | hskp13 | hskp8)),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1437,plain,
% 2.71/2.06 (((hskp27 | hskp13) | hskp8) <=> (hskp27 | hskp13 | hskp8)),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1438,plain,
% 2.71/2.06 ((hskp27 | hskp13) <=> (hskp27 | hskp13)),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1439,plain,
% 2.71/2.06 (((hskp27 | hskp13) | hskp8) <=> ((hskp27 | hskp13) | hskp8)),
% 2.71/2.06 inference(monotonicity,[status(thm)],[1438])).
% 2.71/2.06 tff(1440,plain,
% 2.71/2.06 (((hskp27 | hskp13) | hskp8) <=> (hskp27 | hskp13 | hskp8)),
% 2.71/2.06 inference(transitivity,[status(thm)],[1439, 1437])).
% 2.71/2.06 tff(1441,axiom,((hskp27 | hskp13) | hskp8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 2.71/2.06 tff(1442,plain,
% 2.71/2.06 (hskp27 | hskp13 | hskp8),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1441, 1440])).
% 2.71/2.06 tff(1443,plain,
% 2.71/2.06 (hskp27 | hskp13 | hskp8),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1442, 1436])).
% 2.71/2.06 tff(1444,plain,
% 2.71/2.06 (hskp27 | hskp13 | hskp8),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1443, 1436])).
% 2.71/2.06 tff(1445,plain,
% 2.71/2.06 (hskp27 | hskp13 | hskp8),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1444, 1436])).
% 2.71/2.06 tff(1446,plain,
% 2.71/2.06 (hskp27 | hskp13 | hskp8),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1445, 1436])).
% 2.71/2.06 tff(1447,plain,
% 2.71/2.06 (hskp27 | hskp13 | hskp8),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1446, 1436])).
% 2.71/2.06 tff(1448,plain,
% 2.71/2.06 (hskp27 | hskp13 | hskp8),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1447, 1436])).
% 2.71/2.06 tff(1449,plain,
% 2.71/2.06 (hskp27 | hskp13 | hskp8),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1448, 1436])).
% 2.71/2.06 tff(1450,plain,
% 2.71/2.06 (hskp13),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1449, 1435, 1395])).
% 2.71/2.06 tff(1451,plain,
% 2.71/2.06 (~c3_1(a21)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[831, 1450])).
% 2.71/2.06 tff(1452,plain,
% 2.71/2.06 (~hskp20),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[697, 11, 13, 12, 1379, 530])).
% 2.71/2.06 tff(1453,plain,
% 2.71/2.06 (^[U: $i] : refl((hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))),
% 2.71/2.06 inference(bind,[status(th)],[])).
% 2.71/2.06 tff(1454,plain,
% 2.71/2.06 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.71/2.06 inference(quant_intro,[status(thm)],[1453])).
% 2.71/2.06 tff(1455,plain,
% 2.71/2.06 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1456,plain,
% 2.71/2.06 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp22))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp20) <=> ((hskp22 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp20))), rewrite(((hskp22 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp20) <=> (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp20) <=> (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))))),
% 2.71/2.06 inference(bind,[status(th)],[])).
% 2.71/2.06 tff(1457,plain,
% 2.71/2.06 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp20) <=> ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.71/2.06 inference(quant_intro,[status(thm)],[1456])).
% 2.71/2.06 tff(1458,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 2.71/2.06 tff(1459,plain,
% 2.71/2.06 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1458, 1457])).
% 2.71/2.06 tff(1460,plain,
% 2.71/2.06 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1459, 1455])).
% 2.71/2.06 tff(1461,plain,(
% 2.71/2.06 ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.71/2.06 inference(skolemize,[status(sab)],[1460])).
% 2.71/2.06 tff(1462,plain,
% 2.71/2.06 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1461, 1454])).
% 2.71/2.06 tff(1463,plain,
% 2.71/2.06 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp20 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1464,plain,
% 2.71/2.06 ((hskp22 | hskp20 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15))) <=> (hskp22 | hskp20 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1465,plain,
% 2.71/2.06 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0)))),
% 2.71/2.06 inference(monotonicity,[status(thm)],[1464])).
% 2.71/2.06 tff(1466,plain,
% 2.71/2.06 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp20 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))),
% 2.71/2.06 inference(transitivity,[status(thm)],[1465, 1463])).
% 2.71/2.06 tff(1467,plain,
% 2.71/2.06 ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)))),
% 2.71/2.06 inference(quant_inst,[status(thm)],[])).
% 2.71/2.06 tff(1468,plain,
% 2.71/2.06 ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp20 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 2.71/2.06 tff(1469,plain,
% 2.71/2.06 (hskp22 | hskp20 | c2_1(a15) | (~c3_1(a15))),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1468, 104, 475, 1462])).
% 2.71/2.06 tff(1470,plain,
% 2.71/2.06 (hskp22),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1469, 1452, 752, 1252])).
% 2.71/2.06 tff(1471,plain,
% 2.71/2.06 (((~hskp22) | (~c1_1(a42))) <=> ((~hskp22) | (~c1_1(a42)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1472,plain,
% 2.71/2.06 (((~c1_1(a42)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a42)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1473,axiom,((~c1_1(a42)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 2.71/2.06 tff(1474,plain,
% 2.71/2.06 ((~hskp22) | (~c1_1(a42))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1473, 1472])).
% 2.71/2.06 tff(1475,plain,
% 2.71/2.06 ((~hskp22) | (~c1_1(a42))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1474, 1471])).
% 2.71/2.06 tff(1476,plain,
% 2.71/2.06 (~c1_1(a42)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1475, 1470])).
% 2.71/2.06 tff(1477,plain,
% 2.71/2.06 (c2_1(a21)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[842, 1450])).
% 2.71/2.06 tff(1478,plain,
% 2.71/2.06 (((~hskp22) | c2_1(a42)) <=> ((~hskp22) | c2_1(a42))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1479,axiom,((~hskp22) | c2_1(a42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 2.71/2.06 tff(1480,plain,
% 2.71/2.06 ((~hskp22) | c2_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1479, 1478])).
% 2.71/2.06 tff(1481,plain,
% 2.71/2.06 ((~hskp22) | c2_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1480, 1478])).
% 2.71/2.06 tff(1482,plain,
% 2.71/2.06 ((~hskp22) | c2_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1481, 1478])).
% 2.71/2.06 tff(1483,plain,
% 2.71/2.06 ((~hskp22) | c2_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1482, 1478])).
% 2.71/2.06 tff(1484,plain,
% 2.71/2.06 ((~hskp22) | c2_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1483, 1478])).
% 2.71/2.06 tff(1485,plain,
% 2.71/2.06 ((~hskp22) | c2_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1484, 1478])).
% 2.71/2.06 tff(1486,plain,
% 2.71/2.06 ((~hskp22) | c2_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1485, 1478])).
% 2.71/2.06 tff(1487,plain,
% 2.71/2.06 ((~hskp22) | c2_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1486, 1478])).
% 2.71/2.06 tff(1488,plain,
% 2.71/2.06 (c2_1(a42)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1487, 1470])).
% 2.71/2.06 tff(1489,plain,
% 2.71/2.06 (((~hskp22) | c0_1(a42)) <=> ((~hskp22) | c0_1(a42))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1490,axiom,((~hskp22) | c0_1(a42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 2.71/2.06 tff(1491,plain,
% 2.71/2.06 ((~hskp22) | c0_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1490, 1489])).
% 2.71/2.06 tff(1492,plain,
% 2.71/2.06 ((~hskp22) | c0_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1491, 1489])).
% 2.71/2.06 tff(1493,plain,
% 2.71/2.06 ((~hskp22) | c0_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1492, 1489])).
% 2.71/2.06 tff(1494,plain,
% 2.71/2.06 ((~hskp22) | c0_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1493, 1489])).
% 2.71/2.06 tff(1495,plain,
% 2.71/2.06 ((~hskp22) | c0_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1494, 1489])).
% 2.71/2.06 tff(1496,plain,
% 2.71/2.06 ((~hskp22) | c0_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1495, 1489])).
% 2.71/2.06 tff(1497,plain,
% 2.71/2.06 ((~hskp22) | c0_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1496, 1489])).
% 2.71/2.06 tff(1498,plain,
% 2.71/2.06 ((~hskp22) | c0_1(a42)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1497, 1489])).
% 2.71/2.06 tff(1499,plain,
% 2.71/2.06 (c0_1(a42)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1498, 1470])).
% 2.71/2.06 tff(1500,plain,
% 2.71/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c3_1(a21) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a21) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1501,plain,
% 2.71/2.06 (((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a14) | c0_1(a14) | c3_1(a14)) <=> (c1_1(a42) | c3_1(a21) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1502,plain,
% 2.71/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a14) | c0_1(a14) | c3_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c3_1(a21) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42))))),
% 2.71/2.06 inference(monotonicity,[status(thm)],[1501])).
% 2.71/2.06 tff(1503,plain,
% 2.71/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a14) | c0_1(a14) | c3_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a21) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 2.71/2.06 inference(transitivity,[status(thm)],[1502, 1500])).
% 2.71/2.06 tff(1504,plain,
% 2.71/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a14) | c0_1(a14) | c3_1(a14))),
% 2.71/2.06 inference(quant_inst,[status(thm)],[])).
% 2.71/2.06 tff(1505,plain,
% 2.71/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a21) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 2.71/2.06 tff(1506,plain,
% 2.71/2.06 (~c1_1(a21)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1505, 104, 1499, 1488, 1477, 1476, 1451, 1434, 1409, 1342, 1428])).
% 2.71/2.06 tff(1507,plain,
% 2.71/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | c1_1(a21) | (~c2_1(a21)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1508,plain,
% 2.71/2.06 (((~ndr1_0) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | c1_1(a21) | (~c2_1(a21)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(1509,plain,
% 2.71/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | c1_1(a21) | (~c2_1(a21))))),
% 2.71/2.06 inference(monotonicity,[status(thm)],[1508])).
% 2.71/2.06 tff(1510,plain,
% 2.71/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | c1_1(a21) | (~c2_1(a21)))),
% 2.71/2.06 inference(transitivity,[status(thm)],[1509, 1507])).
% 2.71/2.06 tff(1511,plain,
% 2.71/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 2.71/2.06 inference(quant_inst,[status(thm)],[])).
% 2.71/2.06 tff(1512,plain,
% 2.71/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | c1_1(a21) | (~c2_1(a21))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[1511, 1510])).
% 2.71/2.06 tff(1513,plain,
% 2.71/2.06 ($false),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1512, 104, 476, 1477, 1420, 37, 26, 1451, 1409, 380, 1428, 1506])).
% 2.71/2.06 tff(1514,plain,(hskp0 | c0_1(a58) | c1_1(a58) | c2_1(a15) | (~c3_1(a15)) | c1_1(a15) | c2_1(a2) | c3_1(a2) | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.71/2.06 tff(1515,plain,
% 2.71/2.06 (hskp0),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1514, 13, 26, 752, 1252, 475, 37, 12, 568, 48])).
% 2.71/2.06 tff(1516,plain,
% 2.71/2.06 (~c3_1(a1)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[117, 1515])).
% 2.71/2.06 tff(1517,plain,
% 2.71/2.06 (c2_1(a1)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[128, 1515])).
% 2.71/2.06 tff(1518,plain,
% 2.71/2.06 (c1_1(a1)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[139, 1515])).
% 2.71/2.06 tff(1519,plain,
% 2.71/2.06 (~c0_1(a15)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1262, 104, 1518, 1517, 475, 752, 1252, 1516, 279])).
% 2.71/2.07 tff(1520,plain,
% 2.71/2.07 (~c0_1(a15)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1262, 104, 153, 152, 475, 752, 1252, 151, 279])).
% 2.71/2.07 tff(1521,assumption,(hskp9), introduced(assumption)).
% 2.71/2.07 tff(1522,plain,
% 2.71/2.07 (~c3_1(a16)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[902, 1521])).
% 2.71/2.07 tff(1523,plain,
% 2.71/2.07 (c1_1(a16)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[913, 1521])).
% 2.71/2.07 tff(1524,plain,
% 2.71/2.07 (c2_1(a16)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1305, 104, 1523, 153, 152, 1522, 752, 1252, 151, 734, 1520])).
% 2.71/2.07 tff(1525,plain,
% 2.71/2.07 (c0_1(a16)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[924, 1521])).
% 2.71/2.07 tff(1526,plain,
% 2.71/2.07 (hskp12),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1350, 104, 1525, 1523, 1522, 752, 1252, 987, 1520])).
% 2.71/2.07 tff(1527,plain,
% 2.71/2.07 (~c1_1(a20)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1005, 1526])).
% 2.71/2.07 tff(1528,plain,
% 2.71/2.07 (c2_1(a20)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1016, 1526])).
% 2.71/2.07 tff(1529,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a20) | c3_1(a16) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a20) | c3_1(a16) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1530,plain,
% 2.71/2.07 (((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a20) | c3_1(a16) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1531,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a20) | c3_1(a16) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20))))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[1530])).
% 2.71/2.07 tff(1532,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a20) | c3_1(a16) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))),
% 2.71/2.07 inference(transitivity,[status(thm)],[1531, 1529])).
% 2.71/2.07 tff(1533,plain,
% 2.71/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(1534,plain,
% 2.71/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a20) | c3_1(a16) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 2.71/2.07 tff(1535,plain,
% 2.71/2.07 (~c0_1(a20)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1534, 104, 1528, 1523, 1527, 1522, 14, 13, 12, 1342, 1524])).
% 2.71/2.07 tff(1536,plain,
% 2.71/2.07 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 2.71/2.07 inference(bind,[status(th)],[])).
% 2.71/2.07 tff(1537,plain,
% 2.71/2.07 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.71/2.07 inference(quant_intro,[status(thm)],[1536])).
% 2.71/2.07 tff(1538,plain,
% 2.71/2.07 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1539,plain,
% 2.71/2.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 2.71/2.07 inference(bind,[status(th)],[])).
% 2.71/2.07 tff(1540,plain,
% 2.71/2.07 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.71/2.07 inference(quant_intro,[status(thm)],[1539])).
% 2.71/2.07 tff(1541,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 2.71/2.07 tff(1542,plain,
% 2.71/2.07 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 2.71/2.07 tff(1543,plain,
% 2.71/2.07 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1542, 1538])).
% 2.71/2.07 tff(1544,plain,(
% 2.71/2.07 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.71/2.07 inference(skolemize,[status(sab)],[1543])).
% 2.71/2.07 tff(1545,plain,
% 2.71/2.07 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1544, 1537])).
% 2.71/2.07 tff(1546,plain,
% 2.71/2.07 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c1_1(a20) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a20) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1547,plain,
% 2.71/2.07 ((hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20))) <=> (hskp2 | c1_1(a20) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1548,plain,
% 2.71/2.07 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c1_1(a20) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20))))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[1547])).
% 2.71/2.07 tff(1549,plain,
% 2.71/2.07 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a20) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))),
% 2.71/2.07 inference(transitivity,[status(thm)],[1548, 1546])).
% 2.71/2.07 tff(1550,plain,
% 2.71/2.07 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20)))),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(1551,plain,
% 2.71/2.07 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a20) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 2.71/2.07 tff(1552,plain,
% 2.71/2.07 ($false),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1551, 104, 1119, 1528, 1527, 475, 752, 1252, 1545, 1535])).
% 2.71/2.07 tff(1553,plain,((~hskp9) | hskp2 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.07 tff(1554,plain,
% 2.71/2.07 (~hskp9),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1553, 1119, 475, 752, 1252, 14, 13, 12, 153, 152, 151])).
% 2.71/2.07 tff(1555,plain,
% 2.71/2.07 (hskp7),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1402, 14, 13])).
% 2.71/2.07 tff(1556,plain,
% 2.71/2.07 (~c2_1(a14)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1408, 1555])).
% 2.71/2.07 tff(1557,plain,
% 2.71/2.07 (c1_1(a14)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1419, 1555])).
% 2.71/2.07 tff(1558,plain,
% 2.71/2.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)) | (~c1_1(a14)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1559,plain,
% 2.71/2.07 ((hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14))) <=> (hskp9 | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)) | (~c1_1(a14)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1560,plain,
% 2.71/2.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)) | (~c1_1(a14))))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[1559])).
% 2.71/2.07 tff(1561,plain,
% 2.71/2.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)) | (~c1_1(a14)))),
% 2.71/2.07 inference(transitivity,[status(thm)],[1560, 1558])).
% 2.71/2.07 tff(1562,plain,
% 2.71/2.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(1563,plain,
% 2.71/2.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)) | (~c1_1(a14))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 2.71/2.07 tff(1564,plain,
% 2.71/2.07 (hskp9 | (~c3_1(a14))),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1563, 104, 1557, 153, 152, 1556, 151, 890])).
% 2.71/2.07 tff(1565,plain,
% 2.71/2.07 (~c3_1(a14)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1564, 1554])).
% 2.71/2.07 tff(1566,plain,
% 2.71/2.07 ((hskp17 | hskp9 | hskp2) <=> (hskp17 | hskp9 | hskp2)),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1567,plain,
% 2.71/2.07 (((hskp9 | hskp2) | hskp17) <=> (hskp17 | hskp9 | hskp2)),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1568,plain,
% 2.71/2.07 ((hskp9 | hskp2) <=> (hskp9 | hskp2)),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1569,plain,
% 2.71/2.07 (((hskp9 | hskp2) | hskp17) <=> ((hskp9 | hskp2) | hskp17)),
% 2.71/2.07 inference(monotonicity,[status(thm)],[1568])).
% 2.71/2.07 tff(1570,plain,
% 2.71/2.07 (((hskp9 | hskp2) | hskp17) <=> (hskp17 | hskp9 | hskp2)),
% 2.71/2.07 inference(transitivity,[status(thm)],[1569, 1567])).
% 2.71/2.07 tff(1571,axiom,((hskp9 | hskp2) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 2.71/2.07 tff(1572,plain,
% 2.71/2.07 (hskp17 | hskp9 | hskp2),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 2.71/2.07 tff(1573,plain,
% 2.71/2.07 (hskp17 | hskp9 | hskp2),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1572, 1566])).
% 2.71/2.07 tff(1574,plain,
% 2.71/2.07 (hskp17 | hskp9 | hskp2),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1573, 1566])).
% 2.71/2.07 tff(1575,plain,
% 2.71/2.07 (hskp17 | hskp9 | hskp2),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1574, 1566])).
% 2.71/2.07 tff(1576,plain,
% 2.71/2.07 (hskp17 | hskp9 | hskp2),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1575, 1566])).
% 2.71/2.07 tff(1577,plain,
% 2.71/2.07 (hskp17 | hskp9 | hskp2),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1576, 1566])).
% 2.71/2.07 tff(1578,plain,
% 2.71/2.07 (hskp17 | hskp9 | hskp2),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1577, 1566])).
% 2.71/2.07 tff(1579,plain,
% 2.71/2.07 (hskp17 | hskp9 | hskp2),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1578, 1566])).
% 2.71/2.07 tff(1580,plain,
% 2.71/2.07 (hskp17),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1579, 1554, 1119])).
% 2.71/2.07 tff(1581,plain,
% 2.71/2.07 (((~hskp17) | (~c2_1(a28))) <=> ((~hskp17) | (~c2_1(a28)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1582,plain,
% 2.71/2.07 (((~c2_1(a28)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a28)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1583,axiom,((~c2_1(a28)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 2.71/2.07 tff(1584,plain,
% 2.71/2.07 ((~hskp17) | (~c2_1(a28))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 2.71/2.07 tff(1585,plain,
% 2.71/2.07 ((~hskp17) | (~c2_1(a28))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1584, 1581])).
% 2.71/2.07 tff(1586,plain,
% 2.71/2.07 (~c2_1(a28)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1585, 1580])).
% 2.71/2.07 tff(1587,plain,
% 2.71/2.07 (((~hskp17) | (~c0_1(a28))) <=> ((~hskp17) | (~c0_1(a28)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1588,plain,
% 2.71/2.07 (((~c0_1(a28)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a28)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1589,axiom,((~c0_1(a28)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 2.71/2.07 tff(1590,plain,
% 2.71/2.07 ((~hskp17) | (~c0_1(a28))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 2.71/2.07 tff(1591,plain,
% 2.71/2.07 ((~hskp17) | (~c0_1(a28))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1590, 1587])).
% 2.71/2.07 tff(1592,plain,
% 2.71/2.07 (~c0_1(a28)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1591, 1580])).
% 2.71/2.07 tff(1593,plain,
% 2.71/2.07 (((~hskp17) | c3_1(a28)) <=> ((~hskp17) | c3_1(a28))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1594,axiom,((~hskp17) | c3_1(a28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 2.71/2.07 tff(1595,plain,
% 2.71/2.07 ((~hskp17) | c3_1(a28)),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 2.71/2.07 tff(1596,plain,
% 2.71/2.07 ((~hskp17) | c3_1(a28)),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1595, 1593])).
% 2.71/2.07 tff(1597,plain,
% 2.71/2.07 ((~hskp17) | c3_1(a28)),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1596, 1593])).
% 2.71/2.07 tff(1598,plain,
% 2.71/2.07 ((~hskp17) | c3_1(a28)),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1597, 1593])).
% 2.71/2.07 tff(1599,plain,
% 2.71/2.07 ((~hskp17) | c3_1(a28)),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1598, 1593])).
% 2.71/2.07 tff(1600,plain,
% 2.71/2.07 ((~hskp17) | c3_1(a28)),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1599, 1593])).
% 2.71/2.07 tff(1601,plain,
% 2.71/2.07 ((~hskp17) | c3_1(a28)),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1600, 1593])).
% 2.71/2.07 tff(1602,plain,
% 2.71/2.07 ((~hskp17) | c3_1(a28)),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1601, 1593])).
% 2.71/2.07 tff(1603,plain,
% 2.71/2.07 (c3_1(a28)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1602, 1580])).
% 2.71/2.07 tff(1604,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a28) | c2_1(a28) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | (~c1_1(a14)) | (~c3_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a28) | c2_1(a28) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | (~c1_1(a14)) | (~c3_1(a28)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1605,plain,
% 2.71/2.07 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a28) | c0_1(a28) | (~c3_1(a28))) <=> (c0_1(a28) | c2_1(a28) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | (~c1_1(a14)) | (~c3_1(a28)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1606,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a28) | c0_1(a28) | (~c3_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a28) | c2_1(a28) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | (~c1_1(a14)) | (~c3_1(a28))))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[1605])).
% 2.71/2.07 tff(1607,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a28) | c0_1(a28) | (~c3_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a28) | c2_1(a28) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | (~c1_1(a14)) | (~c3_1(a28)))),
% 2.71/2.07 inference(transitivity,[status(thm)],[1606, 1604])).
% 2.71/2.07 tff(1608,plain,
% 2.71/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a28) | c0_1(a28) | (~c3_1(a28)))),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(1609,plain,
% 2.71/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a28) | c2_1(a28) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | (~c1_1(a14)) | (~c3_1(a28))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 2.71/2.07 tff(1610,plain,
% 2.71/2.07 ($false),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1609, 104, 1603, 1557, 153, 152, 1592, 1586, 1556, 151, 734, 1565])).
% 2.71/2.07 tff(1611,plain,(hskp2 | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.07 tff(1612,plain,
% 2.71/2.07 (hskp2),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1611, 1518, 1517, 1516, 475, 752, 1252, 1379, 13, 12])).
% 2.71/2.07 tff(1613,plain,
% 2.71/2.07 (~c2_1(a3)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[206, 1612])).
% 2.71/2.07 tff(1614,plain,
% 2.71/2.07 (c3_1(a3)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[217, 1612])).
% 2.71/2.07 tff(1615,plain,
% 2.71/2.07 (c1_1(a3)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[228, 1612])).
% 2.71/2.07 tff(1616,plain,
% 2.71/2.07 (hskp9),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1296, 104, 1615, 1614, 1518, 1517, 1613, 1516, 890])).
% 2.71/2.07 tff(1617,plain,
% 2.71/2.07 (~c3_1(a16)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[902, 1616])).
% 2.71/2.07 tff(1618,plain,
% 2.71/2.07 (c1_1(a16)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[913, 1616])).
% 2.71/2.07 tff(1619,plain,
% 2.71/2.07 (c0_1(a16)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[924, 1616])).
% 2.71/2.07 tff(1620,plain,
% 2.71/2.07 (hskp12),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1350, 104, 1619, 1618, 1617, 752, 1252, 987, 1519])).
% 2.71/2.07 tff(1621,plain,
% 2.71/2.07 (~c3_1(a20)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[999, 1620])).
% 2.71/2.07 tff(1622,plain,
% 2.71/2.07 (~c1_1(a20)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1005, 1620])).
% 2.71/2.07 tff(1623,plain,
% 2.71/2.07 (c2_1(a20)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1016, 1620])).
% 2.71/2.07 tff(1624,plain,
% 2.71/2.07 (hskp5),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1164, 104, 1623, 1622, 1621, 1379, 13, 12, 290])).
% 2.71/2.07 tff(1625,plain,
% 2.71/2.07 (~c2_1(a11)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[306, 1624])).
% 2.71/2.07 tff(1626,plain,
% 2.71/2.07 (~c1_1(a11)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[312, 1624])).
% 2.71/2.07 tff(1627,plain,
% 2.71/2.07 (c0_1(a11)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[323, 1624])).
% 2.71/2.07 tff(1628,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c0_1(a15))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1629,plain,
% 2.71/2.07 (((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c0_1(a15))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(1630,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c0_1(a15)))),
% 2.79/2.08 inference(monotonicity,[status(thm)],[1629])).
% 2.79/2.08 tff(1631,plain,
% 2.79/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c0_1(a15))),
% 2.79/2.08 inference(transitivity,[status(thm)],[1630, 1628])).
% 2.79/2.08 tff(1632,plain,
% 2.79/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 2.79/2.08 inference(quant_inst,[status(thm)],[])).
% 2.79/2.08 tff(1633,plain,
% 2.79/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c0_1(a15)),
% 2.79/2.08 inference(modus_ponens,[status(thm)],[1632, 1631])).
% 2.79/2.08 tff(1634,plain,
% 2.79/2.08 ($false),
% 2.79/2.08 inference(unit_resolution,[status(thm)],[1633, 104, 1627, 475, 752, 1252, 1626, 1625, 751, 1519])).
% 2.79/2.08 tff(1635,plain,(c2_1(a2) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a2) | c1_1(a58) | c0_1(a58) | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.79/2.08 tff(1636,plain,
% 2.79/2.08 (c2_1(a2)),
% 2.79/2.08 inference(unit_resolution,[status(thm)],[1635, 12, 752, 1252, 475, 26, 37, 568, 48])).
% 2.79/2.08 tff(1637,plain,
% 2.79/2.08 (~hskp1),
% 2.79/2.08 inference(unit_resolution,[status(thm)],[262, 1636])).
% 2.79/2.08 tff(1638,plain,
% 2.79/2.08 (hskp0),
% 2.79/2.08 inference(unit_resolution,[status(thm)],[587, 1637, 48, 568, 37, 26])).
% 2.79/2.08 tff(1639,plain,
% 2.79/2.08 (~c3_1(a1)),
% 2.79/2.08 inference(unit_resolution,[status(thm)],[117, 1638])).
% 2.79/2.08 tff(1640,plain,
% 2.79/2.08 (c2_1(a1)),
% 2.79/2.08 inference(unit_resolution,[status(thm)],[128, 1638])).
% 2.79/2.08 tff(1641,plain,
% 2.79/2.08 (c1_1(a1)),
% 2.79/2.08 inference(unit_resolution,[status(thm)],[139, 1638])).
% 2.79/2.08 tff(1642,plain,
% 2.79/2.08 (~c0_1(a15)),
% 2.79/2.08 inference(unit_resolution,[status(thm)],[1262, 104, 1641, 1640, 475, 752, 1252, 1639, 279])).
% 2.79/2.08 tff(1643,assumption,(~c0_1(a15)), introduced(assumption)).
% 2.79/2.08 tff(1644,assumption,(c2_1(a2)), introduced(assumption)).
% 2.79/2.08 tff(1645,plain,
% 2.79/2.08 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | (~ndr1_0))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | (~ndr1_0))),
% 2.79/2.08 inference(rewrite,[status(thm)],[])).
% 2.79/2.08 tff(1646,plain,
% 2.79/2.08 ((hskp18 | hskp3 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | (~c2_1(a2))) <=> (hskp18 | hskp3 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | (~ndr1_0))),
% 2.79/2.08 inference(rewrite,[status(thm)],[])).
% 2.79/2.08 tff(1647,plain,
% 2.79/2.08 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | (~c2_1(a2)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | (~ndr1_0)))),
% 2.79/2.08 inference(monotonicity,[status(thm)],[1646])).
% 2.79/2.08 tff(1648,plain,
% 2.79/2.08 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | (~c2_1(a2)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | (~ndr1_0))),
% 2.79/2.08 inference(transitivity,[status(thm)],[1647, 1645])).
% 2.79/2.08 tff(1649,plain,
% 2.79/2.08 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | (~c2_1(a2)))),
% 2.79/2.08 inference(quant_inst,[status(thm)],[])).
% 2.79/2.08 tff(1650,plain,
% 2.79/2.08 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | (~ndr1_0)),
% 2.79/2.08 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 2.79/2.08 tff(1651,plain,
% 2.79/2.08 (hskp18 | c0_1(a2) | (~c2_1(a2))),
% 2.79/2.08 inference(unit_resolution,[status(thm)],[1650, 104, 48, 12, 390])).
% 2.79/2.08 tff(1652,plain,
% 2.79/2.08 (hskp18),
% 2.79/2.08 inference(unit_resolution,[status(thm)],[1651, 14, 1644])).
% 2.79/2.08 tff(1653,plain,
% 2.79/2.08 (~c3_1(a31)),
% 2.79/2.08 inference(unit_resolution,[status(thm)],[403, 1652])).
% 2.79/2.08 tff(1654,plain,
% 2.79/2.08 (c1_1(a31)),
% 2.79/2.08 inference(unit_resolution,[status(thm)],[414, 1652])).
% 2.79/2.08 tff(1655,plain,
% 2.79/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a31) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a31) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31))),
% 2.79/2.08 inference(rewrite,[status(thm)],[])).
% 2.79/2.08 tff(1656,plain,
% 2.79/2.08 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (c3_1(a31) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31))),
% 2.79/2.08 inference(rewrite,[status(thm)],[])).
% 2.79/2.08 tff(1657,plain,
% 2.79/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a31) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31)))),
% 2.79/2.08 inference(monotonicity,[status(thm)],[1656])).
% 2.79/2.08 tff(1658,plain,
% 2.79/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a31) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31))),
% 2.79/2.08 inference(transitivity,[status(thm)],[1657, 1655])).
% 2.79/2.08 tff(1659,plain,
% 2.79/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 2.79/2.08 inference(quant_inst,[status(thm)],[])).
% 2.79/2.08 tff(1660,plain,
% 2.79/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a31) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31)),
% 2.79/2.08 inference(modus_ponens,[status(thm)],[1659, 1658])).
% 2.79/2.08 tff(1661,plain,
% 2.79/2.08 (c2_1(a31)),
% 2.79/2.08 inference(unit_resolution,[status(thm)],[1660, 104, 1654, 153, 152, 1653, 752, 1252, 151, 734, 1643])).
% 2.79/2.08 tff(1662,plain,
% 2.79/2.08 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 2.80/2.08 inference(rewrite,[status(thm)],[])).
% 2.80/2.08 tff(1663,plain,
% 2.80/2.08 ((hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c0_1(a2) | (~c2_1(a2))) <=> (hskp6 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 2.80/2.08 inference(rewrite,[status(thm)],[])).
% 2.80/2.08 tff(1664,plain,
% 2.80/2.08 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c0_1(a2) | (~c2_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))))),
% 2.80/2.08 inference(monotonicity,[status(thm)],[1663])).
% 2.80/2.08 tff(1665,plain,
% 2.80/2.08 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c0_1(a2) | (~c2_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 2.80/2.08 inference(transitivity,[status(thm)],[1664, 1662])).
% 2.80/2.08 tff(1666,plain,
% 2.80/2.08 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c0_1(a2) | (~c2_1(a2)))),
% 2.80/2.08 inference(quant_inst,[status(thm)],[])).
% 2.80/2.08 tff(1667,plain,
% 2.80/2.08 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))),
% 2.80/2.08 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 2.80/2.08 tff(1668,plain,
% 2.80/2.08 (hskp6 | c0_1(a2)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1667, 104, 153, 152, 1644, 12, 151, 171])).
% 2.80/2.08 tff(1669,plain,
% 2.80/2.08 (hskp6),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1668, 14])).
% 2.80/2.08 tff(1670,plain,
% 2.80/2.08 (~c3_1(a13)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[186, 1669])).
% 2.80/2.08 tff(1671,plain,
% 2.80/2.08 (~c1_1(a13)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[192, 1669])).
% 2.80/2.08 tff(1672,plain,
% 2.80/2.08 (~c0_1(a13)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[198, 1669])).
% 2.80/2.08 tff(1673,plain,
% 2.80/2.08 (~hskp1),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[262, 1644])).
% 2.80/2.08 tff(1674,plain,
% 2.80/2.08 (hskp2),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[247, 104, 1673, 1672, 1671, 1670, 47])).
% 2.80/2.08 tff(1675,plain,
% 2.80/2.08 (~c2_1(a3)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[206, 1674])).
% 2.80/2.08 tff(1676,plain,
% 2.80/2.08 (c3_1(a3)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[217, 1674])).
% 2.80/2.08 tff(1677,plain,
% 2.80/2.08 (c1_1(a3)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[228, 1674])).
% 2.80/2.08 tff(1678,plain,
% 2.80/2.08 (~c2_1(a13)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1331, 104, 1673, 1677, 1676, 1672, 1671, 1675, 58])).
% 2.80/2.08 tff(1679,plain,
% 2.80/2.08 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c3_1(a31) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c1_1(a31)) | (~c2_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c3_1(a31) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.80/2.08 inference(rewrite,[status(thm)],[])).
% 2.80/2.08 tff(1680,plain,
% 2.80/2.08 ((hskp9 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp9 | c3_1(a31) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.80/2.08 inference(rewrite,[status(thm)],[])).
% 2.80/2.08 tff(1681,plain,
% 2.80/2.08 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c3_1(a31) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c1_1(a31)) | (~c2_1(a31))))),
% 2.80/2.08 inference(monotonicity,[status(thm)],[1680])).
% 2.80/2.08 tff(1682,plain,
% 2.80/2.08 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c3_1(a31) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.80/2.08 inference(transitivity,[status(thm)],[1681, 1679])).
% 2.80/2.08 tff(1683,plain,
% 2.80/2.08 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.80/2.08 inference(quant_inst,[status(thm)],[])).
% 2.80/2.08 tff(1684,plain,
% 2.80/2.08 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c3_1(a31) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c1_1(a31)) | (~c2_1(a31))),
% 2.80/2.08 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 2.80/2.08 tff(1685,plain,
% 2.80/2.08 (hskp9),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1684, 104, 1654, 1677, 1676, 1653, 1675, 890, 1661])).
% 2.80/2.08 tff(1686,plain,
% 2.80/2.08 (~c3_1(a16)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[902, 1685])).
% 2.80/2.08 tff(1687,plain,
% 2.80/2.08 (c1_1(a16)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[913, 1685])).
% 2.80/2.08 tff(1688,plain,
% 2.80/2.08 (c0_1(a16)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[924, 1685])).
% 2.80/2.08 tff(1689,plain,
% 2.80/2.08 (hskp12),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1350, 104, 1688, 1687, 1686, 752, 1252, 987, 1643])).
% 2.80/2.08 tff(1690,plain,
% 2.80/2.08 (~c1_1(a20)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1005, 1689])).
% 2.80/2.08 tff(1691,plain,
% 2.80/2.08 (c2_1(a20)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1016, 1689])).
% 2.80/2.08 tff(1692,plain,
% 2.80/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a31) | c1_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c0_1(a20)) | (~c2_1(a20)) | (~c1_1(a31)) | (~c2_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a31) | c1_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c0_1(a20)) | (~c2_1(a20)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.80/2.08 inference(rewrite,[status(thm)],[])).
% 2.80/2.08 tff(1693,plain,
% 2.80/2.08 (((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c3_1(a31) | c1_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c0_1(a20)) | (~c2_1(a20)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.80/2.08 inference(rewrite,[status(thm)],[])).
% 2.80/2.08 tff(1694,plain,
% 2.80/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a31) | c1_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c0_1(a20)) | (~c2_1(a20)) | (~c1_1(a31)) | (~c2_1(a31))))),
% 2.80/2.08 inference(monotonicity,[status(thm)],[1693])).
% 2.80/2.08 tff(1695,plain,
% 2.80/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a31) | c1_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c0_1(a20)) | (~c2_1(a20)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.80/2.08 inference(transitivity,[status(thm)],[1694, 1692])).
% 2.80/2.08 tff(1696,plain,
% 2.80/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13))),
% 2.80/2.08 inference(quant_inst,[status(thm)],[])).
% 2.80/2.08 tff(1697,plain,
% 2.80/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a31) | c1_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c0_1(a20)) | (~c2_1(a20)) | (~c1_1(a31)) | (~c2_1(a31))),
% 2.80/2.08 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 2.80/2.08 tff(1698,plain,
% 2.80/2.08 (~c0_1(a20)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1697, 104, 1654, 1691, 1653, 1690, 1672, 1670, 1342, 1678, 1661])).
% 2.80/2.08 tff(1699,plain,
% 2.80/2.08 ($false),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1366, 104, 1673, 1691, 1677, 1676, 1690, 1675, 58, 1698])).
% 2.80/2.08 tff(1700,plain,(c0_1(a2) | c2_1(a15) | (~c3_1(a15)) | c0_1(a15) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | (~c2_1(a2)) | c3_1(a2) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.80/2.08 tff(1701,plain,
% 2.80/2.08 (c0_1(a2)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1700, 1642, 1252, 752, 1641, 1640, 1639, 1636, 12, 48])).
% 2.80/2.08 tff(1702,plain,
% 2.80/2.08 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~c0_1(a2)) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | (~c0_1(a2)) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 2.80/2.08 inference(rewrite,[status(thm)],[])).
% 2.80/2.08 tff(1703,plain,
% 2.80/2.08 ((hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | (~c2_1(a2)) | (~c0_1(a2))) <=> (hskp6 | (~c0_1(a2)) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 2.80/2.08 inference(rewrite,[status(thm)],[])).
% 2.80/2.08 tff(1704,plain,
% 2.80/2.08 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | (~c2_1(a2)) | (~c0_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~c0_1(a2)) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))))),
% 2.80/2.08 inference(monotonicity,[status(thm)],[1703])).
% 2.80/2.08 tff(1705,plain,
% 2.80/2.08 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | (~c2_1(a2)) | (~c0_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | (~c0_1(a2)) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 2.80/2.08 inference(transitivity,[status(thm)],[1704, 1702])).
% 2.80/2.08 tff(1706,plain,
% 2.80/2.08 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | (~c2_1(a2)) | (~c0_1(a2)))),
% 2.80/2.08 inference(quant_inst,[status(thm)],[])).
% 2.80/2.08 tff(1707,plain,
% 2.80/2.08 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | (~c0_1(a2)) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))),
% 2.80/2.08 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 2.80/2.08 tff(1708,plain,
% 2.80/2.08 (hskp6 | (~c0_1(a2))),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1707, 104, 1641, 1640, 1636, 12, 1639, 150])).
% 2.80/2.08 tff(1709,plain,
% 2.80/2.08 (hskp6),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1708, 1701])).
% 2.80/2.08 tff(1710,plain,
% 2.80/2.08 (~c3_1(a13)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[186, 1709])).
% 2.80/2.08 tff(1711,plain,
% 2.80/2.08 (~c1_1(a13)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[192, 1709])).
% 2.80/2.08 tff(1712,plain,
% 2.80/2.08 (~c0_1(a13)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[198, 1709])).
% 2.80/2.08 tff(1713,plain,
% 2.80/2.08 (hskp2),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[247, 104, 1637, 1712, 1711, 1710, 47])).
% 2.80/2.08 tff(1714,plain,
% 2.80/2.08 (~c2_1(a3)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[206, 1713])).
% 2.80/2.08 tff(1715,plain,
% 2.80/2.08 (c3_1(a3)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[217, 1713])).
% 2.80/2.08 tff(1716,plain,
% 2.80/2.08 (c1_1(a3)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[228, 1713])).
% 2.80/2.08 tff(1717,plain,
% 2.80/2.08 (hskp9),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1296, 104, 1716, 1715, 1641, 1640, 1714, 1639, 890])).
% 2.80/2.08 tff(1718,plain,
% 2.80/2.08 (~c3_1(a16)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[902, 1717])).
% 2.80/2.08 tff(1719,plain,
% 2.80/2.08 (c1_1(a16)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[913, 1717])).
% 2.80/2.08 tff(1720,plain,
% 2.80/2.08 (c2_1(a16)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1305, 104, 1719, 1641, 1640, 1718, 752, 1252, 1639, 734, 1642])).
% 2.80/2.08 tff(1721,plain,
% 2.80/2.08 (~c2_1(a13)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1331, 104, 1637, 1716, 1715, 1712, 1711, 1714, 58])).
% 2.80/2.08 tff(1722,plain,
% 2.80/2.08 (c0_1(a16)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[924, 1717])).
% 2.80/2.08 tff(1723,plain,
% 2.80/2.08 (hskp12),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1350, 104, 1722, 1719, 1718, 752, 1252, 987, 1642])).
% 2.80/2.08 tff(1724,plain,
% 2.80/2.08 (~c1_1(a20)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1005, 1723])).
% 2.80/2.08 tff(1725,plain,
% 2.80/2.08 (c2_1(a20)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1016, 1723])).
% 2.80/2.08 tff(1726,plain,
% 2.80/2.08 (~c0_1(a20)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1359, 104, 1725, 1719, 1724, 1718, 1712, 1710, 1342, 1721, 1720])).
% 2.80/2.08 tff(1727,plain,
% 2.80/2.08 ($false),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1366, 104, 1637, 1725, 1716, 1715, 1724, 1714, 58, 1726])).
% 2.80/2.08 tff(1728,plain,(c3_1(a2) | c2_1(a15) | (~c3_1(a15)) | hskp3 | c1_1(a15) | hskp24 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.80/2.08 tff(1729,plain,
% 2.80/2.08 (c3_1(a2)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1728, 568, 1252, 48, 475, 752, 37, 26])).
% 2.80/2.08 tff(1730,plain,
% 2.80/2.08 (~hskp1),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[256, 1729])).
% 2.80/2.08 tff(1731,plain,
% 2.80/2.08 (hskp0),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[587, 1730, 48, 568, 37, 26])).
% 2.80/2.08 tff(1732,plain,
% 2.80/2.08 (~c3_1(a1)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[117, 1731])).
% 2.80/2.08 tff(1733,plain,
% 2.80/2.08 (c2_1(a1)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[128, 1731])).
% 2.80/2.08 tff(1734,plain,
% 2.80/2.08 (c1_1(a1)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[139, 1731])).
% 2.80/2.08 tff(1735,plain,
% 2.80/2.08 (~c0_1(a15)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1262, 104, 1734, 1733, 475, 752, 1252, 1732, 279])).
% 2.80/2.08 tff(1736,plain,
% 2.80/2.08 (hskp6),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[180, 1734, 1733, 1732])).
% 2.80/2.08 tff(1737,plain,
% 2.80/2.08 (~c3_1(a13)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[186, 1736])).
% 2.80/2.08 tff(1738,plain,
% 2.80/2.08 (~c1_1(a13)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[192, 1736])).
% 2.80/2.08 tff(1739,plain,
% 2.80/2.08 (~c0_1(a13)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[198, 1736])).
% 2.80/2.08 tff(1740,plain,
% 2.80/2.08 (hskp2),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[247, 104, 1730, 1739, 1738, 1737, 47])).
% 2.80/2.08 tff(1741,plain,
% 2.80/2.08 (~c2_1(a3)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[206, 1740])).
% 2.80/2.08 tff(1742,plain,
% 2.80/2.08 (c3_1(a3)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[217, 1740])).
% 2.80/2.08 tff(1743,plain,
% 2.80/2.08 (c1_1(a3)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[228, 1740])).
% 2.80/2.08 tff(1744,plain,
% 2.80/2.08 (hskp9),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1296, 104, 1743, 1742, 1734, 1733, 1741, 1732, 890])).
% 2.80/2.08 tff(1745,plain,
% 2.80/2.08 (~c3_1(a16)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[902, 1744])).
% 2.80/2.08 tff(1746,plain,
% 2.80/2.08 (c1_1(a16)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[913, 1744])).
% 2.80/2.08 tff(1747,plain,
% 2.80/2.08 (c2_1(a16)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1305, 104, 1746, 1734, 1733, 1745, 752, 1252, 1732, 734, 1735])).
% 2.80/2.08 tff(1748,plain,
% 2.80/2.08 (~c2_1(a13)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1331, 104, 1730, 1743, 1742, 1739, 1738, 1741, 58])).
% 2.80/2.08 tff(1749,plain,
% 2.80/2.08 (c0_1(a16)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[924, 1744])).
% 2.80/2.08 tff(1750,plain,
% 2.80/2.08 (hskp12),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1350, 104, 1749, 1746, 1745, 752, 1252, 987, 1735])).
% 2.80/2.08 tff(1751,plain,
% 2.80/2.08 (~c1_1(a20)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1005, 1750])).
% 2.80/2.08 tff(1752,plain,
% 2.80/2.08 (c2_1(a20)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1016, 1750])).
% 2.80/2.08 tff(1753,plain,
% 2.80/2.08 (~c0_1(a20)),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1359, 104, 1752, 1746, 1751, 1745, 1739, 1737, 1342, 1748, 1747])).
% 2.80/2.08 tff(1754,plain,
% 2.80/2.08 ($false),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1366, 104, 1730, 1752, 1743, 1742, 1751, 1741, 58, 1753])).
% 2.80/2.08 tff(1755,plain,(hskp24 | c2_1(a15) | (~c3_1(a15)) | c1_1(a15) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.80/2.08 tff(1756,plain,
% 2.80/2.08 (hskp24),
% 2.80/2.08 inference(unit_resolution,[status(thm)],[1755, 752, 1251, 475, 48, 37, 26])).
% 2.80/2.09 tff(1757,plain,
% 2.80/2.09 (c2_1(a58)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[466, 1756])).
% 2.80/2.09 tff(1758,plain,
% 2.80/2.09 (hskp0),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[111, 1757, 26])).
% 2.80/2.09 tff(1759,plain,
% 2.80/2.09 (~c3_1(a1)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[117, 1758])).
% 2.80/2.09 tff(1760,plain,
% 2.80/2.09 (c2_1(a1)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[128, 1758])).
% 2.80/2.09 tff(1761,plain,
% 2.80/2.09 (c1_1(a1)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[139, 1758])).
% 2.80/2.09 tff(1762,plain,
% 2.80/2.09 (~c0_1(a15)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[1262, 104, 1761, 1760, 475, 752, 1251, 1759, 279])).
% 2.80/2.09 tff(1763,plain,
% 2.80/2.09 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 2.80/2.09 inference(bind,[status(th)],[])).
% 2.80/2.09 tff(1764,plain,
% 2.80/2.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.80/2.09 inference(quant_intro,[status(thm)],[1763])).
% 2.80/2.09 tff(1765,plain,
% 2.80/2.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.80/2.09 inference(rewrite,[status(thm)],[])).
% 2.80/2.09 tff(1766,plain,
% 2.80/2.09 (^[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)) | (~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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 2.80/2.09 inference(bind,[status(th)],[])).
% 2.80/2.09 tff(1767,plain,
% 2.80/2.09 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.80/2.09 inference(quant_intro,[status(thm)],[1766])).
% 2.80/2.09 tff(1768,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause202')).
% 2.80/2.09 tff(1769,plain,
% 2.80/2.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.80/2.09 inference(modus_ponens,[status(thm)],[1768, 1767])).
% 2.80/2.09 tff(1770,plain,
% 2.80/2.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.80/2.09 inference(modus_ponens,[status(thm)],[1769, 1765])).
% 2.80/2.09 tff(1771,plain,(
% 2.80/2.09 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.80/2.09 inference(skolemize,[status(sab)],[1770])).
% 2.80/2.09 tff(1772,plain,
% 2.80/2.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.80/2.09 inference(modus_ponens,[status(thm)],[1771, 1764])).
% 2.80/2.09 tff(1773,plain,
% 2.80/2.09 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c2_1(a58)))),
% 2.80/2.09 inference(rewrite,[status(thm)],[])).
% 2.80/2.09 tff(1774,plain,
% 2.80/2.09 ((hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58))) <=> (hskp2 | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c2_1(a58)))),
% 2.80/2.09 inference(rewrite,[status(thm)],[])).
% 2.80/2.09 tff(1775,plain,
% 2.80/2.09 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c2_1(a58))))),
% 2.80/2.09 inference(monotonicity,[status(thm)],[1774])).
% 2.80/2.09 tff(1776,plain,
% 2.80/2.09 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c2_1(a58)))),
% 2.80/2.09 inference(transitivity,[status(thm)],[1775, 1773])).
% 2.80/2.09 tff(1777,plain,
% 2.80/2.09 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))),
% 2.80/2.09 inference(quant_inst,[status(thm)],[])).
% 2.80/2.09 tff(1778,plain,
% 2.80/2.09 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c2_1(a58))),
% 2.80/2.09 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 2.80/2.09 tff(1779,plain,
% 2.80/2.09 (hskp2 | c2_1(a15) | (~c3_1(a15)) | (~c2_1(a58))),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[1778, 104, 37, 26, 475, 1545])).
% 2.80/2.09 tff(1780,plain,
% 2.80/2.09 (hskp2),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[1779, 1757, 752, 1251])).
% 2.80/2.09 tff(1781,plain,
% 2.80/2.09 (~c2_1(a3)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[206, 1780])).
% 2.80/2.09 tff(1782,plain,
% 2.80/2.09 (c3_1(a3)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[217, 1780])).
% 2.80/2.09 tff(1783,plain,
% 2.80/2.09 (c1_1(a3)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[228, 1780])).
% 2.80/2.09 tff(1784,plain,
% 2.80/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 2.80/2.09 inference(rewrite,[status(thm)],[])).
% 2.80/2.09 tff(1785,plain,
% 2.80/2.09 (((~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15))) <=> (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 2.80/2.09 inference(rewrite,[status(thm)],[])).
% 2.80/2.09 tff(1786,plain,
% 2.80/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))))),
% 2.80/2.09 inference(monotonicity,[status(thm)],[1785])).
% 2.80/2.09 tff(1787,plain,
% 2.80/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 2.80/2.09 inference(transitivity,[status(thm)],[1786, 1784])).
% 2.80/2.09 tff(1788,plain,
% 2.80/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15)))),
% 2.80/2.09 inference(quant_inst,[status(thm)],[])).
% 2.80/2.09 tff(1789,plain,
% 2.80/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))),
% 2.80/2.09 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 2.80/2.09 tff(1790,plain,
% 2.80/2.09 (~c0_1(a3)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[1789, 104, 1783, 1782, 475, 752, 1251, 1781, 1772])).
% 2.80/2.09 tff(1791,plain,
% 2.80/2.09 (hskp1),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[237, 1780, 1757, 37, 26])).
% 2.80/2.09 tff(1792,plain,
% 2.80/2.09 (~c3_1(a2)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[256, 1791])).
% 2.80/2.09 tff(1793,plain,
% 2.80/2.09 (~c2_1(a2)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[262, 1791])).
% 2.80/2.09 tff(1794,plain,
% 2.80/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a3) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | (~c3_1(a3)) | c0_1(a3))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a3) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | (~c3_1(a3)) | c0_1(a3))),
% 2.80/2.09 inference(rewrite,[status(thm)],[])).
% 2.80/2.09 tff(1795,plain,
% 2.80/2.09 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c2_1(a3) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | (~c3_1(a3)) | c0_1(a3))),
% 2.80/2.09 inference(rewrite,[status(thm)],[])).
% 2.80/2.09 tff(1796,plain,
% 2.80/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a3) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | (~c3_1(a3)) | c0_1(a3)))),
% 2.80/2.09 inference(monotonicity,[status(thm)],[1795])).
% 2.80/2.09 tff(1797,plain,
% 2.80/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a3) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | (~c3_1(a3)) | c0_1(a3))),
% 2.80/2.09 inference(transitivity,[status(thm)],[1796, 1794])).
% 2.80/2.09 tff(1798,plain,
% 2.80/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 2.80/2.09 inference(quant_inst,[status(thm)],[])).
% 2.80/2.09 tff(1799,plain,
% 2.80/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a3) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | (~c3_1(a3)) | c0_1(a3)),
% 2.80/2.09 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 2.80/2.09 tff(1800,plain,
% 2.80/2.09 (~c1_1(a2)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[1799, 104, 1782, 1761, 1760, 1781, 1793, 1792, 1759, 734, 1790])).
% 2.80/2.09 tff(1801,plain,
% 2.80/2.09 (~c0_1(a2)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[268, 1791])).
% 2.80/2.09 tff(1802,plain,
% 2.80/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.80/2.09 inference(rewrite,[status(thm)],[])).
% 2.80/2.09 tff(1803,plain,
% 2.80/2.09 (((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.80/2.09 inference(rewrite,[status(thm)],[])).
% 2.80/2.09 tff(1804,plain,
% 2.80/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a58)) | (~c3_1(a58))))),
% 2.80/2.09 inference(monotonicity,[status(thm)],[1803])).
% 2.80/2.09 tff(1805,plain,
% 2.80/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.80/2.09 inference(transitivity,[status(thm)],[1804, 1802])).
% 2.80/2.09 tff(1806,plain,
% 2.80/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 2.80/2.09 inference(quant_inst,[status(thm)],[])).
% 2.80/2.09 tff(1807,plain,
% 2.80/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a58)) | (~c3_1(a58))),
% 2.80/2.09 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 2.80/2.09 tff(1808,plain,
% 2.80/2.09 (~c3_1(a58)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[1807, 104, 1757, 26, 1801, 1793, 1792, 362, 1800])).
% 2.80/2.09 tff(1809,plain,
% 2.80/2.09 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 2.80/2.09 inference(rewrite,[status(thm)],[])).
% 2.80/2.09 tff(1810,plain,
% 2.80/2.09 ((hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp5 | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 2.80/2.09 inference(rewrite,[status(thm)],[])).
% 2.80/2.09 tff(1811,plain,
% 2.80/2.09 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)))),
% 2.80/2.09 inference(monotonicity,[status(thm)],[1810])).
% 2.80/2.09 tff(1812,plain,
% 2.80/2.09 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 2.80/2.09 inference(transitivity,[status(thm)],[1811, 1809])).
% 2.80/2.09 tff(1813,plain,
% 2.80/2.09 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 2.80/2.09 inference(quant_inst,[status(thm)],[])).
% 2.80/2.09 tff(1814,plain,
% 2.80/2.09 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)),
% 2.80/2.09 inference(modus_ponens,[status(thm)],[1813, 1812])).
% 2.80/2.09 tff(1815,plain,
% 2.80/2.09 (hskp5),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[1814, 104, 1757, 26, 1801, 1793, 1792, 290, 1808])).
% 2.80/2.09 tff(1816,plain,
% 2.80/2.09 (~c2_1(a11)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[306, 1815])).
% 2.80/2.09 tff(1817,plain,
% 2.80/2.09 (~c1_1(a11)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[312, 1815])).
% 2.80/2.09 tff(1818,plain,
% 2.80/2.09 (c0_1(a11)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[323, 1815])).
% 2.80/2.09 tff(1819,plain,
% 2.80/2.09 ($false),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[1633, 104, 1818, 475, 752, 1251, 1817, 1816, 751, 1762])).
% 2.80/2.09 tff(1820,plain,(c2_1(a15) | c1_1(a15) | c1_1(a58) | c0_1(a58) | hskp3 | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 2.80/2.09 tff(1821,plain,
% 2.80/2.09 (c2_1(a15)),
% 2.80/2.09 inference(unit_resolution,[status(thm)],[1820, 475, 26, 37, 48, 474])).
% 2.80/2.09 tff(1822,plain,
% 2.80/2.09 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 2.80/2.09 inference(rewrite,[status(thm)],[])).
% 2.80/2.09 tff(1823,plain,
% 2.80/2.09 ((hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 2.80/2.09 inference(rewrite,[status(thm)],[])).
% 2.80/2.09 tff(1824,plain,
% 2.80/2.09 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0)))),
% 2.80/2.10 inference(monotonicity,[status(thm)],[1823])).
% 2.80/2.10 tff(1825,plain,
% 2.80/2.10 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 2.80/2.10 inference(transitivity,[status(thm)],[1824, 1822])).
% 2.80/2.10 tff(1826,plain,
% 2.80/2.10 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 2.80/2.10 inference(quant_inst,[status(thm)],[])).
% 2.80/2.10 tff(1827,plain,
% 2.80/2.10 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0)),
% 2.80/2.10 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 2.80/2.10 tff(1828,plain,
% 2.80/2.10 (hskp5 | c0_1(a2) | c2_1(a2)),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[1827, 104, 475, 1821, 468, 12, 290])).
% 2.80/2.10 tff(1829,plain,
% 2.80/2.10 (hskp5),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[1828, 736, 737])).
% 2.80/2.10 tff(1830,plain,
% 2.80/2.10 (~c2_1(a11)),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[306, 1829])).
% 2.80/2.10 tff(1831,plain,
% 2.80/2.10 (~c1_1(a11)),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[312, 1829])).
% 2.80/2.10 tff(1832,plain,
% 2.80/2.10 (c0_1(a11)),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[323, 1829])).
% 2.80/2.10 tff(1833,plain,
% 2.80/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a58)))),
% 2.80/2.10 inference(rewrite,[status(thm)],[])).
% 2.80/2.10 tff(1834,plain,
% 2.80/2.10 (((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a58)))),
% 2.80/2.10 inference(rewrite,[status(thm)],[])).
% 2.80/2.10 tff(1835,plain,
% 2.80/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a58))))),
% 2.80/2.10 inference(monotonicity,[status(thm)],[1834])).
% 2.80/2.10 tff(1836,plain,
% 2.80/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a58)))),
% 2.80/2.10 inference(transitivity,[status(thm)],[1835, 1833])).
% 2.80/2.10 tff(1837,plain,
% 2.80/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 2.80/2.10 inference(quant_inst,[status(thm)],[])).
% 2.80/2.10 tff(1838,plain,
% 2.80/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a58))),
% 2.80/2.10 inference(modus_ponens,[status(thm)],[1837, 1836])).
% 2.80/2.10 tff(1839,plain,
% 2.80/2.10 ($false),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[1838, 104, 476, 1832, 37, 26, 1831, 1830, 751, 741])).
% 2.80/2.10 tff(1840,plain,(hskp0 | c0_1(a58) | c1_1(a58) | c2_1(a38) | c3_1(a2) | c1_1(a15) | c3_1(a15) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.80/2.10 tff(1841,plain,
% 2.80/2.10 (hskp0),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[1840, 12, 26, 474, 37, 475, 468, 48])).
% 2.80/2.10 tff(1842,plain,
% 2.80/2.10 (~c3_1(a1)),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[117, 1841])).
% 2.80/2.10 tff(1843,plain,
% 2.80/2.10 (c2_1(a1)),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[128, 1841])).
% 2.80/2.10 tff(1844,plain,
% 2.80/2.10 (c1_1(a1)),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[139, 1841])).
% 2.80/2.10 tff(1845,assumption,(c2_1(a15)), introduced(assumption)).
% 2.80/2.10 tff(1846,plain,
% 2.80/2.10 (hskp5 | c0_1(a2) | c2_1(a2)),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[1827, 104, 475, 1845, 468, 12, 290])).
% 2.80/2.10 tff(1847,plain,
% 2.80/2.10 (hskp5),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[1846, 14, 13])).
% 2.80/2.10 tff(1848,plain,
% 2.80/2.10 (~c2_1(a11)),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[306, 1847])).
% 2.80/2.10 tff(1849,plain,
% 2.80/2.10 (~c1_1(a11)),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[312, 1847])).
% 2.80/2.10 tff(1850,plain,
% 2.80/2.10 (c0_1(a11)),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[323, 1847])).
% 2.80/2.10 tff(1851,plain,
% 2.80/2.10 (~c3_1(a11)),
% 2.80/2.10 inference(unit_resolution,[status(thm)],[330, 104, 1850, 153, 152, 1849, 1848, 151, 279])).
% 2.80/2.10 tff(1852,plain,
% 2.80/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))),
% 2.80/2.10 inference(rewrite,[status(thm)],[])).
% 2.80/2.10 tff(1853,plain,
% 2.80/2.10 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a15) | (~c2_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))),
% 2.80/2.10 inference(rewrite,[status(thm)],[])).
% 2.80/2.10 tff(1854,plain,
% 2.80/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15))))),
% 2.80/2.10 inference(monotonicity,[status(thm)],[1853])).
% 2.80/2.10 tff(1855,plain,
% 2.80/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))),
% 2.80/2.10 inference(transitivity,[status(thm)],[1854, 1852])).
% 2.80/2.10 tff(1856,plain,
% 2.80/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 2.80/2.10 inference(quant_inst,[status(thm)],[])).
% 2.82/2.10 tff(1857,plain,
% 2.82/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15))),
% 2.82/2.10 inference(modus_ponens,[status(thm)],[1856, 1855])).
% 2.82/2.10 tff(1858,plain,
% 2.82/2.10 (c0_1(a2) | (~c0_1(a15))),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[1857, 104, 153, 152, 475, 1845, 13, 12, 151, 1342])).
% 2.82/2.10 tff(1859,plain,
% 2.82/2.10 (~c0_1(a15)),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[1858, 14])).
% 2.82/2.10 tff(1860,plain,
% 2.82/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~c2_1(a15)) | c3_1(a15) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c2_1(a15)) | c3_1(a15) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | c0_1(a15))),
% 2.82/2.10 inference(rewrite,[status(thm)],[])).
% 2.82/2.10 tff(1861,plain,
% 2.82/2.10 (((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a11) | c1_1(a11) | c3_1(a11)) <=> ((~c2_1(a15)) | c3_1(a15) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | c0_1(a15))),
% 2.82/2.10 inference(rewrite,[status(thm)],[])).
% 2.82/2.10 tff(1862,plain,
% 2.82/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a11) | c1_1(a11) | c3_1(a11))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~c2_1(a15)) | c3_1(a15) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | c0_1(a15)))),
% 2.82/2.10 inference(monotonicity,[status(thm)],[1861])).
% 2.82/2.10 tff(1863,plain,
% 2.82/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a11) | c1_1(a11) | c3_1(a11))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c2_1(a15)) | c3_1(a15) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | c0_1(a15))),
% 2.82/2.10 inference(transitivity,[status(thm)],[1862, 1860])).
% 2.82/2.10 tff(1864,plain,
% 2.82/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a11) | c1_1(a11) | c3_1(a11))),
% 2.82/2.10 inference(quant_inst,[status(thm)],[])).
% 2.82/2.10 tff(1865,plain,
% 2.82/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c2_1(a15)) | c3_1(a15) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | c0_1(a15)),
% 2.82/2.10 inference(modus_ponens,[status(thm)],[1864, 1863])).
% 2.82/2.10 tff(1866,plain,
% 2.82/2.10 ($false),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[1865, 104, 1850, 1845, 468, 1849, 1848, 341, 1859, 1851])).
% 2.82/2.10 tff(1867,plain,(c0_1(a2) | (~c2_1(a15)) | c3_1(a15) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | c1_1(a15) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.82/2.10 tff(1868,plain,
% 2.82/2.10 (c0_1(a2)),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[1867, 13, 468, 153, 152, 151, 475, 1845, 12])).
% 2.82/2.10 tff(1869,plain,
% 2.82/2.10 (~hskp1),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[268, 1868])).
% 2.82/2.10 tff(1870,plain,
% 2.82/2.10 (hskp2 | hskp1),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[247, 104, 342, 293, 292, 47])).
% 2.82/2.10 tff(1871,plain,
% 2.82/2.10 (hskp2),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[1870, 1869])).
% 2.82/2.10 tff(1872,plain,
% 2.82/2.10 (~c2_1(a3)),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[206, 1871])).
% 2.82/2.10 tff(1873,plain,
% 2.82/2.10 (^[U: $i] : refl((hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 2.82/2.10 inference(bind,[status(th)],[])).
% 2.82/2.10 tff(1874,plain,
% 2.82/2.10 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.82/2.10 inference(quant_intro,[status(thm)],[1873])).
% 2.82/2.10 tff(1875,plain,
% 2.82/2.10 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.82/2.10 inference(rewrite,[status(thm)],[])).
% 2.82/2.10 tff(1876,plain,
% 2.82/2.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp10) | hskp1) <=> ((hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp1))), rewrite(((hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp1) <=> (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp10) | hskp1) <=> (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 2.82/2.10 inference(bind,[status(th)],[])).
% 2.82/2.10 tff(1877,plain,
% 2.82/2.10 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp10) | hskp1) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.82/2.10 inference(quant_intro,[status(thm)],[1876])).
% 2.82/2.10 tff(1878,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp10) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 2.82/2.10 tff(1879,plain,
% 2.82/2.10 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.82/2.10 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 2.82/2.10 tff(1880,plain,
% 2.82/2.10 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.82/2.10 inference(modus_ponens,[status(thm)],[1879, 1875])).
% 2.82/2.10 tff(1881,plain,(
% 2.82/2.10 ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.82/2.10 inference(skolemize,[status(sab)],[1880])).
% 2.82/2.10 tff(1882,plain,
% 2.82/2.10 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.82/2.10 inference(modus_ponens,[status(thm)],[1881, 1874])).
% 2.82/2.10 tff(1883,plain,
% 2.82/2.10 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0))),
% 2.82/2.10 inference(rewrite,[status(thm)],[])).
% 2.82/2.10 tff(1884,plain,
% 2.82/2.10 ((hskp10 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15))) <=> (hskp10 | hskp1 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0))),
% 2.82/2.10 inference(rewrite,[status(thm)],[])).
% 2.82/2.10 tff(1885,plain,
% 2.82/2.10 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0)))),
% 2.82/2.10 inference(monotonicity,[status(thm)],[1884])).
% 2.82/2.10 tff(1886,plain,
% 2.82/2.10 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0))),
% 2.82/2.10 inference(transitivity,[status(thm)],[1885, 1883])).
% 2.82/2.10 tff(1887,plain,
% 2.82/2.10 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)))),
% 2.82/2.10 inference(quant_inst,[status(thm)],[])).
% 2.82/2.10 tff(1888,plain,
% 2.82/2.10 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0)),
% 2.82/2.10 inference(modus_ponens,[status(thm)],[1887, 1886])).
% 2.82/2.10 tff(1889,plain,
% 2.82/2.10 (hskp10 | hskp1 | (~c2_1(a15)) | c3_1(a15)),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[1888, 104, 475, 1882])).
% 2.82/2.10 tff(1890,plain,
% 2.82/2.10 (hskp10),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[1889, 1869, 1845, 468])).
% 2.82/2.10 tff(1891,plain,
% 2.82/2.10 (~c1_1(a18)),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[937, 1890])).
% 2.82/2.10 tff(1892,plain,
% 2.82/2.10 (~c0_1(a18)),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[943, 1890])).
% 2.82/2.10 tff(1893,plain,
% 2.82/2.10 (c3_1(a3)),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[217, 1871])).
% 2.82/2.10 tff(1894,plain,
% 2.82/2.10 (c1_1(a3)),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[228, 1871])).
% 2.82/2.10 tff(1895,plain,
% 2.82/2.10 (~c2_1(a18)),
% 2.82/2.10 inference(unit_resolution,[status(thm)],[952, 104, 1869, 1894, 1893, 1892, 1891, 1872, 58])).
% 2.82/2.10 tff(1896,plain,
% 2.82/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.82/2.10 inference(rewrite,[status(thm)],[])).
% 2.82/2.10 tff(1897,plain,
% 2.82/2.10 (((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a2) | (~c0_1(a2)) | (~c1_1(a2)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.82/2.10 inference(rewrite,[status(thm)],[])).
% 2.82/2.10 tff(1898,plain,
% 2.82/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a2) | (~c0_1(a2)) | (~c1_1(a2)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a3)) | (~c1_1(a3))))),
% 2.82/2.10 inference(monotonicity,[status(thm)],[1897])).
% 2.82/2.10 tff(1899,plain,
% 2.82/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a2) | (~c0_1(a2)) | (~c1_1(a2)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.82/2.10 inference(transitivity,[status(thm)],[1898, 1896])).
% 2.82/2.10 tff(1900,plain,
% 2.82/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a2) | (~c0_1(a2)) | (~c1_1(a2)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 2.82/2.10 inference(quant_inst,[status(thm)],[])).
% 2.82/2.11 tff(1901,plain,
% 2.82/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a3)) | (~c1_1(a3))),
% 2.82/2.11 inference(modus_ponens,[status(thm)],[1900, 1899])).
% 2.82/2.11 tff(1902,plain,
% 2.82/2.11 (~c1_1(a2)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1901, 104, 1894, 1893, 342, 293, 292, 1872, 1868, 13, 36])).
% 2.82/2.11 tff(1903,plain,
% 2.82/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~c2_1(a15)) | c3_1(a15) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c2_1(a15)) | c3_1(a15) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))),
% 2.82/2.11 inference(rewrite,[status(thm)],[])).
% 2.82/2.11 tff(1904,plain,
% 2.82/2.11 (((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a2) | c1_1(a2) | c3_1(a2)) <=> ((~c2_1(a15)) | c3_1(a15) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))),
% 2.82/2.11 inference(rewrite,[status(thm)],[])).
% 2.82/2.11 tff(1905,plain,
% 2.82/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a2) | c1_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~c2_1(a15)) | c3_1(a15) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15)))),
% 2.82/2.11 inference(monotonicity,[status(thm)],[1904])).
% 2.82/2.11 tff(1906,plain,
% 2.82/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a2) | c1_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c2_1(a15)) | c3_1(a15) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))),
% 2.82/2.11 inference(transitivity,[status(thm)],[1905, 1903])).
% 2.82/2.11 tff(1907,plain,
% 2.82/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a2) | c1_1(a2) | c3_1(a2))),
% 2.82/2.11 inference(quant_inst,[status(thm)],[])).
% 2.82/2.11 tff(1908,plain,
% 2.82/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c2_1(a15)) | c3_1(a15) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15)),
% 2.82/2.11 inference(modus_ponens,[status(thm)],[1907, 1906])).
% 2.82/2.11 tff(1909,plain,
% 2.82/2.11 ((~c0_1(a2)) | c1_1(a2) | c0_1(a15)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1908, 104, 1845, 468, 13, 12, 341])).
% 2.82/2.11 tff(1910,plain,
% 2.82/2.11 (c0_1(a15)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1909, 1902, 1868])).
% 2.82/2.11 tff(1911,plain,
% 2.82/2.11 (~c2_1(a58)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[237, 1871, 1869, 37, 26])).
% 2.82/2.11 tff(1912,plain,
% 2.82/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)) | c3_1(a58))),
% 2.82/2.11 inference(rewrite,[status(thm)],[])).
% 2.82/2.11 tff(1913,plain,
% 2.82/2.11 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | c3_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)) | c3_1(a58))),
% 2.82/2.11 inference(rewrite,[status(thm)],[])).
% 2.82/2.11 tff(1914,plain,
% 2.82/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)) | c3_1(a58)))),
% 2.82/2.11 inference(monotonicity,[status(thm)],[1913])).
% 2.82/2.11 tff(1915,plain,
% 2.82/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)) | c3_1(a58))),
% 2.82/2.11 inference(transitivity,[status(thm)],[1914, 1912])).
% 2.82/2.11 tff(1916,plain,
% 2.82/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | c3_1(a58))),
% 2.82/2.11 inference(quant_inst,[status(thm)],[])).
% 2.82/2.11 tff(1917,plain,
% 2.82/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)) | c3_1(a58)),
% 2.82/2.11 inference(modus_ponens,[status(thm)],[1916, 1915])).
% 2.82/2.11 tff(1918,plain,
% 2.82/2.11 ((~c0_1(a15)) | c3_1(a58)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1917, 104, 1911, 153, 152, 37, 475, 1845, 151, 1342])).
% 2.82/2.11 tff(1919,plain,
% 2.82/2.11 (c3_1(a58)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1918, 1910])).
% 2.82/2.11 tff(1920,plain,
% 2.82/2.11 (~c2_1(a13)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1331, 104, 1869, 1894, 1893, 342, 293, 1872, 58])).
% 2.82/2.11 tff(1921,plain,
% 2.82/2.11 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 2.82/2.11 inference(rewrite,[status(thm)],[])).
% 2.82/2.11 tff(1922,plain,
% 2.82/2.11 ((hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a13) | c2_1(a13) | c0_1(a13)) <=> (hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 2.82/2.11 inference(rewrite,[status(thm)],[])).
% 2.82/2.11 tff(1923,plain,
% 2.82/2.11 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a13) | c2_1(a13) | c0_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13)))),
% 2.82/2.11 inference(monotonicity,[status(thm)],[1922])).
% 2.82/2.11 tff(1924,plain,
% 2.82/2.11 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a13) | c2_1(a13) | c0_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 2.82/2.11 inference(transitivity,[status(thm)],[1923, 1921])).
% 2.82/2.11 tff(1925,plain,
% 2.82/2.11 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a13) | c2_1(a13) | c0_1(a13))),
% 2.82/2.11 inference(quant_inst,[status(thm)],[])).
% 2.82/2.11 tff(1926,plain,
% 2.82/2.11 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13)),
% 2.82/2.11 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 2.82/2.11 tff(1927,plain,
% 2.82/2.11 (hskp5 | c2_1(a13)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1926, 104, 475, 1845, 468, 342, 292, 290])).
% 2.82/2.11 tff(1928,plain,
% 2.82/2.11 (hskp5),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1927, 1920])).
% 2.82/2.11 tff(1929,plain,
% 2.82/2.11 (~c2_1(a11)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[306, 1928])).
% 2.82/2.11 tff(1930,plain,
% 2.82/2.11 (~c1_1(a11)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[312, 1928])).
% 2.82/2.11 tff(1931,plain,
% 2.82/2.11 (c0_1(a11)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[323, 1928])).
% 2.82/2.11 tff(1932,plain,
% 2.82/2.11 (c3_1(a18)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1037, 1890])).
% 2.82/2.11 tff(1933,plain,
% 2.82/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)) | (~c3_1(a58)))),
% 2.82/2.11 inference(rewrite,[status(thm)],[])).
% 2.82/2.11 tff(1934,plain,
% 2.82/2.11 (((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (c0_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)) | (~c3_1(a58)))),
% 2.82/2.11 inference(rewrite,[status(thm)],[])).
% 2.82/2.11 tff(1935,plain,
% 2.82/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)) | (~c3_1(a58))))),
% 2.82/2.11 inference(monotonicity,[status(thm)],[1934])).
% 2.82/2.11 tff(1936,plain,
% 2.82/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)) | (~c3_1(a58)))),
% 2.82/2.11 inference(transitivity,[status(thm)],[1935, 1933])).
% 2.82/2.11 tff(1937,plain,
% 2.82/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 2.82/2.11 inference(quant_inst,[status(thm)],[])).
% 2.82/2.11 tff(1938,plain,
% 2.82/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)) | (~c3_1(a58))),
% 2.82/2.11 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 2.82/2.11 tff(1939,plain,
% 2.82/2.11 ($false),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1938, 104, 1932, 1931, 37, 26, 1892, 1930, 1929, 751, 1919, 1895])).
% 2.82/2.11 tff(1940,plain,(c2_1(a2) | c0_1(a58) | c1_1(a58) | (~c1_1(a1)) | (~c2_1(a1)) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | c3_1(a15) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.82/2.11 tff(1941,plain,
% 2.82/2.11 (c2_1(a2)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1940, 1844, 26, 37, 1843, 475, 1821, 1842, 468, 12])).
% 2.82/2.11 tff(1942,plain,
% 2.82/2.11 (~hskp1),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[262, 1941])).
% 2.82/2.11 tff(1943,plain,
% 2.82/2.11 (hskp6),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[180, 1844, 1843, 1842])).
% 2.82/2.11 tff(1944,plain,
% 2.82/2.11 (~c3_1(a13)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[186, 1943])).
% 2.82/2.11 tff(1945,plain,
% 2.82/2.11 (~c1_1(a13)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[192, 1943])).
% 2.82/2.11 tff(1946,plain,
% 2.82/2.11 (~c0_1(a13)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[198, 1943])).
% 2.82/2.11 tff(1947,plain,
% 2.82/2.11 (hskp2 | hskp1),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[247, 104, 1946, 1945, 1944, 47])).
% 2.82/2.11 tff(1948,plain,
% 2.82/2.11 (hskp2),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1947, 1942])).
% 2.82/2.11 tff(1949,plain,
% 2.82/2.11 (~c2_1(a3)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[206, 1948])).
% 2.82/2.11 tff(1950,plain,
% 2.82/2.11 (hskp10),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1889, 1942, 1821, 468])).
% 2.82/2.11 tff(1951,plain,
% 2.82/2.11 (~c1_1(a18)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[937, 1950])).
% 2.82/2.11 tff(1952,plain,
% 2.82/2.11 (~c0_1(a18)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[943, 1950])).
% 2.82/2.11 tff(1953,plain,
% 2.82/2.11 (c3_1(a3)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[217, 1948])).
% 2.82/2.11 tff(1954,plain,
% 2.82/2.11 (c1_1(a3)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[228, 1948])).
% 2.82/2.11 tff(1955,plain,
% 2.82/2.11 (~c2_1(a18)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[952, 104, 1942, 1954, 1953, 1952, 1951, 1949, 58])).
% 2.82/2.11 tff(1956,plain,
% 2.82/2.11 (~c2_1(a13)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1331, 104, 1942, 1954, 1953, 1946, 1945, 1949, 58])).
% 2.82/2.11 tff(1957,plain,
% 2.82/2.11 (hskp5 | c2_1(a13)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1926, 104, 475, 1821, 468, 1946, 1944, 290])).
% 2.82/2.11 tff(1958,plain,
% 2.82/2.11 (hskp5),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1957, 1956])).
% 2.82/2.11 tff(1959,plain,
% 2.82/2.11 (~c2_1(a11)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[306, 1958])).
% 2.82/2.11 tff(1960,plain,
% 2.82/2.11 (~c1_1(a11)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[312, 1958])).
% 2.82/2.11 tff(1961,plain,
% 2.82/2.11 (c0_1(a11)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[323, 1958])).
% 2.82/2.11 tff(1962,plain,
% 2.82/2.11 (c3_1(a18)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1037, 1950])).
% 2.82/2.11 tff(1963,plain,
% 2.82/2.11 ($false),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1044, 104, 1962, 1961, 1952, 1951, 1960, 1959, 751, 1955])).
% 2.82/2.11 tff(1964,plain,(c3_1(a2) | c1_1(a15) | c3_1(a15) | c1_1(a58) | c0_1(a58) | c2_1(a38) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.82/2.11 tff(1965,plain,
% 2.82/2.11 (c3_1(a2)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1964, 468, 475, 26, 37, 474, 48])).
% 2.82/2.11 tff(1966,plain,
% 2.82/2.11 (~hskp1),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[256, 1965])).
% 2.82/2.11 tff(1967,plain,
% 2.82/2.11 (hskp0),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[590, 1966, 48, 37, 26])).
% 2.82/2.11 tff(1968,plain,
% 2.82/2.11 (~c3_1(a1)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[117, 1967])).
% 2.82/2.11 tff(1969,plain,
% 2.82/2.11 (c2_1(a1)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[128, 1967])).
% 2.82/2.11 tff(1970,plain,
% 2.82/2.11 (c1_1(a1)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[139, 1967])).
% 2.82/2.11 tff(1971,plain,
% 2.82/2.11 (hskp6),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[180, 1970, 1969, 1968])).
% 2.82/2.11 tff(1972,plain,
% 2.82/2.11 (~c3_1(a13)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[186, 1971])).
% 2.82/2.11 tff(1973,plain,
% 2.82/2.11 (~c1_1(a13)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[192, 1971])).
% 2.82/2.11 tff(1974,plain,
% 2.82/2.11 (~c0_1(a13)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[198, 1971])).
% 2.82/2.11 tff(1975,plain,
% 2.82/2.11 (hskp2),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[247, 104, 1966, 1974, 1973, 1972, 47])).
% 2.82/2.11 tff(1976,plain,
% 2.82/2.11 (~c2_1(a3)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[206, 1975])).
% 2.82/2.11 tff(1977,plain,
% 2.82/2.11 (hskp10),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1889, 1966, 1821, 468])).
% 2.82/2.11 tff(1978,plain,
% 2.82/2.11 (~c1_1(a18)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[937, 1977])).
% 2.82/2.11 tff(1979,plain,
% 2.82/2.11 (~c0_1(a18)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[943, 1977])).
% 2.82/2.11 tff(1980,plain,
% 2.82/2.11 (c3_1(a3)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[217, 1975])).
% 2.82/2.11 tff(1981,plain,
% 2.82/2.11 (c1_1(a3)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[228, 1975])).
% 2.82/2.11 tff(1982,plain,
% 2.82/2.11 (~c2_1(a18)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[952, 104, 1966, 1981, 1980, 1979, 1978, 1976, 58])).
% 2.82/2.11 tff(1983,plain,
% 2.82/2.11 (~c2_1(a13)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1331, 104, 1966, 1981, 1980, 1974, 1973, 1976, 58])).
% 2.82/2.11 tff(1984,plain,
% 2.82/2.11 (hskp5 | c2_1(a13)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1926, 104, 475, 1821, 468, 1974, 1972, 290])).
% 2.82/2.11 tff(1985,plain,
% 2.82/2.11 (hskp5),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1984, 1983])).
% 2.82/2.11 tff(1986,plain,
% 2.82/2.11 (~c2_1(a11)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[306, 1985])).
% 2.82/2.11 tff(1987,plain,
% 2.82/2.11 (~c1_1(a11)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[312, 1985])).
% 2.82/2.11 tff(1988,plain,
% 2.82/2.11 (c0_1(a11)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[323, 1985])).
% 2.82/2.11 tff(1989,plain,
% 2.82/2.11 (c3_1(a18)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1037, 1977])).
% 2.82/2.11 tff(1990,plain,
% 2.82/2.11 ($false),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1044, 104, 1989, 1988, 1979, 1978, 1987, 1986, 751, 1982])).
% 2.82/2.11 tff(1991,plain,(c3_1(a15) | c1_1(a15) | hskp3 | c0_1(a58) | c1_1(a58) | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 2.82/2.11 tff(1992,plain,
% 2.82/2.11 (c3_1(a15)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1991, 475, 48, 37, 26, 474])).
% 2.82/2.11 tff(1993,plain,
% 2.82/2.11 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c0_1(a15))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c0_1(a15))),
% 2.82/2.11 inference(rewrite,[status(thm)],[])).
% 2.82/2.11 tff(1994,plain,
% 2.82/2.11 ((hskp3 | hskp0 | (~ndr1_0) | c1_1(a15) | c0_1(a15) | (~c2_1(a15))) <=> (hskp3 | hskp0 | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c0_1(a15))),
% 2.82/2.11 inference(rewrite,[status(thm)],[])).
% 2.82/2.11 tff(1995,plain,
% 2.82/2.11 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a15) | c0_1(a15) | (~c2_1(a15)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c0_1(a15)))),
% 2.82/2.11 inference(monotonicity,[status(thm)],[1994])).
% 2.82/2.11 tff(1996,plain,
% 2.82/2.11 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a15) | c0_1(a15) | (~c2_1(a15)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c0_1(a15))),
% 2.82/2.11 inference(transitivity,[status(thm)],[1995, 1993])).
% 2.82/2.11 tff(1997,plain,
% 2.82/2.11 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a15) | c0_1(a15) | (~c2_1(a15)))),
% 2.82/2.11 inference(quant_inst,[status(thm)],[])).
% 2.82/2.11 tff(1998,plain,
% 2.82/2.11 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c0_1(a15)),
% 2.82/2.11 inference(modus_ponens,[status(thm)],[1997, 1996])).
% 2.82/2.11 tff(1999,plain,
% 2.82/2.11 (hskp0 | (~c2_1(a15)) | c0_1(a15)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1998, 104, 48, 475, 69])).
% 2.82/2.11 tff(2000,plain,
% 2.82/2.11 (c0_1(a15)),
% 2.82/2.11 inference(unit_resolution,[status(thm)],[1999, 11, 1821])).
% 2.82/2.11 tff(2001,plain,
% 2.82/2.11 (^[U: $i] : refl((hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.82/2.11 inference(bind,[status(th)],[])).
% 2.82/2.11 tff(2002,plain,
% 2.82/2.11 (![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.82/2.11 inference(quant_intro,[status(thm)],[2001])).
% 2.82/2.11 tff(2003,plain,
% 2.82/2.11 (![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.82/2.11 inference(rewrite,[status(thm)],[])).
% 2.82/2.11 tff(2004,plain,
% 2.82/2.11 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp24) <=> ((hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp24) <=> (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.82/2.11 inference(bind,[status(th)],[])).
% 2.82/2.11 tff(2005,plain,
% 2.82/2.11 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp24) <=> ![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.82/2.11 inference(quant_intro,[status(thm)],[2004])).
% 2.82/2.11 tff(2006,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 2.82/2.11 tff(2007,plain,
% 2.82/2.11 (![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.82/2.11 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 2.82/2.11 tff(2008,plain,
% 2.82/2.11 (![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.82/2.11 inference(modus_ponens,[status(thm)],[2007, 2003])).
% 2.82/2.11 tff(2009,plain,(
% 2.82/2.11 ![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.82/2.11 inference(skolemize,[status(sab)],[2008])).
% 2.82/2.11 tff(2010,plain,
% 2.82/2.11 (![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.82/2.11 inference(modus_ponens,[status(thm)],[2009, 2002])).
% 2.82/2.11 tff(2011,plain,
% 2.82/2.11 (((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp13 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))),
% 2.82/2.11 inference(rewrite,[status(thm)],[])).
% 2.82/2.11 tff(2012,plain,
% 2.82/2.11 ((hskp24 | hskp13 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15))) <=> (hskp24 | hskp13 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))),
% 2.82/2.11 inference(rewrite,[status(thm)],[])).
% 2.82/2.11 tff(2013,plain,
% 2.82/2.11 (((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15))))),
% 2.82/2.11 inference(monotonicity,[status(thm)],[2012])).
% 2.82/2.11 tff(2014,plain,
% 2.82/2.11 (((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp13 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))),
% 2.82/2.11 inference(transitivity,[status(thm)],[2013, 2011])).
% 2.82/2.11 tff(2015,plain,
% 2.82/2.12 ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 2.82/2.12 inference(quant_inst,[status(thm)],[])).
% 2.82/2.12 tff(2016,plain,
% 2.82/2.12 ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp13 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15))),
% 2.82/2.12 inference(modus_ponens,[status(thm)],[2015, 2014])).
% 2.82/2.12 tff(2017,plain,
% 2.82/2.12 (hskp24 | hskp13 | (~c3_1(a15)) | (~c0_1(a15))),
% 2.82/2.12 inference(unit_resolution,[status(thm)],[2016, 104, 475, 2010])).
% 2.82/2.12 tff(2018,plain,
% 2.82/2.12 (hskp13),
% 2.82/2.12 inference(unit_resolution,[status(thm)],[2017, 2000, 1992, 594])).
% 2.82/2.12 tff(2019,plain,
% 2.82/2.12 (~c3_1(a21)),
% 2.82/2.12 inference(unit_resolution,[status(thm)],[831, 2018])).
% 2.82/2.12 tff(2020,plain,
% 2.82/2.12 (c2_1(a21)),
% 2.82/2.12 inference(unit_resolution,[status(thm)],[842, 2018])).
% 2.82/2.12 tff(2021,plain,
% 2.82/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c1_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c1_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))),
% 2.82/2.12 inference(rewrite,[status(thm)],[])).
% 2.82/2.12 tff(2022,plain,
% 2.82/2.12 (((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | c0_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c1_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))),
% 2.82/2.12 inference(rewrite,[status(thm)],[])).
% 2.82/2.12 tff(2023,plain,
% 2.82/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c1_1(a21)) | (~c2_1(a21)) | (~c3_1(a58))))),
% 2.82/2.12 inference(monotonicity,[status(thm)],[2022])).
% 2.82/2.12 tff(2024,plain,
% 2.82/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c1_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))),
% 2.82/2.12 inference(transitivity,[status(thm)],[2023, 2021])).
% 2.82/2.12 tff(2025,plain,
% 2.82/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 2.82/2.12 inference(quant_inst,[status(thm)],[])).
% 2.82/2.12 tff(2026,plain,
% 2.82/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c1_1(a21)) | (~c2_1(a21)) | (~c3_1(a58))),
% 2.82/2.12 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 2.82/2.12 tff(2027,plain,
% 2.82/2.12 (~c1_1(a21)),
% 2.82/2.12 inference(unit_resolution,[status(thm)],[2026, 104, 476, 2020, 37, 2019, 593, 12, 734, 724, 716])).
% 2.82/2.12 tff(2028,plain,
% 2.82/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | c1_1(a21) | (~c2_1(a21)))),
% 2.84/2.12 inference(rewrite,[status(thm)],[])).
% 2.84/2.12 tff(2029,plain,
% 2.84/2.12 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | c1_1(a21) | (~c2_1(a21)))),
% 2.84/2.12 inference(rewrite,[status(thm)],[])).
% 2.84/2.12 tff(2030,plain,
% 2.84/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | c1_1(a21) | (~c2_1(a21))))),
% 2.84/2.12 inference(monotonicity,[status(thm)],[2029])).
% 2.84/2.12 tff(2031,plain,
% 2.84/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | c1_1(a21) | (~c2_1(a21)))),
% 2.84/2.12 inference(transitivity,[status(thm)],[2030, 2028])).
% 2.84/2.12 tff(2032,plain,
% 2.84/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 2.84/2.12 inference(quant_inst,[status(thm)],[])).
% 2.84/2.12 tff(2033,plain,
% 2.84/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | c1_1(a21) | (~c2_1(a21))),
% 2.84/2.12 inference(modus_ponens,[status(thm)],[2032, 2031])).
% 2.84/2.12 tff(2034,plain,
% 2.84/2.12 ($false),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[2033, 104, 476, 2020, 37, 26, 2019, 593, 12, 380, 716, 2027])).
% 2.84/2.12 tff(2035,plain,(hskp0 | c0_1(a58) | c1_1(a58) | c3_1(a2) | c2_1(a38) | hskp3 | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.12 tff(2036,plain,
% 2.84/2.12 (hskp0),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[2035, 12, 26, 37, 474, 48, 475])).
% 2.84/2.12 tff(2037,plain,
% 2.84/2.12 (~c3_1(a1)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[117, 2036])).
% 2.84/2.12 tff(2038,plain,
% 2.84/2.12 (c2_1(a1)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[128, 2036])).
% 2.84/2.12 tff(2039,plain,
% 2.84/2.12 (c1_1(a1)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[139, 2036])).
% 2.84/2.12 tff(2040,plain,
% 2.84/2.12 (hskp2),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[248, 200])).
% 2.84/2.12 tff(2041,plain,
% 2.84/2.12 (~c2_1(a3)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[206, 2040])).
% 2.84/2.12 tff(2042,plain,
% 2.84/2.12 (c3_1(a3)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[217, 2040])).
% 2.84/2.12 tff(2043,plain,
% 2.84/2.12 (c1_1(a3)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[228, 2040])).
% 2.84/2.12 tff(2044,plain,
% 2.84/2.12 (~c2_1(a13)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[1331, 104, 200, 2043, 2042, 241, 240, 2041, 58])).
% 2.84/2.12 tff(2045,plain,
% 2.84/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 2.84/2.12 inference(rewrite,[status(thm)],[])).
% 2.84/2.12 tff(2046,plain,
% 2.84/2.12 (((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 2.84/2.12 inference(rewrite,[status(thm)],[])).
% 2.84/2.12 tff(2047,plain,
% 2.84/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))))),
% 2.84/2.12 inference(monotonicity,[status(thm)],[2046])).
% 2.84/2.12 tff(2048,plain,
% 2.84/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 2.84/2.12 inference(transitivity,[status(thm)],[2047, 2045])).
% 2.84/2.12 tff(2049,plain,
% 2.84/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 2.84/2.12 inference(quant_inst,[status(thm)],[])).
% 2.84/2.12 tff(2050,plain,
% 2.84/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))),
% 2.84/2.12 inference(modus_ponens,[status(thm)],[2049, 2048])).
% 2.84/2.12 tff(2051,plain,
% 2.84/2.12 (~c0_1(a3)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[2050, 104, 2043, 2042, 241, 240, 239, 2041, 36])).
% 2.84/2.12 tff(2052,plain,
% 2.84/2.12 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 2.84/2.12 inference(bind,[status(th)],[])).
% 2.84/2.12 tff(2053,plain,
% 2.84/2.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.84/2.12 inference(quant_intro,[status(thm)],[2052])).
% 2.84/2.12 tff(2054,plain,
% 2.84/2.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.84/2.12 inference(rewrite,[status(thm)],[])).
% 2.84/2.12 tff(2055,plain,
% 2.84/2.12 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | 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)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | 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)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 2.84/2.12 inference(bind,[status(th)],[])).
% 2.84/2.12 tff(2056,plain,
% 2.84/2.12 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.84/2.12 inference(quant_intro,[status(thm)],[2055])).
% 2.84/2.12 tff(2057,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 2.84/2.12 tff(2058,plain,
% 2.84/2.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.84/2.12 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 2.84/2.12 tff(2059,plain,
% 2.84/2.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.84/2.12 inference(modus_ponens,[status(thm)],[2058, 2054])).
% 2.84/2.12 tff(2060,plain,(
% 2.84/2.12 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.84/2.12 inference(skolemize,[status(sab)],[2059])).
% 2.84/2.12 tff(2061,plain,
% 2.84/2.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.84/2.12 inference(modus_ponens,[status(thm)],[2060, 2053])).
% 2.84/2.12 tff(2062,plain,
% 2.84/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)))),
% 2.84/2.12 inference(rewrite,[status(thm)],[])).
% 2.84/2.12 tff(2063,plain,
% 2.84/2.12 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3))) <=> (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)))),
% 2.84/2.12 inference(rewrite,[status(thm)],[])).
% 2.84/2.12 tff(2064,plain,
% 2.84/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3))))),
% 2.84/2.12 inference(monotonicity,[status(thm)],[2063])).
% 2.84/2.12 tff(2065,plain,
% 2.84/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)))),
% 2.84/2.12 inference(transitivity,[status(thm)],[2064, 2062])).
% 2.84/2.12 tff(2066,plain,
% 2.84/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3)))),
% 2.84/2.12 inference(quant_inst,[status(thm)],[])).
% 2.84/2.12 tff(2067,plain,
% 2.84/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3))),
% 2.84/2.12 inference(modus_ponens,[status(thm)],[2066, 2065])).
% 2.84/2.12 tff(2068,plain,
% 2.84/2.12 ((~c0_1(a2)) | c0_1(a3)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[2067, 104, 2043, 475, 1845, 1252, 2041, 13, 12, 2061])).
% 2.84/2.12 tff(2069,plain,
% 2.84/2.12 (~c0_1(a2)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[2068, 2051])).
% 2.84/2.12 tff(2070,plain,
% 2.84/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13))),
% 2.84/2.12 inference(rewrite,[status(thm)],[])).
% 2.84/2.12 tff(2071,plain,
% 2.84/2.12 (((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13))),
% 2.84/2.12 inference(rewrite,[status(thm)],[])).
% 2.84/2.12 tff(2072,plain,
% 2.84/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13)))),
% 2.84/2.12 inference(monotonicity,[status(thm)],[2071])).
% 2.84/2.12 tff(2073,plain,
% 2.84/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13))),
% 2.84/2.12 inference(transitivity,[status(thm)],[2072, 2070])).
% 2.84/2.12 tff(2074,plain,
% 2.84/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 2.84/2.12 inference(quant_inst,[status(thm)],[])).
% 2.84/2.12 tff(2075,plain,
% 2.84/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13)),
% 2.84/2.12 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 2.84/2.12 tff(2076,plain,
% 2.84/2.12 (c0_1(a2) | c2_1(a13)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[2075, 104, 475, 1845, 1252, 240, 239, 13, 12, 362])).
% 2.84/2.12 tff(2077,plain,
% 2.84/2.12 ($false),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[2076, 2069, 2044])).
% 2.84/2.12 tff(2078,plain,(hskp1 | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.12 tff(2079,plain,
% 2.84/2.12 (hskp1),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[2078, 13, 1845, 1252, 293, 292, 475, 12, 342])).
% 2.84/2.12 tff(2080,plain,
% 2.84/2.12 (~c0_1(a2)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[268, 2079])).
% 2.84/2.12 tff(2081,plain,
% 2.84/2.12 (c0_1(a2) | c2_1(a13)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[2075, 104, 475, 1845, 1252, 293, 292, 13, 12, 362])).
% 2.84/2.12 tff(2082,plain,
% 2.84/2.12 (c2_1(a13)),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[2081, 2080])).
% 2.84/2.12 tff(2083,plain,
% 2.84/2.12 (hskp5 | c0_1(a2) | c2_1(a2) | (~c2_1(a13))),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[299, 104, 293, 292, 12, 290])).
% 2.84/2.12 tff(2084,plain,
% 2.84/2.12 (hskp5),
% 2.84/2.12 inference(unit_resolution,[status(thm)],[2083, 2082, 13, 2080])).
% 2.84/2.13 tff(2085,plain,
% 2.84/2.13 (~c2_1(a11)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[306, 2084])).
% 2.84/2.13 tff(2086,plain,
% 2.84/2.13 (~c1_1(a11)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[312, 2084])).
% 2.84/2.13 tff(2087,plain,
% 2.84/2.13 (c0_1(a11)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[323, 2084])).
% 2.84/2.13 tff(2088,plain,
% 2.84/2.13 (~c3_1(a11)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[330, 104, 2087, 153, 152, 2086, 2085, 151, 279])).
% 2.84/2.13 tff(2089,plain,
% 2.84/2.13 (((~hskp8) | (~c2_1(a15))) <=> ((~hskp8) | (~c2_1(a15)))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2090,plain,
% 2.84/2.13 (((~c2_1(a15)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a15)))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2091,axiom,((~c2_1(a15)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 2.84/2.13 tff(2092,plain,
% 2.84/2.13 ((~hskp8) | (~c2_1(a15))),
% 2.84/2.13 inference(modus_ponens,[status(thm)],[2091, 2090])).
% 2.84/2.13 tff(2093,plain,
% 2.84/2.13 ((~hskp8) | (~c2_1(a15))),
% 2.84/2.13 inference(modus_ponens,[status(thm)],[2092, 2089])).
% 2.84/2.13 tff(2094,plain,
% 2.84/2.13 (~hskp8),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2093, 1845])).
% 2.84/2.13 tff(2095,plain,
% 2.84/2.13 (hskp7 | c0_1(a2) | c2_1(a2)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[1401, 104, 2094, 12, 1389])).
% 2.84/2.13 tff(2096,plain,
% 2.84/2.13 (hskp7),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2095, 2080, 13])).
% 2.84/2.13 tff(2097,plain,
% 2.84/2.13 (~c2_1(a14)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[1408, 2096])).
% 2.84/2.13 tff(2098,plain,
% 2.84/2.13 (~c0_1(a14)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[1433, 2096])).
% 2.84/2.13 tff(2099,plain,
% 2.84/2.13 (c1_1(a14)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[1419, 2096])).
% 2.84/2.13 tff(2100,plain,
% 2.84/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a14) | c2_1(a14) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c1_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a14) | c2_1(a14) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c1_1(a14)))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2101,plain,
% 2.84/2.13 (((~ndr1_0) | c3_1(a11) | c2_1(a11) | (~c0_1(a11)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14))) <=> (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a14) | c2_1(a14) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c1_1(a14)))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2102,plain,
% 2.84/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a11) | c2_1(a11) | (~c0_1(a11)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a14) | c2_1(a14) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c1_1(a14))))),
% 2.84/2.13 inference(monotonicity,[status(thm)],[2101])).
% 2.84/2.13 tff(2103,plain,
% 2.84/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a11) | c2_1(a11) | (~c0_1(a11)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a14) | c2_1(a14) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c1_1(a14)))),
% 2.84/2.13 inference(transitivity,[status(thm)],[2102, 2100])).
% 2.84/2.13 tff(2104,plain,
% 2.84/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a11) | c2_1(a11) | (~c0_1(a11)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))),
% 2.84/2.13 inference(quant_inst,[status(thm)],[])).
% 2.84/2.13 tff(2105,plain,
% 2.84/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a14) | c2_1(a14) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c1_1(a14))),
% 2.84/2.13 inference(modus_ponens,[status(thm)],[2104, 2103])).
% 2.84/2.13 tff(2106,plain,
% 2.84/2.13 ($false),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2105, 104, 2099, 2087, 475, 1845, 1252, 2098, 2097, 2085, 2061, 2088])).
% 2.84/2.13 tff(2107,plain,(c2_1(a2) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.13 tff(2108,plain,
% 2.84/2.13 (c2_1(a2)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2107, 2039, 1821, 1992, 475, 2038, 2037, 12])).
% 2.84/2.13 tff(2109,plain,
% 2.84/2.13 (~hskp1),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[262, 2108])).
% 2.84/2.13 tff(2110,plain,
% 2.84/2.13 (hskp6),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[180, 2039, 2038, 2037])).
% 2.84/2.13 tff(2111,plain,
% 2.84/2.13 (~c3_1(a13)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[186, 2110])).
% 2.84/2.13 tff(2112,plain,
% 2.84/2.13 (~c1_1(a13)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[192, 2110])).
% 2.84/2.13 tff(2113,plain,
% 2.84/2.13 (~c0_1(a13)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[198, 2110])).
% 2.84/2.13 tff(2114,plain,
% 2.84/2.13 (hskp2 | hskp1),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[247, 104, 2113, 2112, 2111, 47])).
% 2.84/2.13 tff(2115,plain,
% 2.84/2.13 (hskp2),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2114, 2109])).
% 2.84/2.13 tff(2116,plain,
% 2.84/2.13 (~c2_1(a3)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[206, 2115])).
% 2.84/2.13 tff(2117,plain,
% 2.84/2.13 (c3_1(a3)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[217, 2115])).
% 2.84/2.13 tff(2118,plain,
% 2.84/2.13 (c1_1(a3)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[228, 2115])).
% 2.84/2.13 tff(2119,plain,
% 2.84/2.13 (~c2_1(a13)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[1331, 104, 2109, 2118, 2117, 2113, 2112, 2116, 58])).
% 2.84/2.13 tff(2120,plain,
% 2.84/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2121,plain,
% 2.84/2.13 (((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2122,plain,
% 2.84/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13)))),
% 2.84/2.13 inference(monotonicity,[status(thm)],[2121])).
% 2.84/2.13 tff(2123,plain,
% 2.84/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 2.84/2.13 inference(transitivity,[status(thm)],[2122, 2120])).
% 2.84/2.13 tff(2124,plain,
% 2.84/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c3_1(a13))),
% 2.84/2.13 inference(quant_inst,[status(thm)],[])).
% 2.84/2.13 tff(2125,plain,
% 2.84/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13)),
% 2.84/2.13 inference(modus_ponens,[status(thm)],[2124, 2123])).
% 2.84/2.13 tff(2126,plain,
% 2.84/2.13 ($false),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2125, 104, 475, 1821, 1992, 2113, 2112, 2111, 362, 2119])).
% 2.84/2.13 tff(2127,plain,(c3_1(a2) | c1_1(a15) | c1_1(a58) | c0_1(a58) | c2_1(a38) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.84/2.13 tff(2128,plain,
% 2.84/2.13 (c3_1(a2)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2127, 475, 26, 37, 474, 48])).
% 2.84/2.13 tff(2129,plain,
% 2.84/2.13 (~hskp1),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[256, 2128])).
% 2.84/2.13 tff(2130,plain,
% 2.84/2.13 (hskp0),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[590, 2129, 48, 37, 26])).
% 2.84/2.13 tff(2131,plain,
% 2.84/2.13 (~c3_1(a1)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[117, 2130])).
% 2.84/2.13 tff(2132,plain,
% 2.84/2.13 (c2_1(a1)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[128, 2130])).
% 2.84/2.13 tff(2133,plain,
% 2.84/2.13 (c1_1(a1)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[139, 2130])).
% 2.84/2.13 tff(2134,plain,
% 2.84/2.13 (hskp6),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[180, 2133, 2132, 2131])).
% 2.84/2.13 tff(2135,plain,
% 2.84/2.13 (~c3_1(a13)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[186, 2134])).
% 2.84/2.13 tff(2136,plain,
% 2.84/2.13 (~c1_1(a13)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[192, 2134])).
% 2.84/2.13 tff(2137,plain,
% 2.84/2.13 (~c0_1(a13)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[198, 2134])).
% 2.84/2.13 tff(2138,plain,
% 2.84/2.13 (hskp2),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[247, 104, 2129, 2137, 2136, 2135, 47])).
% 2.84/2.13 tff(2139,plain,
% 2.84/2.13 (~c2_1(a3)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[206, 2138])).
% 2.84/2.13 tff(2140,plain,
% 2.84/2.13 (c3_1(a3)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[217, 2138])).
% 2.84/2.13 tff(2141,plain,
% 2.84/2.13 (c1_1(a3)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[228, 2138])).
% 2.84/2.13 tff(2142,plain,
% 2.84/2.13 (~c2_1(a13)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[1331, 104, 2129, 2141, 2140, 2137, 2136, 2139, 58])).
% 2.84/2.13 tff(2143,plain,
% 2.84/2.13 ($false),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2125, 104, 475, 1821, 1992, 2137, 2136, 2135, 362, 2142])).
% 2.84/2.13 tff(2144,plain,(c1_1(a15) | hskp3 | c0_1(a58) | c1_1(a58) | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.13 tff(2145,plain,
% 2.84/2.13 (c1_1(a15)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2144, 474, 37, 26, 48])).
% 2.84/2.13 tff(2146,plain,
% 2.84/2.13 (hskp0),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[590, 200, 48, 37, 26])).
% 2.84/2.13 tff(2147,plain,
% 2.84/2.13 (~c3_1(a1)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[117, 2146])).
% 2.84/2.13 tff(2148,plain,
% 2.84/2.13 (c2_1(a1)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[128, 2146])).
% 2.84/2.13 tff(2149,plain,
% 2.84/2.13 (c1_1(a1)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[139, 2146])).
% 2.84/2.13 tff(2150,plain,
% 2.84/2.13 (hskp6),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[180, 2149, 2148, 2147])).
% 2.84/2.13 tff(2151,plain,
% 2.84/2.13 (~c3_1(a13)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[186, 2150])).
% 2.84/2.13 tff(2152,plain,
% 2.84/2.13 (~c1_1(a13)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[192, 2150])).
% 2.84/2.13 tff(2153,plain,
% 2.84/2.13 (~c0_1(a13)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[198, 2150])).
% 2.84/2.13 tff(2154,plain,
% 2.84/2.13 (hskp2),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[247, 104, 200, 2153, 2152, 2151, 47])).
% 2.84/2.13 tff(2155,plain,
% 2.84/2.13 (~c2_1(a3)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[206, 2154])).
% 2.84/2.13 tff(2156,assumption,(c1_1(a15)), introduced(assumption)).
% 2.84/2.13 tff(2157,plain,
% 2.84/2.13 (c3_1(a3)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[217, 2154])).
% 2.84/2.13 tff(2158,plain,
% 2.84/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2159,plain,
% 2.84/2.13 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> ((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2160,plain,
% 2.84/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3)))),
% 2.84/2.13 inference(monotonicity,[status(thm)],[2159])).
% 2.84/2.13 tff(2161,plain,
% 2.84/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 2.84/2.13 inference(transitivity,[status(thm)],[2160, 2158])).
% 2.84/2.13 tff(2162,plain,
% 2.84/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 2.84/2.13 inference(quant_inst,[status(thm)],[])).
% 2.84/2.13 tff(2163,plain,
% 2.84/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3)),
% 2.84/2.13 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 2.84/2.13 tff(2164,plain,
% 2.84/2.13 (c0_1(a3)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2163, 104, 2157, 2149, 2148, 2156, 752, 468, 2155, 2147, 734])).
% 2.84/2.13 tff(2165,plain,
% 2.84/2.13 (c1_1(a3)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[228, 2154])).
% 2.84/2.13 tff(2166,plain,
% 2.84/2.13 ($false),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2050, 104, 2165, 2157, 2153, 2152, 2151, 2155, 36, 2164])).
% 2.84/2.13 tff(2167,plain,(hskp1 | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.13 tff(2168,plain,
% 2.84/2.13 (hskp1),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2167, 752, 2145, 468, 48, 37, 26])).
% 2.84/2.13 tff(2169,plain,
% 2.84/2.13 (~c3_1(a2)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[256, 2168])).
% 2.84/2.13 tff(2170,plain,
% 2.84/2.13 (~c2_1(a2)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[262, 2168])).
% 2.84/2.13 tff(2171,plain,
% 2.84/2.13 (~c0_1(a2)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[268, 2168])).
% 2.84/2.13 tff(2172,plain,
% 2.84/2.13 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~c1_1(a15)) | c2_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | (~c1_1(a15)) | c2_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a15)))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2173,plain,
% 2.84/2.13 ((hskp27 | (~ndr1_0) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp27 | (~c1_1(a15)) | c2_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a15)))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2174,plain,
% 2.84/2.13 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~c1_1(a15)) | c2_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a15))))),
% 2.84/2.13 inference(monotonicity,[status(thm)],[2173])).
% 2.84/2.13 tff(2175,plain,
% 2.84/2.13 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | (~c1_1(a15)) | c2_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a15)))),
% 2.84/2.13 inference(transitivity,[status(thm)],[2174, 2172])).
% 2.84/2.13 tff(2176,plain,
% 2.84/2.13 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 2.84/2.13 inference(quant_inst,[status(thm)],[])).
% 2.84/2.13 tff(2177,plain,
% 2.84/2.13 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | (~c1_1(a15)) | c2_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a15))),
% 2.84/2.13 inference(modus_ponens,[status(thm)],[2176, 2175])).
% 2.84/2.13 tff(2178,plain,
% 2.84/2.13 (hskp27 | (~c0_1(a15))),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2177, 104, 2145, 752, 2171, 2170, 2169, 668])).
% 2.84/2.13 tff(2179,plain,
% 2.84/2.13 (~c0_1(a15)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2178, 634])).
% 2.84/2.13 tff(2180,plain,
% 2.84/2.13 (((~hskp8) | (~c1_1(a15))) <=> ((~hskp8) | (~c1_1(a15)))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2181,plain,
% 2.84/2.13 (((~c1_1(a15)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a15)))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2182,axiom,((~c1_1(a15)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 2.84/2.13 tff(2183,plain,
% 2.84/2.13 ((~hskp8) | (~c1_1(a15))),
% 2.84/2.13 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 2.84/2.13 tff(2184,plain,
% 2.84/2.13 ((~hskp8) | (~c1_1(a15))),
% 2.84/2.13 inference(modus_ponens,[status(thm)],[2183, 2180])).
% 2.84/2.13 tff(2185,plain,
% 2.84/2.13 (~hskp8),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2184, 2145])).
% 2.84/2.13 tff(2186,plain,
% 2.84/2.13 (hskp13),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[1449, 634, 2185])).
% 2.84/2.13 tff(2187,plain,
% 2.84/2.13 (~c3_1(a21)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[831, 2186])).
% 2.84/2.13 tff(2188,plain,
% 2.84/2.13 (~hskp20),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[697, 11, 2169, 2170, 2171, 530])).
% 2.84/2.13 tff(2189,plain,
% 2.84/2.13 (~hskp21),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[678, 634, 474, 2170, 2169, 2171])).
% 2.84/2.13 tff(2190,plain,
% 2.84/2.13 (c3_1(a58)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[723, 2189, 476, 2188])).
% 2.84/2.13 tff(2191,plain,
% 2.84/2.13 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | (~c3_1(a58)))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2192,plain,
% 2.84/2.13 ((hskp22 | hskp20 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58))) <=> (hskp22 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | (~c3_1(a58)))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2193,plain,
% 2.84/2.13 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | (~c3_1(a58))))),
% 2.84/2.13 inference(monotonicity,[status(thm)],[2192])).
% 2.84/2.13 tff(2194,plain,
% 2.84/2.13 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | (~c3_1(a58)))),
% 2.84/2.13 inference(transitivity,[status(thm)],[2193, 2191])).
% 2.84/2.13 tff(2195,plain,
% 2.84/2.13 ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)))),
% 2.84/2.13 inference(quant_inst,[status(thm)],[])).
% 2.84/2.13 tff(2196,plain,
% 2.84/2.13 ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | (~c3_1(a58))),
% 2.84/2.13 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 2.84/2.13 tff(2197,plain,
% 2.84/2.13 (hskp22 | hskp20 | c2_1(a58) | (~c3_1(a58))),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2196, 104, 26, 1462])).
% 2.84/2.13 tff(2198,plain,
% 2.84/2.13 (hskp22),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[2197, 2190, 476, 2188])).
% 2.84/2.13 tff(2199,plain,
% 2.84/2.13 (~c1_1(a42)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[1475, 2198])).
% 2.84/2.13 tff(2200,plain,
% 2.84/2.13 (c2_1(a21)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[842, 2186])).
% 2.84/2.13 tff(2201,plain,
% 2.84/2.13 (c2_1(a42)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[1487, 2198])).
% 2.84/2.13 tff(2202,plain,
% 2.84/2.13 (c0_1(a42)),
% 2.84/2.13 inference(unit_resolution,[status(thm)],[1498, 2198])).
% 2.84/2.13 tff(2203,plain,
% 2.84/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c3_1(a21) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a21) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2204,plain,
% 2.84/2.13 (((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a15) | c0_1(a15) | c3_1(a15)) <=> (c1_1(a42) | c3_1(a21) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 2.84/2.13 inference(rewrite,[status(thm)],[])).
% 2.84/2.13 tff(2205,plain,
% 2.84/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a15) | c0_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c3_1(a21) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42))))),
% 2.84/2.13 inference(monotonicity,[status(thm)],[2204])).
% 2.84/2.13 tff(2206,plain,
% 2.84/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a15) | c0_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a21) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 2.84/2.13 inference(transitivity,[status(thm)],[2205, 2203])).
% 2.84/2.13 tff(2207,plain,
% 2.84/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a15) | c0_1(a15) | c3_1(a15))),
% 2.84/2.13 inference(quant_inst,[status(thm)],[])).
% 2.84/2.13 tff(2208,plain,
% 2.84/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a21) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42))),
% 2.84/2.14 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 2.84/2.14 tff(2209,plain,
% 2.84/2.14 (~c1_1(a21)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[2208, 104, 2202, 2201, 2200, 2199, 2187, 752, 468, 1342, 2179])).
% 2.84/2.14 tff(2210,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 2.84/2.14 inference(rewrite,[status(thm)],[])).
% 2.84/2.14 tff(2211,plain,
% 2.84/2.14 (((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 2.84/2.14 inference(rewrite,[status(thm)],[])).
% 2.84/2.14 tff(2212,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21))))),
% 2.84/2.14 inference(monotonicity,[status(thm)],[2211])).
% 2.84/2.14 tff(2213,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 2.84/2.14 inference(transitivity,[status(thm)],[2212, 2210])).
% 2.84/2.14 tff(2214,plain,
% 2.84/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 2.84/2.14 inference(quant_inst,[status(thm)],[])).
% 2.84/2.14 tff(2215,plain,
% 2.84/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21))),
% 2.84/2.14 inference(modus_ponens,[status(thm)],[2214, 2213])).
% 2.84/2.14 tff(2216,plain,
% 2.84/2.14 ($false),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[2215, 104, 476, 2200, 37, 26, 2187, 2145, 752, 468, 380, 2209])).
% 2.84/2.14 tff(2217,plain,(hskp0 | c0_1(a58) | c1_1(a58) | c2_1(a15) | c3_1(a15) | c2_1(a38) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.84/2.14 tff(2218,plain,
% 2.84/2.14 (hskp0),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[2217, 752, 26, 37, 468, 474, 48])).
% 2.84/2.14 tff(2219,plain,
% 2.84/2.14 (~c3_1(a1)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[117, 2218])).
% 2.84/2.14 tff(2220,plain,
% 2.84/2.14 (hskp7),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[1401, 104, 2185, 2171, 2170, 2169, 1389])).
% 2.84/2.14 tff(2221,plain,
% 2.84/2.14 (~c2_1(a14)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[1408, 2220])).
% 2.84/2.14 tff(2222,plain,
% 2.84/2.14 (~c0_1(a14)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[1433, 2220])).
% 2.84/2.14 tff(2223,plain,
% 2.84/2.14 (c2_1(a1)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[128, 2218])).
% 2.84/2.14 tff(2224,plain,
% 2.84/2.14 (c1_1(a1)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[139, 2218])).
% 2.84/2.14 tff(2225,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a14) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a14) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)))),
% 2.84/2.14 inference(rewrite,[status(thm)],[])).
% 2.84/2.14 tff(2226,plain,
% 2.84/2.14 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14))) <=> ((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a14) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)))),
% 2.84/2.14 inference(rewrite,[status(thm)],[])).
% 2.84/2.14 tff(2227,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a14) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14))))),
% 2.84/2.14 inference(monotonicity,[status(thm)],[2226])).
% 2.84/2.14 tff(2228,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a14) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)))),
% 2.84/2.14 inference(transitivity,[status(thm)],[2227, 2225])).
% 2.84/2.14 tff(2229,plain,
% 2.84/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)))),
% 2.84/2.14 inference(quant_inst,[status(thm)],[])).
% 2.84/2.14 tff(2230,plain,
% 2.84/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a14) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14))),
% 2.84/2.14 inference(modus_ponens,[status(thm)],[2229, 2228])).
% 2.84/2.14 tff(2231,plain,
% 2.84/2.14 (~c3_1(a14)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[2230, 104, 2224, 2223, 2145, 752, 468, 2222, 2221, 2219, 734])).
% 2.84/2.14 tff(2232,plain,
% 2.84/2.14 (hskp6),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[180, 2224, 2223, 2219])).
% 2.84/2.14 tff(2233,plain,
% 2.84/2.14 (~c3_1(a13)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[186, 2232])).
% 2.84/2.14 tff(2234,plain,
% 2.84/2.14 (~c1_1(a13)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[192, 2232])).
% 2.84/2.14 tff(2235,plain,
% 2.84/2.14 (~c0_1(a13)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[198, 2232])).
% 2.84/2.14 tff(2236,plain,
% 2.84/2.14 (~c2_1(a13)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[350, 2224, 2223, 2219, 2171, 2170, 2169])).
% 2.84/2.14 tff(2237,assumption,(~c3_1(a14)), introduced(assumption)).
% 2.84/2.14 tff(2238,assumption,(~c2_1(a14)), introduced(assumption)).
% 2.84/2.14 tff(2239,assumption,(~c0_1(a14)), introduced(assumption)).
% 2.84/2.14 tff(2240,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c0_1(a14) | c2_1(a14) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c3_1(a14) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c0_1(a14) | c2_1(a14) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c3_1(a14) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.84/2.14 inference(rewrite,[status(thm)],[])).
% 2.84/2.14 tff(2241,plain,
% 2.84/2.14 (((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a14) | c0_1(a14) | c3_1(a14)) <=> (c1_1(a58) | c0_1(a14) | c2_1(a14) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c3_1(a14) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.84/2.14 inference(rewrite,[status(thm)],[])).
% 2.84/2.14 tff(2242,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a14) | c0_1(a14) | c3_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c0_1(a14) | c2_1(a14) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c3_1(a14) | (~c2_1(a58)) | (~c3_1(a58))))),
% 2.84/2.14 inference(monotonicity,[status(thm)],[2241])).
% 2.84/2.14 tff(2243,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a14) | c0_1(a14) | c3_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c0_1(a14) | c2_1(a14) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c3_1(a14) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.84/2.14 inference(transitivity,[status(thm)],[2242, 2240])).
% 2.84/2.14 tff(2244,plain,
% 2.84/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a14) | c0_1(a14) | c3_1(a14))),
% 2.84/2.14 inference(quant_inst,[status(thm)],[])).
% 2.84/2.14 tff(2245,plain,
% 2.84/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c0_1(a14) | c2_1(a14) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c3_1(a14) | (~c2_1(a58)) | (~c3_1(a58))),
% 2.84/2.14 inference(modus_ponens,[status(thm)],[2244, 2243])).
% 2.84/2.14 tff(2246,plain,
% 2.84/2.14 (c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58))),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[2245, 104, 26, 2239, 2238, 240, 239, 362, 2237])).
% 2.84/2.14 tff(2247,plain,
% 2.84/2.14 (~c3_1(a58)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[2246, 352, 59])).
% 2.84/2.14 tff(2248,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))),
% 2.84/2.14 inference(rewrite,[status(thm)],[])).
% 2.84/2.14 tff(2249,plain,
% 2.84/2.14 (((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13)) <=> (c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))),
% 2.84/2.14 inference(rewrite,[status(thm)],[])).
% 2.84/2.14 tff(2250,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58)))),
% 2.84/2.14 inference(monotonicity,[status(thm)],[2249])).
% 2.84/2.14 tff(2251,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))),
% 2.84/2.14 inference(transitivity,[status(thm)],[2250, 2248])).
% 2.84/2.14 tff(2252,plain,
% 2.84/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13))),
% 2.84/2.14 inference(quant_inst,[status(thm)],[])).
% 2.84/2.14 tff(2253,plain,
% 2.84/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58)),
% 2.84/2.14 inference(modus_ponens,[status(thm)],[2252, 2251])).
% 2.84/2.14 tff(2254,plain,
% 2.84/2.14 ($false),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[2253, 104, 59, 26, 2156, 752, 468, 241, 240, 380, 352, 2247])).
% 2.84/2.14 tff(2255,plain,(c2_1(a13) | (~c2_1(a58)) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | c0_1(a14) | c2_1(a14) | c3_1(a13) | c3_1(a14)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.14 tff(2256,plain,
% 2.84/2.14 (~c2_1(a58)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[2255, 2236, 26, 2145, 752, 468, 2235, 2234, 2222, 2221, 2233, 2231])).
% 2.84/2.14 tff(2257,plain,
% 2.84/2.14 (~hskp24),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[466, 2256])).
% 2.84/2.14 tff(2258,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))),
% 2.84/2.14 inference(rewrite,[status(thm)],[])).
% 2.84/2.14 tff(2259,plain,
% 2.84/2.14 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))),
% 2.84/2.14 inference(rewrite,[status(thm)],[])).
% 2.84/2.14 tff(2260,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58))))),
% 2.84/2.14 inference(monotonicity,[status(thm)],[2259])).
% 2.84/2.14 tff(2261,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))),
% 2.84/2.14 inference(transitivity,[status(thm)],[2260, 2258])).
% 2.84/2.14 tff(2262,plain,
% 2.84/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 2.84/2.14 inference(quant_inst,[status(thm)],[])).
% 2.84/2.14 tff(2263,plain,
% 2.84/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58))),
% 2.84/2.14 inference(modus_ponens,[status(thm)],[2262, 2261])).
% 2.84/2.14 tff(2264,plain,
% 2.84/2.14 (~c3_1(a58)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[2263, 104, 780, 2224, 2223, 37, 2145, 752, 468, 2219, 734])).
% 2.84/2.14 tff(2265,assumption,(~c3_1(a58)), introduced(assumption)).
% 2.84/2.14 tff(2266,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a58) | c1_1(a58) | c2_1(a38) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a58) | c2_1(a38) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58))),
% 2.84/2.14 inference(rewrite,[status(thm)],[])).
% 2.84/2.14 tff(2267,plain,
% 2.84/2.14 (((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a58) | c0_1(a58) | c3_1(a58)) <=> (c0_1(a58) | c1_1(a58) | c2_1(a38) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58))),
% 2.84/2.14 inference(rewrite,[status(thm)],[])).
% 2.84/2.14 tff(2268,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a58) | c1_1(a58) | c2_1(a38) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58)))),
% 2.84/2.14 inference(monotonicity,[status(thm)],[2267])).
% 2.84/2.14 tff(2269,plain,
% 2.84/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a58) | c2_1(a38) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58))),
% 2.84/2.14 inference(transitivity,[status(thm)],[2268, 2266])).
% 2.84/2.14 tff(2270,plain,
% 2.84/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a58) | c0_1(a58) | c3_1(a58))),
% 2.84/2.14 inference(quant_inst,[status(thm)],[])).
% 2.84/2.14 tff(2271,plain,
% 2.84/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a58) | c2_1(a38) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58)),
% 2.84/2.14 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 2.84/2.14 tff(2272,plain,
% 2.84/2.14 ((~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[2271, 104, 37, 26, 474, 36])).
% 2.84/2.14 tff(2273,plain,
% 2.84/2.14 (~c3_1(a38)),
% 2.84/2.14 inference(unit_resolution,[status(thm)],[2272, 647, 2265, 658])).
% 2.84/2.14 tff(2274,plain,
% 2.84/2.14 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))))),
% 2.84/2.14 inference(bind,[status(th)],[])).
% 2.84/2.14 tff(2275,plain,
% 2.84/2.14 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 2.84/2.14 inference(quant_intro,[status(thm)],[2274])).
% 2.84/2.14 tff(2276,plain,
% 2.84/2.14 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 2.84/2.14 inference(rewrite,[status(thm)],[])).
% 2.84/2.14 tff(2277,plain,
% 2.84/2.14 (^[V: $i, U: $i] : 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)) | (~c0_1(V)) | (~c1_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))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))))),
% 2.84/2.14 inference(bind,[status(th)],[])).
% 2.84/2.14 tff(2278,plain,
% 2.84/2.14 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 2.84/2.14 inference(quant_intro,[status(thm)],[2277])).
% 2.84/2.14 tff(2279,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 2.84/2.14 tff(2280,plain,
% 2.84/2.14 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 2.84/2.15 inference(modus_ponens,[status(thm)],[2279, 2278])).
% 2.84/2.15 tff(2281,plain,
% 2.84/2.15 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 2.84/2.15 inference(modus_ponens,[status(thm)],[2280, 2276])).
% 2.84/2.15 tff(2282,plain,(
% 2.84/2.15 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 2.84/2.15 inference(skolemize,[status(sab)],[2281])).
% 2.84/2.15 tff(2283,plain,
% 2.84/2.15 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 2.84/2.15 inference(modus_ponens,[status(thm)],[2282, 2275])).
% 2.84/2.15 tff(2284,plain,
% 2.84/2.15 (hskp27),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[678, 636, 474, 13, 12, 14])).
% 2.84/2.15 tff(2285,plain,
% 2.84/2.15 (c3_1(a12)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[605, 2284])).
% 2.84/2.15 tff(2286,plain,
% 2.84/2.15 (c1_1(a12)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[616, 2284])).
% 2.84/2.15 tff(2287,plain,
% 2.84/2.15 (c0_1(a12)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[1192, 2284])).
% 2.84/2.15 tff(2288,assumption,(~hskp8), introduced(assumption)).
% 2.84/2.15 tff(2289,plain,
% 2.84/2.15 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 2.84/2.15 inference(rewrite,[status(thm)],[])).
% 2.84/2.15 tff(2290,plain,
% 2.84/2.15 ((hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38))) <=> (hskp8 | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 2.84/2.15 inference(rewrite,[status(thm)],[])).
% 2.84/2.15 tff(2291,plain,
% 2.84/2.15 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))))),
% 2.84/2.15 inference(monotonicity,[status(thm)],[2290])).
% 2.84/2.15 tff(2292,plain,
% 2.84/2.15 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 2.84/2.15 inference(transitivity,[status(thm)],[2291, 2289])).
% 2.84/2.15 tff(2293,plain,
% 2.84/2.15 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.84/2.15 inference(quant_inst,[status(thm)],[])).
% 2.84/2.15 tff(2294,plain,
% 2.84/2.15 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))),
% 2.84/2.15 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 2.84/2.15 tff(2295,plain,
% 2.84/2.15 ($false),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2294, 104, 2288, 2287, 2286, 2285, 647, 658, 2283, 2273])).
% 2.84/2.15 tff(2296,plain,((~hskp21) | hskp8 | c3_1(a58) | c0_1(a58) | c1_1(a58) | c2_1(a38) | c2_1(a2) | c3_1(a2) | c0_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.15 tff(2297,plain,
% 2.84/2.15 (~hskp21),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2296, 2264, 2185, 37, 26, 474, 2170, 2169, 2171])).
% 2.84/2.15 tff(2298,plain,
% 2.84/2.15 (hskp20),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[723, 2297, 780, 2264])).
% 2.84/2.15 tff(2299,plain,
% 2.84/2.15 (c3_1(a37)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[555, 2298])).
% 2.84/2.15 tff(2300,plain,
% 2.84/2.15 (c1_1(a37)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[566, 2298])).
% 2.84/2.15 tff(2301,plain,
% 2.84/2.15 (~c2_1(a37)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[571, 104, 568, 48, 2300, 2299, 10])).
% 2.84/2.15 tff(2302,plain,
% 2.84/2.15 (hskp13),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[825, 2297, 568])).
% 2.84/2.15 tff(2303,plain,
% 2.84/2.15 (~c3_1(a21)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[831, 2302])).
% 2.84/2.15 tff(2304,plain,
% 2.84/2.15 (c2_1(a21)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[842, 2302])).
% 2.84/2.15 tff(2305,plain,
% 2.84/2.15 (c1_1(a21)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2215, 104, 780, 2304, 37, 26, 2303, 2145, 752, 468, 380])).
% 2.84/2.15 tff(2306,plain,
% 2.84/2.15 (~c0_1(a37)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[685, 2298])).
% 2.84/2.15 tff(2307,plain,
% 2.84/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | c2_1(a37) | (~c3_1(a37)))),
% 2.84/2.15 inference(rewrite,[status(thm)],[])).
% 2.84/2.15 tff(2308,plain,
% 2.84/2.15 (((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37))) <=> (c0_1(a37) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | c2_1(a37) | (~c3_1(a37)))),
% 2.84/2.15 inference(rewrite,[status(thm)],[])).
% 2.84/2.15 tff(2309,plain,
% 2.84/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | c2_1(a37) | (~c3_1(a37))))),
% 2.84/2.15 inference(monotonicity,[status(thm)],[2308])).
% 2.84/2.15 tff(2310,plain,
% 2.84/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | c2_1(a37) | (~c3_1(a37)))),
% 2.84/2.15 inference(transitivity,[status(thm)],[2309, 2307])).
% 2.84/2.15 tff(2311,plain,
% 2.84/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))),
% 2.84/2.15 inference(quant_inst,[status(thm)],[])).
% 2.84/2.15 tff(2312,plain,
% 2.84/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | c2_1(a37) | (~c3_1(a37))),
% 2.84/2.15 inference(modus_ponens,[status(thm)],[2311, 2310])).
% 2.84/2.15 tff(2313,plain,
% 2.84/2.15 ($false),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2312, 104, 2299, 2304, 2306, 2303, 2145, 752, 468, 734, 2305, 2301])).
% 2.84/2.15 tff(2314,plain,(c2_1(a58) | c2_1(a15) | c3_1(a15) | c0_1(a58) | c1_1(a58) | hskp24 | hskp3 | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.15 tff(2315,plain,
% 2.84/2.15 ($false),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2314, 2257, 2256, 468, 37, 26, 752, 48, 474])).
% 2.84/2.15 tff(2316,plain,(c2_1(a15) | c3_1(a15) | c0_1(a58) | c1_1(a58) | hskp3 | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.15 tff(2317,plain,
% 2.84/2.15 (c2_1(a15)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2316, 468, 37, 26, 48, 474])).
% 2.84/2.15 tff(2318,plain,
% 2.84/2.15 (~c0_1(a3)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2050, 104, 2165, 2157, 2153, 2152, 2151, 2155, 36])).
% 2.84/2.15 tff(2319,plain,
% 2.84/2.15 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.84/2.15 inference(rewrite,[status(thm)],[])).
% 2.84/2.15 tff(2320,plain,
% 2.84/2.15 ((hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.84/2.15 inference(rewrite,[status(thm)],[])).
% 2.84/2.15 tff(2321,plain,
% 2.84/2.15 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3))))),
% 2.84/2.15 inference(monotonicity,[status(thm)],[2320])).
% 2.84/2.15 tff(2322,plain,
% 2.84/2.15 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.84/2.15 inference(transitivity,[status(thm)],[2321, 2319])).
% 2.84/2.15 tff(2323,plain,
% 2.84/2.15 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.84/2.15 inference(quant_inst,[status(thm)],[])).
% 2.84/2.15 tff(2324,plain,
% 2.84/2.15 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3))),
% 2.84/2.15 inference(modus_ponens,[status(thm)],[2323, 2322])).
% 2.84/2.15 tff(2325,plain,
% 2.84/2.15 (hskp9),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2324, 104, 2165, 2157, 2156, 1845, 468, 2155, 890])).
% 2.84/2.15 tff(2326,plain,
% 2.84/2.15 (~c3_1(a16)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[902, 2325])).
% 2.84/2.15 tff(2327,plain,
% 2.84/2.15 (c1_1(a16)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[913, 2325])).
% 2.84/2.15 tff(2328,plain,
% 2.84/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))),
% 2.84/2.15 inference(rewrite,[status(thm)],[])).
% 2.84/2.15 tff(2329,plain,
% 2.84/2.15 (((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))),
% 2.84/2.15 inference(rewrite,[status(thm)],[])).
% 2.84/2.15 tff(2330,plain,
% 2.84/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16)))),
% 2.84/2.15 inference(monotonicity,[status(thm)],[2329])).
% 2.84/2.15 tff(2331,plain,
% 2.84/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))),
% 2.84/2.15 inference(transitivity,[status(thm)],[2330, 2328])).
% 2.84/2.15 tff(2332,plain,
% 2.84/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 2.84/2.15 inference(quant_inst,[status(thm)],[])).
% 2.84/2.15 tff(2333,plain,
% 2.84/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16)),
% 2.84/2.15 inference(modus_ponens,[status(thm)],[2332, 2331])).
% 2.84/2.15 tff(2334,plain,
% 2.84/2.15 (c2_1(a16)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2333, 104, 2327, 2157, 2326, 2156, 1845, 468, 2155, 734, 2318])).
% 2.84/2.15 tff(2335,plain,
% 2.84/2.15 (~c2_1(a13)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[1331, 104, 200, 2165, 2157, 2153, 2152, 2155, 58])).
% 2.84/2.15 tff(2336,plain,
% 2.84/2.15 (c0_1(a16)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[924, 2325])).
% 2.84/2.15 tff(2337,plain,
% 2.84/2.15 (hskp12),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[993, 104, 2336, 2327, 2157, 2326, 2155, 987, 2318])).
% 2.84/2.15 tff(2338,plain,
% 2.84/2.15 (~c1_1(a20)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[1005, 2337])).
% 2.84/2.15 tff(2339,plain,
% 2.84/2.15 (c2_1(a20)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[1016, 2337])).
% 2.84/2.15 tff(2340,plain,
% 2.84/2.15 (~c0_1(a20)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[1359, 104, 2339, 2327, 2338, 2326, 2153, 2151, 1342, 2335, 2334])).
% 2.84/2.15 tff(2341,plain,
% 2.84/2.15 ($false),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[1366, 104, 200, 2339, 2165, 2157, 2338, 2155, 58, 2340])).
% 2.84/2.15 tff(2342,plain,(hskp1 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.15 tff(2343,plain,
% 2.84/2.15 (hskp1),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2342, 2317, 2145, 468, 48, 37, 26])).
% 2.84/2.15 tff(2344,plain,
% 2.84/2.15 (~c3_1(a2)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[256, 2343])).
% 2.84/2.15 tff(2345,plain,
% 2.84/2.15 (~c0_1(a2)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[268, 2343])).
% 2.84/2.15 tff(2346,plain,
% 2.84/2.15 (~c2_1(a2)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[262, 2343])).
% 2.84/2.15 tff(2347,plain,
% 2.84/2.15 (~hskp20),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[697, 592, 12, 13, 11, 530])).
% 2.84/2.15 tff(2348,plain,
% 2.84/2.15 (~hskp27),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[633, 594, 11, 530, 48])).
% 2.84/2.15 tff(2349,plain,
% 2.84/2.15 (~hskp21),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[678, 2348, 474, 13, 12, 592])).
% 2.84/2.15 tff(2350,plain,
% 2.84/2.15 (c1_1(a2)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[715, 2349, 13, 2347])).
% 2.84/2.15 tff(2351,plain,
% 2.84/2.15 (c3_1(a58)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[723, 2349, 476, 2347])).
% 2.84/2.15 tff(2352,plain,
% 2.84/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a58)))),
% 2.84/2.15 inference(rewrite,[status(thm)],[])).
% 2.84/2.15 tff(2353,plain,
% 2.84/2.15 (((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a58)))),
% 2.84/2.15 inference(rewrite,[status(thm)],[])).
% 2.84/2.15 tff(2354,plain,
% 2.84/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a58))))),
% 2.84/2.15 inference(monotonicity,[status(thm)],[2353])).
% 2.84/2.15 tff(2355,plain,
% 2.84/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a58)))),
% 2.84/2.15 inference(transitivity,[status(thm)],[2354, 2352])).
% 2.84/2.15 tff(2356,plain,
% 2.84/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 2.84/2.15 inference(quant_inst,[status(thm)],[])).
% 2.84/2.15 tff(2357,plain,
% 2.84/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a58))),
% 2.84/2.15 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 2.84/2.15 tff(2358,plain,
% 2.84/2.15 ($false),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2357, 104, 476, 37, 2145, 2317, 468, 13, 12, 734, 2351, 2350])).
% 2.84/2.15 tff(2359,plain,(hskp0 | c0_1(a58) | c3_1(a15) | c2_1(a2) | c3_1(a2) | c1_1(a58) | c2_1(a38) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.84/2.15 tff(2360,plain,
% 2.84/2.15 (hskp0),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2359, 13, 468, 37, 12, 26, 474, 48])).
% 2.84/2.15 tff(2361,plain,
% 2.84/2.15 (~c3_1(a1)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[117, 2360])).
% 2.84/2.15 tff(2362,plain,
% 2.84/2.15 (c2_1(a1)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[128, 2360])).
% 2.84/2.15 tff(2363,plain,
% 2.84/2.15 (c1_1(a1)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[139, 2360])).
% 2.84/2.15 tff(2364,plain,
% 2.84/2.15 (hskp6),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[180, 2363, 2362, 2361])).
% 2.84/2.15 tff(2365,plain,
% 2.84/2.15 (~c1_1(a13)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[192, 2364])).
% 2.84/2.15 tff(2366,plain,
% 2.84/2.15 (~c3_1(a13)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[186, 2364])).
% 2.84/2.15 tff(2367,plain,
% 2.84/2.15 (~c0_1(a13)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[198, 2364])).
% 2.84/2.15 tff(2368,plain,
% 2.84/2.15 (~c2_1(a13)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[350, 14, 2362, 2361, 2363, 13, 12])).
% 2.84/2.15 tff(2369,plain,
% 2.84/2.15 (~c2_1(a58)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[453, 2368, 2367, 2366, 26, 2365, 48, 37, 14, 13, 12])).
% 2.84/2.15 tff(2370,plain,
% 2.84/2.15 (~hskp24),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[466, 2369])).
% 2.84/2.15 tff(2371,plain,
% 2.84/2.15 (~hskp21),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2296, 2265, 2185, 37, 26, 474, 13, 12, 14])).
% 2.84/2.15 tff(2372,plain,
% 2.84/2.15 (hskp20),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[723, 2371, 780, 2265])).
% 2.84/2.15 tff(2373,plain,
% 2.84/2.15 (c3_1(a37)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[555, 2372])).
% 2.84/2.15 tff(2374,plain,
% 2.84/2.15 (c1_1(a37)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[566, 2372])).
% 2.84/2.15 tff(2375,plain,
% 2.84/2.15 (~c2_1(a37)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[571, 104, 568, 48, 2374, 2373, 10])).
% 2.84/2.15 tff(2376,plain,
% 2.84/2.15 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.84/2.15 inference(rewrite,[status(thm)],[])).
% 2.84/2.15 tff(2377,plain,
% 2.84/2.15 ((hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))) <=> (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.84/2.15 inference(rewrite,[status(thm)],[])).
% 2.84/2.15 tff(2378,plain,
% 2.84/2.15 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))))),
% 2.84/2.15 inference(monotonicity,[status(thm)],[2377])).
% 2.84/2.15 tff(2379,plain,
% 2.84/2.15 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.84/2.15 inference(transitivity,[status(thm)],[2378, 2376])).
% 2.84/2.15 tff(2380,plain,
% 2.84/2.15 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.84/2.15 inference(quant_inst,[status(thm)],[])).
% 2.84/2.15 tff(2381,plain,
% 2.84/2.15 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 2.84/2.15 inference(modus_ponens,[status(thm)],[2380, 2379])).
% 2.84/2.15 tff(2382,plain,
% 2.84/2.15 (hskp9),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[2381, 104, 2374, 2373, 2145, 2317, 468, 890, 2375])).
% 2.84/2.15 tff(2383,plain,
% 2.84/2.15 (~c3_1(a16)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[902, 2382])).
% 2.84/2.15 tff(2384,plain,
% 2.84/2.15 (c1_1(a16)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[913, 2382])).
% 2.84/2.15 tff(2385,plain,
% 2.84/2.15 (c0_1(a16)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[924, 2382])).
% 2.84/2.15 tff(2386,plain,
% 2.84/2.15 (hskp10),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[931, 104, 2371, 2385, 2384, 2383, 876])).
% 2.84/2.15 tff(2387,plain,
% 2.84/2.15 (~c1_1(a18)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[937, 2386])).
% 2.84/2.15 tff(2388,plain,
% 2.84/2.15 (c3_1(a18)),
% 2.84/2.15 inference(unit_resolution,[status(thm)],[1037, 2386])).
% 2.84/2.15 tff(2389,plain,
% 2.84/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a18) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a18) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a58))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2390,plain,
% 2.84/2.16 (((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a58) | c0_1(a58) | c3_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a18) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a58))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2391,plain,
% 2.84/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a18) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a58)))),
% 2.84/2.16 inference(monotonicity,[status(thm)],[2390])).
% 2.84/2.16 tff(2392,plain,
% 2.84/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a18) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a58))),
% 2.84/2.16 inference(transitivity,[status(thm)],[2391, 2389])).
% 2.84/2.16 tff(2393,plain,
% 2.84/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a58) | c0_1(a58) | c3_1(a58))),
% 2.84/2.16 inference(quant_inst,[status(thm)],[])).
% 2.84/2.16 tff(2394,plain,
% 2.84/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a18) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a58)),
% 2.84/2.16 inference(modus_ponens,[status(thm)],[2393, 2392])).
% 2.84/2.16 tff(2395,plain,
% 2.84/2.16 (~c2_1(a18)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2394, 104, 780, 2388, 37, 2387, 2365, 2366, 362, 2368, 2265])).
% 2.84/2.16 tff(2396,plain,
% 2.84/2.16 (~c0_1(a37)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[685, 2372])).
% 2.84/2.16 tff(2397,plain,
% 2.84/2.16 (hskp12),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1154, 104, 2373, 2385, 2384, 2396, 2383, 987, 2375])).
% 2.84/2.16 tff(2398,plain,
% 2.84/2.16 (~c3_1(a20)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[999, 2397])).
% 2.84/2.16 tff(2399,plain,
% 2.84/2.16 (~c1_1(a20)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1005, 2397])).
% 2.84/2.16 tff(2400,plain,
% 2.84/2.16 (c2_1(a20)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1016, 2397])).
% 2.84/2.16 tff(2401,plain,
% 2.84/2.16 (hskp5),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1023, 104, 2400, 2399, 2398, 2367, 2366, 290, 2368])).
% 2.84/2.16 tff(2402,plain,
% 2.84/2.16 (~c2_1(a11)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[306, 2401])).
% 2.84/2.16 tff(2403,plain,
% 2.84/2.16 (~c1_1(a11)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[312, 2401])).
% 2.84/2.16 tff(2404,plain,
% 2.84/2.16 (~c0_1(a18)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[943, 2386])).
% 2.84/2.16 tff(2405,plain,
% 2.84/2.16 (c0_1(a11)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[323, 2401])).
% 2.84/2.16 tff(2406,plain,
% 2.84/2.16 ($false),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1044, 104, 2388, 2405, 2404, 2387, 2403, 2402, 751, 2395])).
% 2.84/2.16 tff(2407,plain,(c3_1(a58) | c2_1(a58) | c0_1(a58) | c3_1(a15) | hskp24 | hskp3 | c1_1(a58) | c2_1(a38) | c2_1(a2) | c3_1(a2) | c0_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.16 tff(2408,plain,
% 2.84/2.16 (c3_1(a58)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2407, 2369, 37, 468, 2370, 48, 26, 474, 13, 12, 14])).
% 2.84/2.16 tff(2409,plain,
% 2.84/2.16 (c3_1(a58)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2407, 780, 37, 468, 568, 48, 26, 474, 13, 12, 14])).
% 2.84/2.16 tff(2410,assumption,(c3_1(a58)), introduced(assumption)).
% 2.84/2.16 tff(2411,plain,
% 2.84/2.16 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2412,plain,
% 2.84/2.16 ((hskp21 | hskp20 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c2_1(a13)) <=> (hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2413,plain,
% 2.84/2.16 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13)))),
% 2.84/2.16 inference(monotonicity,[status(thm)],[2412])).
% 2.84/2.16 tff(2414,plain,
% 2.84/2.16 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 2.84/2.16 inference(transitivity,[status(thm)],[2413, 2411])).
% 2.84/2.16 tff(2415,plain,
% 2.84/2.16 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c2_1(a13))),
% 2.84/2.16 inference(quant_inst,[status(thm)],[])).
% 2.84/2.16 tff(2416,plain,
% 2.84/2.16 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13)),
% 2.84/2.16 inference(modus_ponens,[status(thm)],[2415, 2414])).
% 2.84/2.16 tff(2417,plain,
% 2.84/2.16 (hskp21 | hskp20 | c2_1(a13)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2416, 104, 240, 239, 708])).
% 2.84/2.16 tff(2418,plain,
% 2.84/2.16 (hskp20),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2417, 811, 352])).
% 2.84/2.16 tff(2419,plain,
% 2.84/2.16 (c3_1(a37)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[555, 2418])).
% 2.84/2.16 tff(2420,plain,
% 2.84/2.16 (c1_1(a37)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[566, 2418])).
% 2.84/2.16 tff(2421,plain,
% 2.84/2.16 (~c2_1(a37)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[571, 104, 568, 48, 2420, 2419, 10])).
% 2.84/2.16 tff(2422,plain,
% 2.84/2.16 (hskp9),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2381, 104, 2420, 2419, 2156, 1845, 468, 890, 2421])).
% 2.84/2.16 tff(2423,plain,
% 2.84/2.16 (~c3_1(a16)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[902, 2422])).
% 2.84/2.16 tff(2424,plain,
% 2.84/2.16 (c1_1(a16)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[913, 2422])).
% 2.84/2.16 tff(2425,plain,
% 2.84/2.16 (c0_1(a16)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[924, 2422])).
% 2.84/2.16 tff(2426,plain,
% 2.84/2.16 (hskp10),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[931, 104, 811, 2425, 2424, 2423, 876])).
% 2.84/2.16 tff(2427,plain,
% 2.84/2.16 (~c1_1(a18)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[937, 2426])).
% 2.84/2.16 tff(2428,plain,
% 2.84/2.16 (~c0_1(a18)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[943, 2426])).
% 2.84/2.16 tff(2429,plain,
% 2.84/2.16 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c2_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c2_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a58)))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2430,plain,
% 2.84/2.16 ((hskp2 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (hskp2 | c2_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a58)))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2431,plain,
% 2.84/2.16 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c2_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a58))))),
% 2.84/2.16 inference(monotonicity,[status(thm)],[2430])).
% 2.84/2.16 tff(2432,plain,
% 2.84/2.16 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c2_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a58)))),
% 2.84/2.16 inference(transitivity,[status(thm)],[2431, 2429])).
% 2.84/2.16 tff(2433,plain,
% 2.84/2.16 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 2.84/2.16 inference(quant_inst,[status(thm)],[])).
% 2.84/2.16 tff(2434,plain,
% 2.84/2.16 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c2_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a58))),
% 2.84/2.16 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 2.84/2.16 tff(2435,plain,
% 2.84/2.16 (~c2_1(a18)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2434, 104, 1119, 780, 26, 2428, 2427, 1545, 2410])).
% 2.84/2.16 tff(2436,plain,
% 2.84/2.16 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a58) | c0_1(a58) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a58) | c0_1(a58) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a58)))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2437,plain,
% 2.84/2.16 ((hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (hskp12 | c2_1(a58) | c0_1(a58) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a58)))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2438,plain,
% 2.84/2.16 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a58) | c0_1(a58) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a58))))),
% 2.84/2.16 inference(monotonicity,[status(thm)],[2437])).
% 2.84/2.16 tff(2439,plain,
% 2.84/2.16 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a58) | c0_1(a58) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a58)))),
% 2.84/2.16 inference(transitivity,[status(thm)],[2438, 2436])).
% 2.84/2.16 tff(2440,plain,
% 2.84/2.16 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 2.84/2.16 inference(quant_inst,[status(thm)],[])).
% 2.84/2.16 tff(2441,plain,
% 2.84/2.16 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a58) | c0_1(a58) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a58))),
% 2.84/2.16 inference(modus_ponens,[status(thm)],[2440, 2439])).
% 2.84/2.16 tff(2442,plain,
% 2.84/2.16 (hskp12),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2441, 104, 780, 2425, 2424, 37, 2423, 987, 2410])).
% 2.84/2.16 tff(2443,plain,
% 2.84/2.16 (~c3_1(a20)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[999, 2442])).
% 2.84/2.16 tff(2444,plain,
% 2.84/2.16 (~c1_1(a20)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1005, 2442])).
% 2.84/2.16 tff(2445,plain,
% 2.84/2.16 (c2_1(a20)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1016, 2442])).
% 2.84/2.16 tff(2446,plain,
% 2.84/2.16 (hskp5),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1023, 104, 2445, 2444, 2443, 241, 239, 290, 352])).
% 2.84/2.16 tff(2447,plain,
% 2.84/2.16 (~c2_1(a11)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[306, 2446])).
% 2.84/2.16 tff(2448,plain,
% 2.84/2.16 (~c1_1(a11)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[312, 2446])).
% 2.84/2.16 tff(2449,plain,
% 2.84/2.16 (c0_1(a11)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[323, 2446])).
% 2.84/2.16 tff(2450,plain,
% 2.84/2.16 (c3_1(a18)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1037, 2426])).
% 2.84/2.16 tff(2451,plain,
% 2.84/2.16 ($false),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1938, 104, 2450, 2449, 37, 26, 2428, 2448, 2447, 751, 2410, 2435])).
% 2.84/2.16 tff(2452,plain,(hskp21 | c0_1(a58) | c1_1(a58) | (~c3_1(a58)) | hskp2 | c2_1(a58) | c0_1(a13) | c3_1(a13) | c2_1(a13) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | hskp24 | hskp3 | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.16 tff(2453,plain,
% 2.84/2.16 (hskp21),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2452, 2409, 26, 37, 1119, 780, 2367, 2366, 2368, 2145, 2317, 468, 568, 48, 2365])).
% 2.84/2.16 tff(2454,plain,
% 2.84/2.16 (c0_1(a38)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[646, 2453])).
% 2.84/2.16 tff(2455,plain,
% 2.84/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a58) | c1_1(a58) | c2_1(a38) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a58) | c1_1(a58) | c2_1(a38) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58)))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2456,plain,
% 2.84/2.16 (((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a38) | (~c3_1(a38)) | (~c0_1(a38)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | c1_1(a58) | c2_1(a38) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58)))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2457,plain,
% 2.84/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a38) | (~c3_1(a38)) | (~c0_1(a38)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a58) | c1_1(a58) | c2_1(a38) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58))))),
% 2.84/2.16 inference(monotonicity,[status(thm)],[2456])).
% 2.84/2.16 tff(2458,plain,
% 2.84/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a38) | (~c3_1(a38)) | (~c0_1(a38)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a58) | c1_1(a58) | c2_1(a38) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58)))),
% 2.84/2.16 inference(transitivity,[status(thm)],[2457, 2455])).
% 2.84/2.16 tff(2459,plain,
% 2.84/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a38) | (~c3_1(a38)) | (~c0_1(a38)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))),
% 2.84/2.16 inference(quant_inst,[status(thm)],[])).
% 2.84/2.16 tff(2460,plain,
% 2.84/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a58) | c1_1(a58) | c2_1(a38) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58))),
% 2.84/2.16 inference(modus_ponens,[status(thm)],[2459, 2458])).
% 2.84/2.16 tff(2461,plain,
% 2.84/2.16 ((~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58))),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2460, 104, 780, 26, 474, 2145, 2317, 468, 279])).
% 2.84/2.16 tff(2462,plain,
% 2.84/2.16 (~c3_1(a38)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2461, 2454, 2409])).
% 2.84/2.16 tff(2463,plain,
% 2.84/2.16 (c1_1(a38)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[657, 2453])).
% 2.84/2.16 tff(2464,plain,
% 2.84/2.16 (hskp27),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[678, 2453, 474, 13, 12, 14])).
% 2.84/2.16 tff(2465,plain,
% 2.84/2.16 (c3_1(a12)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[605, 2464])).
% 2.84/2.16 tff(2466,plain,
% 2.84/2.16 (c1_1(a12)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[616, 2464])).
% 2.84/2.16 tff(2467,plain,
% 2.84/2.16 (c0_1(a12)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1192, 2464])).
% 2.84/2.16 tff(2468,plain,
% 2.84/2.16 ($false),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2294, 104, 2185, 2467, 2466, 2465, 2454, 2463, 2283, 2462])).
% 2.84/2.16 tff(2469,plain,(c2_1(a58) | c1_1(a58) | c2_1(a38) | c3_1(a15) | c2_1(a2) | c3_1(a2) | c0_1(a2) | c0_1(a58) | hskp2 | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.84/2.16 tff(2470,plain,
% 2.84/2.16 (hskp2),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2469, 2370, 474, 468, 13, 12, 14, 37, 2369, 26, 48])).
% 2.84/2.16 tff(2471,plain,
% 2.84/2.16 (~c2_1(a3)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[206, 2470])).
% 2.84/2.16 tff(2472,plain,
% 2.84/2.16 (c3_1(a3)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[217, 2470])).
% 2.84/2.16 tff(2473,plain,
% 2.84/2.16 (c1_1(a3)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[228, 2470])).
% 2.84/2.16 tff(2474,plain,
% 2.84/2.16 (hskp9),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2324, 104, 2473, 2472, 2145, 2317, 468, 2471, 890])).
% 2.84/2.16 tff(2475,plain,
% 2.84/2.16 (~c3_1(a16)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[902, 2474])).
% 2.84/2.16 tff(2476,plain,
% 2.84/2.16 (c1_1(a16)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[913, 2474])).
% 2.84/2.16 tff(2477,plain,
% 2.84/2.16 (c0_1(a16)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[924, 2474])).
% 2.84/2.16 tff(2478,plain,
% 2.84/2.16 (hskp12),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2441, 104, 2369, 2477, 2476, 37, 2475, 987, 2408])).
% 2.84/2.16 tff(2479,plain,
% 2.84/2.16 (~c3_1(a20)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[999, 2478])).
% 2.84/2.16 tff(2480,plain,
% 2.84/2.16 (~c1_1(a20)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1005, 2478])).
% 2.84/2.16 tff(2481,plain,
% 2.84/2.16 (c2_1(a20)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1016, 2478])).
% 2.84/2.16 tff(2482,plain,
% 2.84/2.16 (hskp5),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1023, 104, 2481, 2480, 2479, 2367, 2366, 290, 2368])).
% 2.84/2.16 tff(2483,plain,
% 2.84/2.16 (~c2_1(a11)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[306, 2482])).
% 2.84/2.16 tff(2484,plain,
% 2.84/2.16 (~c1_1(a11)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[312, 2482])).
% 2.84/2.16 tff(2485,plain,
% 2.84/2.16 (c0_1(a11)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[323, 2482])).
% 2.84/2.16 tff(2486,plain,
% 2.84/2.16 ($false),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[1838, 104, 2369, 2485, 37, 26, 2484, 2483, 751, 2408])).
% 2.84/2.16 tff(2487,plain,(c0_1(a2) | c0_1(a58) | c1_1(a58) | c3_1(a15) | c2_1(a38) | c2_1(a2) | c3_1(a2) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.84/2.16 tff(2488,plain,
% 2.84/2.16 ($false),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2487, 2346, 2345, 26, 468, 474, 37, 2344, 48])).
% 2.84/2.16 tff(2489,plain,(c3_1(a15) | c1_1(a58) | c2_1(a38) | c0_1(a58) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.84/2.16 tff(2490,plain,
% 2.84/2.16 (c2_1(a38)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2489, 468, 26, 37, 48])).
% 2.84/2.16 tff(2491,plain,
% 2.84/2.16 (((~hskp21) | (~c2_1(a38))) <=> ((~hskp21) | (~c2_1(a38)))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2492,plain,
% 2.84/2.16 (((~c2_1(a38)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a38)))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2493,axiom,((~c2_1(a38)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 2.84/2.16 tff(2494,plain,
% 2.84/2.16 ((~hskp21) | (~c2_1(a38))),
% 2.84/2.16 inference(modus_ponens,[status(thm)],[2493, 2492])).
% 2.84/2.16 tff(2495,plain,
% 2.84/2.16 ((~hskp21) | (~c2_1(a38))),
% 2.84/2.16 inference(modus_ponens,[status(thm)],[2494, 2491])).
% 2.84/2.16 tff(2496,plain,
% 2.84/2.16 (~hskp21),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2495, 2490])).
% 2.84/2.16 tff(2497,plain,
% 2.84/2.16 (hskp13),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[825, 2496, 473])).
% 2.84/2.16 tff(2498,plain,
% 2.84/2.16 (c0_1(a21)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[853, 2497])).
% 2.84/2.16 tff(2499,plain,
% 2.84/2.16 (~c3_1(a21)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[831, 2497])).
% 2.84/2.16 tff(2500,plain,
% 2.84/2.16 (c2_1(a21)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[842, 2497])).
% 2.84/2.16 tff(2501,assumption,(c1_1(a13)), introduced(assumption)).
% 2.84/2.16 tff(2502,plain,
% 2.84/2.16 (~hskp6),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[192, 2501])).
% 2.84/2.16 tff(2503,plain,
% 2.84/2.16 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a13) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a13) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2504,plain,
% 2.84/2.16 ((hskp6 | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a13)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13))) <=> (hskp6 | c0_1(a13) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2505,plain,
% 2.84/2.16 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a13)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a13) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13))))),
% 2.84/2.16 inference(monotonicity,[status(thm)],[2504])).
% 2.84/2.16 tff(2506,plain,
% 2.84/2.16 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a13)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a13) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 2.84/2.16 inference(transitivity,[status(thm)],[2505, 2503])).
% 2.84/2.16 tff(2507,plain,
% 2.84/2.16 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a13)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)))),
% 2.84/2.16 inference(quant_inst,[status(thm)],[])).
% 2.84/2.16 tff(2508,plain,
% 2.84/2.16 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a13) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13))),
% 2.84/2.16 inference(modus_ponens,[status(thm)],[2507, 2506])).
% 2.84/2.16 tff(2509,plain,
% 2.84/2.16 (hskp6 | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13))),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2508, 104, 239, 171])).
% 2.84/2.16 tff(2510,plain,
% 2.84/2.16 (~c2_1(a13)),
% 2.84/2.16 inference(unit_resolution,[status(thm)],[2509, 2502, 241, 2501])).
% 2.84/2.16 tff(2511,assumption,(~c3_1(a21)), introduced(assumption)).
% 2.84/2.16 tff(2512,assumption,(c2_1(a21)), introduced(assumption)).
% 2.84/2.16 tff(2513,assumption,(c0_1(a21)), introduced(assumption)).
% 2.84/2.16 tff(2514,plain,
% 2.84/2.16 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2515,plain,
% 2.84/2.16 ((hskp6 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21))) <=> (hskp6 | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.84/2.16 inference(rewrite,[status(thm)],[])).
% 2.84/2.16 tff(2516,plain,
% 2.84/2.16 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21))))),
% 2.84/2.17 inference(monotonicity,[status(thm)],[2515])).
% 2.84/2.17 tff(2517,plain,
% 2.84/2.17 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.84/2.17 inference(transitivity,[status(thm)],[2516, 2514])).
% 2.84/2.17 tff(2518,plain,
% 2.84/2.17 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))),
% 2.84/2.17 inference(quant_inst,[status(thm)],[])).
% 2.84/2.17 tff(2519,plain,
% 2.84/2.17 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21))),
% 2.84/2.17 inference(modus_ponens,[status(thm)],[2518, 2517])).
% 2.84/2.17 tff(2520,plain,
% 2.84/2.17 (hskp6 | (~c1_1(a21))),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2519, 104, 2513, 2512, 2511, 150])).
% 2.84/2.17 tff(2521,plain,
% 2.84/2.17 (~c1_1(a21)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2520, 2502])).
% 2.84/2.17 tff(2522,plain,
% 2.84/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))),
% 2.84/2.17 inference(rewrite,[status(thm)],[])).
% 2.84/2.17 tff(2523,plain,
% 2.84/2.17 (((~ndr1_0) | c3_1(a13) | c2_1(a13) | (~c1_1(a13)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))),
% 2.84/2.17 inference(rewrite,[status(thm)],[])).
% 2.84/2.17 tff(2524,plain,
% 2.84/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a13) | c2_1(a13) | (~c1_1(a13)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21))))),
% 2.84/2.17 inference(monotonicity,[status(thm)],[2523])).
% 2.84/2.17 tff(2525,plain,
% 2.84/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a13) | c2_1(a13) | (~c1_1(a13)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))),
% 2.84/2.17 inference(transitivity,[status(thm)],[2524, 2522])).
% 2.84/2.17 tff(2526,plain,
% 2.84/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a13) | c2_1(a13) | (~c1_1(a13)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 2.84/2.17 inference(quant_inst,[status(thm)],[])).
% 2.84/2.17 tff(2527,plain,
% 2.84/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21))),
% 2.84/2.17 inference(modus_ponens,[status(thm)],[2526, 2525])).
% 2.84/2.17 tff(2528,plain,
% 2.84/2.17 ((~c1_1(a13)) | c2_1(a13) | c1_1(a21)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2527, 104, 780, 2512, 37, 26, 2511, 239, 380])).
% 2.84/2.17 tff(2529,plain,
% 2.84/2.17 ($false),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2528, 2521, 2510, 2501])).
% 2.84/2.17 tff(2530,plain,((~c1_1(a13)) | c2_1(a58) | (~c2_1(a21)) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c3_1(a13) | (~c0_1(a21)) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.17 tff(2531,plain,
% 2.84/2.17 (~c1_1(a13)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2530, 2500, 472, 37, 26, 2499, 239, 2498, 241])).
% 2.84/2.17 tff(2532,plain,
% 2.84/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 2.84/2.17 inference(rewrite,[status(thm)],[])).
% 2.84/2.17 tff(2533,plain,
% 2.84/2.17 (((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 2.84/2.17 inference(rewrite,[status(thm)],[])).
% 2.84/2.17 tff(2534,plain,
% 2.84/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13))))),
% 2.84/2.17 inference(monotonicity,[status(thm)],[2533])).
% 2.84/2.17 tff(2535,plain,
% 2.84/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 2.84/2.17 inference(transitivity,[status(thm)],[2534, 2532])).
% 2.84/2.17 tff(2536,plain,
% 2.84/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 2.84/2.17 inference(quant_inst,[status(thm)],[])).
% 2.84/2.17 tff(2537,plain,
% 2.84/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13))),
% 2.84/2.17 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 2.84/2.17 tff(2538,plain,
% 2.84/2.17 ((~c1_1(a15)) | c2_1(a15) | c1_1(a13) | (~c2_1(a13))),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2537, 104, 472, 37, 26, 468, 239, 380])).
% 2.84/2.17 tff(2539,plain,
% 2.84/2.17 (~c2_1(a13)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2538, 2156, 240, 752])).
% 2.84/2.17 tff(2540,plain,
% 2.84/2.17 (hskp21 | hskp20 | c1_1(a13) | c2_1(a13)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2416, 104, 239, 708])).
% 2.84/2.17 tff(2541,plain,
% 2.84/2.17 (hskp20),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2540, 2539, 2496, 240])).
% 2.84/2.17 tff(2542,plain,
% 2.84/2.17 (c3_1(a37)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[555, 2541])).
% 2.84/2.17 tff(2543,plain,
% 2.84/2.17 (c1_1(a37)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[566, 2541])).
% 2.84/2.17 tff(2544,plain,
% 2.84/2.17 (~c2_1(a37)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[571, 104, 473, 48, 2543, 2542, 10])).
% 2.84/2.17 tff(2545,plain,
% 2.84/2.17 ((~c1_1(a15)) | c2_1(a15) | c1_1(a21)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2215, 104, 472, 2500, 37, 26, 2499, 468, 380])).
% 2.84/2.17 tff(2546,plain,
% 2.84/2.17 (c1_1(a21)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2545, 2156, 752])).
% 2.84/2.17 tff(2547,plain,
% 2.84/2.17 (~c0_1(a37)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[685, 2541])).
% 2.84/2.17 tff(2548,plain,
% 2.84/2.17 ($false),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2312, 104, 2542, 2500, 2547, 2499, 2156, 752, 468, 734, 2546, 2544])).
% 2.84/2.17 tff(2549,plain,((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | hskp3 | c1_1(a13) | c3_1(a13) | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.17 tff(2550,plain,
% 2.84/2.17 (~c1_1(a15)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2549, 752, 468, 48, 240, 239, 37, 26])).
% 2.84/2.17 tff(2551,plain,
% 2.84/2.17 (hskp20 | c1_1(a15) | c2_1(a15)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[801, 104, 2496, 468, 708])).
% 2.84/2.17 tff(2552,plain,
% 2.84/2.17 (hskp20),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2551, 475, 752])).
% 2.84/2.17 tff(2553,assumption,(hskp0), introduced(assumption)).
% 2.84/2.17 tff(2554,plain,
% 2.84/2.17 (~c3_1(a1)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[117, 2553])).
% 2.84/2.17 tff(2555,plain,
% 2.84/2.17 (c1_1(a1)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[139, 2553])).
% 2.84/2.17 tff(2556,plain,
% 2.84/2.17 (c2_1(a1)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[128, 2553])).
% 2.84/2.17 tff(2557,plain,
% 2.84/2.17 ($false),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[1170, 2556, 2555, 468, 811, 12, 13, 752, 14, 475, 2554, 568, 48])).
% 2.84/2.17 tff(2558,plain,((~hskp0) | c3_1(a15) | hskp21 | c3_1(a2) | c2_1(a2) | c2_1(a15) | c0_1(a2) | c1_1(a15) | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.84/2.17 tff(2559,plain,
% 2.84/2.17 (~hskp0),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2558, 475, 2496, 12, 13, 752, 14, 468, 473, 48])).
% 2.84/2.17 tff(2560,plain,
% 2.84/2.17 (~hskp28),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[529, 2559, 48, 37, 26])).
% 2.84/2.17 tff(2561,plain,
% 2.84/2.17 ($false),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[697, 2560, 2559, 12, 13, 14, 2552])).
% 2.84/2.17 tff(2562,plain,(c1_1(a15) | c3_1(a2) | c2_1(a2) | c0_1(a2) | hskp3 | c0_1(a58) | c1_1(a58) | c2_1(a15) | c3_1(a15)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.17 tff(2563,plain,
% 2.84/2.17 (c0_1(a2)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2562, 2550, 13, 12, 48, 37, 26, 752, 468])).
% 2.84/2.17 tff(2564,plain,
% 2.84/2.17 (~hskp1),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[268, 2563])).
% 2.84/2.17 tff(2565,plain,
% 2.84/2.17 (hskp0),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[590, 2564, 48, 37, 26])).
% 2.84/2.17 tff(2566,plain,
% 2.84/2.17 (c1_1(a1)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[139, 2565])).
% 2.84/2.17 tff(2567,plain,
% 2.84/2.17 (c2_1(a1)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[128, 2565])).
% 2.84/2.17 tff(2568,plain,
% 2.84/2.17 (~c3_1(a1)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[117, 2565])).
% 2.84/2.17 tff(2569,plain,
% 2.84/2.17 ($false),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[1046, 2568, 2567, 468, 2496, 752, 2550, 48, 2564, 2566, 473])).
% 2.84/2.17 tff(2570,plain,(c2_1(a15) | c3_1(a15) | hskp3 | c0_1(a58) | c1_1(a58) | c2_1(a2) | c3_1(a2) | c1_1(a13) | c3_1(a13)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.17 tff(2571,plain,
% 2.84/2.17 (c2_1(a15)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2570, 240, 48, 37, 26, 13, 12, 468, 239])).
% 2.84/2.17 tff(2572,plain,
% 2.84/2.17 ($false),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[1940, 2556, 2555, 26, 37, 468, 12, 13, 1845, 475, 2554])).
% 2.84/2.17 tff(2573,plain,((~hskp0) | c1_1(a58) | c0_1(a58) | c3_1(a15) | c3_1(a2) | c2_1(a2) | (~c2_1(a15)) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.17 tff(2574,plain,
% 2.84/2.17 (~hskp0),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2573, 475, 37, 468, 12, 13, 1845, 26])).
% 2.84/2.17 tff(2575,plain,
% 2.84/2.17 (~hskp28),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[529, 2574, 48, 37, 26])).
% 2.84/2.17 tff(2576,plain,
% 2.84/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)))),
% 2.84/2.17 inference(rewrite,[status(thm)],[])).
% 2.84/2.17 tff(2577,plain,
% 2.84/2.17 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)))),
% 2.84/2.17 inference(rewrite,[status(thm)],[])).
% 2.84/2.17 tff(2578,plain,
% 2.84/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2))))),
% 2.84/2.17 inference(monotonicity,[status(thm)],[2577])).
% 2.84/2.17 tff(2579,plain,
% 2.84/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)))),
% 2.84/2.17 inference(transitivity,[status(thm)],[2578, 2576])).
% 2.84/2.17 tff(2580,plain,
% 2.84/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 2.84/2.17 inference(quant_inst,[status(thm)],[])).
% 2.84/2.17 tff(2581,plain,
% 2.84/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2))),
% 2.84/2.17 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 2.84/2.17 tff(2582,plain,
% 2.84/2.17 (c1_1(a15) | (~c2_1(a15)) | c2_1(a2) | (~c1_1(a2))),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2581, 104, 472, 37, 26, 468, 12, 380])).
% 2.84/2.17 tff(2583,plain,
% 2.84/2.17 (~c1_1(a2)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2582, 475, 13, 1845])).
% 2.84/2.17 tff(2584,plain,
% 2.84/2.17 (hskp20),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[715, 2583, 2496, 13])).
% 2.84/2.17 tff(2585,plain,
% 2.84/2.17 (c3_1(a37)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[555, 2584])).
% 2.84/2.17 tff(2586,plain,
% 2.84/2.17 (c1_1(a37)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[566, 2584])).
% 2.84/2.17 tff(2587,plain,
% 2.84/2.17 (~c2_1(a37)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[571, 104, 473, 48, 2586, 2585, 10])).
% 2.84/2.17 tff(2588,plain,
% 2.84/2.17 (hskp28 | hskp0),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[585, 104, 2586, 2585, 582, 2587])).
% 2.84/2.17 tff(2589,plain,
% 2.84/2.17 ($false),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2588, 2575, 2574])).
% 2.84/2.17 tff(2590,plain,(c1_1(a15) | hskp3 | c0_1(a58) | c1_1(a58) | c3_1(a15) | c3_1(a2) | c2_1(a2) | (~c2_1(a15))), inference(lemma,lemma(discharge,[]))).
% 2.84/2.17 tff(2591,plain,
% 2.84/2.17 (c1_1(a15)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2590, 2571, 37, 26, 468, 12, 13, 48])).
% 2.84/2.17 tff(2592,plain,
% 2.84/2.17 (hskp1),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2342, 2591, 468, 2571, 48, 37, 26])).
% 2.84/2.17 tff(2593,plain,
% 2.84/2.17 (~c0_1(a2)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[268, 2592])).
% 2.84/2.17 tff(2594,plain,
% 2.84/2.17 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 2.84/2.17 inference(rewrite,[status(thm)],[])).
% 2.84/2.17 tff(2595,plain,
% 2.84/2.17 ((hskp3 | hskp0 | (~ndr1_0) | c1_1(a13) | c0_1(a13) | (~c2_1(a13))) <=> (hskp3 | hskp0 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 2.84/2.17 inference(rewrite,[status(thm)],[])).
% 2.84/2.17 tff(2596,plain,
% 2.84/2.17 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a13) | c0_1(a13) | (~c2_1(a13)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13))))),
% 2.84/2.17 inference(monotonicity,[status(thm)],[2595])).
% 2.84/2.17 tff(2597,plain,
% 2.84/2.17 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a13) | c0_1(a13) | (~c2_1(a13)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 2.84/2.17 inference(transitivity,[status(thm)],[2596, 2594])).
% 2.84/2.17 tff(2598,plain,
% 2.84/2.17 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a13) | c0_1(a13) | (~c2_1(a13)))),
% 2.84/2.17 inference(quant_inst,[status(thm)],[])).
% 2.84/2.17 tff(2599,plain,
% 2.84/2.17 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13))),
% 2.84/2.17 inference(modus_ponens,[status(thm)],[2598, 2597])).
% 2.84/2.17 tff(2600,plain,
% 2.84/2.17 (hskp0 | c1_1(a13) | (~c2_1(a13))),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2599, 104, 48, 241, 69])).
% 2.84/2.17 tff(2601,plain,
% 2.84/2.17 (~c2_1(a13)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2600, 11, 240])).
% 2.84/2.17 tff(2602,plain,
% 2.84/2.17 ($false),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[697, 530, 11, 12, 13, 14, 680])).
% 2.84/2.17 tff(2603,plain,(hskp0 | c3_1(a2) | c2_1(a2) | c0_1(a2) | (~hskp20) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.17 tff(2604,plain,
% 2.84/2.17 (~hskp20),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2603, 11, 13, 12, 14, 48, 37, 26])).
% 2.84/2.17 tff(2605,plain,
% 2.84/2.17 ($false),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2540, 2604, 2601, 811, 240])).
% 2.84/2.17 tff(2606,plain,(hskp0 | hskp21 | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | c0_1(a2) | hskp3 | c0_1(a58) | c1_1(a58) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.17 tff(2607,plain,
% 2.84/2.17 (hskp0),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2606, 240, 2496, 239, 13, 12, 2593, 48, 37, 26, 241])).
% 2.84/2.17 tff(2608,plain,
% 2.84/2.17 (~c3_1(a1)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[117, 2607])).
% 2.84/2.17 tff(2609,plain,
% 2.84/2.17 (c2_1(a1)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[128, 2607])).
% 2.84/2.17 tff(2610,plain,
% 2.84/2.17 (c1_1(a1)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[139, 2607])).
% 2.84/2.17 tff(2611,plain,
% 2.84/2.17 (~c2_1(a13)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[350, 2609, 2593, 2608, 2610, 13, 12])).
% 2.84/2.17 tff(2612,plain,
% 2.84/2.17 (hskp20),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2540, 2611, 2496, 240])).
% 2.84/2.17 tff(2613,plain,
% 2.84/2.17 (c3_1(a37)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[555, 2612])).
% 2.84/2.17 tff(2614,plain,
% 2.84/2.17 (c1_1(a37)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[566, 2612])).
% 2.84/2.17 tff(2615,plain,
% 2.84/2.17 (~c2_1(a37)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[571, 104, 473, 48, 2614, 2613, 10])).
% 2.84/2.17 tff(2616,plain,
% 2.84/2.17 (hskp9),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2381, 104, 2614, 2613, 2591, 2571, 468, 890, 2615])).
% 2.84/2.17 tff(2617,plain,
% 2.84/2.17 (~c3_1(a16)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[902, 2616])).
% 2.84/2.17 tff(2618,plain,
% 2.84/2.17 (~c0_1(a37)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[685, 2612])).
% 2.84/2.17 tff(2619,plain,
% 2.84/2.17 (c1_1(a16)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[913, 2616])).
% 2.84/2.17 tff(2620,plain,
% 2.84/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))),
% 2.84/2.17 inference(rewrite,[status(thm)],[])).
% 2.84/2.17 tff(2621,plain,
% 2.84/2.17 (((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37))) <=> (c0_1(a37) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))),
% 2.84/2.17 inference(rewrite,[status(thm)],[])).
% 2.84/2.17 tff(2622,plain,
% 2.84/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37))))),
% 2.84/2.17 inference(monotonicity,[status(thm)],[2621])).
% 2.84/2.17 tff(2623,plain,
% 2.84/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))),
% 2.84/2.17 inference(transitivity,[status(thm)],[2622, 2620])).
% 2.84/2.17 tff(2624,plain,
% 2.84/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))),
% 2.84/2.17 inference(quant_inst,[status(thm)],[])).
% 2.84/2.17 tff(2625,plain,
% 2.84/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37))),
% 2.84/2.17 inference(modus_ponens,[status(thm)],[2624, 2623])).
% 2.84/2.17 tff(2626,plain,
% 2.84/2.17 (c2_1(a16)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2625, 104, 2613, 2619, 2618, 2617, 2591, 2571, 468, 734, 2615])).
% 2.84/2.17 tff(2627,plain,
% 2.84/2.17 (c0_1(a16)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[924, 2616])).
% 2.84/2.17 tff(2628,plain,
% 2.84/2.17 (hskp12),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[1154, 104, 2613, 2627, 2619, 2618, 2617, 987, 2615])).
% 2.84/2.17 tff(2629,plain,
% 2.84/2.17 (~c3_1(a20)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[999, 2628])).
% 2.84/2.17 tff(2630,plain,
% 2.84/2.17 (c2_1(a20)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[1016, 2628])).
% 2.84/2.17 tff(2631,plain,
% 2.84/2.17 (~c1_1(a20)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[1005, 2628])).
% 2.84/2.17 tff(2632,plain,
% 2.84/2.17 (~c2_1(a13)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[350, 14, 152, 151, 153, 13, 12])).
% 2.84/2.17 tff(2633,assumption,(~c3_1(a20)), introduced(assumption)).
% 2.84/2.17 tff(2634,assumption,(~c1_1(a20)), introduced(assumption)).
% 2.84/2.17 tff(2635,assumption,(c2_1(a16)), introduced(assumption)).
% 2.84/2.17 tff(2636,assumption,(~c3_1(a16)), introduced(assumption)).
% 2.84/2.17 tff(2637,assumption,(c1_1(a16)), introduced(assumption)).
% 2.84/2.17 tff(2638,assumption,(c2_1(a20)), introduced(assumption)).
% 2.84/2.17 tff(2639,plain,
% 2.84/2.17 (c0_1(a2) | (~c0_1(a20))),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[1534, 104, 2638, 2637, 2634, 2636, 13, 12, 1342, 2635])).
% 2.84/2.17 tff(2640,plain,
% 2.84/2.17 (~c0_1(a20)),
% 2.84/2.17 inference(unit_resolution,[status(thm)],[2639, 14])).
% 2.84/2.17 tff(2641,plain,
% 2.84/2.17 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | c3_1(a20) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c3_1(a20) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))),
% 2.84/2.18 inference(rewrite,[status(thm)],[])).
% 2.84/2.18 tff(2642,plain,
% 2.84/2.18 ((hskp18 | hskp3 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c2_1(a20))) <=> (hskp18 | hskp3 | c3_1(a20) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))),
% 2.84/2.18 inference(rewrite,[status(thm)],[])).
% 2.84/2.18 tff(2643,plain,
% 2.84/2.18 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | c3_1(a20) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20))))),
% 2.84/2.18 inference(monotonicity,[status(thm)],[2642])).
% 2.84/2.18 tff(2644,plain,
% 2.84/2.18 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c3_1(a20) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))),
% 2.84/2.18 inference(transitivity,[status(thm)],[2643, 2641])).
% 2.84/2.18 tff(2645,plain,
% 2.84/2.18 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)))),
% 2.84/2.18 inference(quant_inst,[status(thm)],[])).
% 2.84/2.18 tff(2646,plain,
% 2.84/2.18 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c3_1(a20) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20))),
% 2.84/2.18 inference(modus_ponens,[status(thm)],[2645, 2644])).
% 2.84/2.18 tff(2647,plain,
% 2.84/2.18 (hskp18 | c0_1(a20)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2646, 104, 48, 2638, 2633, 390])).
% 2.84/2.18 tff(2648,plain,
% 2.84/2.18 (hskp18),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2647, 2640])).
% 2.84/2.18 tff(2649,plain,
% 2.84/2.18 (~c3_1(a31)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[403, 2648])).
% 2.84/2.18 tff(2650,plain,
% 2.84/2.18 (c1_1(a31)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[414, 2648])).
% 2.84/2.18 tff(2651,plain,
% 2.84/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a31) | c1_1(a20) | c3_1(a20) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)) | (~c1_1(a31)) | c2_1(a31))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a31) | c1_1(a20) | c3_1(a20) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)) | (~c1_1(a31)) | c2_1(a31))),
% 2.84/2.18 inference(rewrite,[status(thm)],[])).
% 2.84/2.18 tff(2652,plain,
% 2.84/2.18 (((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c0_1(a13)) <=> (c3_1(a31) | c1_1(a20) | c3_1(a20) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)) | (~c1_1(a31)) | c2_1(a31))),
% 2.84/2.18 inference(rewrite,[status(thm)],[])).
% 2.84/2.18 tff(2653,plain,
% 2.84/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a31) | c1_1(a20) | c3_1(a20) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)) | (~c1_1(a31)) | c2_1(a31)))),
% 2.84/2.18 inference(monotonicity,[status(thm)],[2652])).
% 2.84/2.18 tff(2654,plain,
% 2.84/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a31) | c1_1(a20) | c3_1(a20) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)) | (~c1_1(a31)) | c2_1(a31))),
% 2.84/2.18 inference(transitivity,[status(thm)],[2653, 2651])).
% 2.84/2.18 tff(2655,plain,
% 2.84/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c0_1(a13))),
% 2.84/2.18 inference(quant_inst,[status(thm)],[])).
% 2.84/2.18 tff(2656,plain,
% 2.84/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a31) | c1_1(a20) | c3_1(a20) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)) | (~c1_1(a31)) | c2_1(a31)),
% 2.84/2.18 inference(modus_ponens,[status(thm)],[2655, 2654])).
% 2.84/2.18 tff(2657,plain,
% 2.84/2.18 (c2_1(a31)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2656, 104, 2650, 2638, 2649, 2634, 2633, 342, 293, 380, 2632])).
% 2.84/2.18 tff(2658,plain,
% 2.84/2.18 (hskp5 | c0_1(a2) | c2_1(a2)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[1164, 104, 2638, 2634, 2633, 12, 290])).
% 2.84/2.18 tff(2659,plain,
% 2.84/2.18 (hskp5),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2658, 14, 13])).
% 2.84/2.18 tff(2660,plain,
% 2.84/2.18 (~c2_1(a11)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[306, 2659])).
% 2.84/2.18 tff(2661,plain,
% 2.84/2.18 (~c1_1(a11)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[312, 2659])).
% 2.84/2.18 tff(2662,plain,
% 2.84/2.18 (c0_1(a11)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[323, 2659])).
% 2.84/2.18 tff(2663,plain,
% 2.84/2.18 (~c3_1(a11)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[438, 104, 2650, 2662, 2649, 2661, 2660, 279, 2657])).
% 2.84/2.18 tff(2664,plain,
% 2.84/2.18 (~c2_1(a58)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[453, 2632, 342, 292, 26, 293, 48, 37, 14, 13, 12])).
% 2.84/2.18 tff(2665,plain,
% 2.84/2.18 (~c3_1(a58)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[1838, 104, 2664, 2662, 37, 26, 2661, 2660, 751])).
% 2.84/2.18 tff(2666,plain,
% 2.84/2.18 (~c0_1(a31)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[444, 2648])).
% 2.84/2.18 tff(2667,plain,
% 2.84/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | c1_1(a58) | c0_1(a31) | c3_1(a31) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | c1_1(a58) | c0_1(a31) | c3_1(a31) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)) | c3_1(a58))),
% 2.84/2.18 inference(rewrite,[status(thm)],[])).
% 2.84/2.18 tff(2668,plain,
% 2.84/2.18 (((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a58) | c1_1(a58) | c3_1(a58)) <=> (c2_1(a58) | c1_1(a58) | c0_1(a31) | c3_1(a31) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)) | c3_1(a58))),
% 2.84/2.18 inference(rewrite,[status(thm)],[])).
% 2.84/2.18 tff(2669,plain,
% 2.84/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | c1_1(a58) | c0_1(a31) | c3_1(a31) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)) | c3_1(a58)))),
% 2.84/2.18 inference(monotonicity,[status(thm)],[2668])).
% 2.84/2.18 tff(2670,plain,
% 2.84/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | c1_1(a58) | c0_1(a31) | c3_1(a31) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)) | c3_1(a58))),
% 2.84/2.18 inference(transitivity,[status(thm)],[2669, 2667])).
% 2.84/2.18 tff(2671,plain,
% 2.84/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a58) | c1_1(a58) | c3_1(a58))),
% 2.84/2.18 inference(quant_inst,[status(thm)],[])).
% 2.84/2.18 tff(2672,plain,
% 2.84/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | c1_1(a58) | c0_1(a31) | c3_1(a31) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)) | c3_1(a58)),
% 2.84/2.18 inference(modus_ponens,[status(thm)],[2671, 2670])).
% 2.84/2.18 tff(2673,plain,
% 2.84/2.18 ($false),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2672, 104, 2664, 2662, 26, 2666, 2649, 2661, 341, 2665, 2663, 2657])).
% 2.84/2.18 tff(2674,plain,(c0_1(a2) | c1_1(a58) | (~c2_1(a20)) | c1_1(a20) | c3_1(a20) | c0_1(a58) | hskp3 | c2_1(a2) | c3_1(a2) | (~c1_1(a16)) | c3_1(a16) | (~c2_1(a16)) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1))), inference(lemma,lemma(discharge,[]))).
% 2.84/2.18 tff(2675,plain,
% 2.84/2.18 ($false),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2674, 2631, 2630, 2593, 2610, 2629, 37, 48, 13, 12, 2619, 2617, 2626, 2609, 2608, 26])).
% 2.84/2.18 tff(2676,plain,(c1_1(a13) | c0_1(a58) | hskp3 | c2_1(a2) | c3_1(a2) | c1_1(a58) | c3_1(a15) | c3_1(a13) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.18 tff(2677,plain,
% 2.84/2.18 (c2_1(a2)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2676, 2531, 48, 37, 12, 26, 468, 239, 241])).
% 2.84/2.18 tff(2678,plain,
% 2.84/2.18 (~hskp1),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[262, 2677])).
% 2.84/2.18 tff(2679,plain,
% 2.84/2.18 (hskp2 | hskp1 | c0_1(a13) | c1_1(a13)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[247, 104, 239, 47])).
% 2.84/2.18 tff(2680,plain,
% 2.84/2.18 (hskp2),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2679, 2678, 241, 2531])).
% 2.84/2.18 tff(2681,plain,
% 2.84/2.18 (~c2_1(a3)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[206, 2680])).
% 2.84/2.18 tff(2682,plain,
% 2.84/2.18 (c3_1(a3)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[217, 2680])).
% 2.84/2.18 tff(2683,plain,
% 2.84/2.18 (c1_1(a3)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[228, 2680])).
% 2.84/2.18 tff(2684,plain,
% 2.84/2.18 (~c2_1(a13)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[1331, 104, 2678, 2683, 2682, 241, 2531, 2681, 58])).
% 2.84/2.18 tff(2685,plain,
% 2.84/2.18 (hskp20),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2540, 2684, 2496, 2531])).
% 2.84/2.18 tff(2686,plain,
% 2.84/2.18 (c3_1(a37)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[555, 2685])).
% 2.84/2.18 tff(2687,plain,
% 2.84/2.18 (c1_1(a37)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[566, 2685])).
% 2.84/2.18 tff(2688,plain,
% 2.84/2.18 (~c2_1(a37)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[571, 104, 473, 48, 2687, 2686, 10])).
% 2.84/2.18 tff(2689,plain,
% 2.84/2.18 (hskp0),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[590, 2678, 48, 37, 26])).
% 2.84/2.18 tff(2690,plain,
% 2.84/2.18 (~c3_1(a1)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[117, 2689])).
% 2.84/2.18 tff(2691,plain,
% 2.84/2.18 (c2_1(a1)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[128, 2689])).
% 2.84/2.18 tff(2692,plain,
% 2.84/2.18 (c1_1(a1)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[139, 2689])).
% 2.84/2.18 tff(2693,plain,
% 2.84/2.18 (hskp9),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[1296, 104, 2683, 2682, 2692, 2691, 2681, 2690, 890])).
% 2.84/2.18 tff(2694,plain,
% 2.84/2.18 (~c3_1(a16)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[902, 2693])).
% 2.84/2.18 tff(2695,plain,
% 2.84/2.18 (c1_1(a16)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[913, 2693])).
% 2.84/2.18 tff(2696,plain,
% 2.84/2.18 (c0_1(a16)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[924, 2693])).
% 2.84/2.18 tff(2697,plain,
% 2.84/2.18 (hskp10),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[931, 104, 2496, 2696, 2695, 2694, 876])).
% 2.84/2.18 tff(2698,plain,
% 2.84/2.18 (~c1_1(a18)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[937, 2697])).
% 2.84/2.18 tff(2699,plain,
% 2.84/2.18 (~c0_1(a18)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[943, 2697])).
% 2.84/2.18 tff(2700,plain,
% 2.84/2.18 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.84/2.18 inference(rewrite,[status(thm)],[])).
% 2.84/2.18 tff(2701,plain,
% 2.84/2.18 ((hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (hskp1 | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.84/2.18 inference(rewrite,[status(thm)],[])).
% 2.84/2.18 tff(2702,plain,
% 2.84/2.18 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))))),
% 2.84/2.18 inference(monotonicity,[status(thm)],[2701])).
% 2.84/2.18 tff(2703,plain,
% 2.84/2.18 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.84/2.18 inference(transitivity,[status(thm)],[2702, 2700])).
% 2.84/2.18 tff(2704,plain,
% 2.84/2.18 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 2.84/2.18 inference(quant_inst,[status(thm)],[])).
% 2.84/2.18 tff(2705,plain,
% 2.84/2.18 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 2.84/2.18 inference(modus_ponens,[status(thm)],[2704, 2703])).
% 2.84/2.18 tff(2706,plain,
% 2.84/2.18 (~c2_1(a18)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2705, 104, 2678, 2687, 2686, 2699, 2698, 58, 2688])).
% 2.84/2.18 tff(2707,plain,
% 2.84/2.18 (~c0_1(a3)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2050, 104, 2683, 2682, 241, 2531, 239, 2681, 36])).
% 2.84/2.18 tff(2708,plain,
% 2.84/2.18 (hskp12),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[993, 104, 2696, 2695, 2682, 2694, 2681, 987, 2707])).
% 2.84/2.18 tff(2709,plain,
% 2.84/2.18 (~c3_1(a20)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[999, 2708])).
% 2.84/2.18 tff(2710,plain,
% 2.84/2.18 (~c1_1(a20)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[1005, 2708])).
% 2.84/2.18 tff(2711,plain,
% 2.84/2.18 (c2_1(a20)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[1016, 2708])).
% 2.84/2.18 tff(2712,plain,
% 2.84/2.18 (hskp5),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[1023, 104, 2711, 2710, 2709, 241, 239, 290, 2684])).
% 2.84/2.18 tff(2713,plain,
% 2.84/2.18 (~c2_1(a11)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[306, 2712])).
% 2.84/2.18 tff(2714,plain,
% 2.84/2.18 (~c1_1(a11)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[312, 2712])).
% 2.84/2.18 tff(2715,plain,
% 2.84/2.18 (c0_1(a11)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[323, 2712])).
% 2.84/2.18 tff(2716,plain,
% 2.84/2.18 (c3_1(a18)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[1037, 2697])).
% 2.84/2.18 tff(2717,plain,
% 2.84/2.18 ($false),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[1044, 104, 2716, 2715, 2699, 2698, 2714, 2713, 751, 2706])).
% 2.84/2.18 tff(2718,plain,(c3_1(a15) | c0_1(a13) | c3_1(a13) | hskp3 | c0_1(a58) | c1_1(a58) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.18 tff(2719,plain,
% 2.84/2.18 ($false),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2718, 471, 470, 12, 48, 37, 26, 468])).
% 2.84/2.18 tff(2720,plain,((~hskp6) | c3_1(a2) | hskp3 | c0_1(a58) | c1_1(a58) | c3_1(a15)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.18 tff(2721,plain,
% 2.84/2.18 (~hskp6),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2720, 468, 48, 37, 26, 12])).
% 2.84/2.18 tff(2722,plain,
% 2.84/2.18 (hskp13),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[825, 2496, 467])).
% 2.84/2.18 tff(2723,plain,
% 2.84/2.18 (~c3_1(a21)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[831, 2722])).
% 2.84/2.18 tff(2724,plain,
% 2.84/2.18 (c2_1(a21)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[842, 2722])).
% 2.84/2.18 tff(2725,plain,
% 2.84/2.18 (c0_1(a21)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[853, 2722])).
% 2.84/2.18 tff(2726,plain,
% 2.84/2.18 (hskp6 | (~c1_1(a21))),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2519, 104, 2725, 2724, 2723, 150])).
% 2.84/2.18 tff(2727,plain,
% 2.84/2.18 (~c1_1(a21)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2726, 2721])).
% 2.84/2.18 tff(2728,plain,
% 2.84/2.18 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 2.84/2.18 inference(bind,[status(th)],[])).
% 2.84/2.18 tff(2729,plain,
% 2.84/2.18 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.84/2.18 inference(quant_intro,[status(thm)],[2728])).
% 2.84/2.18 tff(2730,plain,
% 2.84/2.18 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.84/2.18 inference(rewrite,[status(thm)],[])).
% 2.84/2.18 tff(2731,plain,
% 2.84/2.18 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | 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)) | (~c0_1(V))) | c1_1(U)) | 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)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp18) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 2.84/2.18 inference(bind,[status(th)],[])).
% 2.84/2.18 tff(2732,plain,
% 2.84/2.18 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.84/2.18 inference(quant_intro,[status(thm)],[2731])).
% 2.84/2.18 tff(2733,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 2.84/2.18 tff(2734,plain,
% 2.84/2.18 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.84/2.18 inference(modus_ponens,[status(thm)],[2733, 2732])).
% 2.84/2.18 tff(2735,plain,
% 2.84/2.18 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.84/2.18 inference(modus_ponens,[status(thm)],[2734, 2730])).
% 2.84/2.18 tff(2736,plain,(
% 2.84/2.18 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.84/2.18 inference(skolemize,[status(sab)],[2735])).
% 2.84/2.18 tff(2737,plain,
% 2.84/2.18 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.84/2.18 inference(modus_ponens,[status(thm)],[2736, 2729])).
% 2.84/2.18 tff(2738,plain,
% 2.84/2.18 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.84/2.18 inference(rewrite,[status(thm)],[])).
% 2.84/2.18 tff(2739,plain,
% 2.84/2.18 ((hskp18 | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21))) <=> (hskp18 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.84/2.18 inference(rewrite,[status(thm)],[])).
% 2.84/2.18 tff(2740,plain,
% 2.84/2.18 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21))))),
% 2.84/2.18 inference(monotonicity,[status(thm)],[2739])).
% 2.84/2.18 tff(2741,plain,
% 2.84/2.18 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.84/2.18 inference(transitivity,[status(thm)],[2740, 2738])).
% 2.84/2.18 tff(2742,plain,
% 2.84/2.18 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))),
% 2.84/2.18 inference(quant_inst,[status(thm)],[])).
% 2.84/2.18 tff(2743,plain,
% 2.84/2.18 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21))),
% 2.84/2.18 inference(modus_ponens,[status(thm)],[2742, 2741])).
% 2.84/2.18 tff(2744,plain,
% 2.84/2.18 (hskp18),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[2743, 104, 2725, 2724, 2723, 2737, 2727])).
% 2.84/2.18 tff(2745,plain,
% 2.84/2.18 (~c3_1(a31)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[403, 2744])).
% 2.84/2.18 tff(2746,plain,
% 2.84/2.18 (c1_1(a31)),
% 2.84/2.18 inference(unit_resolution,[status(thm)],[414, 2744])).
% 2.84/2.18 tff(2747,plain,
% 2.84/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c1_1(a31)) | c2_1(a31))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c1_1(a31)) | c2_1(a31))),
% 2.84/2.18 inference(rewrite,[status(thm)],[])).
% 2.84/2.18 tff(2748,plain,
% 2.84/2.18 (((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c1_1(a31)) | c2_1(a31))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2749,plain,
% 2.84/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c1_1(a31)) | c2_1(a31)))),
% 2.84/2.19 inference(monotonicity,[status(thm)],[2748])).
% 2.84/2.19 tff(2750,plain,
% 2.84/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c1_1(a31)) | c2_1(a31))),
% 2.84/2.19 inference(transitivity,[status(thm)],[2749, 2747])).
% 2.84/2.19 tff(2751,plain,
% 2.84/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 2.84/2.19 inference(quant_inst,[status(thm)],[])).
% 2.84/2.19 tff(2752,plain,
% 2.84/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c1_1(a31)) | c2_1(a31)),
% 2.84/2.19 inference(modus_ponens,[status(thm)],[2751, 2750])).
% 2.84/2.19 tff(2753,plain,
% 2.84/2.19 (c2_1(a31)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2752, 104, 456, 2746, 2724, 37, 26, 2745, 2723, 380, 2727])).
% 2.84/2.19 tff(2754,plain,
% 2.84/2.19 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a31) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a31) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2755,plain,
% 2.84/2.19 ((hskp6 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21))) <=> (hskp6 | c3_1(a31) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2756,plain,
% 2.84/2.19 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a31) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31))))),
% 2.84/2.19 inference(monotonicity,[status(thm)],[2755])).
% 2.84/2.19 tff(2757,plain,
% 2.84/2.19 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a31) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.84/2.19 inference(transitivity,[status(thm)],[2756, 2754])).
% 2.84/2.19 tff(2758,plain,
% 2.84/2.19 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))),
% 2.84/2.19 inference(quant_inst,[status(thm)],[])).
% 2.84/2.19 tff(2759,plain,
% 2.84/2.19 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a31) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31))),
% 2.84/2.19 inference(modus_ponens,[status(thm)],[2758, 2757])).
% 2.84/2.19 tff(2760,plain,
% 2.84/2.19 ($false),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2759, 104, 2721, 2746, 2725, 2724, 2745, 2723, 150, 2753])).
% 2.84/2.19 tff(2761,plain,(c3_1(a15) | c0_1(a58) | c1_1(a58) | hskp3 | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.19 tff(2762,plain,
% 2.84/2.19 (c3_1(a15)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2761, 12, 26, 48, 37])).
% 2.84/2.19 tff(2763,plain,
% 2.84/2.19 (c1_1(a15)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[1728, 752, 473, 48, 1252, 12, 37, 26])).
% 2.84/2.19 tff(2764,plain,
% 2.84/2.19 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2765,plain,
% 2.84/2.19 ((hskp28 | hskp0 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15))) <=> (hskp28 | hskp0 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2766,plain,
% 2.84/2.19 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0)))),
% 2.84/2.19 inference(monotonicity,[status(thm)],[2765])).
% 2.84/2.19 tff(2767,plain,
% 2.84/2.19 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))),
% 2.84/2.19 inference(transitivity,[status(thm)],[2766, 2764])).
% 2.84/2.19 tff(2768,plain,
% 2.84/2.19 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))),
% 2.84/2.19 inference(quant_inst,[status(thm)],[])).
% 2.84/2.19 tff(2769,plain,
% 2.84/2.19 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0)),
% 2.84/2.19 inference(modus_ponens,[status(thm)],[2768, 2767])).
% 2.84/2.19 tff(2770,plain,
% 2.84/2.19 (hskp28 | hskp0 | c2_1(a15) | (~c3_1(a15))),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2769, 104, 2156, 582])).
% 2.84/2.19 tff(2771,plain,
% 2.84/2.19 ($false),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2770, 530, 11, 1252, 752])).
% 2.84/2.19 tff(2772,plain,(hskp0 | (~c3_1(a15)) | c2_1(a15) | (~c1_1(a15)) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.19 tff(2773,plain,
% 2.84/2.19 (hskp0),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2772, 752, 1252, 2156, 48, 37, 26])).
% 2.84/2.19 tff(2774,plain,
% 2.84/2.19 (c1_1(a1)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[139, 2773])).
% 2.84/2.19 tff(2775,plain,
% 2.84/2.19 (~c3_1(a1)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[117, 2773])).
% 2.84/2.19 tff(2776,plain,
% 2.84/2.19 (c2_1(a1)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[128, 2773])).
% 2.84/2.19 tff(2777,plain,
% 2.84/2.19 (hskp6),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[180, 2774, 2776, 2775])).
% 2.84/2.19 tff(2778,plain,
% 2.84/2.19 (~c3_1(a13)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[186, 2777])).
% 2.84/2.19 tff(2779,plain,
% 2.84/2.19 (~c1_1(a13)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[192, 2777])).
% 2.84/2.19 tff(2780,plain,
% 2.84/2.19 (~c0_1(a13)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[198, 2777])).
% 2.84/2.19 tff(2781,plain,
% 2.84/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c0_1(a15)))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2782,plain,
% 2.84/2.19 (((~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c2_1(a15) | (~c0_1(a15)) | (~c1_1(a15)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> ((~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c0_1(a15)))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2783,plain,
% 2.84/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c2_1(a15) | (~c0_1(a15)) | (~c1_1(a15)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c0_1(a15))))),
% 2.84/2.19 inference(monotonicity,[status(thm)],[2782])).
% 2.84/2.19 tff(2784,plain,
% 2.84/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c2_1(a15) | (~c0_1(a15)) | (~c1_1(a15)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c0_1(a15)))),
% 2.84/2.19 inference(transitivity,[status(thm)],[2783, 2781])).
% 2.84/2.19 tff(2785,plain,
% 2.84/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c2_1(a15) | (~c0_1(a15)) | (~c1_1(a15)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 2.84/2.19 inference(quant_inst,[status(thm)],[])).
% 2.84/2.19 tff(2786,plain,
% 2.84/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c0_1(a15))),
% 2.84/2.19 inference(modus_ponens,[status(thm)],[2785, 2784])).
% 2.84/2.19 tff(2787,plain,
% 2.84/2.19 (~c0_1(a15)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2786, 104, 2156, 752, 1252, 2780, 2779, 2778, 36])).
% 2.84/2.19 tff(2788,plain,
% 2.84/2.19 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2789,plain,
% 2.84/2.19 ((hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15))) <=> (hskp9 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2790,plain,
% 2.84/2.19 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))))),
% 2.84/2.19 inference(monotonicity,[status(thm)],[2789])).
% 2.84/2.19 tff(2791,plain,
% 2.84/2.19 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 2.84/2.19 inference(transitivity,[status(thm)],[2790, 2788])).
% 2.84/2.19 tff(2792,plain,
% 2.84/2.19 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))),
% 2.84/2.19 inference(quant_inst,[status(thm)],[])).
% 2.84/2.19 tff(2793,plain,
% 2.84/2.19 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))),
% 2.84/2.19 inference(modus_ponens,[status(thm)],[2792, 2791])).
% 2.84/2.19 tff(2794,plain,
% 2.84/2.19 (hskp9),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2793, 104, 2774, 2776, 2156, 752, 1252, 2775, 890])).
% 2.84/2.19 tff(2795,plain,
% 2.84/2.19 (~c3_1(a16)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[902, 2794])).
% 2.84/2.19 tff(2796,plain,
% 2.84/2.19 (c1_1(a16)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[913, 2794])).
% 2.84/2.19 tff(2797,plain,
% 2.84/2.19 (c2_1(a16)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[1305, 104, 2796, 2774, 2776, 2795, 752, 1252, 2775, 734, 2787])).
% 2.84/2.19 tff(2798,plain,
% 2.84/2.19 (c0_1(a16)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[924, 2794])).
% 2.84/2.19 tff(2799,assumption,(c0_1(a16)), introduced(assumption)).
% 2.84/2.19 tff(2800,plain,
% 2.84/2.19 (~c0_1(a3)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[976, 104, 2799, 2637, 2043, 2042, 2636, 2041, 970])).
% 2.84/2.19 tff(2801,plain,
% 2.84/2.19 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2802,plain,
% 2.84/2.19 ((hskp1 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13))) <=> (hskp1 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2803,plain,
% 2.84/2.19 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13))))),
% 2.84/2.19 inference(monotonicity,[status(thm)],[2802])).
% 2.84/2.19 tff(2804,plain,
% 2.84/2.19 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 2.84/2.19 inference(transitivity,[status(thm)],[2803, 2801])).
% 2.84/2.19 tff(2805,plain,
% 2.84/2.19 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))),
% 2.84/2.19 inference(quant_inst,[status(thm)],[])).
% 2.84/2.19 tff(2806,plain,
% 2.84/2.19 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13))),
% 2.84/2.19 inference(modus_ponens,[status(thm)],[2805, 2804])).
% 2.84/2.19 tff(2807,plain,
% 2.84/2.19 (hskp1 | (~c2_1(a13))),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2806, 104, 2156, 752, 1252, 241, 240, 58])).
% 2.84/2.19 tff(2808,plain,
% 2.84/2.19 (~c2_1(a13)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2807, 200])).
% 2.84/2.19 tff(2809,plain,
% 2.84/2.19 (~c0_1(a15)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2786, 104, 2156, 752, 1252, 241, 240, 239, 36])).
% 2.84/2.19 tff(2810,plain,
% 2.84/2.19 (hskp12),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[1350, 104, 2799, 2637, 2636, 752, 1252, 987, 2809])).
% 2.84/2.19 tff(2811,plain,
% 2.84/2.19 (~c3_1(a20)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[999, 2810])).
% 2.84/2.19 tff(2812,plain,
% 2.84/2.19 (~c1_1(a20)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[1005, 2810])).
% 2.84/2.19 tff(2813,plain,
% 2.84/2.19 (c2_1(a20)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[1016, 2810])).
% 2.84/2.19 tff(2814,plain,
% 2.84/2.19 (hskp5 | c2_1(a13)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[1023, 104, 2813, 2812, 2811, 241, 239, 290])).
% 2.84/2.19 tff(2815,plain,
% 2.84/2.19 (hskp5),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2814, 2808])).
% 2.84/2.19 tff(2816,plain,
% 2.84/2.19 (~c2_1(a11)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[306, 2815])).
% 2.84/2.19 tff(2817,plain,
% 2.84/2.19 (~c1_1(a11)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[312, 2815])).
% 2.84/2.19 tff(2818,plain,
% 2.84/2.19 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c1_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a20)))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2819,plain,
% 2.84/2.19 ((hskp10 | hskp1 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20))) <=> (hskp10 | hskp1 | c1_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a20)))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2820,plain,
% 2.84/2.19 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c1_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a20))))),
% 2.84/2.19 inference(monotonicity,[status(thm)],[2819])).
% 2.84/2.19 tff(2821,plain,
% 2.84/2.19 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a20)))),
% 2.84/2.19 inference(transitivity,[status(thm)],[2820, 2818])).
% 2.84/2.19 tff(2822,plain,
% 2.84/2.19 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)))),
% 2.84/2.19 inference(quant_inst,[status(thm)],[])).
% 2.84/2.19 tff(2823,plain,
% 2.84/2.19 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a20))),
% 2.84/2.19 inference(modus_ponens,[status(thm)],[2822, 2821])).
% 2.84/2.19 tff(2824,plain,
% 2.84/2.19 (hskp10 | hskp1),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2823, 104, 2813, 2812, 2811, 1882])).
% 2.84/2.19 tff(2825,plain,
% 2.84/2.19 (hskp10),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2824, 200])).
% 2.84/2.19 tff(2826,plain,
% 2.84/2.19 (~c1_1(a18)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[937, 2825])).
% 2.84/2.19 tff(2827,plain,
% 2.84/2.19 (~c0_1(a18)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[943, 2825])).
% 2.84/2.19 tff(2828,plain,
% 2.84/2.19 (c0_1(a11)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[323, 2815])).
% 2.84/2.19 tff(2829,plain,
% 2.84/2.19 (c3_1(a18)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[1037, 2825])).
% 2.84/2.19 tff(2830,plain,
% 2.84/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c0_1(a11)) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c0_1(a11)) | (~c3_1(a18)))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2831,plain,
% 2.84/2.19 (((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18))) <=> (c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c0_1(a11)) | (~c3_1(a18)))),
% 2.84/2.19 inference(rewrite,[status(thm)],[])).
% 2.84/2.19 tff(2832,plain,
% 2.84/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c0_1(a11)) | (~c3_1(a18))))),
% 2.84/2.19 inference(monotonicity,[status(thm)],[2831])).
% 2.84/2.19 tff(2833,plain,
% 2.84/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c0_1(a11)) | (~c3_1(a18)))),
% 2.84/2.19 inference(transitivity,[status(thm)],[2832, 2830])).
% 2.84/2.19 tff(2834,plain,
% 2.84/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))),
% 2.84/2.19 inference(quant_inst,[status(thm)],[])).
% 2.84/2.19 tff(2835,plain,
% 2.84/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c0_1(a11)) | (~c3_1(a18))),
% 2.84/2.19 inference(modus_ponens,[status(thm)],[2834, 2833])).
% 2.84/2.19 tff(2836,plain,
% 2.84/2.19 ($false),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2835, 104, 2829, 2828, 2042, 2827, 2826, 2817, 2816, 2041, 751, 2800])).
% 2.84/2.19 tff(2837,plain,(hskp1 | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.19 tff(2838,plain,
% 2.84/2.19 (hskp1),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2837, 2798, 2796, 2795, 2780, 2778, 2156, 752, 1252, 2779])).
% 2.84/2.19 tff(2839,plain,
% 2.84/2.19 (~c3_1(a2)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[256, 2838])).
% 2.84/2.19 tff(2840,plain,
% 2.84/2.19 (hskp12),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[1350, 104, 2798, 2796, 2795, 752, 1252, 987, 2787])).
% 2.84/2.19 tff(2841,plain,
% 2.84/2.19 (~c3_1(a20)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[999, 2840])).
% 2.84/2.19 tff(2842,plain,
% 2.84/2.19 (~c1_1(a20)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[1005, 2840])).
% 2.84/2.19 tff(2843,plain,
% 2.84/2.19 (c2_1(a20)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[1016, 2840])).
% 2.84/2.19 tff(2844,plain,
% 2.84/2.19 (~c0_1(a2)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[268, 2838])).
% 2.84/2.19 tff(2845,plain,
% 2.84/2.19 (~c2_1(a2)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[262, 2838])).
% 2.84/2.19 tff(2846,plain,
% 2.84/2.19 ($false),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2674, 2845, 2844, 2843, 2842, 2841, 37, 48, 26, 2839, 2796, 2795, 2797, 2776, 2775, 2774])).
% 2.84/2.19 tff(2847,plain,(c2_1(a15) | c0_1(a58) | hskp3 | c1_1(a58) | (~c1_1(a15)) | (~c3_1(a15))), inference(lemma,lemma(discharge,[]))).
% 2.84/2.19 tff(2848,plain,
% 2.84/2.19 ($false),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2847, 2763, 752, 48, 26, 37, 1252])).
% 2.84/2.19 tff(2849,plain,(c2_1(a15) | hskp3 | c1_1(a58) | c0_1(a58) | (~c3_1(a15)) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.19 tff(2850,plain,
% 2.84/2.19 (c2_1(a15)),
% 2.84/2.19 inference(unit_resolution,[status(thm)],[2849, 2762, 26, 37, 48, 12])).
% 2.84/2.19 tff(2851,plain,
% 2.84/2.19 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~c1_1(a15)) | (~c2_1(a15)) | (~c3_1(a15)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~c1_1(a15)) | (~c2_1(a15)) | (~c3_1(a15)) | (~ndr1_0))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2852,plain,
% 2.84/2.20 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15))) <=> (hskp24 | hskp3 | (~c1_1(a15)) | (~c2_1(a15)) | (~c3_1(a15)) | (~ndr1_0))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2853,plain,
% 2.84/2.20 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~c1_1(a15)) | (~c2_1(a15)) | (~c3_1(a15)) | (~ndr1_0)))),
% 2.84/2.20 inference(monotonicity,[status(thm)],[2852])).
% 2.84/2.20 tff(2854,plain,
% 2.84/2.20 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~c1_1(a15)) | (~c2_1(a15)) | (~c3_1(a15)) | (~ndr1_0))),
% 2.84/2.20 inference(transitivity,[status(thm)],[2853, 2851])).
% 2.84/2.20 tff(2855,plain,
% 2.84/2.20 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)))),
% 2.84/2.20 inference(quant_inst,[status(thm)],[])).
% 2.84/2.20 tff(2856,plain,
% 2.84/2.20 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~c1_1(a15)) | (~c2_1(a15)) | (~c3_1(a15)) | (~ndr1_0)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2855, 2854])).
% 2.84/2.20 tff(2857,plain,
% 2.84/2.20 (~c1_1(a15)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2856, 104, 467, 48, 2850, 2762, 10])).
% 2.84/2.20 tff(2858,plain,
% 2.84/2.20 (c2_1(a38)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2127, 2857, 26, 37, 12, 48])).
% 2.84/2.20 tff(2859,plain,
% 2.84/2.20 (~hskp21),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2495, 2858])).
% 2.84/2.20 tff(2860,plain,
% 2.84/2.20 (hskp13),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[825, 2859, 467])).
% 2.84/2.20 tff(2861,plain,
% 2.84/2.20 (c0_1(a21)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[853, 2860])).
% 2.84/2.20 tff(2862,plain,
% 2.84/2.20 (c2_1(a21)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[842, 2860])).
% 2.84/2.20 tff(2863,plain,
% 2.84/2.20 (~c3_1(a21)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[831, 2860])).
% 2.84/2.20 tff(2864,plain,
% 2.84/2.20 (hskp6 | (~c1_1(a21))),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2519, 104, 2861, 2862, 2863, 150])).
% 2.84/2.20 tff(2865,plain,
% 2.84/2.20 (~c1_1(a21)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2864, 25])).
% 2.84/2.20 tff(2866,plain,
% 2.84/2.20 (c2_1(a2) | (~c1_1(a2)) | c1_1(a21)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2033, 104, 456, 2862, 37, 26, 2863, 12, 380])).
% 2.84/2.20 tff(2867,plain,
% 2.84/2.20 (~c1_1(a2)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2866, 2865, 13])).
% 2.84/2.20 tff(2868,plain,
% 2.84/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2869,plain,
% 2.84/2.20 (((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2870,plain,
% 2.84/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2)))),
% 2.84/2.20 inference(monotonicity,[status(thm)],[2869])).
% 2.84/2.20 tff(2871,plain,
% 2.84/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 2.84/2.20 inference(transitivity,[status(thm)],[2870, 2868])).
% 2.84/2.20 tff(2872,plain,
% 2.84/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 2.84/2.20 inference(quant_inst,[status(thm)],[])).
% 2.84/2.20 tff(2873,plain,
% 2.84/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2872, 2871])).
% 2.84/2.20 tff(2874,plain,
% 2.84/2.20 (c0_1(a2) | c1_1(a2)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2873, 104, 2857, 2850, 2762, 13, 12, 362])).
% 2.84/2.20 tff(2875,plain,
% 2.84/2.20 (c0_1(a2)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2874, 2867])).
% 2.84/2.20 tff(2876,plain,
% 2.84/2.20 (~hskp1),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[268, 2875])).
% 2.84/2.20 tff(2877,plain,
% 2.84/2.20 (hskp0),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[590, 2876, 48, 37, 26])).
% 2.84/2.20 tff(2878,plain,
% 2.84/2.20 (~c3_1(a1)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[117, 2877])).
% 2.84/2.20 tff(2879,plain,
% 2.84/2.20 (c1_1(a1)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[139, 2877])).
% 2.84/2.20 tff(2880,plain,
% 2.84/2.20 (c2_1(a1)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[128, 2877])).
% 2.84/2.20 tff(2881,plain,
% 2.84/2.20 ($false),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[180, 2880, 2879, 25, 2878])).
% 2.84/2.20 tff(2882,plain,(hskp6 | hskp3 | c0_1(a58) | c1_1(a58) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.20 tff(2883,plain,
% 2.84/2.20 (hskp6),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2882, 13, 37, 26, 48, 12])).
% 2.84/2.20 tff(2884,plain,
% 2.84/2.20 (~c0_1(a13)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[198, 2883])).
% 2.84/2.20 tff(2885,plain,
% 2.84/2.20 (~c3_1(a13)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[186, 2883])).
% 2.84/2.20 tff(2886,plain,
% 2.84/2.20 (~c1_1(a13)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2530, 241, 780, 37, 26, 2511, 2512, 2513, 239])).
% 2.84/2.20 tff(2887,plain,
% 2.84/2.20 (hskp1),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2078, 2886, 1252, 1845, 12, 475, 13, 239, 241])).
% 2.84/2.20 tff(2888,plain,
% 2.84/2.20 (~c0_1(a2)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[268, 2887])).
% 2.84/2.20 tff(2889,plain,
% 2.84/2.20 (c0_1(a2) | c1_1(a2)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2873, 104, 475, 1845, 1252, 13, 12, 362])).
% 2.84/2.20 tff(2890,plain,
% 2.84/2.20 (c1_1(a2)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2889, 2888])).
% 2.84/2.20 tff(2891,plain,
% 2.84/2.20 (c1_1(a13) | c0_1(a2) | c2_1(a13)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2075, 104, 475, 1845, 1252, 239, 13, 12, 362])).
% 2.84/2.20 tff(2892,plain,
% 2.84/2.20 (c2_1(a13)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2891, 2888, 2886])).
% 2.84/2.20 tff(2893,plain,
% 2.84/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a13)))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2894,plain,
% 2.84/2.20 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a13)))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2895,plain,
% 2.84/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a13))))),
% 2.84/2.20 inference(monotonicity,[status(thm)],[2894])).
% 2.84/2.20 tff(2896,plain,
% 2.84/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a13)))),
% 2.84/2.20 inference(transitivity,[status(thm)],[2895, 2893])).
% 2.84/2.20 tff(2897,plain,
% 2.84/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 2.84/2.20 inference(quant_inst,[status(thm)],[])).
% 2.84/2.20 tff(2898,plain,
% 2.84/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a13))),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2897, 2896])).
% 2.84/2.20 tff(2899,plain,
% 2.84/2.20 (c1_1(a13) | (~c1_1(a2)) | (~c2_1(a13))),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2898, 104, 780, 37, 26, 239, 13, 12, 380])).
% 2.84/2.20 tff(2900,plain,
% 2.84/2.20 ($false),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2899, 2892, 2890, 2886])).
% 2.84/2.20 tff(2901,plain,(c0_1(a13) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a13) | c2_1(a2) | c3_1(a2) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21))), inference(lemma,lemma(discharge,[]))).
% 2.84/2.20 tff(2902,plain,
% 2.84/2.20 ($false),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2901, 2885, 2884, 37, 26, 456, 13, 12, 2857, 2850, 2762, 2863, 2862, 2861])).
% 2.84/2.20 tff(2903,plain,(c2_1(a2) | c0_1(a58) | c1_1(a58) | c3_1(a2) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.84/2.20 tff(2904,plain,
% 2.84/2.20 (c2_1(a2)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2903, 12, 26, 37, 48])).
% 2.84/2.20 tff(2905,plain,
% 2.84/2.20 (~hskp1),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[262, 2904])).
% 2.84/2.20 tff(2906,plain,
% 2.84/2.20 (hskp0),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[590, 2905, 48, 37, 26])).
% 2.84/2.20 tff(2907,plain,
% 2.84/2.20 (~c3_1(a1)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[117, 2906])).
% 2.84/2.20 tff(2908,plain,
% 2.84/2.20 (c1_1(a1)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[139, 2906])).
% 2.84/2.20 tff(2909,plain,
% 2.84/2.20 (c2_1(a1)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[128, 2906])).
% 2.84/2.20 tff(2910,plain,
% 2.84/2.20 (hskp6),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[180, 2909, 2908, 2907])).
% 2.84/2.20 tff(2911,plain,
% 2.84/2.20 (~c3_1(a13)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[186, 2910])).
% 2.84/2.20 tff(2912,plain,
% 2.84/2.20 (~c1_1(a13)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[192, 2910])).
% 2.84/2.20 tff(2913,plain,
% 2.84/2.20 (~c0_1(a13)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[198, 2910])).
% 2.84/2.20 tff(2914,plain,
% 2.84/2.20 (hskp2),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[247, 104, 2905, 2913, 2912, 2911, 47])).
% 2.84/2.20 tff(2915,plain,
% 2.84/2.20 (~c2_1(a3)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[206, 2914])).
% 2.84/2.20 tff(2916,plain,
% 2.84/2.20 (c3_1(a3)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[217, 2914])).
% 2.84/2.20 tff(2917,plain,
% 2.84/2.20 (c1_1(a3)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[228, 2914])).
% 2.84/2.20 tff(2918,plain,
% 2.84/2.20 (~c2_1(a13)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[1331, 104, 2905, 2917, 2916, 2913, 2912, 2915, 58])).
% 2.84/2.20 tff(2919,plain,
% 2.84/2.20 ($false),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2125, 104, 2857, 2850, 2762, 2913, 2912, 2911, 362, 2918])).
% 2.84/2.20 tff(2920,plain,(c3_1(a2) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.20 tff(2921,plain,
% 2.84/2.20 (c3_1(a2)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2920, 48, 37, 26])).
% 2.84/2.20 tff(2922,plain,
% 2.84/2.20 (~hskp1),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[256, 2921])).
% 2.84/2.20 tff(2923,plain,
% 2.84/2.20 (hskp0),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[590, 2922, 48, 37, 26])).
% 2.84/2.20 tff(2924,plain,
% 2.84/2.20 (~c3_1(a1)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[117, 2923])).
% 2.84/2.20 tff(2925,plain,
% 2.84/2.20 (c1_1(a1)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[139, 2923])).
% 2.84/2.20 tff(2926,plain,
% 2.84/2.20 (c2_1(a1)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[128, 2923])).
% 2.84/2.20 tff(2927,plain,
% 2.84/2.20 (hskp6),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[180, 2926, 2925, 2924])).
% 2.84/2.20 tff(2928,plain,
% 2.84/2.20 (~c3_1(a13)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[186, 2927])).
% 2.84/2.20 tff(2929,plain,
% 2.84/2.20 (~c1_1(a13)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[192, 2927])).
% 2.84/2.20 tff(2930,plain,
% 2.84/2.20 (~c0_1(a13)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[198, 2927])).
% 2.84/2.20 tff(2931,plain,
% 2.84/2.20 (hskp2),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[247, 104, 2922, 2930, 2929, 2928, 47])).
% 2.84/2.20 tff(2932,plain,
% 2.84/2.20 (~c2_1(a3)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[206, 2931])).
% 2.84/2.20 tff(2933,plain,
% 2.84/2.20 (c3_1(a3)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[217, 2931])).
% 2.84/2.20 tff(2934,plain,
% 2.84/2.20 (c1_1(a3)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[228, 2931])).
% 2.84/2.20 tff(2935,plain,
% 2.84/2.20 (~c0_1(a3)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2050, 104, 2934, 2933, 2930, 2929, 2928, 2932, 36])).
% 2.84/2.20 tff(2936,plain,
% 2.84/2.20 (hskp9),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[1296, 104, 2934, 2933, 2925, 2926, 2932, 2924, 890])).
% 2.84/2.20 tff(2937,plain,
% 2.84/2.20 (~c3_1(a16)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[902, 2936])).
% 2.84/2.20 tff(2938,plain,
% 2.84/2.20 (c1_1(a16)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[913, 2936])).
% 2.84/2.20 tff(2939,plain,
% 2.84/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a16) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2940,plain,
% 2.84/2.20 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c3_1(a16) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2941,plain,
% 2.84/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a16) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16)))),
% 2.84/2.20 inference(monotonicity,[status(thm)],[2940])).
% 2.84/2.20 tff(2942,plain,
% 2.84/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))),
% 2.84/2.20 inference(transitivity,[status(thm)],[2941, 2939])).
% 2.84/2.20 tff(2943,plain,
% 2.84/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 2.84/2.20 inference(quant_inst,[status(thm)],[])).
% 2.84/2.20 tff(2944,plain,
% 2.84/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2943, 2942])).
% 2.84/2.20 tff(2945,plain,
% 2.84/2.20 (c2_1(a16)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2944, 104, 2938, 2933, 2925, 2926, 2937, 2932, 2924, 734, 2935])).
% 2.84/2.20 tff(2946,plain,
% 2.84/2.20 (~c2_1(a13)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[1331, 104, 2922, 2934, 2933, 2930, 2929, 2932, 58])).
% 2.84/2.20 tff(2947,plain,
% 2.84/2.20 (c0_1(a16)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[924, 2936])).
% 2.84/2.20 tff(2948,plain,
% 2.84/2.20 (hskp12),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[993, 104, 2947, 2938, 2933, 2937, 2932, 987, 2935])).
% 2.84/2.20 tff(2949,plain,
% 2.84/2.20 (~c1_1(a20)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[1005, 2948])).
% 2.84/2.20 tff(2950,plain,
% 2.84/2.20 (c2_1(a20)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[1016, 2948])).
% 2.84/2.20 tff(2951,plain,
% 2.84/2.20 (~c0_1(a20)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[1359, 104, 2950, 2938, 2949, 2937, 2930, 2928, 1342, 2946, 2945])).
% 2.84/2.20 tff(2952,plain,
% 2.84/2.20 ($false),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[1366, 104, 2922, 2950, 2934, 2933, 2949, 2932, 58, 2951])).
% 2.84/2.20 tff(2953,plain,(hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.20 tff(2954,plain,
% 2.84/2.20 (hskp3),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2953, 37, 26])).
% 2.84/2.20 tff(2955,plain,
% 2.84/2.20 (((~hskp3) | (~c2_1(a7))) <=> ((~hskp3) | (~c2_1(a7)))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2956,plain,
% 2.84/2.20 (((~c2_1(a7)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a7)))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2957,axiom,((~c2_1(a7)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 2.84/2.20 tff(2958,plain,
% 2.84/2.20 ((~hskp3) | (~c2_1(a7))),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2957, 2956])).
% 2.84/2.20 tff(2959,plain,
% 2.84/2.20 ((~hskp3) | (~c2_1(a7))),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2958, 2955])).
% 2.84/2.20 tff(2960,plain,
% 2.84/2.20 (~c2_1(a7)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2959, 2954])).
% 2.84/2.20 tff(2961,plain,
% 2.84/2.20 (~hskp24),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[466, 780])).
% 2.84/2.20 tff(2962,assumption,(~c1_1(a7)), introduced(assumption)).
% 2.84/2.20 tff(2963,plain,
% 2.84/2.20 (((~hskp3) | c3_1(a7)) <=> ((~hskp3) | c3_1(a7))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2964,axiom,((~hskp3) | c3_1(a7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 2.84/2.20 tff(2965,plain,
% 2.84/2.20 ((~hskp3) | c3_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2964, 2963])).
% 2.84/2.20 tff(2966,plain,
% 2.84/2.20 ((~hskp3) | c3_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2965, 2963])).
% 2.84/2.20 tff(2967,plain,
% 2.84/2.20 ((~hskp3) | c3_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2966, 2963])).
% 2.84/2.20 tff(2968,plain,
% 2.84/2.20 ((~hskp3) | c3_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2967, 2963])).
% 2.84/2.20 tff(2969,plain,
% 2.84/2.20 ((~hskp3) | c3_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2968, 2963])).
% 2.84/2.20 tff(2970,plain,
% 2.84/2.20 ((~hskp3) | c3_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2969, 2963])).
% 2.84/2.20 tff(2971,plain,
% 2.84/2.20 ((~hskp3) | c3_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2970, 2963])).
% 2.84/2.20 tff(2972,plain,
% 2.84/2.20 ((~hskp3) | c3_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2971, 2963])).
% 2.84/2.20 tff(2973,plain,
% 2.84/2.20 (c3_1(a7)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2972, 2954])).
% 2.84/2.20 tff(2974,plain,
% 2.84/2.20 (((~hskp3) | c0_1(a7)) <=> ((~hskp3) | c0_1(a7))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2975,axiom,((~hskp3) | c0_1(a7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 2.84/2.20 tff(2976,plain,
% 2.84/2.20 ((~hskp3) | c0_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2975, 2974])).
% 2.84/2.20 tff(2977,plain,
% 2.84/2.20 ((~hskp3) | c0_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2976, 2974])).
% 2.84/2.20 tff(2978,plain,
% 2.84/2.20 ((~hskp3) | c0_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2977, 2974])).
% 2.84/2.20 tff(2979,plain,
% 2.84/2.20 ((~hskp3) | c0_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2978, 2974])).
% 2.84/2.20 tff(2980,plain,
% 2.84/2.20 ((~hskp3) | c0_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2979, 2974])).
% 2.84/2.20 tff(2981,plain,
% 2.84/2.20 ((~hskp3) | c0_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2980, 2974])).
% 2.84/2.20 tff(2982,plain,
% 2.84/2.20 ((~hskp3) | c0_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2981, 2974])).
% 2.84/2.20 tff(2983,plain,
% 2.84/2.20 ((~hskp3) | c0_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2982, 2974])).
% 2.84/2.20 tff(2984,plain,
% 2.84/2.20 (c0_1(a7)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2983, 2954])).
% 2.84/2.20 tff(2985,plain,
% 2.84/2.20 (((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))) <=> ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp13 | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2986,plain,
% 2.84/2.20 ((hskp24 | hskp13 | (~ndr1_0) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7))) <=> (hskp24 | hskp13 | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2987,plain,
% 2.84/2.20 (((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7)))) <=> ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7)))),
% 2.84/2.20 inference(monotonicity,[status(thm)],[2986])).
% 2.84/2.20 tff(2988,plain,
% 2.84/2.20 (((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7)))) <=> ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp13 | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))),
% 2.84/2.20 inference(transitivity,[status(thm)],[2987, 2985])).
% 2.84/2.20 tff(2989,plain,
% 2.84/2.20 ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7)))),
% 2.84/2.20 inference(quant_inst,[status(thm)],[])).
% 2.84/2.20 tff(2990,plain,
% 2.84/2.20 ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp13 | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7)),
% 2.84/2.20 inference(modus_ponens,[status(thm)],[2989, 2988])).
% 2.84/2.20 tff(2991,plain,
% 2.84/2.20 (hskp24 | hskp13 | c1_1(a7)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2990, 104, 2984, 2973, 2010])).
% 2.84/2.20 tff(2992,plain,
% 2.84/2.20 (hskp13),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[2991, 2961, 2962])).
% 2.84/2.20 tff(2993,plain,
% 2.84/2.20 (~c3_1(a21)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[831, 2992])).
% 2.84/2.20 tff(2994,plain,
% 2.84/2.20 (c2_1(a21)),
% 2.84/2.20 inference(unit_resolution,[status(thm)],[842, 2992])).
% 2.84/2.20 tff(2995,plain,
% 2.84/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a21) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a21)) | (~c2_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a21) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a21)) | (~c2_1(a21)))),
% 2.84/2.20 inference(rewrite,[status(thm)],[])).
% 2.84/2.20 tff(2996,plain,
% 2.84/2.20 (((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7))) <=> (c3_1(a21) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a21)) | (~c2_1(a21)))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(2997,plain,
% 2.84/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a21) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a21)) | (~c2_1(a21))))),
% 2.84/2.21 inference(monotonicity,[status(thm)],[2996])).
% 2.84/2.21 tff(2998,plain,
% 2.84/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a21) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a21)) | (~c2_1(a21)))),
% 2.84/2.21 inference(transitivity,[status(thm)],[2997, 2995])).
% 2.84/2.21 tff(2999,plain,
% 2.84/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))),
% 2.84/2.21 inference(quant_inst,[status(thm)],[])).
% 2.84/2.21 tff(3000,plain,
% 2.84/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a21) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a21)) | (~c2_1(a21))),
% 2.84/2.21 inference(modus_ponens,[status(thm)],[2999, 2998])).
% 2.84/2.21 tff(3001,plain,
% 2.84/2.21 (~c1_1(a21)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3000, 104, 2994, 2984, 2973, 2993, 2960, 279, 2962])).
% 2.84/2.21 tff(3002,plain,
% 2.84/2.21 (c0_1(a21)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[853, 2992])).
% 2.84/2.21 tff(3003,plain,
% 2.84/2.21 (hskp18),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[2743, 104, 3002, 2994, 2993, 2737, 3001])).
% 2.84/2.21 tff(3004,plain,
% 2.84/2.21 (~c3_1(a31)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[403, 3003])).
% 2.84/2.21 tff(3005,plain,
% 2.84/2.21 (c1_1(a31)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[414, 3003])).
% 2.84/2.21 tff(3006,plain,
% 2.84/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a31) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a31)) | (~c2_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a31) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3007,plain,
% 2.84/2.21 (((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7))) <=> (c3_1(a31) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3008,plain,
% 2.84/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a31) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a31)) | (~c2_1(a31))))),
% 2.84/2.21 inference(monotonicity,[status(thm)],[3007])).
% 2.84/2.21 tff(3009,plain,
% 2.84/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a31) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.84/2.21 inference(transitivity,[status(thm)],[3008, 3006])).
% 2.84/2.21 tff(3010,plain,
% 2.84/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))),
% 2.84/2.21 inference(quant_inst,[status(thm)],[])).
% 2.84/2.21 tff(3011,plain,
% 2.84/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a31) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a31)) | (~c2_1(a31))),
% 2.84/2.21 inference(modus_ponens,[status(thm)],[3010, 3009])).
% 2.84/2.21 tff(3012,plain,
% 2.84/2.21 (~c2_1(a31)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3011, 104, 3005, 2984, 2973, 3004, 2960, 279, 2962])).
% 2.84/2.21 tff(3013,plain,
% 2.84/2.21 ($false),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[2752, 104, 780, 3005, 2994, 37, 26, 3004, 2993, 380, 3001, 3012])).
% 2.84/2.21 tff(3014,plain,(c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a7)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.21 tff(3015,plain,
% 2.84/2.21 (c1_1(a7)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3014, 780, 26, 37])).
% 2.84/2.21 tff(3016,plain,
% 2.84/2.21 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | c2_1(a7) | (~ndr1_0) | (~c0_1(a7)) | (~c1_1(a7)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a7) | (~ndr1_0) | (~c0_1(a7)) | (~c1_1(a7)))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3017,plain,
% 2.84/2.21 ((hskp24 | hskp6 | (~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7))) <=> (hskp24 | hskp6 | c2_1(a7) | (~ndr1_0) | (~c0_1(a7)) | (~c1_1(a7)))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3018,plain,
% 2.84/2.21 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | c2_1(a7) | (~ndr1_0) | (~c0_1(a7)) | (~c1_1(a7))))),
% 2.84/2.21 inference(monotonicity,[status(thm)],[3017])).
% 2.84/2.21 tff(3019,plain,
% 2.84/2.21 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a7) | (~ndr1_0) | (~c0_1(a7)) | (~c1_1(a7)))),
% 2.84/2.21 inference(transitivity,[status(thm)],[3018, 3016])).
% 2.84/2.21 tff(3020,plain,
% 2.84/2.21 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7)))),
% 2.84/2.21 inference(quant_inst,[status(thm)],[])).
% 2.84/2.21 tff(3021,plain,
% 2.84/2.21 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a7) | (~ndr1_0) | (~c0_1(a7)) | (~c1_1(a7))),
% 2.84/2.21 inference(modus_ponens,[status(thm)],[3020, 3019])).
% 2.84/2.21 tff(3022,plain,
% 2.84/2.21 (hskp24 | hskp6 | (~c1_1(a7))),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3021, 104, 2984, 2960, 1059])).
% 2.84/2.21 tff(3023,plain,
% 2.84/2.21 ($false),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3022, 3015, 2961, 25])).
% 2.84/2.21 tff(3024,plain,(c2_1(a58) | hskp6 | c1_1(a58) | c0_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.21 tff(3025,plain,
% 2.84/2.21 (hskp6),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3024, 780, 26, 37])).
% 2.84/2.21 tff(3026,plain,
% 2.84/2.21 (~c1_1(a13)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[192, 3025])).
% 2.84/2.21 tff(3027,plain,
% 2.84/2.21 (~c0_1(a13)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[198, 3025])).
% 2.84/2.21 tff(3028,plain,
% 2.84/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3029,plain,
% 2.84/2.21 (((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3030,plain,
% 2.84/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7))))),
% 2.84/2.21 inference(monotonicity,[status(thm)],[3029])).
% 2.84/2.21 tff(3031,plain,
% 2.84/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))),
% 2.84/2.21 inference(transitivity,[status(thm)],[3030, 3028])).
% 2.84/2.21 tff(3032,plain,
% 2.84/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 2.84/2.21 inference(quant_inst,[status(thm)],[])).
% 2.84/2.21 tff(3033,plain,
% 2.84/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7))),
% 2.84/2.21 inference(modus_ponens,[status(thm)],[3032, 3031])).
% 2.84/2.21 tff(3034,plain,
% 2.84/2.21 ($false),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3033, 104, 2984, 2973, 3027, 3026, 239, 2960, 36, 3015])).
% 2.84/2.21 tff(3035,plain,(c2_1(a58) | c3_1(a13) | c1_1(a58) | c0_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.21 tff(3036,plain,
% 2.84/2.21 (c3_1(a13)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3035, 780, 26, 37])).
% 2.84/2.21 tff(3037,plain,
% 2.84/2.21 ($false),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[186, 3036, 3025])).
% 2.84/2.21 tff(3038,plain,(c2_1(a58) | c1_1(a58) | c0_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.21 tff(3039,plain,
% 2.84/2.21 (c2_1(a58)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3038, 37, 26])).
% 2.84/2.21 tff(3040,plain,
% 2.84/2.21 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a58)))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3041,plain,
% 2.84/2.21 ((hskp1 | (~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58))) <=> (hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a58)))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3042,plain,
% 2.84/2.21 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a58))))),
% 2.84/2.21 inference(monotonicity,[status(thm)],[3041])).
% 2.84/2.21 tff(3043,plain,
% 2.84/2.21 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a58)))),
% 2.84/2.21 inference(transitivity,[status(thm)],[3042, 3040])).
% 2.84/2.21 tff(3044,plain,
% 2.84/2.21 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))),
% 2.84/2.21 inference(quant_inst,[status(thm)],[])).
% 2.84/2.21 tff(3045,plain,
% 2.84/2.21 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a58))),
% 2.84/2.21 inference(modus_ponens,[status(thm)],[3044, 3043])).
% 2.84/2.21 tff(3046,plain,
% 2.84/2.21 (hskp1 | (~c1_1(a7)) | (~c2_1(a58))),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3045, 104, 2973, 37, 26, 2960, 58])).
% 2.84/2.21 tff(3047,plain,
% 2.84/2.21 (~c1_1(a7)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3046, 200, 59])).
% 2.84/2.21 tff(3048,plain,
% 2.84/2.21 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | (~c2_1(a58)))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3049,plain,
% 2.84/2.21 ((hskp2 | (~ndr1_0) | c1_1(a7) | c2_1(a7) | (~c3_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58))) <=> (hskp2 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | (~c2_1(a58)))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3050,plain,
% 2.84/2.21 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a7) | c2_1(a7) | (~c3_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | (~c2_1(a58))))),
% 2.84/2.21 inference(monotonicity,[status(thm)],[3049])).
% 2.84/2.21 tff(3051,plain,
% 2.84/2.21 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a7) | c2_1(a7) | (~c3_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | (~c2_1(a58)))),
% 2.84/2.21 inference(transitivity,[status(thm)],[3050, 3048])).
% 2.84/2.21 tff(3052,plain,
% 2.84/2.21 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a7) | c2_1(a7) | (~c3_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))),
% 2.84/2.21 inference(quant_inst,[status(thm)],[])).
% 2.84/2.21 tff(3053,plain,
% 2.84/2.21 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | (~c2_1(a58))),
% 2.84/2.21 inference(modus_ponens,[status(thm)],[3052, 3051])).
% 2.84/2.21 tff(3054,plain,
% 2.84/2.21 ($false),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3053, 104, 238, 59, 2973, 37, 26, 2960, 1545, 3047])).
% 2.84/2.21 tff(3055,plain,(hskp1 | (~c2_1(a58)) | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.84/2.21 tff(3056,plain,
% 2.84/2.21 (hskp1),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3055, 3039, 37, 26])).
% 2.84/2.21 tff(3057,plain,
% 2.84/2.21 (~c3_1(a2)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[256, 3056])).
% 2.84/2.21 tff(3058,plain,
% 2.84/2.21 (~c2_1(a2)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[262, 3056])).
% 2.84/2.21 tff(3059,plain,
% 2.84/2.21 (~c0_1(a2)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[268, 3056])).
% 2.84/2.21 tff(3060,plain,
% 2.84/2.21 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3061,plain,
% 2.84/2.21 ((hskp0 | (~ndr1_0) | c0_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp0 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3062,plain,
% 2.84/2.21 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58))))),
% 2.84/2.21 inference(monotonicity,[status(thm)],[3061])).
% 2.84/2.21 tff(3063,plain,
% 2.84/2.21 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.84/2.21 inference(transitivity,[status(thm)],[3062, 3060])).
% 2.84/2.21 tff(3064,plain,
% 2.84/2.21 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 2.84/2.21 inference(quant_inst,[status(thm)],[])).
% 2.84/2.21 tff(3065,plain,
% 2.84/2.21 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58))),
% 2.84/2.21 inference(modus_ponens,[status(thm)],[3064, 3063])).
% 2.84/2.21 tff(3066,plain,
% 2.84/2.21 (hskp0 | (~c3_1(a58))),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3065, 104, 3039, 37, 3059, 3058, 3057, 24])).
% 2.84/2.21 tff(3067,plain,
% 2.84/2.21 (~c3_1(a58)),
% 2.84/2.21 inference(unit_resolution,[status(thm)],[3066, 11])).
% 2.84/2.21 tff(3068,plain,
% 2.84/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)) | c3_1(a58))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3069,plain,
% 2.84/2.21 (((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a58) | c0_1(a58) | c3_1(a58)) <=> (c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)) | c3_1(a58))),
% 2.84/2.21 inference(rewrite,[status(thm)],[])).
% 2.84/2.21 tff(3070,plain,
% 2.84/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)) | c3_1(a58)))),
% 2.93/2.22 inference(monotonicity,[status(thm)],[3069])).
% 2.93/2.22 tff(3071,plain,
% 2.93/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)) | c3_1(a58))),
% 2.93/2.22 inference(transitivity,[status(thm)],[3070, 3068])).
% 2.93/2.22 tff(3072,plain,
% 2.93/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a58) | c0_1(a58) | c3_1(a58))),
% 2.93/2.22 inference(quant_inst,[status(thm)],[])).
% 2.93/2.22 tff(3073,plain,
% 2.93/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)) | c3_1(a58)),
% 2.93/2.22 inference(modus_ponens,[status(thm)],[3072, 3071])).
% 2.93/2.22 tff(3074,plain,
% 2.93/2.22 ((~c1_1(a7)) | c3_1(a58)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3073, 104, 2984, 2973, 37, 26, 2960, 36])).
% 2.93/2.22 tff(3075,plain,
% 2.93/2.22 (~c1_1(a7)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3074, 3067])).
% 2.93/2.22 tff(3076,plain,
% 2.93/2.22 (hskp2),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3053, 104, 3039, 2973, 37, 26, 2960, 1545, 3075])).
% 2.93/2.22 tff(3077,plain,
% 2.93/2.22 (~c2_1(a3)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[206, 3076])).
% 2.93/2.22 tff(3078,plain,
% 2.93/2.22 (c3_1(a3)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[217, 3076])).
% 2.93/2.22 tff(3079,plain,
% 2.93/2.22 (c1_1(a3)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[228, 3076])).
% 2.93/2.22 tff(3080,plain,
% 2.93/2.22 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3081,plain,
% 2.93/2.22 ((hskp28 | hskp0 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp28 | hskp0 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3082,plain,
% 2.93/2.22 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3))))),
% 2.93/2.22 inference(monotonicity,[status(thm)],[3081])).
% 2.93/2.22 tff(3083,plain,
% 2.93/2.22 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.93/2.22 inference(transitivity,[status(thm)],[3082, 3080])).
% 2.93/2.22 tff(3084,plain,
% 2.93/2.22 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.93/2.22 inference(quant_inst,[status(thm)],[])).
% 2.93/2.22 tff(3085,plain,
% 2.93/2.22 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3))),
% 2.93/2.22 inference(modus_ponens,[status(thm)],[3084, 3083])).
% 2.93/2.22 tff(3086,plain,
% 2.93/2.22 (hskp28),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3085, 104, 11, 3079, 3078, 3077, 582])).
% 2.93/2.22 tff(3087,plain,
% 2.93/2.22 (c3_1(a25)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[487, 3086])).
% 2.93/2.22 tff(3088,plain,
% 2.93/2.22 (c1_1(a25)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[498, 3086])).
% 2.93/2.22 tff(3089,plain,
% 2.93/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a7) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | c1_1(a7) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | c1_1(a7) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3090,plain,
% 2.93/2.22 (((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7))) <=> (c2_1(a7) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | c1_1(a7) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3091,plain,
% 2.93/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a7) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | c1_1(a7) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25))))),
% 2.93/2.22 inference(monotonicity,[status(thm)],[3090])).
% 2.93/2.22 tff(3092,plain,
% 2.93/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | c1_1(a7) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 2.93/2.22 inference(transitivity,[status(thm)],[3091, 3089])).
% 2.93/2.22 tff(3093,plain,
% 2.93/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))),
% 2.93/2.22 inference(quant_inst,[status(thm)],[])).
% 2.93/2.22 tff(3094,plain,
% 2.93/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | c1_1(a7) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25))),
% 2.93/2.22 inference(modus_ponens,[status(thm)],[3093, 3092])).
% 2.93/2.22 tff(3095,plain,
% 2.93/2.22 (~c0_1(a25)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3094, 104, 3088, 3087, 2973, 3079, 3078, 2960, 3077, 1772, 3075])).
% 2.93/2.22 tff(3096,plain,
% 2.93/2.22 (c2_1(a25)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[509, 3086])).
% 2.93/2.22 tff(3097,plain,
% 2.93/2.22 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3098,plain,
% 2.93/2.22 ((hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3099,plain,
% 2.93/2.22 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25)))),
% 2.93/2.22 inference(monotonicity,[status(thm)],[3098])).
% 2.93/2.22 tff(3100,plain,
% 2.93/2.22 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))),
% 2.93/2.22 inference(transitivity,[status(thm)],[3099, 3097])).
% 2.93/2.22 tff(3101,plain,
% 2.93/2.22 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 2.93/2.22 inference(quant_inst,[status(thm)],[])).
% 2.93/2.22 tff(3102,plain,
% 2.93/2.22 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25)),
% 2.93/2.22 inference(modus_ponens,[status(thm)],[3101, 3100])).
% 2.93/2.22 tff(3103,plain,
% 2.93/2.22 ($false),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3102, 104, 11, 3096, 3087, 3059, 3058, 3057, 24, 3095])).
% 2.93/2.22 tff(3104,plain,(hskp0 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.22 tff(3105,plain,
% 2.93/2.22 (hskp0),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3104, 37, 26])).
% 2.93/2.22 tff(3106,plain,
% 2.93/2.22 (~c3_1(a1)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[117, 3105])).
% 2.93/2.22 tff(3107,plain,
% 2.93/2.22 (c1_1(a1)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[139, 3105])).
% 2.93/2.22 tff(3108,plain,
% 2.93/2.22 (c2_1(a1)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[128, 3105])).
% 2.93/2.22 tff(3109,plain,
% 2.93/2.22 (hskp6),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[180, 3108, 3107, 3106])).
% 2.93/2.22 tff(3110,plain,
% 2.93/2.22 (~c3_1(a13)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[186, 3109])).
% 2.93/2.22 tff(3111,plain,
% 2.93/2.22 (~c1_1(a13)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[192, 3109])).
% 2.93/2.22 tff(3112,plain,
% 2.93/2.22 (~c0_1(a13)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[198, 3109])).
% 2.93/2.22 tff(3113,plain,
% 2.93/2.22 (~c1_1(a7)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3033, 104, 2984, 2973, 3112, 3111, 3110, 2960, 36])).
% 2.93/2.22 tff(3114,plain,
% 2.93/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3115,plain,
% 2.93/2.22 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7))) <=> (c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3116,plain,
% 2.93/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7)))),
% 2.93/2.22 inference(monotonicity,[status(thm)],[3115])).
% 2.93/2.22 tff(3117,plain,
% 2.93/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))),
% 2.93/2.22 inference(transitivity,[status(thm)],[3116, 3114])).
% 2.93/2.22 tff(3118,plain,
% 2.93/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))),
% 2.93/2.22 inference(quant_inst,[status(thm)],[])).
% 2.93/2.22 tff(3119,plain,
% 2.93/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7)),
% 2.93/2.22 inference(modus_ponens,[status(thm)],[3118, 3117])).
% 2.93/2.22 tff(3120,plain,
% 2.93/2.22 ($false),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3119, 104, 2984, 2973, 3107, 3108, 2960, 3106, 279, 3113])).
% 2.93/2.22 tff(3121,plain,(c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.22 tff(3122,plain,
% 2.93/2.22 (c0_1(a58)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3121, 26])).
% 2.93/2.22 tff(3123,plain,
% 2.93/2.22 (((~hskp24) | (~c0_1(a58))) <=> ((~hskp24) | (~c0_1(a58)))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3124,plain,
% 2.93/2.22 (((~c0_1(a58)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a58)))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3125,axiom,((~c0_1(a58)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 2.93/2.22 tff(3126,plain,
% 2.93/2.22 ((~hskp24) | (~c0_1(a58))),
% 2.93/2.22 inference(modus_ponens,[status(thm)],[3125, 3124])).
% 2.93/2.22 tff(3127,plain,
% 2.93/2.22 ((~hskp24) | (~c0_1(a58))),
% 2.93/2.22 inference(modus_ponens,[status(thm)],[3126, 3123])).
% 2.93/2.22 tff(3128,plain,
% 2.93/2.22 (~hskp24),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3127, 3122])).
% 2.93/2.22 tff(3129,plain,
% 2.93/2.22 ($false),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[522, 104, 568, 48, 499, 510, 488, 10])).
% 2.93/2.22 tff(3130,plain,((~hskp28) | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.93/2.22 tff(3131,plain,
% 2.93/2.22 (~hskp28),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3130, 48, 3128])).
% 2.93/2.22 tff(3132,plain,
% 2.93/2.22 (~c2_1(a37)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[571, 104, 568, 48, 695, 687, 10])).
% 2.93/2.22 tff(3133,plain,
% 2.93/2.22 (~hskp28),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3130, 48, 568])).
% 2.93/2.22 tff(3134,plain,
% 2.93/2.22 ($false),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[585, 104, 3133, 11, 695, 687, 582, 3132])).
% 2.93/2.22 tff(3135,plain,((~hskp20) | hskp0 | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.93/2.22 tff(3136,plain,
% 2.93/2.22 (~hskp20),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3135, 11, 3128, 48])).
% 2.93/2.22 tff(3137,plain,
% 2.93/2.22 (hskp1),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[544, 3136, 3131])).
% 2.93/2.22 tff(3138,plain,
% 2.93/2.22 (~c0_1(a2)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[268, 3137])).
% 2.93/2.22 tff(3139,plain,
% 2.93/2.22 (~c2_1(a2)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[262, 3137])).
% 2.93/2.22 tff(3140,plain,
% 2.93/2.22 (~hskp27),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[633, 11, 3131, 3128, 48])).
% 2.93/2.22 tff(3141,plain,
% 2.93/2.22 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 2.93/2.22 inference(bind,[status(th)],[])).
% 2.93/2.22 tff(3142,plain,
% 2.93/2.22 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.93/2.22 inference(quant_intro,[status(thm)],[3141])).
% 2.93/2.22 tff(3143,plain,
% 2.93/2.22 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3144,plain,
% 2.93/2.22 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 2.93/2.22 inference(bind,[status(th)],[])).
% 2.93/2.22 tff(3145,plain,
% 2.93/2.22 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.93/2.22 inference(quant_intro,[status(thm)],[3144])).
% 2.93/2.22 tff(3146,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 2.93/2.22 tff(3147,plain,
% 2.93/2.22 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.93/2.22 inference(modus_ponens,[status(thm)],[3146, 3145])).
% 2.93/2.22 tff(3148,plain,
% 2.93/2.22 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.93/2.22 inference(modus_ponens,[status(thm)],[3147, 3143])).
% 2.93/2.22 tff(3149,plain,(
% 2.93/2.22 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.93/2.22 inference(skolemize,[status(sab)],[3148])).
% 2.93/2.22 tff(3150,plain,
% 2.93/2.22 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.93/2.22 inference(modus_ponens,[status(thm)],[3149, 3142])).
% 2.93/2.22 tff(3151,plain,
% 2.93/2.22 (hskp13),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[825, 811, 3128])).
% 2.93/2.22 tff(3152,plain,
% 2.93/2.22 (~c3_1(a21)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[831, 3151])).
% 2.93/2.22 tff(3153,plain,
% 2.93/2.22 (c2_1(a21)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[842, 3151])).
% 2.93/2.22 tff(3154,plain,
% 2.93/2.22 (~c2_1(a38)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[2495, 636])).
% 2.93/2.22 tff(3155,plain,
% 2.93/2.22 ($false),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[1065, 104, 568, 25, 647, 658, 3154, 1059])).
% 2.93/2.22 tff(3156,plain,((~hskp21) | hskp24 | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.93/2.22 tff(3157,plain,
% 2.93/2.22 (~hskp21),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3156, 25, 3128])).
% 2.93/2.22 tff(3158,plain,
% 2.93/2.22 (hskp13),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[825, 3157, 3128])).
% 2.93/2.22 tff(3159,plain,
% 2.93/2.22 (~c3_1(a21)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[831, 3158])).
% 2.93/2.22 tff(3160,plain,
% 2.93/2.22 (c2_1(a21)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[842, 3158])).
% 2.93/2.22 tff(3161,plain,
% 2.93/2.22 (c0_1(a21)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[853, 3158])).
% 2.93/2.22 tff(3162,plain,
% 2.93/2.22 (~c1_1(a21)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[2519, 104, 25, 3161, 3160, 3159, 150])).
% 2.93/2.22 tff(3163,plain,
% 2.93/2.22 (hskp18),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[2743, 104, 3161, 3160, 3159, 2737, 3162])).
% 2.93/2.22 tff(3164,plain,
% 2.93/2.22 (~c3_1(a31)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[403, 3163])).
% 2.93/2.22 tff(3165,plain,
% 2.93/2.22 (c1_1(a31)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[414, 3163])).
% 2.93/2.22 tff(3166,plain,
% 2.93/2.22 (~c2_1(a31)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[2759, 104, 25, 3165, 3161, 3160, 3164, 3159, 150])).
% 2.93/2.22 tff(3167,plain,
% 2.93/2.22 (~c0_1(a31)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[444, 3163])).
% 2.93/2.22 tff(3168,assumption,(~hskp20), introduced(assumption)).
% 2.93/2.22 tff(3169,plain,
% 2.93/2.22 (c3_1(a58)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[723, 3168, 780, 811])).
% 2.93/2.22 tff(3170,plain,
% 2.93/2.22 (c0_1(a21)),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[853, 3151])).
% 2.93/2.22 tff(3171,plain,
% 2.93/2.22 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3172,plain,
% 2.93/2.22 ((hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58))) <=> (hskp20 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3173,plain,
% 2.93/2.22 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c3_1(a58))))),
% 2.93/2.22 inference(monotonicity,[status(thm)],[3172])).
% 2.93/2.22 tff(3174,plain,
% 2.93/2.22 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))),
% 2.93/2.22 inference(transitivity,[status(thm)],[3173, 3171])).
% 2.93/2.22 tff(3175,plain,
% 2.93/2.22 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))),
% 2.93/2.22 inference(quant_inst,[status(thm)],[])).
% 2.93/2.22 tff(3176,plain,
% 2.93/2.22 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c3_1(a58))),
% 2.93/2.22 inference(modus_ponens,[status(thm)],[3175, 3174])).
% 2.93/2.22 tff(3177,plain,
% 2.93/2.22 (hskp20 | (~c3_1(a58))),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3176, 104, 3170, 3153, 3122, 26, 3152, 3150])).
% 2.93/2.22 tff(3178,plain,
% 2.93/2.22 ($false),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3177, 3169, 3168])).
% 2.93/2.22 tff(3179,plain,(hskp20 | c1_1(a58) | c2_1(a58) | hskp21), inference(lemma,lemma(discharge,[]))).
% 2.93/2.22 tff(3180,plain,
% 2.93/2.22 (hskp20),
% 2.93/2.22 inference(unit_resolution,[status(thm)],[3179, 3157, 780, 26])).
% 2.93/2.22 tff(3181,assumption,(~c2_1(a31)), introduced(assumption)).
% 2.93/2.22 tff(3182,assumption,(~c3_1(a31)), introduced(assumption)).
% 2.93/2.22 tff(3183,assumption,(~c0_1(a31)), introduced(assumption)).
% 2.93/2.22 tff(3184,plain,
% 2.93/2.22 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a37) | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c2_1(a37)) | (~c3_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a37) | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c2_1(a37)) | (~c3_1(a37)))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3185,plain,
% 2.93/2.22 ((hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31)) <=> (hskp0 | c0_1(a37) | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c2_1(a37)) | (~c3_1(a37)))),
% 2.93/2.22 inference(rewrite,[status(thm)],[])).
% 2.93/2.22 tff(3186,plain,
% 2.93/2.22 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a37) | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c2_1(a37)) | (~c3_1(a37))))),
% 2.93/2.22 inference(monotonicity,[status(thm)],[3185])).
% 2.93/2.22 tff(3187,plain,
% 2.93/2.22 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a37) | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c2_1(a37)) | (~c3_1(a37)))),
% 2.93/2.22 inference(transitivity,[status(thm)],[3186, 3184])).
% 2.93/2.22 tff(3188,plain,
% 2.93/2.22 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31))),
% 2.93/2.23 inference(quant_inst,[status(thm)],[])).
% 2.93/2.23 tff(3189,plain,
% 2.93/2.23 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a37) | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c2_1(a37)) | (~c3_1(a37))),
% 2.93/2.23 inference(modus_ponens,[status(thm)],[3188, 3187])).
% 2.93/2.23 tff(3190,plain,
% 2.93/2.23 (~c2_1(a37)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3189, 104, 11, 687, 686, 3183, 3182, 24, 3181])).
% 2.93/2.23 tff(3191,plain,
% 2.93/2.23 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.93/2.23 inference(rewrite,[status(thm)],[])).
% 2.93/2.23 tff(3192,plain,
% 2.93/2.23 ((hskp6 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31)) <=> (hskp6 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.93/2.23 inference(rewrite,[status(thm)],[])).
% 2.93/2.23 tff(3193,plain,
% 2.93/2.23 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))))),
% 2.93/2.23 inference(monotonicity,[status(thm)],[3192])).
% 2.93/2.23 tff(3194,plain,
% 2.93/2.23 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 2.93/2.23 inference(transitivity,[status(thm)],[3193, 3191])).
% 2.93/2.23 tff(3195,plain,
% 2.93/2.23 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31))),
% 2.93/2.23 inference(quant_inst,[status(thm)],[])).
% 2.93/2.23 tff(3196,plain,
% 2.93/2.23 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 2.93/2.23 inference(modus_ponens,[status(thm)],[3195, 3194])).
% 2.93/2.23 tff(3197,plain,
% 2.93/2.23 ($false),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3196, 104, 25, 695, 687, 3183, 3182, 1316, 3181, 3190])).
% 2.93/2.23 tff(3198,plain,((~hskp20) | hskp6 | c0_1(a31) | c3_1(a31) | c2_1(a31) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.93/2.23 tff(3199,plain,
% 2.93/2.23 (hskp0),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3198, 3180, 3167, 3164, 3166, 25])).
% 2.93/2.23 tff(3200,plain,
% 2.93/2.23 (~c3_1(a1)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[117, 3199])).
% 2.93/2.23 tff(3201,plain,
% 2.93/2.23 (c1_1(a1)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[139, 3199])).
% 2.93/2.23 tff(3202,plain,
% 2.93/2.23 (c2_1(a1)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[128, 3199])).
% 2.93/2.23 tff(3203,plain,
% 2.93/2.23 ($false),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[180, 3202, 3201, 25, 3200])).
% 2.93/2.23 tff(3204,plain,(hskp6 | c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.23 tff(3205,plain,
% 2.93/2.23 (hskp6),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3204, 780, 26])).
% 2.93/2.23 tff(3206,plain,
% 2.93/2.23 (~c3_1(a13)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[186, 3205])).
% 2.93/2.23 tff(3207,plain,
% 2.93/2.23 (~c1_1(a13)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[192, 3205])).
% 2.93/2.23 tff(3208,plain,
% 2.93/2.23 (~c0_1(a13)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[198, 3205])).
% 2.93/2.23 tff(3209,plain,
% 2.93/2.23 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))),
% 2.93/2.23 inference(rewrite,[status(thm)],[])).
% 2.93/2.23 tff(3210,plain,
% 2.93/2.23 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13)) <=> (hskp1 | hskp0 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))),
% 2.93/2.23 inference(rewrite,[status(thm)],[])).
% 2.93/2.23 tff(3211,plain,
% 2.93/2.23 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0)))),
% 2.93/2.23 inference(monotonicity,[status(thm)],[3210])).
% 2.93/2.23 tff(3212,plain,
% 2.93/2.23 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))),
% 2.93/2.23 inference(transitivity,[status(thm)],[3211, 3209])).
% 2.93/2.23 tff(3213,plain,
% 2.93/2.23 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13))),
% 2.93/2.23 inference(quant_inst,[status(thm)],[])).
% 2.93/2.23 tff(3214,plain,
% 2.93/2.23 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0)),
% 2.93/2.23 inference(modus_ponens,[status(thm)],[3213, 3212])).
% 2.93/2.23 tff(3215,plain,
% 2.93/2.23 (hskp1 | hskp0),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3214, 104, 3208, 3207, 3206, 763])).
% 2.93/2.23 tff(3216,plain,
% 2.93/2.23 (hskp1),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3215, 11])).
% 2.93/2.23 tff(3217,plain,
% 2.93/2.23 (~c2_1(a2)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[262, 3216])).
% 2.93/2.23 tff(3218,plain,
% 2.93/2.23 (~c0_1(a2)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[268, 3216])).
% 2.93/2.23 tff(3219,plain,
% 2.93/2.23 (~hskp27),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[633, 3131, 11, 3128, 48])).
% 2.93/2.23 tff(3220,plain,
% 2.93/2.23 (~hskp20),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[697, 3131, 12, 3217, 11, 3218])).
% 2.93/2.23 tff(3221,plain,
% 2.93/2.23 (hskp21),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3179, 3220, 780, 26])).
% 2.93/2.23 tff(3222,plain,
% 2.93/2.23 (~c2_1(a38)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[2495, 3221])).
% 2.93/2.23 tff(3223,plain,
% 2.93/2.23 ($false),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[678, 3222, 3221, 3219, 3217, 12, 3218])).
% 2.93/2.23 tff(3224,plain,(hskp3 | c3_1(a2) | c2_1(a58) | c1_1(a58) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.93/2.23 tff(3225,plain,
% 2.93/2.23 (hskp3),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3224, 11, 780, 26, 12])).
% 2.93/2.23 tff(3226,plain,
% 2.93/2.23 (~c2_1(a7)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[2959, 3225])).
% 2.93/2.23 tff(3227,plain,
% 2.93/2.23 (c3_1(a7)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[2972, 3225])).
% 2.93/2.23 tff(3228,plain,
% 2.93/2.23 (c0_1(a7)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[2983, 3225])).
% 2.93/2.23 tff(3229,plain,
% 2.93/2.23 (~c1_1(a7)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3033, 104, 3228, 3227, 3208, 3207, 3206, 3226, 36])).
% 2.93/2.23 tff(3230,plain,
% 2.93/2.23 (hskp13 | c1_1(a7)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[2990, 104, 3128, 3228, 3227, 2010])).
% 2.93/2.23 tff(3231,plain,
% 2.93/2.23 (hskp13),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3230, 3229])).
% 2.93/2.23 tff(3232,plain,
% 2.93/2.23 (~c3_1(a21)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[831, 3231])).
% 2.93/2.23 tff(3233,plain,
% 2.93/2.23 (c2_1(a21)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[842, 3231])).
% 2.93/2.23 tff(3234,plain,
% 2.93/2.23 (c0_1(a21)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[853, 3231])).
% 2.93/2.23 tff(3235,plain,
% 2.93/2.23 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c3_1(a21) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c0_1(a21)) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c3_1(a21) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.93/2.23 inference(rewrite,[status(thm)],[])).
% 2.93/2.23 tff(3236,plain,
% 2.93/2.23 ((hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7))) <=> (hskp20 | c3_1(a21) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.93/2.23 inference(rewrite,[status(thm)],[])).
% 2.93/2.23 tff(3237,plain,
% 2.93/2.23 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c3_1(a21) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c0_1(a21)) | (~c2_1(a21))))),
% 2.93/2.23 inference(monotonicity,[status(thm)],[3236])).
% 2.93/2.23 tff(3238,plain,
% 2.93/2.23 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c3_1(a21) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.93/2.23 inference(transitivity,[status(thm)],[3237, 3235])).
% 2.93/2.23 tff(3239,plain,
% 2.93/2.23 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7)))),
% 2.93/2.23 inference(quant_inst,[status(thm)],[])).
% 2.93/2.23 tff(3240,plain,
% 2.93/2.23 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c3_1(a21) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c0_1(a21)) | (~c2_1(a21))),
% 2.93/2.23 inference(modus_ponens,[status(thm)],[3239, 3238])).
% 2.93/2.23 tff(3241,plain,
% 2.93/2.23 (hskp20),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3240, 104, 3234, 3233, 3228, 3227, 3232, 3150, 3229])).
% 2.93/2.23 tff(3242,plain,
% 2.93/2.23 (~c0_1(a37)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[685, 3241])).
% 2.93/2.23 tff(3243,plain,
% 2.93/2.23 (c3_1(a37)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[555, 3241])).
% 2.93/2.23 tff(3244,plain,
% 2.93/2.23 (~c2_1(a37)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[693, 104, 11, 3243, 3242, 3218, 3217, 12, 24])).
% 2.93/2.23 tff(3245,plain,
% 2.93/2.23 (c1_1(a37)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[566, 3241])).
% 2.93/2.23 tff(3246,plain,
% 2.93/2.23 (hskp28),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[697, 3241, 12, 3217, 11, 3218])).
% 2.93/2.23 tff(3247,plain,
% 2.93/2.23 (c3_1(a25)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[487, 3246])).
% 2.93/2.23 tff(3248,plain,
% 2.93/2.23 (c1_1(a25)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[498, 3246])).
% 2.93/2.23 tff(3249,plain,
% 2.93/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 2.93/2.23 inference(rewrite,[status(thm)],[])).
% 2.93/2.23 tff(3250,plain,
% 2.93/2.23 (((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7))) <=> (c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 2.93/2.23 inference(rewrite,[status(thm)],[])).
% 2.93/2.23 tff(3251,plain,
% 2.93/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25))))),
% 2.93/2.23 inference(monotonicity,[status(thm)],[3250])).
% 2.93/2.23 tff(3252,plain,
% 2.93/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 2.93/2.23 inference(transitivity,[status(thm)],[3251, 3249])).
% 2.93/2.23 tff(3253,plain,
% 2.93/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))),
% 2.93/2.23 inference(quant_inst,[status(thm)],[])).
% 2.93/2.23 tff(3254,plain,
% 2.93/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25))),
% 2.93/2.23 inference(modus_ponens,[status(thm)],[3253, 3252])).
% 2.93/2.23 tff(3255,plain,
% 2.93/2.23 (~c0_1(a25)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3254, 104, 3248, 3247, 3245, 3243, 3227, 3226, 1772, 3229, 3244])).
% 2.93/2.23 tff(3256,plain,
% 2.93/2.23 (~c1_1(a21)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3000, 104, 3233, 3228, 3227, 3232, 3226, 279, 3229])).
% 2.93/2.23 tff(3257,plain,
% 2.93/2.23 (hskp18),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[2743, 104, 3234, 3233, 3232, 2737, 3256])).
% 2.93/2.23 tff(3258,plain,
% 2.93/2.23 (~c3_1(a31)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[403, 3257])).
% 2.93/2.23 tff(3259,plain,
% 2.93/2.23 (c1_1(a31)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[414, 3257])).
% 2.93/2.23 tff(3260,plain,
% 2.93/2.23 (~c2_1(a31)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3011, 104, 3259, 3228, 3227, 3258, 3226, 279, 3229])).
% 2.93/2.23 tff(3261,plain,
% 2.93/2.23 (~c0_1(a31)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[444, 3257])).
% 2.93/2.23 tff(3262,plain,
% 2.93/2.23 (c2_1(a25)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[509, 3246])).
% 2.93/2.23 tff(3263,plain,
% 2.93/2.23 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))),
% 2.93/2.23 inference(rewrite,[status(thm)],[])).
% 2.93/2.23 tff(3264,plain,
% 2.93/2.23 ((hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a31) | c2_1(a31) | c0_1(a31)) <=> (hskp0 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))),
% 2.93/2.23 inference(rewrite,[status(thm)],[])).
% 2.93/2.23 tff(3265,plain,
% 2.93/2.23 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25)))),
% 2.93/2.23 inference(monotonicity,[status(thm)],[3264])).
% 2.93/2.23 tff(3266,plain,
% 2.93/2.23 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))),
% 2.93/2.23 inference(transitivity,[status(thm)],[3265, 3263])).
% 2.93/2.23 tff(3267,plain,
% 2.93/2.23 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a31) | c2_1(a31) | c0_1(a31))),
% 2.93/2.23 inference(quant_inst,[status(thm)],[])).
% 2.93/2.23 tff(3268,plain,
% 2.93/2.23 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25)),
% 2.93/2.23 inference(modus_ponens,[status(thm)],[3267, 3266])).
% 2.93/2.23 tff(3269,plain,
% 2.93/2.23 ($false),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3268, 104, 11, 3262, 3247, 3261, 3258, 24, 3260, 3255])).
% 2.93/2.23 tff(3270,plain,(hskp0 | c3_1(a2) | c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.23 tff(3271,plain,
% 2.93/2.23 (hskp0),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3270, 12, 780, 26])).
% 2.93/2.23 tff(3272,plain,
% 2.93/2.23 (~c3_1(a1)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[117, 3271])).
% 2.93/2.23 tff(3273,plain,
% 2.93/2.23 (c2_1(a1)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[128, 3271])).
% 2.93/2.23 tff(3274,plain,
% 2.93/2.23 (c1_1(a1)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[139, 3271])).
% 2.93/2.23 tff(3275,plain,
% 2.93/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))),
% 2.93/2.23 inference(rewrite,[status(thm)],[])).
% 2.93/2.23 tff(3276,plain,
% 2.93/2.23 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))),
% 2.93/2.23 inference(rewrite,[status(thm)],[])).
% 2.93/2.23 tff(3277,plain,
% 2.93/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58))))),
% 2.93/2.23 inference(monotonicity,[status(thm)],[3276])).
% 2.93/2.23 tff(3278,plain,
% 2.93/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))),
% 2.93/2.23 inference(transitivity,[status(thm)],[3277, 3275])).
% 2.93/2.23 tff(3279,plain,
% 2.93/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))),
% 2.93/2.23 inference(quant_inst,[status(thm)],[])).
% 2.93/2.23 tff(3280,plain,
% 2.93/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58))),
% 2.93/2.23 inference(modus_ponens,[status(thm)],[3279, 3278])).
% 2.93/2.23 tff(3281,plain,
% 2.93/2.23 (~c3_1(a58)),
% 2.93/2.23 inference(unit_resolution,[status(thm)],[3280, 104, 780, 3274, 3273, 3122, 26, 3272, 279])).
% 2.93/2.23 tff(3282,plain,
% 2.93/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c3_1(a58))),
% 2.93/2.23 inference(rewrite,[status(thm)],[])).
% 2.93/2.23 tff(3283,plain,
% 2.93/2.23 (((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a58) | c1_1(a58) | c3_1(a58)) <=> (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c3_1(a58))),
% 2.93/2.24 inference(rewrite,[status(thm)],[])).
% 2.93/2.24 tff(3284,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c3_1(a58)))),
% 2.93/2.24 inference(monotonicity,[status(thm)],[3283])).
% 2.93/2.24 tff(3285,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c3_1(a58))),
% 2.93/2.24 inference(transitivity,[status(thm)],[3284, 3282])).
% 2.93/2.24 tff(3286,plain,
% 2.93/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a58) | c1_1(a58) | c3_1(a58))),
% 2.93/2.24 inference(quant_inst,[status(thm)],[])).
% 2.93/2.24 tff(3287,plain,
% 2.93/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c3_1(a58)),
% 2.93/2.24 inference(modus_ponens,[status(thm)],[3286, 3285])).
% 2.93/2.24 tff(3288,plain,
% 2.93/2.24 (c0_1(a1)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[3287, 104, 780, 3273, 3122, 26, 3272, 341, 3281])).
% 2.93/2.24 tff(3289,assumption,(c0_1(a1)), introduced(assumption)).
% 2.93/2.24 tff(3290,assumption,(hskp3), introduced(assumption)).
% 2.93/2.24 tff(3291,plain,
% 2.93/2.24 (~c2_1(a7)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[2959, 3290])).
% 2.93/2.24 tff(3292,plain,
% 2.93/2.24 (c3_1(a7)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[2972, 3290])).
% 2.93/2.24 tff(3293,plain,
% 2.93/2.24 (c0_1(a7)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[2983, 3290])).
% 2.93/2.24 tff(3294,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))),
% 2.93/2.24 inference(rewrite,[status(thm)],[])).
% 2.93/2.24 tff(3295,plain,
% 2.93/2.24 (((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7))) <=> (c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))),
% 2.93/2.24 inference(rewrite,[status(thm)],[])).
% 2.93/2.24 tff(3296,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7))))),
% 2.93/2.24 inference(monotonicity,[status(thm)],[3295])).
% 2.93/2.24 tff(3297,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))),
% 2.93/2.24 inference(transitivity,[status(thm)],[3296, 3294])).
% 2.93/2.24 tff(3298,plain,
% 2.93/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7)))),
% 2.93/2.24 inference(quant_inst,[status(thm)],[])).
% 2.93/2.24 tff(3299,plain,
% 2.93/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7))),
% 2.93/2.24 inference(modus_ponens,[status(thm)],[3298, 3297])).
% 2.93/2.24 tff(3300,plain,
% 2.93/2.24 (~c1_1(a7)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[3299, 104, 3293, 3292, 153, 3291, 151, 970, 3289])).
% 2.93/2.24 tff(3301,plain,
% 2.93/2.24 ($false),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[3119, 104, 3293, 3292, 153, 152, 3291, 151, 279, 3300])).
% 2.93/2.24 tff(3302,plain,((~hskp3) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a1))), inference(lemma,lemma(discharge,[]))).
% 2.93/2.24 tff(3303,plain,
% 2.93/2.24 (~hskp3),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[3302, 3274, 3273, 3272, 3288])).
% 2.93/2.24 tff(3304,plain,
% 2.93/2.24 (~hskp28),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[3130, 3303, 3128])).
% 2.93/2.24 tff(3305,plain,
% 2.93/2.24 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 2.93/2.24 inference(bind,[status(th)],[])).
% 2.93/2.24 tff(3306,plain,
% 2.93/2.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.24 inference(quant_intro,[status(thm)],[3305])).
% 2.93/2.24 tff(3307,plain,
% 2.93/2.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.24 inference(rewrite,[status(thm)],[])).
% 2.93/2.24 tff(3308,plain,
% 2.93/2.24 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 2.93/2.24 inference(bind,[status(th)],[])).
% 2.93/2.24 tff(3309,plain,
% 2.93/2.24 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.24 inference(quant_intro,[status(thm)],[3308])).
% 2.93/2.24 tff(3310,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 2.93/2.24 tff(3311,plain,
% 2.93/2.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.24 inference(modus_ponens,[status(thm)],[3310, 3309])).
% 2.93/2.24 tff(3312,plain,
% 2.93/2.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.24 inference(modus_ponens,[status(thm)],[3311, 3307])).
% 2.93/2.24 tff(3313,plain,(
% 2.93/2.24 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.24 inference(skolemize,[status(sab)],[3312])).
% 2.93/2.24 tff(3314,plain,
% 2.93/2.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.24 inference(modus_ponens,[status(thm)],[3313, 3306])).
% 2.93/2.24 tff(3315,assumption,(c0_1(a2)), introduced(assumption)).
% 2.93/2.24 tff(3316,plain,
% 2.93/2.24 (~hskp1),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[268, 3315])).
% 2.93/2.24 tff(3317,plain,
% 2.93/2.24 (hskp20),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[544, 3316, 3131])).
% 2.93/2.24 tff(3318,plain,
% 2.93/2.24 (c3_1(a37)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[555, 3317])).
% 2.93/2.24 tff(3319,plain,
% 2.93/2.24 (c1_1(a37)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[566, 3317])).
% 2.93/2.24 tff(3320,plain,
% 2.93/2.24 (~c2_1(a37)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[571, 104, 3128, 48, 3319, 3318, 10])).
% 2.93/2.24 tff(3321,plain,
% 2.93/2.24 (hskp2 | hskp1),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[247, 104, 3208, 3207, 3206, 47])).
% 2.93/2.24 tff(3322,plain,
% 2.93/2.24 (hskp2),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[3321, 3316])).
% 2.93/2.24 tff(3323,plain,
% 2.93/2.24 (~c2_1(a3)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[206, 3322])).
% 2.93/2.24 tff(3324,plain,
% 2.93/2.24 (c3_1(a3)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[217, 3322])).
% 2.93/2.24 tff(3325,plain,
% 2.93/2.24 (c1_1(a3)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[228, 3322])).
% 2.93/2.24 tff(3326,plain,
% 2.93/2.24 (hskp9),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[1296, 104, 3325, 3324, 3274, 3273, 3323, 3272, 890])).
% 2.93/2.24 tff(3327,plain,
% 2.93/2.24 (~c3_1(a16)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[902, 3326])).
% 2.93/2.24 tff(3328,plain,
% 2.93/2.24 (~c0_1(a37)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[685, 3317])).
% 2.93/2.24 tff(3329,plain,
% 2.93/2.24 (c1_1(a16)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[913, 3326])).
% 2.93/2.24 tff(3330,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a16) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))),
% 2.93/2.24 inference(rewrite,[status(thm)],[])).
% 2.93/2.24 tff(3331,plain,
% 2.93/2.24 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37))) <=> (c0_1(a37) | c3_1(a16) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))),
% 2.93/2.24 inference(rewrite,[status(thm)],[])).
% 2.93/2.24 tff(3332,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a16) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37))))),
% 2.93/2.24 inference(monotonicity,[status(thm)],[3331])).
% 2.93/2.24 tff(3333,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))),
% 2.93/2.24 inference(transitivity,[status(thm)],[3332, 3330])).
% 2.93/2.24 tff(3334,plain,
% 2.93/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))),
% 2.93/2.24 inference(quant_inst,[status(thm)],[])).
% 2.93/2.24 tff(3335,plain,
% 2.93/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37))),
% 2.93/2.24 inference(modus_ponens,[status(thm)],[3334, 3333])).
% 2.93/2.24 tff(3336,plain,
% 2.93/2.24 (c2_1(a16)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[3335, 104, 3318, 3329, 3274, 3273, 3328, 3327, 3272, 734, 3320])).
% 2.93/2.24 tff(3337,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a58))),
% 2.93/2.24 inference(rewrite,[status(thm)],[])).
% 2.93/2.24 tff(3338,plain,
% 2.93/2.24 (((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c3_1(a58)) <=> (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a58))),
% 2.93/2.24 inference(rewrite,[status(thm)],[])).
% 2.93/2.24 tff(3339,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a58)))),
% 2.93/2.24 inference(monotonicity,[status(thm)],[3338])).
% 2.93/2.24 tff(3340,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a58))),
% 2.93/2.24 inference(transitivity,[status(thm)],[3339, 3337])).
% 2.93/2.24 tff(3341,plain,
% 2.93/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c3_1(a58))),
% 2.93/2.24 inference(quant_inst,[status(thm)],[])).
% 2.93/2.24 tff(3342,plain,
% 2.93/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a58)),
% 2.93/2.24 inference(modus_ponens,[status(thm)],[3341, 3340])).
% 2.93/2.24 tff(3343,plain,
% 2.93/2.24 (~c2_1(a13)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[3342, 104, 780, 3122, 26, 3208, 3206, 341, 3281])).
% 2.93/2.24 tff(3344,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 2.93/2.24 inference(rewrite,[status(thm)],[])).
% 2.93/2.24 tff(3345,plain,
% 2.93/2.24 (((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_1(a3)) | (~c0_1(a3))) <=> (c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 2.93/2.24 inference(rewrite,[status(thm)],[])).
% 2.93/2.24 tff(3346,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_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) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))))),
% 2.93/2.24 inference(monotonicity,[status(thm)],[3345])).
% 2.93/2.24 tff(3347,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_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) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 2.93/2.24 inference(transitivity,[status(thm)],[3346, 3344])).
% 2.93/2.24 tff(3348,plain,
% 2.93/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_1(a3)) | (~c0_1(a3)))),
% 2.93/2.24 inference(quant_inst,[status(thm)],[])).
% 2.93/2.24 tff(3349,plain,
% 2.93/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))),
% 2.93/2.24 inference(modus_ponens,[status(thm)],[3348, 3347])).
% 2.93/2.24 tff(3350,plain,
% 2.93/2.24 (~c0_1(a3)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[3349, 104, 3325, 3324, 3274, 3323, 3272, 970, 3288])).
% 2.93/2.24 tff(3351,plain,
% 2.93/2.24 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 2.93/2.24 inference(rewrite,[status(thm)],[])).
% 2.93/2.24 tff(3352,plain,
% 2.93/2.24 ((hskp12 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (hskp12 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 2.93/2.24 inference(rewrite,[status(thm)],[])).
% 2.93/2.24 tff(3353,plain,
% 2.93/2.24 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3)))),
% 2.93/2.24 inference(monotonicity,[status(thm)],[3352])).
% 2.93/2.24 tff(3354,plain,
% 2.93/2.24 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 2.93/2.24 inference(transitivity,[status(thm)],[3353, 3351])).
% 2.93/2.24 tff(3355,plain,
% 2.93/2.24 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 2.93/2.24 inference(quant_inst,[status(thm)],[])).
% 2.93/2.24 tff(3356,plain,
% 2.93/2.24 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3)),
% 2.93/2.24 inference(modus_ponens,[status(thm)],[3355, 3354])).
% 2.93/2.24 tff(3357,plain,
% 2.93/2.24 (hskp12),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[3356, 104, 3324, 3274, 3323, 3272, 987, 3288, 3350])).
% 2.93/2.24 tff(3358,plain,
% 2.93/2.24 (~c1_1(a20)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[1005, 3357])).
% 2.93/2.24 tff(3359,plain,
% 2.93/2.24 (c2_1(a20)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[1016, 3357])).
% 2.93/2.24 tff(3360,plain,
% 2.93/2.24 (~c0_1(a20)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[1359, 104, 3359, 3329, 3358, 3327, 3208, 3206, 1342, 3343, 3336])).
% 2.93/2.24 tff(3361,plain,
% 2.93/2.24 (~c1_1(a2)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[1799, 104, 3324, 3274, 3273, 3323, 13, 12, 3272, 734, 3350])).
% 2.93/2.24 tff(3362,plain,
% 2.93/2.24 (~c3_1(a20)),
% 2.93/2.24 inference(unit_resolution,[status(thm)],[999, 3357])).
% 2.93/2.24 tff(3363,plain,
% 2.93/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | c1_1(a58) | c3_1(a20) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a20) | (~c2_1(a20)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | c1_1(a58) | c3_1(a20) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a20) | (~c2_1(a20)) | c3_1(a58))),
% 2.93/2.24 inference(rewrite,[status(thm)],[])).
% 2.93/2.24 tff(3364,plain,
% 2.93/2.24 (((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a58) | c1_1(a58) | c3_1(a58)) <=> (c2_1(a58) | c1_1(a58) | c3_1(a20) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a20) | (~c2_1(a20)) | c3_1(a58))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3365,plain,
% 2.93/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | c1_1(a58) | c3_1(a20) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a20) | (~c2_1(a20)) | c3_1(a58)))),
% 2.93/2.25 inference(monotonicity,[status(thm)],[3364])).
% 2.93/2.25 tff(3366,plain,
% 2.93/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | c1_1(a58) | c3_1(a20) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a20) | (~c2_1(a20)) | c3_1(a58))),
% 2.93/2.25 inference(transitivity,[status(thm)],[3365, 3363])).
% 2.93/2.25 tff(3367,plain,
% 2.93/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a58) | c1_1(a58) | c3_1(a58))),
% 2.93/2.25 inference(quant_inst,[status(thm)],[])).
% 2.93/2.25 tff(3368,plain,
% 2.93/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | c1_1(a58) | c3_1(a20) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a20) | (~c2_1(a20)) | c3_1(a58)),
% 2.93/2.25 inference(modus_ponens,[status(thm)],[3367, 3366])).
% 2.93/2.25 tff(3369,plain,
% 2.93/2.25 ($false),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3368, 104, 780, 3359, 26, 3362, 3315, 12, 341, 3281, 3361, 3360])).
% 2.93/2.25 tff(3370,plain,((~c0_1(a2)) | c2_1(a58) | c1_1(a58) | c3_1(a2) | c2_1(a2) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.93/2.25 tff(3371,plain,
% 2.93/2.25 (~c0_1(a2)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3370, 48, 26, 12, 13, 780])).
% 2.93/2.25 tff(3372,plain,
% 2.93/2.25 (c2_1(a38)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[1201, 475, 2556, 568, 468, 752, 12, 14, 13, 48, 2554, 2555])).
% 2.93/2.25 tff(3373,plain,
% 2.93/2.25 (hskp21),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[2558, 475, 568, 12, 2553, 13, 14, 468, 752, 48])).
% 2.93/2.25 tff(3374,plain,
% 2.93/2.25 ($false),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[2495, 3373, 3372])).
% 2.93/2.25 tff(3375,plain,(c1_1(a15) | hskp24 | c3_1(a2) | (~hskp0) | c2_1(a2) | c0_1(a2) | c3_1(a15) | c2_1(a15) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.93/2.25 tff(3376,plain,
% 2.93/2.25 (c1_1(a15)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3375, 752, 12, 3271, 13, 14, 468, 3128, 48])).
% 2.93/2.25 tff(3377,plain,
% 2.93/2.25 (~hskp8),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[2184, 3376])).
% 2.93/2.25 tff(3378,plain,
% 2.93/2.25 (hskp8 | hskp7 | c0_1(a2) | c2_1(a2)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[1401, 104, 12, 1389])).
% 2.93/2.25 tff(3379,plain,
% 2.93/2.25 (hskp7),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3378, 3377, 14, 13])).
% 2.93/2.25 tff(3380,plain,
% 2.93/2.25 (~c2_1(a14)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[1408, 3379])).
% 2.93/2.25 tff(3381,plain,
% 2.93/2.25 (~c0_1(a14)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[1433, 3379])).
% 2.93/2.25 tff(3382,plain,
% 2.93/2.25 (c1_1(a14)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[1419, 3379])).
% 2.93/2.25 tff(3383,plain,
% 2.93/2.25 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | (~c1_1(a14)))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3384,plain,
% 2.93/2.25 ((hskp9 | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14))) <=> (hskp9 | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | (~c1_1(a14)))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3385,plain,
% 2.93/2.25 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | (~c1_1(a14))))),
% 2.93/2.25 inference(monotonicity,[status(thm)],[3384])).
% 2.93/2.25 tff(3386,plain,
% 2.93/2.25 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | (~c1_1(a14)))),
% 2.93/2.25 inference(transitivity,[status(thm)],[3385, 3383])).
% 2.93/2.25 tff(3387,plain,
% 2.93/2.25 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))),
% 2.93/2.25 inference(quant_inst,[status(thm)],[])).
% 2.93/2.25 tff(3388,plain,
% 2.93/2.25 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | (~c1_1(a14))),
% 2.93/2.25 inference(modus_ponens,[status(thm)],[3387, 3386])).
% 2.93/2.25 tff(3389,plain,
% 2.93/2.25 (hskp9),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3388, 104, 3382, 3274, 3273, 3381, 3380, 3314, 3288])).
% 2.93/2.25 tff(3390,plain,
% 2.93/2.25 (~c3_1(a16)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[902, 3389])).
% 2.93/2.25 tff(3391,plain,
% 2.93/2.25 (c1_1(a16)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[913, 3389])).
% 2.93/2.25 tff(3392,plain,
% 2.93/2.25 (c0_1(a16)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[924, 3389])).
% 2.93/2.25 tff(3393,plain,
% 2.93/2.25 (hskp20),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3179, 811, 780, 26])).
% 2.93/2.25 tff(3394,plain,
% 2.93/2.25 (c3_1(a37)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[555, 3393])).
% 2.93/2.25 tff(3395,plain,
% 2.93/2.25 (c1_1(a37)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[566, 3393])).
% 2.93/2.25 tff(3396,plain,
% 2.93/2.25 (~c2_1(a37)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[571, 104, 3128, 48, 3395, 3394, 10])).
% 2.93/2.25 tff(3397,plain,
% 2.93/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3398,plain,
% 2.93/2.25 (((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a13) | c1_1(a13) | c0_1(a13)) <=> (c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3399,plain,
% 2.93/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21))))),
% 2.93/2.25 inference(monotonicity,[status(thm)],[3398])).
% 2.93/2.25 tff(3400,plain,
% 2.93/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))),
% 2.93/2.25 inference(transitivity,[status(thm)],[3399, 3397])).
% 2.93/2.25 tff(3401,plain,
% 2.93/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a13) | c1_1(a13) | c0_1(a13))),
% 2.93/2.25 inference(quant_inst,[status(thm)],[])).
% 2.93/2.25 tff(3402,plain,
% 2.93/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21))),
% 2.93/2.25 inference(modus_ponens,[status(thm)],[3401, 3400])).
% 2.93/2.25 tff(3403,plain,
% 2.93/2.25 (c1_1(a21)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3402, 104, 3153, 3152, 2156, 752, 468, 3208, 3207, 380, 352])).
% 2.93/2.25 tff(3404,plain,
% 2.93/2.25 (~c0_1(a37)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[685, 3393])).
% 2.93/2.25 tff(3405,plain,
% 2.93/2.25 ($false),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[2312, 104, 3394, 3153, 3404, 3152, 2156, 752, 468, 734, 3403, 3396])).
% 2.93/2.25 tff(3406,plain,(hskp21 | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a13) | hskp3 | c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.25 tff(3407,plain,
% 2.93/2.25 (hskp21),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3406, 3376, 752, 468, 3343, 48, 780, 26])).
% 2.93/2.25 tff(3408,plain,
% 2.93/2.25 (~c2_1(a38)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[2495, 3407])).
% 2.93/2.25 tff(3409,plain,
% 2.93/2.25 (hskp27),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[678, 3408, 3407, 13, 12, 14])).
% 2.93/2.25 tff(3410,plain,
% 2.93/2.25 (c3_1(a12)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[605, 3409])).
% 2.93/2.25 tff(3411,plain,
% 2.93/2.25 (c1_1(a12)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[616, 3409])).
% 2.93/2.25 tff(3412,plain,
% 2.93/2.25 (c0_1(a12)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[1192, 3409])).
% 2.93/2.25 tff(3413,plain,
% 2.93/2.25 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3414,plain,
% 2.93/2.25 ((hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16))) <=> (hskp8 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3415,plain,
% 2.93/2.25 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))))),
% 2.93/2.25 inference(monotonicity,[status(thm)],[3414])).
% 2.93/2.25 tff(3416,plain,
% 2.93/2.25 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 2.93/2.25 inference(transitivity,[status(thm)],[3415, 3413])).
% 2.93/2.25 tff(3417,plain,
% 2.93/2.25 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)))),
% 2.93/2.25 inference(quant_inst,[status(thm)],[])).
% 2.93/2.25 tff(3418,plain,
% 2.93/2.25 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))),
% 2.93/2.25 inference(modus_ponens,[status(thm)],[3417, 3416])).
% 2.93/2.25 tff(3419,plain,
% 2.93/2.25 ($false),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3418, 104, 3377, 3412, 3411, 3410, 3392, 3391, 3390, 2283])).
% 2.93/2.25 tff(3420,plain,(c2_1(a15) | c2_1(a2) | c3_1(a2) | c0_1(a2) | c3_1(a15) | hskp3 | c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.25 tff(3421,plain,
% 2.93/2.25 (c2_1(a15)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3420, 14, 12, 13, 468, 48, 780, 26])).
% 2.93/2.25 tff(3422,plain,
% 2.93/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | c3_1(a58))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3423,plain,
% 2.93/2.25 (((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c3_1(a58)) <=> (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | c3_1(a58))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3424,plain,
% 2.93/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | c3_1(a58)))),
% 2.93/2.25 inference(monotonicity,[status(thm)],[3423])).
% 2.93/2.25 tff(3425,plain,
% 2.93/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | c3_1(a58))),
% 2.93/2.25 inference(transitivity,[status(thm)],[3424, 3422])).
% 2.93/2.25 tff(3426,plain,
% 2.93/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c3_1(a58))),
% 2.93/2.25 inference(quant_inst,[status(thm)],[])).
% 2.93/2.25 tff(3427,plain,
% 2.93/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | c3_1(a58)),
% 2.93/2.25 inference(modus_ponens,[status(thm)],[3426, 3425])).
% 2.93/2.25 tff(3428,plain,
% 2.93/2.25 ((~c2_1(a15)) | c0_1(a15)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3427, 104, 780, 3122, 26, 468, 341, 3281])).
% 2.93/2.25 tff(3429,plain,
% 2.93/2.25 (c0_1(a15)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3428, 3421])).
% 2.93/2.25 tff(3430,plain,
% 2.93/2.25 (~hskp8),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[2093, 3421])).
% 2.93/2.25 tff(3431,plain,
% 2.93/2.25 (hskp7),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3378, 3430, 14, 13])).
% 2.93/2.25 tff(3432,plain,
% 2.93/2.25 (~c2_1(a14)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[1408, 3431])).
% 2.93/2.25 tff(3433,plain,
% 2.93/2.25 (~c0_1(a14)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[1433, 3431])).
% 2.93/2.25 tff(3434,plain,
% 2.93/2.25 (c1_1(a15)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[1867, 3421, 3273, 3272, 13, 468, 14, 3274, 12])).
% 2.93/2.25 tff(3435,plain,
% 2.93/2.25 (c1_1(a14)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[1419, 3431])).
% 2.93/2.25 tff(3436,plain,
% 2.93/2.25 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c0_1(a15)))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3437,plain,
% 2.93/2.25 ((hskp9 | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14))) <=> (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c0_1(a15)))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3438,plain,
% 2.93/2.25 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c0_1(a15))))),
% 2.93/2.25 inference(monotonicity,[status(thm)],[3437])).
% 2.93/2.25 tff(3439,plain,
% 2.93/2.25 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c0_1(a15)))),
% 2.93/2.25 inference(transitivity,[status(thm)],[3438, 3436])).
% 2.93/2.25 tff(3440,plain,
% 2.93/2.25 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))),
% 2.93/2.25 inference(quant_inst,[status(thm)],[])).
% 2.93/2.25 tff(3441,plain,
% 2.93/2.25 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c0_1(a15))),
% 2.93/2.25 inference(modus_ponens,[status(thm)],[3440, 3439])).
% 2.93/2.25 tff(3442,plain,
% 2.93/2.25 (hskp9),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3441, 104, 3435, 3434, 3421, 3433, 3432, 3314, 3429])).
% 2.93/2.25 tff(3443,plain,
% 2.93/2.25 (~c3_1(a16)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[902, 3442])).
% 2.93/2.25 tff(3444,plain,
% 2.93/2.25 (c1_1(a16)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[913, 3442])).
% 2.93/2.25 tff(3445,plain,
% 2.93/2.25 (c0_1(a16)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[924, 3442])).
% 2.93/2.25 tff(3446,plain,
% 2.93/2.25 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp10 | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3447,plain,
% 2.93/2.25 ((hskp21 | hskp10 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1))) <=> (hskp21 | hskp10 | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3448,plain,
% 2.93/2.25 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1))))),
% 2.93/2.25 inference(monotonicity,[status(thm)],[3447])).
% 2.93/2.25 tff(3449,plain,
% 2.93/2.25 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp10 | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)))),
% 2.93/2.25 inference(transitivity,[status(thm)],[3448, 3446])).
% 2.93/2.25 tff(3450,plain,
% 2.93/2.25 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)))),
% 2.93/2.25 inference(quant_inst,[status(thm)],[])).
% 2.93/2.25 tff(3451,plain,
% 2.93/2.25 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp10 | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1))),
% 2.93/2.25 inference(modus_ponens,[status(thm)],[3450, 3449])).
% 2.93/2.25 tff(3452,plain,
% 2.93/2.25 (hskp21 | hskp10 | (~c0_1(a1))),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3451, 104, 153, 151, 876])).
% 2.93/2.25 tff(3453,plain,
% 2.93/2.25 (hskp10),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[3452, 811, 3289])).
% 2.93/2.25 tff(3454,plain,
% 2.93/2.25 (~c1_1(a18)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[937, 3453])).
% 2.93/2.25 tff(3455,plain,
% 2.93/2.25 (~c0_1(a18)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[943, 3453])).
% 2.93/2.25 tff(3456,plain,
% 2.93/2.25 (c3_1(a18)),
% 2.93/2.25 inference(unit_resolution,[status(thm)],[1037, 3453])).
% 2.93/2.25 tff(3457,plain,
% 2.93/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a18) | c1_1(a18) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a18) | c1_1(a18) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c3_1(a18)))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3458,plain,
% 2.93/2.25 (((~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18))) <=> (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a18) | c1_1(a18) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c3_1(a18)))),
% 2.93/2.25 inference(rewrite,[status(thm)],[])).
% 2.93/2.25 tff(3459,plain,
% 2.93/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a18) | c1_1(a18) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c3_1(a18))))),
% 2.93/2.25 inference(monotonicity,[status(thm)],[3458])).
% 2.93/2.25 tff(3460,plain,
% 2.93/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a18) | c1_1(a18) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c3_1(a18)))),
% 2.93/2.25 inference(transitivity,[status(thm)],[3459, 3457])).
% 2.93/2.25 tff(3461,plain,
% 2.93/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))),
% 2.93/2.26 inference(quant_inst,[status(thm)],[])).
% 2.93/2.26 tff(3462,plain,
% 2.93/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a18) | c1_1(a18) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c3_1(a18))),
% 2.93/2.26 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 2.93/2.26 tff(3463,plain,
% 2.93/2.26 (~c3_1(a14)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3462, 104, 780, 3456, 3122, 26, 3455, 3454, 2239, 2238, 751])).
% 2.93/2.26 tff(3464,assumption,(c1_1(a14)), introduced(assumption)).
% 2.93/2.26 tff(3465,plain,
% 2.93/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | (~c1_1(a16)) | (~c2_1(a16)) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | (~c1_1(a16)) | (~c2_1(a16)) | c2_1(a37) | (~c3_1(a37)))),
% 2.93/2.26 inference(rewrite,[status(thm)],[])).
% 2.93/2.26 tff(3466,plain,
% 2.93/2.26 (((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37))) <=> (c0_1(a37) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | (~c1_1(a16)) | (~c2_1(a16)) | c2_1(a37) | (~c3_1(a37)))),
% 2.93/2.26 inference(rewrite,[status(thm)],[])).
% 2.93/2.26 tff(3467,plain,
% 2.93/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | (~c1_1(a16)) | (~c2_1(a16)) | c2_1(a37) | (~c3_1(a37))))),
% 2.93/2.26 inference(monotonicity,[status(thm)],[3466])).
% 2.93/2.26 tff(3468,plain,
% 2.93/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | (~c1_1(a16)) | (~c2_1(a16)) | c2_1(a37) | (~c3_1(a37)))),
% 2.93/2.26 inference(transitivity,[status(thm)],[3467, 3465])).
% 2.93/2.26 tff(3469,plain,
% 2.93/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))),
% 2.93/2.26 inference(quant_inst,[status(thm)],[])).
% 2.93/2.26 tff(3470,plain,
% 2.93/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | (~c1_1(a16)) | (~c2_1(a16)) | c2_1(a37) | (~c3_1(a37))),
% 2.93/2.26 inference(modus_ponens,[status(thm)],[3469, 3468])).
% 2.93/2.26 tff(3471,plain,
% 2.93/2.26 (~c2_1(a16)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3470, 104, 3394, 2637, 3464, 3404, 2636, 2238, 734, 3463, 3396])).
% 2.93/2.26 tff(3472,plain,
% 2.93/2.26 ($false),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[2625, 104, 3394, 2637, 3404, 2636, 2156, 1845, 468, 734, 3471, 3396])).
% 2.93/2.26 tff(3473,plain,(hskp21 | (~c1_1(a16)) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~c1_1(a14)) | c2_1(a14) | c2_1(a58) | c1_1(a58) | c0_1(a14) | hskp3 | (~c0_1(a1)) | (~c1_1(a1)) | c3_1(a1)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.26 tff(3474,plain,
% 2.93/2.26 (hskp21),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3473, 3444, 3443, 3434, 3421, 468, 3435, 3432, 780, 26, 3433, 48, 3288, 3274, 3272])).
% 2.93/2.26 tff(3475,plain,
% 2.93/2.26 (~c2_1(a38)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[2495, 3474])).
% 2.93/2.26 tff(3476,plain,
% 2.93/2.26 (hskp27),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[678, 3475, 3474, 13, 12, 14])).
% 2.93/2.26 tff(3477,plain,
% 2.93/2.26 (c3_1(a12)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[605, 3476])).
% 2.93/2.26 tff(3478,plain,
% 2.93/2.26 (c1_1(a12)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[616, 3476])).
% 2.93/2.26 tff(3479,plain,
% 2.93/2.26 (c0_1(a12)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[1192, 3476])).
% 2.93/2.26 tff(3480,plain,
% 2.93/2.26 ($false),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3418, 104, 3430, 3479, 3478, 3477, 3445, 3444, 3443, 2283])).
% 2.93/2.26 tff(3481,plain,(c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a15) | c2_1(a58) | c1_1(a58) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.93/2.26 tff(3482,plain,
% 2.93/2.26 (c3_1(a15)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3481, 3371, 12, 13, 780, 26, 48])).
% 2.93/2.26 tff(3483,plain,
% 2.93/2.26 (~hskp8),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[1394, 3482])).
% 2.93/2.26 tff(3484,plain,
% 2.93/2.26 (hskp7),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3378, 3483, 3371, 13])).
% 2.93/2.26 tff(3485,plain,
% 2.93/2.26 (~c2_1(a14)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[1408, 3484])).
% 2.93/2.26 tff(3486,plain,
% 2.93/2.26 (~c0_1(a14)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[1433, 3484])).
% 2.93/2.26 tff(3487,plain,
% 2.93/2.26 (c1_1(a14)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[1419, 3484])).
% 2.93/2.26 tff(3488,plain,
% 2.93/2.26 (hskp9),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3388, 104, 3487, 3274, 3273, 3486, 3485, 3314, 3288])).
% 2.93/2.26 tff(3489,plain,
% 2.93/2.26 (~c3_1(a16)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[902, 3488])).
% 2.93/2.26 tff(3490,plain,
% 2.93/2.26 (c1_1(a16)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[913, 3488])).
% 2.93/2.26 tff(3491,plain,
% 2.93/2.26 (c0_1(a16)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[924, 3488])).
% 2.93/2.26 tff(3492,plain,
% 2.93/2.26 (~c3_1(a58)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3280, 104, 780, 153, 152, 3122, 26, 151, 279])).
% 2.93/2.26 tff(3493,plain,
% 2.93/2.26 (c0_1(a1)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3287, 104, 780, 152, 3122, 26, 151, 341, 3492])).
% 2.93/2.26 tff(3494,plain,
% 2.93/2.26 (hskp10),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3452, 811, 3493])).
% 2.93/2.26 tff(3495,plain,
% 2.93/2.26 (~c1_1(a18)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[937, 3494])).
% 2.93/2.26 tff(3496,plain,
% 2.93/2.26 (~c0_1(a18)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[943, 3494])).
% 2.93/2.26 tff(3497,plain,
% 2.93/2.26 (c3_1(a18)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[1037, 3494])).
% 2.93/2.26 tff(3498,plain,
% 2.93/2.26 (~c3_1(a14)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3462, 104, 780, 3497, 3122, 26, 3496, 3495, 2239, 2238, 751])).
% 2.93/2.26 tff(3499,plain,
% 2.93/2.26 (hskp9),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3388, 104, 3464, 153, 152, 2239, 2238, 3314, 3493])).
% 2.93/2.26 tff(3500,plain,
% 2.93/2.26 (~c3_1(a16)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[902, 3499])).
% 2.93/2.26 tff(3501,plain,
% 2.93/2.26 (c1_1(a16)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[913, 3499])).
% 2.93/2.26 tff(3502,plain,
% 2.93/2.26 (~c2_1(a16)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3470, 104, 3394, 3501, 3464, 3404, 3500, 2238, 734, 3498, 3396])).
% 2.93/2.26 tff(3503,plain,
% 2.93/2.26 ($false),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3335, 104, 3394, 3501, 153, 152, 3404, 3500, 151, 734, 3502, 3396])).
% 2.93/2.26 tff(3504,plain,(hskp21 | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a14)) | c2_1(a14) | c2_1(a58) | c1_1(a58) | c0_1(a14) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.93/2.26 tff(3505,plain,
% 2.93/2.26 (hskp21),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3504, 3487, 3273, 3272, 3274, 3485, 780, 26, 3486, 48])).
% 2.93/2.26 tff(3506,plain,
% 2.93/2.26 (~c2_1(a38)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[2495, 3505])).
% 2.93/2.26 tff(3507,plain,
% 2.93/2.26 (hskp27),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[678, 3506, 3505, 13, 12, 3371])).
% 2.93/2.26 tff(3508,plain,
% 2.93/2.26 (c3_1(a12)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[605, 3507])).
% 2.93/2.26 tff(3509,plain,
% 2.93/2.26 (c1_1(a12)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[616, 3507])).
% 2.93/2.26 tff(3510,plain,
% 2.93/2.26 (c0_1(a12)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[1192, 3507])).
% 2.93/2.26 tff(3511,plain,
% 2.93/2.26 ($false),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3418, 104, 3483, 3510, 3509, 3508, 3491, 3490, 3489, 2283])).
% 2.93/2.26 tff(3512,plain,(hskp3 | c2_1(a2) | c3_1(a2) | c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.26 tff(3513,plain,
% 2.93/2.26 (c2_1(a2)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3512, 3303, 12, 780, 26])).
% 2.93/2.26 tff(3514,plain,
% 2.93/2.26 (~hskp1),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[262, 3513])).
% 2.93/2.26 tff(3515,plain,
% 2.93/2.26 (hskp20),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[544, 3514, 3304])).
% 2.93/2.26 tff(3516,plain,
% 2.93/2.26 (c3_1(a37)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[555, 3515])).
% 2.93/2.26 tff(3517,plain,
% 2.93/2.26 (c1_1(a37)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[566, 3515])).
% 2.93/2.26 tff(3518,plain,
% 2.93/2.26 (~c2_1(a37)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[571, 104, 3128, 3303, 3517, 3516, 10])).
% 2.93/2.26 tff(3519,plain,
% 2.93/2.26 (hskp2),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3321, 3514])).
% 2.93/2.26 tff(3520,plain,
% 2.93/2.26 (~c2_1(a3)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[206, 3519])).
% 2.93/2.26 tff(3521,plain,
% 2.93/2.26 (c3_1(a3)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[217, 3519])).
% 2.93/2.26 tff(3522,plain,
% 2.93/2.26 (c1_1(a3)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[228, 3519])).
% 2.93/2.26 tff(3523,plain,
% 2.93/2.26 (~c0_1(a3)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3349, 104, 3522, 3521, 3274, 3520, 3272, 970, 3288])).
% 2.93/2.26 tff(3524,plain,
% 2.93/2.26 (^[U: $i] : refl((hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))),
% 2.93/2.26 inference(bind,[status(th)],[])).
% 2.93/2.26 tff(3525,plain,
% 2.93/2.26 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.93/2.26 inference(quant_intro,[status(thm)],[3524])).
% 2.93/2.26 tff(3526,plain,
% 2.93/2.26 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.93/2.26 inference(rewrite,[status(thm)],[])).
% 2.93/2.26 tff(3527,plain,
% 2.93/2.26 (^[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)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp7) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp7) <=> (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp7) <=> (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))))),
% 2.93/2.26 inference(bind,[status(th)],[])).
% 2.93/2.26 tff(3528,plain,
% 2.93/2.26 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp7) <=> ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.93/2.26 inference(quant_intro,[status(thm)],[3527])).
% 2.93/2.26 tff(3529,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 2.93/2.26 tff(3530,plain,
% 2.93/2.26 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.93/2.26 inference(modus_ponens,[status(thm)],[3529, 3528])).
% 2.93/2.26 tff(3531,plain,
% 2.93/2.26 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.93/2.26 inference(modus_ponens,[status(thm)],[3530, 3526])).
% 2.93/2.26 tff(3532,plain,(
% 2.93/2.26 ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.93/2.26 inference(skolemize,[status(sab)],[3531])).
% 2.93/2.26 tff(3533,plain,
% 2.93/2.26 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.93/2.26 inference(modus_ponens,[status(thm)],[3532, 3525])).
% 2.93/2.26 tff(3534,plain,
% 2.93/2.26 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp7 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp7 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3))),
% 2.93/2.26 inference(rewrite,[status(thm)],[])).
% 2.93/2.26 tff(3535,plain,
% 2.93/2.26 ((hskp28 | hskp7 | (~ndr1_0) | c0_1(a3) | c2_1(a3) | (~c3_1(a3))) <=> (hskp28 | hskp7 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3))),
% 2.93/2.26 inference(rewrite,[status(thm)],[])).
% 2.93/2.26 tff(3536,plain,
% 2.93/2.26 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp7 | (~ndr1_0) | c0_1(a3) | c2_1(a3) | (~c3_1(a3)))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp7 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3)))),
% 2.93/2.26 inference(monotonicity,[status(thm)],[3535])).
% 2.93/2.26 tff(3537,plain,
% 2.93/2.26 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp7 | (~ndr1_0) | c0_1(a3) | c2_1(a3) | (~c3_1(a3)))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp7 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3))),
% 2.93/2.26 inference(transitivity,[status(thm)],[3536, 3534])).
% 2.93/2.26 tff(3538,plain,
% 2.93/2.26 ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp7 | (~ndr1_0) | c0_1(a3) | c2_1(a3) | (~c3_1(a3)))),
% 2.93/2.26 inference(quant_inst,[status(thm)],[])).
% 2.93/2.26 tff(3539,plain,
% 2.93/2.26 ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp7 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3)),
% 2.93/2.26 inference(modus_ponens,[status(thm)],[3538, 3537])).
% 2.93/2.26 tff(3540,plain,
% 2.93/2.26 (hskp7),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3539, 104, 3304, 3521, 3520, 3533, 3523])).
% 2.93/2.26 tff(3541,plain,
% 2.93/2.26 (~c0_1(a14)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[1433, 3540])).
% 2.93/2.26 tff(3542,plain,
% 2.93/2.26 (~c2_1(a14)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[1408, 3540])).
% 2.93/2.26 tff(3543,plain,
% 2.93/2.26 (c1_1(a14)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[1419, 3540])).
% 2.93/2.26 tff(3544,plain,
% 2.93/2.26 (hskp21),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3504, 3543, 3273, 3272, 3274, 3542, 780, 26, 3541, 3303])).
% 2.93/2.26 tff(3545,plain,
% 2.93/2.26 (~c2_1(a38)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[2495, 3544])).
% 2.93/2.26 tff(3546,plain,
% 2.93/2.26 (c1_1(a38)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[657, 3544])).
% 2.93/2.26 tff(3547,plain,
% 2.93/2.26 (c0_1(a38)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[646, 3544])).
% 2.93/2.26 tff(3548,plain,
% 2.93/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.93/2.26 inference(rewrite,[status(thm)],[])).
% 2.93/2.26 tff(3549,plain,
% 2.93/2.26 (((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.93/2.26 inference(rewrite,[status(thm)],[])).
% 2.93/2.26 tff(3550,plain,
% 2.93/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c0_1(a38)) | (~c1_1(a38))))),
% 2.93/2.26 inference(monotonicity,[status(thm)],[3549])).
% 2.93/2.26 tff(3551,plain,
% 2.93/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.93/2.26 inference(transitivity,[status(thm)],[3550, 3548])).
% 2.93/2.26 tff(3552,plain,
% 2.93/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 2.93/2.26 inference(quant_inst,[status(thm)],[])).
% 2.93/2.26 tff(3553,plain,
% 2.93/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c0_1(a38)) | (~c1_1(a38))),
% 2.93/2.26 inference(modus_ponens,[status(thm)],[3552, 3551])).
% 2.93/2.26 tff(3554,plain,
% 2.93/2.26 ($false),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3553, 104, 3547, 3546, 3517, 3516, 3545, 3208, 3207, 3206, 36, 3518])).
% 2.93/2.26 tff(3555,plain,(c3_1(a2) | c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.26 tff(3556,plain,
% 2.93/2.26 (c3_1(a2)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3555, 780, 26])).
% 2.93/2.26 tff(3557,plain,
% 2.93/2.26 (~hskp1),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[256, 3556])).
% 2.93/2.26 tff(3558,plain,
% 2.93/2.26 (hskp2),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3321, 3557])).
% 2.93/2.26 tff(3559,plain,
% 2.93/2.26 (~c2_1(a3)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[206, 3558])).
% 2.93/2.26 tff(3560,plain,
% 2.93/2.26 (hskp0),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3215, 3557])).
% 2.93/2.26 tff(3561,plain,
% 2.93/2.26 (c1_1(a1)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[139, 3560])).
% 2.93/2.26 tff(3562,plain,
% 2.93/2.26 (~c3_1(a1)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[117, 3560])).
% 2.93/2.26 tff(3563,plain,
% 2.93/2.26 (c2_1(a1)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[128, 3560])).
% 2.93/2.26 tff(3564,plain,
% 2.93/2.26 (~c3_1(a58)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3280, 104, 780, 3561, 3563, 3122, 26, 3562, 279])).
% 2.93/2.26 tff(3565,plain,
% 2.93/2.26 (c0_1(a1)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3287, 104, 780, 3563, 3122, 26, 3562, 341, 3564])).
% 2.93/2.26 tff(3566,plain,
% 2.93/2.26 (~hskp3),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3302, 3565, 3563, 3562, 3561])).
% 2.93/2.26 tff(3567,plain,
% 2.93/2.26 (c3_1(a3)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[217, 3558])).
% 2.93/2.26 tff(3568,plain,
% 2.93/2.26 (c1_1(a3)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[228, 3558])).
% 2.93/2.26 tff(3569,plain,
% 2.93/2.26 (~c0_1(a3)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[2050, 104, 3568, 3567, 3208, 3207, 3206, 3559, 36])).
% 2.93/2.26 tff(3570,plain,
% 2.93/2.26 (~hskp28),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3130, 3566, 3128])).
% 2.93/2.26 tff(3571,plain,
% 2.93/2.26 (hskp28 | hskp7 | c0_1(a3)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3539, 104, 3567, 3559, 3533])).
% 2.93/2.26 tff(3572,plain,
% 2.93/2.26 (hskp7),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3571, 3570, 3569])).
% 2.93/2.26 tff(3573,plain,
% 2.93/2.26 (~c0_1(a14)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[1433, 3572])).
% 2.93/2.26 tff(3574,plain,
% 2.93/2.26 (~c2_1(a14)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[1408, 3572])).
% 2.93/2.26 tff(3575,plain,
% 2.93/2.26 (c1_1(a14)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[1419, 3572])).
% 2.93/2.26 tff(3576,plain,
% 2.93/2.26 (hskp21),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3504, 3575, 3563, 3562, 3561, 3574, 780, 26, 3573, 3566])).
% 2.93/2.26 tff(3577,plain,
% 2.93/2.26 (~c2_1(a38)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[2495, 3576])).
% 2.93/2.26 tff(3578,plain,
% 2.93/2.26 (c1_1(a38)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[657, 3576])).
% 2.93/2.26 tff(3579,plain,
% 2.93/2.26 (c0_1(a38)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[646, 3576])).
% 2.93/2.26 tff(3580,plain,
% 2.93/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.93/2.26 inference(rewrite,[status(thm)],[])).
% 2.93/2.26 tff(3581,plain,
% 2.93/2.26 (((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.93/2.26 inference(rewrite,[status(thm)],[])).
% 2.93/2.26 tff(3582,plain,
% 2.93/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a38)) | (~c1_1(a38))))),
% 2.93/2.26 inference(monotonicity,[status(thm)],[3581])).
% 2.93/2.26 tff(3583,plain,
% 2.93/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.93/2.26 inference(transitivity,[status(thm)],[3582, 3580])).
% 2.93/2.26 tff(3584,plain,
% 2.93/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 2.93/2.26 inference(quant_inst,[status(thm)],[])).
% 2.93/2.26 tff(3585,plain,
% 2.93/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a38)) | (~c1_1(a38))),
% 2.93/2.26 inference(modus_ponens,[status(thm)],[3584, 3583])).
% 2.93/2.26 tff(3586,plain,
% 2.93/2.26 ($false),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3585, 104, 3579, 3578, 3568, 3567, 3577, 3208, 3207, 3206, 3559, 36])).
% 2.93/2.26 tff(3587,plain,(c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.26 tff(3588,plain,
% 2.93/2.26 (c2_1(a58)),
% 2.93/2.26 inference(unit_resolution,[status(thm)],[3587, 26])).
% 2.93/2.26 tff(3589,plain,
% 2.93/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a58)) | c1_1(a58) | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a58)))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3590,plain,
% 2.93/2.27 (((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> ((~c0_1(a58)) | c1_1(a58) | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a58)))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3591,plain,
% 2.93/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a58)) | c1_1(a58) | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a58))))),
% 2.93/2.27 inference(monotonicity,[status(thm)],[3590])).
% 2.93/2.27 tff(3592,plain,
% 2.93/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a58)))),
% 2.93/2.27 inference(transitivity,[status(thm)],[3591, 3589])).
% 2.93/2.27 tff(3593,plain,
% 2.93/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 2.93/2.27 inference(quant_inst,[status(thm)],[])).
% 2.93/2.27 tff(3594,plain,
% 2.93/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a58))),
% 2.93/2.27 inference(modus_ponens,[status(thm)],[3593, 3592])).
% 2.93/2.27 tff(3595,plain,
% 2.93/2.27 (c0_1(a2) | (~c1_1(a21))),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3594, 104, 3588, 3153, 3122, 26, 3152, 13, 12, 1342])).
% 2.93/2.27 tff(3596,plain,
% 2.93/2.27 (~c1_1(a21)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3595, 14])).
% 2.93/2.27 tff(3597,plain,
% 2.93/2.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3598,plain,
% 2.93/2.27 ((hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp5 | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3599,plain,
% 2.93/2.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21))))),
% 2.93/2.27 inference(monotonicity,[status(thm)],[3598])).
% 2.93/2.27 tff(3600,plain,
% 2.93/2.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 2.93/2.27 inference(transitivity,[status(thm)],[3599, 3597])).
% 2.93/2.27 tff(3601,plain,
% 2.93/2.27 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 2.93/2.27 inference(quant_inst,[status(thm)],[])).
% 2.93/2.27 tff(3602,plain,
% 2.93/2.27 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21))),
% 2.93/2.27 inference(modus_ponens,[status(thm)],[3601, 3600])).
% 2.93/2.27 tff(3603,plain,
% 2.93/2.27 (hskp5 | c0_1(a2) | c1_1(a21)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3602, 104, 3153, 3152, 13, 12, 290])).
% 2.93/2.27 tff(3604,plain,
% 2.93/2.27 (hskp5),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3603, 14, 3596])).
% 2.93/2.27 tff(3605,plain,
% 2.93/2.27 (~c1_1(a11)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[312, 3604])).
% 2.93/2.27 tff(3606,plain,
% 2.93/2.27 (c0_1(a11)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[323, 3604])).
% 2.93/2.27 tff(3607,plain,
% 2.93/2.27 (~hskp20),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[697, 14, 12, 11, 625, 13])).
% 2.93/2.27 tff(3608,plain,
% 2.93/2.27 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c3_1(a21) | c1_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c0_1(a21)) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c3_1(a21) | c1_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3609,plain,
% 2.93/2.27 ((hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a11) | (~c3_1(a11)) | (~c0_1(a11))) <=> (hskp20 | c3_1(a21) | c1_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3610,plain,
% 2.93/2.27 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a11) | (~c3_1(a11)) | (~c0_1(a11)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c3_1(a21) | c1_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c0_1(a21)) | (~c2_1(a21))))),
% 2.93/2.27 inference(monotonicity,[status(thm)],[3609])).
% 2.93/2.27 tff(3611,plain,
% 2.93/2.27 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a11) | (~c3_1(a11)) | (~c0_1(a11)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c3_1(a21) | c1_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.93/2.27 inference(transitivity,[status(thm)],[3610, 3608])).
% 2.93/2.27 tff(3612,plain,
% 2.93/2.27 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a11) | (~c3_1(a11)) | (~c0_1(a11)))),
% 2.93/2.27 inference(quant_inst,[status(thm)],[])).
% 2.93/2.27 tff(3613,plain,
% 2.93/2.27 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c3_1(a21) | c1_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c0_1(a21)) | (~c2_1(a21))),
% 2.93/2.27 inference(modus_ponens,[status(thm)],[3612, 3611])).
% 2.93/2.27 tff(3614,plain,
% 2.93/2.27 (~c3_1(a11)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3613, 104, 3607, 3170, 3153, 3606, 3152, 3605, 3150])).
% 2.93/2.27 tff(3615,plain,
% 2.93/2.27 (~c2_1(a11)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[306, 3604])).
% 2.93/2.27 tff(3616,plain,
% 2.93/2.27 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3617,plain,
% 2.93/2.27 ((hskp21 | hskp20 | (~ndr1_0) | c3_1(a11) | c1_1(a11) | c2_1(a11)) <=> (hskp21 | hskp20 | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3618,plain,
% 2.93/2.27 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a11) | c1_1(a11) | c2_1(a11))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11)))),
% 2.93/2.27 inference(monotonicity,[status(thm)],[3617])).
% 2.93/2.27 tff(3619,plain,
% 2.93/2.27 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a11) | c1_1(a11) | c2_1(a11))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11))),
% 2.93/2.27 inference(transitivity,[status(thm)],[3618, 3616])).
% 2.93/2.27 tff(3620,plain,
% 2.93/2.27 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a11) | c1_1(a11) | c2_1(a11))),
% 2.93/2.27 inference(quant_inst,[status(thm)],[])).
% 2.93/2.27 tff(3621,plain,
% 2.93/2.27 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11)),
% 2.93/2.27 inference(modus_ponens,[status(thm)],[3620, 3619])).
% 2.93/2.27 tff(3622,plain,
% 2.93/2.27 ($false),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3621, 104, 811, 3607, 3605, 3615, 708, 3614])).
% 2.93/2.27 tff(3623,plain,(c0_1(a2) | hskp21 | c2_1(a2) | c3_1(a2) | c1_1(a58) | hskp0 | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.93/2.27 tff(3624,plain,
% 2.93/2.27 (hskp21),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3623, 3138, 3139, 12, 26, 11, 3131])).
% 2.93/2.27 tff(3625,plain,
% 2.93/2.27 (~c2_1(a38)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[2495, 3624])).
% 2.93/2.27 tff(3626,plain,
% 2.93/2.27 ($false),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[678, 3625, 3624, 3140, 3139, 12, 3138])).
% 2.93/2.27 tff(3627,plain,(hskp0 | c3_1(a2) | c1_1(a58) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.93/2.27 tff(3628,plain,
% 2.93/2.27 (hskp0),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3627, 12, 26, 48])).
% 2.93/2.27 tff(3629,plain,
% 2.93/2.27 (~c3_1(a1)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[117, 3628])).
% 2.93/2.27 tff(3630,plain,
% 2.93/2.27 (c2_1(a1)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[128, 3628])).
% 2.93/2.27 tff(3631,plain,
% 2.93/2.27 (c1_1(a1)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[139, 3628])).
% 2.93/2.27 tff(3632,plain,
% 2.93/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a58)) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a58)))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3633,plain,
% 2.93/2.27 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> ((~c0_1(a58)) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a58)))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3634,plain,
% 2.93/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a58)) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a58))))),
% 2.93/2.27 inference(monotonicity,[status(thm)],[3633])).
% 2.93/2.27 tff(3635,plain,
% 2.93/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a58)))),
% 2.93/2.27 inference(transitivity,[status(thm)],[3634, 3632])).
% 2.93/2.27 tff(3636,plain,
% 2.93/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 2.93/2.27 inference(quant_inst,[status(thm)],[])).
% 2.93/2.27 tff(3637,plain,
% 2.93/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a58))),
% 2.93/2.27 inference(modus_ponens,[status(thm)],[3636, 3635])).
% 2.93/2.27 tff(3638,plain,
% 2.93/2.27 (c0_1(a2)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3637, 104, 3588, 3631, 3630, 3122, 26, 13, 12, 3629, 1342])).
% 2.93/2.27 tff(3639,plain,
% 2.93/2.27 (~hskp1),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[268, 3638])).
% 2.93/2.27 tff(3640,plain,
% 2.93/2.27 (hskp20),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[544, 3639, 3131])).
% 2.93/2.27 tff(3641,plain,
% 2.93/2.27 (c3_1(a37)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[555, 3640])).
% 2.93/2.27 tff(3642,plain,
% 2.93/2.27 (c1_1(a37)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[566, 3640])).
% 2.93/2.27 tff(3643,plain,
% 2.93/2.27 (~c2_1(a37)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[571, 104, 3128, 48, 3642, 3641, 10])).
% 2.93/2.27 tff(3644,plain,
% 2.93/2.27 (hskp6),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[180, 3630, 3631, 3629])).
% 2.93/2.27 tff(3645,plain,
% 2.93/2.27 (~c3_1(a13)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[186, 3644])).
% 2.93/2.27 tff(3646,plain,
% 2.93/2.27 (~c1_1(a13)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[192, 3644])).
% 2.93/2.27 tff(3647,plain,
% 2.93/2.27 (~c0_1(a13)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[198, 3644])).
% 2.93/2.27 tff(3648,plain,
% 2.93/2.27 (hskp2 | hskp1),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[247, 104, 3647, 3646, 3645, 47])).
% 2.93/2.27 tff(3649,plain,
% 2.93/2.27 (hskp2),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3648, 3639])).
% 2.93/2.27 tff(3650,plain,
% 2.93/2.27 (~c2_1(a3)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[206, 3649])).
% 2.93/2.27 tff(3651,plain,
% 2.93/2.27 (c3_1(a3)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[217, 3649])).
% 2.93/2.27 tff(3652,plain,
% 2.93/2.27 (c1_1(a3)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[228, 3649])).
% 2.93/2.27 tff(3653,plain,
% 2.93/2.27 (~c1_1(a2)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[1901, 104, 3652, 3651, 3647, 3646, 3645, 3650, 3638, 13, 36])).
% 2.93/2.27 tff(3654,plain,
% 2.93/2.27 (~c0_1(a3)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[2050, 104, 3652, 3651, 3647, 3646, 3645, 3650, 36])).
% 2.93/2.27 tff(3655,plain,
% 2.93/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a58) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c2_1(a58)) | (~c3_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)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a58) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3656,plain,
% 2.93/2.27 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3))) <=> (c1_1(a58) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3657,plain,
% 2.93/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a58) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c2_1(a58)) | (~c3_1(a58))))),
% 2.93/2.27 inference(monotonicity,[status(thm)],[3656])).
% 2.93/2.27 tff(3658,plain,
% 2.93/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a58) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c2_1(a58)) | (~c3_1(a58)))),
% 2.93/2.27 inference(transitivity,[status(thm)],[3657, 3655])).
% 2.93/2.27 tff(3659,plain,
% 2.93/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3)))),
% 2.93/2.27 inference(quant_inst,[status(thm)],[])).
% 2.93/2.27 tff(3660,plain,
% 2.93/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a58) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c2_1(a58)) | (~c3_1(a58))),
% 2.93/2.27 inference(modus_ponens,[status(thm)],[3659, 3658])).
% 2.93/2.27 tff(3661,plain,
% 2.93/2.27 (c0_1(a3) | (~c3_1(a58))),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3660, 104, 3588, 3652, 26, 3650, 3638, 13, 12, 2061])).
% 2.93/2.27 tff(3662,plain,
% 2.93/2.27 (~c3_1(a58)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3661, 3654])).
% 2.93/2.27 tff(3663,plain,
% 2.93/2.27 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3664,plain,
% 2.93/2.27 ((hskp10 | hskp1 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58))) <=> (hskp10 | hskp1 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3665,plain,
% 2.93/2.27 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)))),
% 2.93/2.27 inference(monotonicity,[status(thm)],[3664])).
% 2.93/2.27 tff(3666,plain,
% 2.93/2.27 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 2.93/2.27 inference(transitivity,[status(thm)],[3665, 3663])).
% 2.93/2.27 tff(3667,plain,
% 2.93/2.27 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)))),
% 2.93/2.27 inference(quant_inst,[status(thm)],[])).
% 2.93/2.27 tff(3668,plain,
% 2.93/2.27 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)),
% 2.93/2.27 inference(modus_ponens,[status(thm)],[3667, 3666])).
% 2.93/2.27 tff(3669,plain,
% 2.93/2.27 (hskp10 | hskp1 | (~c2_1(a58)) | c3_1(a58)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3668, 104, 26, 1882])).
% 2.93/2.27 tff(3670,plain,
% 2.93/2.27 (hskp10),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3669, 3662, 3588, 3639])).
% 2.93/2.27 tff(3671,plain,
% 2.93/2.27 (~c1_1(a18)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[937, 3670])).
% 2.93/2.27 tff(3672,plain,
% 2.93/2.27 (~c0_1(a18)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[943, 3670])).
% 2.93/2.27 tff(3673,plain,
% 2.93/2.27 (~c0_1(a37)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[685, 3640])).
% 2.93/2.27 tff(3674,plain,
% 2.93/2.27 (c3_1(a18)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[1037, 3670])).
% 2.93/2.27 tff(3675,plain,
% 2.93/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c0_1(a18) | c1_1(a18) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c0_1(a18) | c1_1(a18) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3676,plain,
% 2.93/2.27 (((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18))) <=> (c0_1(a37) | c0_1(a18) | c1_1(a18) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))),
% 2.93/2.27 inference(rewrite,[status(thm)],[])).
% 2.93/2.27 tff(3677,plain,
% 2.93/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c0_1(a18) | c1_1(a18) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37))))),
% 2.93/2.27 inference(monotonicity,[status(thm)],[3676])).
% 2.93/2.27 tff(3678,plain,
% 2.93/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c0_1(a18) | c1_1(a18) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))),
% 2.93/2.27 inference(transitivity,[status(thm)],[3677, 3675])).
% 2.93/2.27 tff(3679,plain,
% 2.93/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))),
% 2.93/2.27 inference(quant_inst,[status(thm)],[])).
% 2.93/2.27 tff(3680,plain,
% 2.93/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c0_1(a18) | c1_1(a18) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37))),
% 2.93/2.27 inference(modus_ponens,[status(thm)],[3679, 3678])).
% 2.93/2.27 tff(3681,plain,
% 2.93/2.27 ($false),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3680, 104, 3641, 3674, 3673, 3672, 3671, 3638, 13, 751, 3653, 3643])).
% 2.93/2.27 tff(3682,plain,(c2_1(a2) | c1_1(a58) | c3_1(a2) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.93/2.27 tff(3683,plain,
% 2.93/2.27 (c2_1(a2)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3682, 12, 26, 48])).
% 2.93/2.27 tff(3684,plain,
% 2.93/2.27 (~hskp1),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[262, 3683])).
% 2.93/2.27 tff(3685,plain,
% 2.93/2.27 (hskp2),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[3648, 3684])).
% 2.93/2.27 tff(3686,plain,
% 2.93/2.27 (~c2_1(a3)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[206, 3685])).
% 2.93/2.27 tff(3687,plain,
% 2.93/2.27 (c3_1(a3)),
% 2.93/2.27 inference(unit_resolution,[status(thm)],[217, 3685])).
% 2.93/2.28 tff(3688,plain,
% 2.93/2.28 (c1_1(a3)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[228, 3685])).
% 2.93/2.28 tff(3689,plain,
% 2.93/2.28 (~c2_1(a13)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[1331, 104, 3684, 3688, 3687, 3647, 3646, 3686, 58])).
% 2.93/2.28 tff(3690,plain,
% 2.93/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a13) | (~c2_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a13) | (~c2_1(a58)))),
% 2.93/2.28 inference(rewrite,[status(thm)],[])).
% 2.93/2.28 tff(3691,plain,
% 2.93/2.28 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a13) | c0_1(a13) | c3_1(a13)) <=> ((~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a13) | (~c2_1(a58)))),
% 2.93/2.28 inference(rewrite,[status(thm)],[])).
% 2.93/2.28 tff(3692,plain,
% 2.93/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a13) | (~c2_1(a58))))),
% 2.93/2.28 inference(monotonicity,[status(thm)],[3691])).
% 2.93/2.28 tff(3693,plain,
% 2.93/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a13) | (~c2_1(a58)))),
% 2.93/2.28 inference(transitivity,[status(thm)],[3692, 3690])).
% 2.93/2.28 tff(3694,plain,
% 2.93/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a13) | c0_1(a13) | c3_1(a13))),
% 2.93/2.28 inference(quant_inst,[status(thm)],[])).
% 2.93/2.28 tff(3695,plain,
% 2.93/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a13) | (~c2_1(a58))),
% 2.93/2.28 inference(modus_ponens,[status(thm)],[3694, 3693])).
% 2.93/2.28 tff(3696,plain,
% 2.93/2.28 ($false),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3695, 104, 3588, 3631, 3630, 3122, 26, 3647, 3645, 3629, 1342, 3689])).
% 2.93/2.28 tff(3697,plain,(c3_1(a2) | c1_1(a58) | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.93/2.28 tff(3698,plain,
% 2.93/2.28 (c3_1(a2)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3697, 48, 26])).
% 2.93/2.28 tff(3699,plain,
% 2.93/2.28 (~hskp1),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[256, 3698])).
% 2.93/2.28 tff(3700,plain,
% 2.93/2.28 (hskp20),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[544, 3699, 3131])).
% 2.93/2.28 tff(3701,plain,
% 2.93/2.28 (c3_1(a37)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[555, 3700])).
% 2.93/2.28 tff(3702,plain,
% 2.93/2.28 (c1_1(a37)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[566, 3700])).
% 2.93/2.28 tff(3703,plain,
% 2.93/2.28 (~c2_1(a37)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[571, 104, 3128, 48, 3702, 3701, 10])).
% 2.93/2.28 tff(3704,plain,
% 2.93/2.28 (hskp0),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3135, 3700, 3128, 48])).
% 2.93/2.28 tff(3705,plain,
% 2.93/2.28 (~c3_1(a1)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[117, 3704])).
% 2.93/2.28 tff(3706,plain,
% 2.93/2.28 (c1_1(a1)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[139, 3704])).
% 2.93/2.28 tff(3707,plain,
% 2.93/2.28 (c2_1(a1)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[128, 3704])).
% 2.93/2.28 tff(3708,plain,
% 2.93/2.28 (hskp6),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[180, 3707, 3706, 3705])).
% 2.93/2.28 tff(3709,plain,
% 2.93/2.28 (~c1_1(a13)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[192, 3708])).
% 2.93/2.28 tff(3710,plain,
% 2.93/2.28 (~c0_1(a13)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[198, 3708])).
% 2.93/2.28 tff(3711,plain,
% 2.93/2.28 (~c2_1(a13)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[959, 104, 3699, 3702, 3701, 3710, 3709, 58, 3703])).
% 2.93/2.28 tff(3712,plain,
% 2.93/2.28 (~c3_1(a13)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[186, 3708])).
% 2.93/2.28 tff(3713,plain,
% 2.93/2.28 ($false),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3695, 104, 3588, 3706, 3707, 3122, 26, 3710, 3712, 3705, 1342, 3711])).
% 2.93/2.28 tff(3714,plain,(hskp3 | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.28 tff(3715,plain,
% 2.93/2.28 (hskp3),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3714, 26])).
% 2.93/2.28 tff(3716,plain,
% 2.93/2.28 (~c2_1(a7)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[2959, 3715])).
% 2.93/2.28 tff(3717,plain,
% 2.93/2.28 (c3_1(a7)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[2972, 3715])).
% 2.93/2.28 tff(3718,plain,
% 2.93/2.28 (c0_1(a7)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[2983, 3715])).
% 2.93/2.28 tff(3719,plain,
% 2.93/2.28 (hskp6),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3156, 636, 568])).
% 2.93/2.28 tff(3720,plain,
% 2.93/2.28 (~c3_1(a13)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[186, 3719])).
% 2.93/2.28 tff(3721,plain,
% 2.93/2.28 (~c1_1(a13)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[192, 3719])).
% 2.93/2.28 tff(3722,plain,
% 2.93/2.28 (~c0_1(a13)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[198, 3719])).
% 2.93/2.28 tff(3723,plain,
% 2.93/2.28 (~c3_1(a38)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[1076, 104, 647, 658, 3154, 3722, 3721, 3720, 36])).
% 2.93/2.28 tff(3724,assumption,(~c2_1(a7)), introduced(assumption)).
% 2.93/2.28 tff(3725,assumption,(c3_1(a7)), introduced(assumption)).
% 2.93/2.28 tff(3726,assumption,(c0_1(a7)), introduced(assumption)).
% 2.93/2.28 tff(3727,plain,
% 2.93/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a38) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a38) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.93/2.28 inference(rewrite,[status(thm)],[])).
% 2.93/2.28 tff(3728,plain,
% 2.93/2.28 (((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38))) <=> (c2_1(a38) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.93/2.28 inference(rewrite,[status(thm)],[])).
% 2.93/2.28 tff(3729,plain,
% 2.93/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a38) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38))))),
% 2.93/2.28 inference(monotonicity,[status(thm)],[3728])).
% 2.93/2.28 tff(3730,plain,
% 2.93/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a38) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 2.93/2.28 inference(transitivity,[status(thm)],[3729, 3727])).
% 2.93/2.28 tff(3731,plain,
% 2.93/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))),
% 2.93/2.28 inference(quant_inst,[status(thm)],[])).
% 2.93/2.28 tff(3732,plain,
% 2.93/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a38) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38))),
% 2.93/2.28 inference(modus_ponens,[status(thm)],[3731, 3730])).
% 2.93/2.28 tff(3733,plain,
% 2.93/2.28 ($false),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3732, 104, 647, 658, 3726, 3725, 3154, 3724, 970, 3723])).
% 2.93/2.28 tff(3734,plain,((~hskp21) | (~c0_1(a7)) | (~c3_1(a7)) | c2_1(a7) | hskp24), inference(lemma,lemma(discharge,[]))).
% 2.93/2.28 tff(3735,plain,
% 2.93/2.28 (~hskp21),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3734, 3718, 3717, 3716, 3128])).
% 2.93/2.28 tff(3736,plain,
% 2.93/2.28 (hskp13),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[825, 3735, 3128])).
% 2.93/2.28 tff(3737,plain,
% 2.93/2.28 (c0_1(a21)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[853, 3736])).
% 2.93/2.28 tff(3738,plain,
% 2.93/2.28 (hskp6),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[180, 2556, 2555, 2554])).
% 2.93/2.28 tff(3739,plain,
% 2.93/2.28 (~c3_1(a13)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[186, 3738])).
% 2.93/2.28 tff(3740,plain,
% 2.93/2.28 (~c1_1(a13)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[192, 3738])).
% 2.93/2.28 tff(3741,plain,
% 2.93/2.28 (~c0_1(a13)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[198, 3738])).
% 2.93/2.28 tff(3742,plain,
% 2.93/2.28 (~c1_1(a7)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3033, 104, 3726, 3725, 3741, 3740, 3739, 3724, 36])).
% 2.93/2.28 tff(3743,plain,
% 2.93/2.28 ($false),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3119, 104, 3726, 3725, 2555, 2556, 3724, 2554, 279, 3742])).
% 2.93/2.28 tff(3744,plain,((~hskp0) | (~c0_1(a7)) | (~c3_1(a7)) | c2_1(a7)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.28 tff(3745,plain,
% 2.93/2.28 (~hskp0),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3744, 3718, 3717, 3716])).
% 2.93/2.28 tff(3746,plain,
% 2.93/2.28 (~c1_1(a13)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[192, 469])).
% 2.93/2.28 tff(3747,plain,
% 2.93/2.28 ($false),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3214, 104, 200, 11, 470, 3746, 471, 763])).
% 2.93/2.28 tff(3748,plain,((~hskp6) | hskp1 | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.93/2.28 tff(3749,plain,
% 2.93/2.28 (~hskp6),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3748, 200, 3745])).
% 2.93/2.28 tff(3750,plain,
% 2.93/2.28 (~c3_1(a21)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[831, 3736])).
% 2.93/2.28 tff(3751,plain,
% 2.93/2.28 (c2_1(a21)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[842, 3736])).
% 2.93/2.28 tff(3752,plain,
% 2.93/2.28 (hskp6 | (~c1_1(a21))),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[2519, 104, 3737, 3751, 3750, 150])).
% 2.93/2.28 tff(3753,plain,
% 2.93/2.28 (~c1_1(a21)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3752, 3749])).
% 2.93/2.28 tff(3754,plain,
% 2.93/2.28 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a58)))),
% 2.93/2.28 inference(rewrite,[status(thm)],[])).
% 2.93/2.28 tff(3755,plain,
% 2.93/2.28 ((hskp18 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21))) <=> (hskp18 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a58)))),
% 2.93/2.28 inference(rewrite,[status(thm)],[])).
% 2.93/2.28 tff(3756,plain,
% 2.93/2.28 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a58))))),
% 2.93/2.28 inference(monotonicity,[status(thm)],[3755])).
% 2.93/2.28 tff(3757,plain,
% 2.93/2.28 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a58)))),
% 2.93/2.28 inference(transitivity,[status(thm)],[3756, 3754])).
% 2.93/2.28 tff(3758,plain,
% 2.93/2.28 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))),
% 2.93/2.28 inference(quant_inst,[status(thm)],[])).
% 2.93/2.28 tff(3759,plain,
% 2.93/2.28 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a58))),
% 2.93/2.28 inference(modus_ponens,[status(thm)],[3758, 3757])).
% 2.93/2.28 tff(3760,plain,
% 2.93/2.28 (hskp18 | c1_1(a21)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3759, 104, 3588, 3737, 3122, 26, 3750, 2737])).
% 2.93/2.28 tff(3761,plain,
% 2.93/2.28 (hskp18),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3760, 3753])).
% 2.93/2.28 tff(3762,plain,
% 2.93/2.28 (c1_1(a31)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[414, 3761])).
% 2.93/2.28 tff(3763,plain,
% 2.93/2.28 (~c3_1(a31)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[403, 3761])).
% 2.93/2.28 tff(3764,plain,
% 2.93/2.28 (~c0_1(a31)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[444, 3761])).
% 2.93/2.28 tff(3765,plain,
% 2.93/2.28 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 2.93/2.28 inference(rewrite,[status(thm)],[])).
% 2.93/2.28 tff(3766,plain,
% 2.93/2.28 ((hskp10 | hskp1 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21))) <=> (hskp10 | hskp1 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 2.93/2.28 inference(rewrite,[status(thm)],[])).
% 2.93/2.28 tff(3767,plain,
% 2.93/2.28 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21))))),
% 2.93/2.28 inference(monotonicity,[status(thm)],[3766])).
% 2.93/2.28 tff(3768,plain,
% 2.93/2.28 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 2.93/2.28 inference(transitivity,[status(thm)],[3767, 3765])).
% 2.93/2.28 tff(3769,plain,
% 2.93/2.28 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)))),
% 2.93/2.28 inference(quant_inst,[status(thm)],[])).
% 2.93/2.28 tff(3770,plain,
% 2.93/2.28 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21))),
% 2.93/2.28 inference(modus_ponens,[status(thm)],[3769, 3768])).
% 2.93/2.28 tff(3771,plain,
% 2.93/2.28 (hskp10 | hskp1 | c1_1(a21)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3770, 104, 3751, 3750, 1882])).
% 2.93/2.28 tff(3772,plain,
% 2.93/2.28 (hskp10),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3771, 3753, 200])).
% 2.93/2.28 tff(3773,plain,
% 2.93/2.28 (~c1_1(a18)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[937, 3772])).
% 2.93/2.28 tff(3774,plain,
% 2.93/2.28 (c3_1(a18)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[1037, 3772])).
% 2.93/2.28 tff(3775,plain,
% 2.93/2.28 (~c0_1(a18)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[943, 3772])).
% 2.93/2.28 tff(3776,assumption,(c1_1(a31)), introduced(assumption)).
% 2.93/2.28 tff(3777,plain,
% 2.93/2.28 (hskp6 | (~c2_1(a31))),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[2759, 104, 3776, 2513, 2512, 3182, 2511, 150])).
% 2.93/2.28 tff(3778,plain,
% 2.93/2.28 (~c2_1(a31)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3777, 25])).
% 2.93/2.28 tff(3779,assumption,(~c0_1(a18)), introduced(assumption)).
% 2.93/2.28 tff(3780,assumption,(c3_1(a18)), introduced(assumption)).
% 2.93/2.28 tff(3781,plain,
% 2.93/2.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a31) | c3_1(a31) | c0_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a31) | c3_1(a31) | c0_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a31))),
% 2.93/2.28 inference(rewrite,[status(thm)],[])).
% 2.93/2.28 tff(3782,plain,
% 2.93/2.28 ((hskp0 | (~ndr1_0) | c0_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a31) | c2_1(a31) | c0_1(a31)) <=> (hskp0 | c0_1(a31) | c3_1(a31) | c0_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a31))),
% 2.93/2.28 inference(rewrite,[status(thm)],[])).
% 2.93/2.28 tff(3783,plain,
% 2.93/2.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a31) | c3_1(a31) | c0_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a31)))),
% 2.93/2.28 inference(monotonicity,[status(thm)],[3782])).
% 2.93/2.28 tff(3784,plain,
% 2.93/2.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a31) | c3_1(a31) | c0_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a31))),
% 2.93/2.28 inference(transitivity,[status(thm)],[3783, 3781])).
% 2.93/2.28 tff(3785,plain,
% 2.93/2.28 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a31) | c2_1(a31) | c0_1(a31))),
% 2.93/2.28 inference(quant_inst,[status(thm)],[])).
% 2.93/2.28 tff(3786,plain,
% 2.93/2.28 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a31) | c3_1(a31) | c0_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a31)),
% 2.93/2.28 inference(modus_ponens,[status(thm)],[3785, 3784])).
% 2.93/2.28 tff(3787,plain,
% 2.93/2.28 ((~c2_1(a18)) | c2_1(a31)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3786, 104, 11, 3780, 3183, 3182, 3779, 24])).
% 2.93/2.28 tff(3788,plain,
% 2.93/2.28 (~c2_1(a18)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3787, 3778])).
% 2.93/2.28 tff(3789,plain,
% 2.93/2.28 (~c1_1(a21)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[2520, 25])).
% 2.93/2.28 tff(3790,plain,
% 2.93/2.28 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c0_1(a31) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c2_1(a31))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c0_1(a31) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c2_1(a31))),
% 2.93/2.28 inference(rewrite,[status(thm)],[])).
% 2.93/2.28 tff(3791,plain,
% 2.93/2.28 ((hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a31) | c2_1(a31) | c0_1(a31)) <=> (hskp5 | c0_1(a31) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c2_1(a31))),
% 2.93/2.28 inference(rewrite,[status(thm)],[])).
% 2.93/2.28 tff(3792,plain,
% 2.93/2.28 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c0_1(a31) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c2_1(a31)))),
% 2.93/2.28 inference(monotonicity,[status(thm)],[3791])).
% 2.93/2.28 tff(3793,plain,
% 2.93/2.28 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c0_1(a31) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c2_1(a31))),
% 2.93/2.28 inference(transitivity,[status(thm)],[3792, 3790])).
% 2.93/2.28 tff(3794,plain,
% 2.93/2.28 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a31) | c2_1(a31) | c0_1(a31))),
% 2.93/2.28 inference(quant_inst,[status(thm)],[])).
% 2.93/2.28 tff(3795,plain,
% 2.93/2.28 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c0_1(a31) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c2_1(a31)),
% 2.93/2.28 inference(modus_ponens,[status(thm)],[3794, 3793])).
% 2.93/2.28 tff(3796,plain,
% 2.93/2.28 (hskp5 | c1_1(a21) | c2_1(a31)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3795, 104, 2512, 3183, 3182, 2511, 290])).
% 2.93/2.28 tff(3797,plain,
% 2.93/2.28 (hskp5),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3796, 3778, 3789])).
% 2.93/2.28 tff(3798,plain,
% 2.93/2.28 (~c2_1(a11)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[306, 3797])).
% 2.93/2.28 tff(3799,plain,
% 2.93/2.28 (~c1_1(a11)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[312, 3797])).
% 2.93/2.28 tff(3800,assumption,(~c1_1(a18)), introduced(assumption)).
% 2.93/2.28 tff(3801,plain,
% 2.93/2.28 (c0_1(a11)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[323, 3797])).
% 2.93/2.28 tff(3802,plain,
% 2.93/2.28 ($false),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[1044, 104, 3780, 3801, 3779, 3800, 3799, 3798, 751, 3788])).
% 2.93/2.28 tff(3803,plain,(hskp6 | (~c3_1(a18)) | c0_1(a18) | c1_1(a18) | (~c2_1(a21)) | c0_1(a31) | c3_1(a31) | c3_1(a21) | hskp0 | (~c1_1(a31)) | (~c0_1(a21))), inference(lemma,lemma(discharge,[]))).
% 2.93/2.28 tff(3804,plain,
% 2.93/2.28 ($false),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3803, 3775, 3774, 3749, 3773, 3751, 3764, 3763, 3750, 3745, 3762, 3737])).
% 2.93/2.28 tff(3805,plain,(hskp1 | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.28 tff(3806,plain,
% 2.93/2.28 (hskp1),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3805, 26])).
% 2.93/2.28 tff(3807,plain,
% 2.93/2.28 (~c3_1(a2)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[256, 3806])).
% 2.93/2.28 tff(3808,plain,
% 2.93/2.28 (~c0_1(a2)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[268, 3806])).
% 2.93/2.28 tff(3809,plain,
% 2.93/2.28 (~c2_1(a2)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[262, 3806])).
% 2.93/2.28 tff(3810,plain,
% 2.93/2.28 (c0_1(a2) | (~c1_1(a21))),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3594, 104, 3588, 3751, 3122, 26, 3750, 13, 12, 1342])).
% 2.93/2.28 tff(3811,plain,
% 2.93/2.28 (~c1_1(a21)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3810, 14])).
% 2.93/2.28 tff(3812,plain,
% 2.93/2.28 (~c1_1(a21)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3594, 104, 3588, 3153, 3122, 26, 3152, 14, 13, 12, 1342])).
% 2.93/2.28 tff(3813,plain,
% 2.93/2.28 (hskp5),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3602, 104, 3153, 3152, 14, 13, 12, 290, 3812])).
% 2.93/2.28 tff(3814,plain,
% 2.93/2.28 (~c1_1(a11)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[312, 3813])).
% 2.93/2.28 tff(3815,plain,
% 2.93/2.28 (c0_1(a11)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[323, 3813])).
% 2.93/2.28 tff(3816,plain,
% 2.93/2.28 (~c3_1(a11)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3613, 104, 3168, 3170, 3153, 3815, 3152, 3814, 3150])).
% 2.93/2.28 tff(3817,plain,
% 2.93/2.28 (~c2_1(a11)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[306, 3813])).
% 2.93/2.28 tff(3818,plain,
% 2.93/2.28 ($false),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3621, 104, 811, 3168, 3814, 3817, 708, 3816])).
% 2.93/2.28 tff(3819,plain,(hskp21 | hskp20 | c0_1(a2) | c2_1(a2) | c3_1(a2) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.28 tff(3820,plain,
% 2.93/2.28 (c0_1(a2)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3819, 3168, 3735, 13, 12, 26])).
% 2.93/2.28 tff(3821,plain,
% 2.93/2.28 (hskp20 | c2_1(a2) | c1_1(a2)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[714, 104, 3735, 12, 708])).
% 2.93/2.28 tff(3822,plain,
% 2.93/2.28 (c1_1(a2)),
% 2.93/2.28 inference(unit_resolution,[status(thm)],[3821, 3168, 13])).
% 2.93/2.28 tff(3823,plain,
% 2.93/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a7) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a7)) | (~c0_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a7) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a7)) | (~c0_1(a7)))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3824,plain,
% 2.93/2.29 (((~ndr1_0) | c3_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2))) <=> (c2_1(a7) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a7)) | (~c0_1(a7)))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3825,plain,
% 2.93/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a7) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a7)) | (~c0_1(a7))))),
% 2.93/2.29 inference(monotonicity,[status(thm)],[3824])).
% 2.93/2.29 tff(3826,plain,
% 2.93/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a7) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a7)) | (~c0_1(a7)))),
% 2.93/2.29 inference(transitivity,[status(thm)],[3825, 3823])).
% 2.93/2.29 tff(3827,plain,
% 2.93/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)))),
% 2.93/2.29 inference(quant_inst,[status(thm)],[])).
% 2.93/2.29 tff(3828,plain,
% 2.93/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a7) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a7)) | (~c0_1(a7))),
% 2.93/2.29 inference(modus_ponens,[status(thm)],[3827, 3826])).
% 2.93/2.29 tff(3829,plain,
% 2.93/2.29 ((~c0_1(a2)) | (~c1_1(a2))),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3828, 104, 3718, 3717, 3716, 13, 12, 970])).
% 2.93/2.29 tff(3830,plain,
% 2.93/2.29 ($false),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3829, 3822, 3820])).
% 2.93/2.29 tff(3831,plain,(hskp20 | c2_1(a2) | c3_1(a2) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.29 tff(3832,plain,
% 2.93/2.29 (hskp20),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3831, 13, 12, 26])).
% 2.93/2.29 tff(3833,plain,
% 2.93/2.29 (hskp18),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3760, 3811])).
% 2.93/2.29 tff(3834,plain,
% 2.93/2.29 (~c0_1(a31)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[444, 3833])).
% 2.93/2.29 tff(3835,plain,
% 2.93/2.29 (~c3_1(a31)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[403, 3833])).
% 2.93/2.29 tff(3836,plain,
% 2.93/2.29 (hskp0 | c0_1(a2) | (~c2_1(a37))),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[693, 104, 687, 686, 13, 12, 24])).
% 2.93/2.29 tff(3837,plain,
% 2.93/2.29 (~c2_1(a37)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3836, 11, 14])).
% 2.93/2.29 tff(3838,plain,
% 2.93/2.29 (hskp6),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3198, 11, 680, 3183, 3182, 3181])).
% 2.93/2.29 tff(3839,plain,
% 2.93/2.29 (~c3_1(a13)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[186, 3838])).
% 2.93/2.29 tff(3840,plain,
% 2.93/2.29 (~c1_1(a13)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[192, 3838])).
% 2.93/2.29 tff(3841,plain,
% 2.93/2.29 (~c0_1(a13)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[198, 3838])).
% 2.93/2.29 tff(3842,plain,
% 2.93/2.29 (~c1_1(a7)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3033, 104, 3726, 3725, 3841, 3840, 3839, 3724, 36])).
% 2.93/2.29 tff(3843,plain,
% 2.93/2.29 (hskp28),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[697, 11, 12, 680, 14, 13])).
% 2.93/2.29 tff(3844,plain,
% 2.93/2.29 (c3_1(a25)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[487, 3843])).
% 2.93/2.29 tff(3845,plain,
% 2.93/2.29 (c1_1(a25)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[498, 3843])).
% 2.93/2.29 tff(3846,plain,
% 2.93/2.29 (~c0_1(a25)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3254, 104, 3845, 3844, 695, 687, 3725, 3724, 1772, 3842, 3837])).
% 2.93/2.29 tff(3847,plain,
% 2.93/2.29 (c2_1(a25)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[509, 3843])).
% 2.93/2.29 tff(3848,plain,
% 2.93/2.29 ($false),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3268, 104, 11, 3847, 3844, 3183, 3182, 24, 3181, 3846])).
% 2.93/2.29 tff(3849,plain,(hskp0 | c0_1(a31) | c3_1(a31) | c2_1(a31) | (~c3_1(a7)) | c2_1(a7) | (~c0_1(a7)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~hskp20)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.29 tff(3850,plain,
% 2.93/2.29 (c2_1(a31)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3849, 3835, 3745, 3834, 3717, 3716, 3718, 14, 13, 12, 3832])).
% 2.93/2.29 tff(3851,plain,
% 2.93/2.29 (c1_1(a31)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[414, 3833])).
% 2.93/2.29 tff(3852,plain,
% 2.93/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a31) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a31) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3853,plain,
% 2.93/2.29 (((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c3_1(a31) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3854,plain,
% 2.93/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a31) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31))))),
% 2.93/2.29 inference(monotonicity,[status(thm)],[3853])).
% 2.93/2.29 tff(3855,plain,
% 2.93/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a31) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 2.93/2.29 inference(transitivity,[status(thm)],[3854, 3852])).
% 2.93/2.29 tff(3856,plain,
% 2.93/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 2.93/2.29 inference(quant_inst,[status(thm)],[])).
% 2.93/2.29 tff(3857,plain,
% 2.93/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a31) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31))),
% 2.93/2.29 inference(modus_ponens,[status(thm)],[3856, 3855])).
% 2.93/2.29 tff(3858,plain,
% 2.93/2.29 ($false),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3857, 104, 3851, 3737, 3751, 3835, 14, 13, 12, 1342, 3850, 3811])).
% 2.93/2.29 tff(3859,plain,(c0_1(a2) | c2_1(a2) | c3_1(a2) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.29 tff(3860,plain,
% 2.93/2.29 ($false),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3859, 3809, 3808, 3807, 26])).
% 2.93/2.29 tff(3861,plain,(c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.29 tff(3862,plain,
% 2.93/2.29 (((~hskp24) | (~c1_1(a58))) <=> ((~hskp24) | (~c1_1(a58)))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3863,plain,
% 2.93/2.29 (((~c1_1(a58)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a58)))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3864,axiom,((~c1_1(a58)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 2.93/2.29 tff(3865,plain,
% 2.93/2.29 ((~hskp24) | (~c1_1(a58))),
% 2.93/2.29 inference(modus_ponens,[status(thm)],[3864, 3863])).
% 2.93/2.29 tff(3866,plain,
% 2.93/2.29 ((~hskp24) | (~c1_1(a58))),
% 2.93/2.29 inference(modus_ponens,[status(thm)],[3865, 3862])).
% 2.93/2.29 tff(3867,plain,
% 2.93/2.29 (~hskp24),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3866, 3861])).
% 2.93/2.29 tff(3868,plain,
% 2.93/2.29 ((~hskp21) | hskp6),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3156, 3867])).
% 2.93/2.29 tff(3869,plain,
% 2.93/2.29 (~hskp21),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3868, 25])).
% 2.93/2.29 tff(3870,plain,
% 2.93/2.29 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 2.93/2.29 inference(bind,[status(th)],[])).
% 2.93/2.29 tff(3871,plain,
% 2.93/2.29 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.29 inference(quant_intro,[status(thm)],[3870])).
% 2.93/2.29 tff(3872,plain,
% 2.93/2.29 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3873,plain,
% 2.93/2.29 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 2.93/2.29 inference(bind,[status(th)],[])).
% 2.93/2.29 tff(3874,plain,
% 2.93/2.29 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.29 inference(quant_intro,[status(thm)],[3873])).
% 2.93/2.29 tff(3875,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 2.93/2.29 tff(3876,plain,
% 2.93/2.29 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.29 inference(modus_ponens,[status(thm)],[3875, 3874])).
% 2.93/2.29 tff(3877,plain,
% 2.93/2.29 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.29 inference(modus_ponens,[status(thm)],[3876, 3872])).
% 2.93/2.29 tff(3878,plain,(
% 2.93/2.29 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.29 inference(skolemize,[status(sab)],[3877])).
% 2.93/2.29 tff(3879,plain,
% 2.93/2.29 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.93/2.29 inference(modus_ponens,[status(thm)],[3878, 3871])).
% 2.93/2.29 tff(3880,plain,
% 2.93/2.29 (hskp21 | hskp13),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[825, 3867])).
% 2.93/2.29 tff(3881,plain,
% 2.93/2.29 (hskp13),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3880, 3869])).
% 2.93/2.29 tff(3882,plain,
% 2.93/2.29 (c2_1(a21)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[842, 3881])).
% 2.93/2.29 tff(3883,plain,
% 2.93/2.29 (c0_1(a21)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[853, 3881])).
% 2.93/2.29 tff(3884,plain,
% 2.93/2.29 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3885,plain,
% 2.93/2.29 ((hskp6 | (~ndr1_0) | (~c2_1(a21)) | (~c1_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58))) <=> (hskp6 | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3886,plain,
% 2.93/2.29 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a21)) | (~c1_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21))))),
% 2.93/2.29 inference(monotonicity,[status(thm)],[3885])).
% 2.93/2.29 tff(3887,plain,
% 2.93/2.29 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a21)) | (~c1_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 2.93/2.29 inference(transitivity,[status(thm)],[3886, 3884])).
% 2.93/2.29 tff(3888,plain,
% 2.93/2.29 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a21)) | (~c1_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)))),
% 2.93/2.29 inference(quant_inst,[status(thm)],[])).
% 2.93/2.29 tff(3889,plain,
% 2.93/2.29 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21))),
% 2.93/2.29 inference(modus_ponens,[status(thm)],[3888, 3887])).
% 2.93/2.29 tff(3890,plain,
% 2.93/2.29 (~c1_1(a21)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3889, 104, 25, 780, 3883, 3882, 37, 3861, 3879])).
% 2.93/2.29 tff(3891,plain,
% 2.93/2.29 (~c3_1(a21)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[831, 3881])).
% 2.93/2.29 tff(3892,plain,
% 2.93/2.29 (hskp18),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[2743, 104, 3883, 3882, 3891, 2737, 3890])).
% 2.93/2.29 tff(3893,plain,
% 2.93/2.29 (~c0_1(a31)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[444, 3892])).
% 2.93/2.29 tff(3894,plain,
% 2.93/2.29 (~c3_1(a31)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[403, 3892])).
% 2.93/2.29 tff(3895,plain,
% 2.93/2.29 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a58) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a58) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a58)))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3896,plain,
% 2.93/2.29 ((hskp6 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp6 | c2_1(a58) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a58)))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3897,plain,
% 2.93/2.29 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a58) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a58))))),
% 2.93/2.29 inference(monotonicity,[status(thm)],[3896])).
% 2.93/2.29 tff(3898,plain,
% 2.93/2.29 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a58) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a58)))),
% 2.93/2.29 inference(transitivity,[status(thm)],[3897, 3895])).
% 2.93/2.29 tff(3899,plain,
% 2.93/2.29 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 2.93/2.29 inference(quant_inst,[status(thm)],[])).
% 2.93/2.29 tff(3900,plain,
% 2.93/2.29 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a58) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a58))),
% 2.93/2.29 inference(modus_ponens,[status(thm)],[3899, 3898])).
% 2.93/2.29 tff(3901,plain,
% 2.93/2.29 (hskp6 | c0_1(a2) | (~c3_1(a58))),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3900, 104, 780, 3861, 13, 12, 1316])).
% 2.93/2.29 tff(3902,plain,
% 2.93/2.29 (~c3_1(a58)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3901, 25, 14])).
% 2.93/2.29 tff(3903,plain,
% 2.93/2.29 (c1_1(a31)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[414, 3892])).
% 2.93/2.29 tff(3904,plain,
% 2.93/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | c0_1(a58) | c3_1(a31) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c3_1(a31) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)) | c3_1(a58))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3905,plain,
% 2.93/2.29 (((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | c3_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c3_1(a31) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)) | c3_1(a58))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3906,plain,
% 2.93/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | c0_1(a58) | c3_1(a31) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)) | c3_1(a58)))),
% 2.93/2.29 inference(monotonicity,[status(thm)],[3905])).
% 2.93/2.29 tff(3907,plain,
% 2.93/2.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c3_1(a31) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)) | c3_1(a58))),
% 2.93/2.29 inference(transitivity,[status(thm)],[3906, 3904])).
% 2.93/2.29 tff(3908,plain,
% 2.93/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | c3_1(a58))),
% 2.93/2.29 inference(quant_inst,[status(thm)],[])).
% 2.93/2.29 tff(3909,plain,
% 2.93/2.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c3_1(a31) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)) | c3_1(a58)),
% 2.93/2.29 inference(modus_ponens,[status(thm)],[3908, 3907])).
% 2.93/2.29 tff(3910,plain,
% 2.93/2.29 (~c2_1(a31)),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3909, 104, 780, 3903, 3883, 3882, 37, 3894, 1342, 3902, 3890])).
% 2.93/2.29 tff(3911,plain,
% 2.93/2.29 (~hskp20),
% 2.93/2.29 inference(unit_resolution,[status(thm)],[3198, 3910, 11, 3894, 3893, 25])).
% 2.93/2.29 tff(3912,plain,
% 2.93/2.29 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c2_1(a58) | c0_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c2_1(a58) | c0_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3913,plain,
% 2.93/2.29 ((hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58) | c2_1(a58) | c0_1(a58)) <=> (hskp5 | c2_1(a58) | c0_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58))),
% 2.93/2.29 inference(rewrite,[status(thm)],[])).
% 2.93/2.29 tff(3914,plain,
% 2.93/2.29 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58) | c2_1(a58) | c0_1(a58))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c2_1(a58) | c0_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58)))),
% 2.93/2.29 inference(monotonicity,[status(thm)],[3913])).
% 2.93/2.29 tff(3915,plain,
% 2.93/2.29 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58) | c2_1(a58) | c0_1(a58))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c2_1(a58) | c0_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58))),
% 2.93/2.30 inference(transitivity,[status(thm)],[3914, 3912])).
% 2.93/2.30 tff(3916,plain,
% 2.93/2.30 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58) | c2_1(a58) | c0_1(a58))),
% 2.93/2.30 inference(quant_inst,[status(thm)],[])).
% 2.93/2.30 tff(3917,plain,
% 2.93/2.30 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c2_1(a58) | c0_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58)),
% 2.93/2.30 inference(modus_ponens,[status(thm)],[3916, 3915])).
% 2.93/2.30 tff(3918,plain,
% 2.93/2.30 (hskp5),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[3917, 104, 780, 3882, 37, 3891, 290, 3902, 3890])).
% 2.93/2.30 tff(3919,plain,
% 2.93/2.30 (~c1_1(a11)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[312, 3918])).
% 2.93/2.30 tff(3920,plain,
% 2.93/2.30 (c0_1(a11)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[323, 3918])).
% 2.93/2.30 tff(3921,plain,
% 2.93/2.30 (hskp20 | (~c3_1(a11))),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[3613, 104, 3883, 3882, 3920, 3891, 3919, 3150])).
% 2.93/2.30 tff(3922,plain,
% 2.93/2.30 (~c3_1(a11)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[3921, 3911])).
% 2.93/2.30 tff(3923,plain,
% 2.93/2.30 (~c2_1(a11)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[306, 3918])).
% 2.93/2.30 tff(3924,plain,
% 2.93/2.30 (hskp20 | c3_1(a11)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[3621, 104, 3869, 3919, 3923, 708])).
% 2.93/2.30 tff(3925,plain,
% 2.93/2.30 ($false),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[3924, 3922, 3911])).
% 2.93/2.30 tff(3926,plain,(hskp6 | hskp0 | c2_1(a58) | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.30 tff(3927,plain,
% 2.93/2.30 (hskp6),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[3926, 37, 780, 11, 14, 13, 12])).
% 2.93/2.30 tff(3928,plain,
% 2.93/2.30 (~c3_1(a13)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[186, 3927])).
% 2.93/2.30 tff(3929,plain,
% 2.93/2.30 (~c1_1(a13)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[192, 3927])).
% 2.93/2.30 tff(3930,plain,
% 2.93/2.30 (~c0_1(a13)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[198, 3927])).
% 2.93/2.30 tff(3931,plain,
% 2.93/2.30 (~c3_1(a38)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[1076, 104, 647, 658, 3154, 3930, 3929, 3928, 36])).
% 2.93/2.30 tff(3932,plain,
% 2.93/2.30 (^[U: $i] : refl((hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 2.93/2.30 inference(bind,[status(th)],[])).
% 2.93/2.30 tff(3933,plain,
% 2.93/2.30 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.93/2.30 inference(quant_intro,[status(thm)],[3932])).
% 2.93/2.30 tff(3934,plain,
% 2.93/2.30 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.93/2.30 inference(rewrite,[status(thm)],[])).
% 2.93/2.30 tff(3935,plain,
% 2.93/2.30 (^[U: $i] : 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)) | hskp22) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp0) <=> ((hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0))), rewrite(((hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp0) <=> (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 2.93/2.30 inference(bind,[status(th)],[])).
% 2.93/2.30 tff(3936,plain,
% 2.93/2.30 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp0) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.93/2.30 inference(quant_intro,[status(thm)],[3935])).
% 2.93/2.30 tff(3937,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 2.93/2.30 tff(3938,plain,
% 2.93/2.30 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.93/2.30 inference(modus_ponens,[status(thm)],[3937, 3936])).
% 2.93/2.30 tff(3939,plain,
% 2.93/2.30 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.93/2.30 inference(modus_ponens,[status(thm)],[3938, 3934])).
% 2.93/2.30 tff(3940,plain,(
% 2.93/2.30 ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.93/2.30 inference(skolemize,[status(sab)],[3939])).
% 2.93/2.30 tff(3941,plain,
% 2.93/2.30 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.93/2.30 inference(modus_ponens,[status(thm)],[3940, 3933])).
% 2.93/2.30 tff(3942,plain,
% 2.93/2.30 (hskp27),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[678, 3154, 636, 13, 12, 14])).
% 2.93/2.30 tff(3943,plain,
% 2.93/2.30 (c3_1(a12)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[605, 3942])).
% 2.93/2.30 tff(3944,plain,
% 2.93/2.30 (c1_1(a12)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[616, 3942])).
% 2.93/2.30 tff(3945,plain,
% 2.93/2.30 (c0_1(a12)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[1192, 3942])).
% 2.93/2.30 tff(3946,plain,
% 2.93/2.30 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 2.93/2.30 inference(rewrite,[status(thm)],[])).
% 2.93/2.30 tff(3947,plain,
% 2.93/2.30 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 2.93/2.30 inference(quant_inst,[status(thm)],[])).
% 2.93/2.30 tff(3948,plain,
% 2.93/2.30 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))),
% 2.93/2.30 inference(modus_ponens,[status(thm)],[3947, 3946])).
% 2.93/2.30 tff(3949,plain,
% 2.93/2.30 (hskp22),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[3948, 104, 11, 3945, 3944, 3943, 3941])).
% 2.93/2.30 tff(3950,plain,
% 2.93/2.30 (~c1_1(a42)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[1475, 3949])).
% 2.93/2.30 tff(3951,plain,
% 2.93/2.30 (c2_1(a42)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[1487, 3949])).
% 2.93/2.30 tff(3952,plain,
% 2.93/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | c1_1(a42) | c2_1(a38) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~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)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | c1_1(a42) | c2_1(a38) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 2.93/2.30 inference(rewrite,[status(thm)],[])).
% 2.93/2.30 tff(3953,plain,
% 2.93/2.30 (((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58))) <=> (c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | c1_1(a42) | c2_1(a38) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 2.93/2.30 inference(rewrite,[status(thm)],[])).
% 2.93/2.30 tff(3954,plain,
% 2.93/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a58) | c0_1(a58) | (~c1_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)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | c1_1(a42) | c2_1(a38) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42))))),
% 2.93/2.30 inference(monotonicity,[status(thm)],[3953])).
% 2.93/2.30 tff(3955,plain,
% 2.93/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a58) | c0_1(a58) | (~c1_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)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | c1_1(a42) | c2_1(a38) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 2.93/2.30 inference(transitivity,[status(thm)],[3954, 3952])).
% 2.93/2.30 tff(3956,plain,
% 2.93/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)))),
% 2.93/2.30 inference(quant_inst,[status(thm)],[])).
% 2.93/2.30 tff(3957,plain,
% 2.93/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | c1_1(a42) | c2_1(a38) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42))),
% 2.93/2.30 inference(modus_ponens,[status(thm)],[3956, 3955])).
% 2.93/2.30 tff(3958,plain,
% 2.93/2.30 (~c3_1(a42)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[3957, 104, 780, 3951, 647, 37, 3861, 3950, 3154, 2061, 3931])).
% 2.93/2.30 tff(3959,plain,
% 2.93/2.30 (hskp8),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[2294, 104, 3945, 3944, 3943, 647, 658, 2283, 3931])).
% 2.93/2.30 tff(3960,plain,
% 2.93/2.30 (~c3_1(a15)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[1394, 3959])).
% 2.93/2.30 tff(3961,plain,
% 2.93/2.30 (~c2_1(a15)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[2093, 3959])).
% 2.93/2.30 tff(3962,plain,
% 2.93/2.30 (~c1_1(a15)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[2184, 3959])).
% 2.93/2.30 tff(3963,plain,
% 2.93/2.30 (c0_1(a42)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[1498, 3949])).
% 2.93/2.30 tff(3964,plain,
% 2.93/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a42) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a42) | (~c0_1(a42)))),
% 2.93/2.30 inference(rewrite,[status(thm)],[])).
% 2.93/2.30 tff(3965,plain,
% 2.93/2.30 (((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15)) <=> (c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a42) | (~c0_1(a42)))),
% 2.93/2.30 inference(rewrite,[status(thm)],[])).
% 2.93/2.30 tff(3966,plain,
% 2.93/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a42) | (~c0_1(a42))))),
% 2.93/2.30 inference(monotonicity,[status(thm)],[3965])).
% 2.93/2.30 tff(3967,plain,
% 2.93/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a42) | (~c0_1(a42)))),
% 2.93/2.30 inference(transitivity,[status(thm)],[3966, 3964])).
% 2.93/2.30 tff(3968,plain,
% 2.93/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15))),
% 2.93/2.30 inference(quant_inst,[status(thm)],[])).
% 2.93/2.30 tff(3969,plain,
% 2.93/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a42) | (~c0_1(a42))),
% 2.93/2.30 inference(modus_ponens,[status(thm)],[3968, 3967])).
% 2.93/2.30 tff(3970,plain,
% 2.93/2.30 (~c2_1(a13)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[3969, 104, 3963, 3950, 3962, 3961, 3960, 3930, 3928, 341, 3958])).
% 2.93/2.30 tff(3971,plain,
% 2.93/2.30 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c3_1(a42) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c3_1(a42) | (~c0_1(a42)))),
% 2.93/2.30 inference(rewrite,[status(thm)],[])).
% 2.93/2.30 tff(3972,plain,
% 2.93/2.30 ((hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42))) <=> (hskp18 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c3_1(a42) | (~c0_1(a42)))),
% 2.93/2.30 inference(rewrite,[status(thm)],[])).
% 2.93/2.30 tff(3973,plain,
% 2.93/2.30 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c3_1(a42) | (~c0_1(a42))))),
% 2.93/2.30 inference(monotonicity,[status(thm)],[3972])).
% 2.93/2.30 tff(3974,plain,
% 2.93/2.30 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c3_1(a42) | (~c0_1(a42)))),
% 2.93/2.30 inference(transitivity,[status(thm)],[3973, 3971])).
% 2.93/2.30 tff(3975,plain,
% 2.93/2.30 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)))),
% 2.93/2.30 inference(quant_inst,[status(thm)],[])).
% 2.93/2.30 tff(3976,plain,
% 2.93/2.30 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c3_1(a42) | (~c0_1(a42))),
% 2.93/2.30 inference(modus_ponens,[status(thm)],[3975, 3974])).
% 2.93/2.30 tff(3977,plain,
% 2.93/2.30 (hskp18),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[3976, 104, 3963, 3951, 3950, 2737, 3958])).
% 2.93/2.30 tff(3978,plain,
% 2.93/2.30 (~c3_1(a31)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[403, 3977])).
% 2.93/2.30 tff(3979,plain,
% 2.93/2.30 (c1_1(a31)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[414, 3977])).
% 2.93/2.30 tff(3980,plain,
% 2.93/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c3_1(a31) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | (~c2_1(a31)) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a31) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | (~c2_1(a31)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 2.93/2.30 inference(rewrite,[status(thm)],[])).
% 2.93/2.30 tff(3981,plain,
% 2.93/2.30 (((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c1_1(a42) | c3_1(a31) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | (~c2_1(a31)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 2.93/2.30 inference(rewrite,[status(thm)],[])).
% 2.93/2.30 tff(3982,plain,
% 2.93/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c3_1(a31) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | (~c2_1(a31)) | (~c2_1(a42)) | (~c0_1(a42))))),
% 2.93/2.30 inference(monotonicity,[status(thm)],[3981])).
% 2.93/2.30 tff(3983,plain,
% 2.93/2.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a31) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | (~c2_1(a31)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 2.93/2.30 inference(transitivity,[status(thm)],[3982, 3980])).
% 2.93/2.30 tff(3984,plain,
% 2.93/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a13) | c0_1(a13) | c3_1(a13))),
% 2.93/2.30 inference(quant_inst,[status(thm)],[])).
% 2.93/2.30 tff(3985,plain,
% 2.93/2.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a31) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | (~c2_1(a31)) | (~c2_1(a42)) | (~c0_1(a42))),
% 2.93/2.30 inference(modus_ponens,[status(thm)],[3984, 3983])).
% 2.93/2.30 tff(3986,plain,
% 2.93/2.30 (~c2_1(a31)),
% 2.93/2.30 inference(unit_resolution,[status(thm)],[3985, 104, 3963, 3951, 3979, 3950, 3978, 3930, 3928, 1342, 3970])).
% 2.93/2.30 tff(3987,plain,
% 2.93/2.30 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 2.93/2.30 inference(bind,[status(th)],[])).
% 2.93/2.30 tff(3988,plain,
% 2.93/2.30 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.93/2.30 inference(quant_intro,[status(thm)],[3987])).
% 2.93/2.30 tff(3989,plain,
% 2.93/2.30 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.93/2.30 inference(rewrite,[status(thm)],[])).
% 2.93/2.30 tff(3990,plain,
% 2.93/2.30 (^[V: $i, U: $i] : 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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp12) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 2.93/2.30 inference(bind,[status(th)],[])).
% 2.93/2.30 tff(3991,plain,
% 2.93/2.30 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.93/2.30 inference(quant_intro,[status(thm)],[3990])).
% 2.93/2.30 tff(3992,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 2.93/2.30 tff(3993,plain,
% 2.93/2.30 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.93/2.30 inference(modus_ponens,[status(thm)],[3992, 3991])).
% 2.93/2.30 tff(3994,plain,
% 2.93/2.30 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.93/2.30 inference(modus_ponens,[status(thm)],[3993, 3989])).
% 2.93/2.30 tff(3995,plain,(
% 2.93/2.30 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.93/2.30 inference(skolemize,[status(sab)],[3994])).
% 2.93/2.30 tff(3996,plain,
% 2.93/2.30 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.93/2.30 inference(modus_ponens,[status(thm)],[3995, 3988])).
% 2.93/2.30 tff(3997,plain,
% 2.93/2.30 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 2.93/2.31 inference(rewrite,[status(thm)],[])).
% 2.93/2.31 tff(3998,plain,
% 2.93/2.31 ((hskp12 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42))) <=> (hskp12 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 2.93/2.31 inference(rewrite,[status(thm)],[])).
% 2.93/2.31 tff(3999,plain,
% 2.93/2.31 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))))),
% 2.93/2.31 inference(monotonicity,[status(thm)],[3998])).
% 2.93/2.31 tff(4000,plain,
% 2.93/2.31 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 2.93/2.31 inference(transitivity,[status(thm)],[3999, 3997])).
% 2.93/2.31 tff(4001,plain,
% 2.93/2.31 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)))),
% 2.93/2.31 inference(quant_inst,[status(thm)],[])).
% 2.93/2.31 tff(4002,plain,
% 2.93/2.31 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))),
% 2.93/2.31 inference(modus_ponens,[status(thm)],[4001, 4000])).
% 2.93/2.31 tff(4003,plain,
% 2.93/2.31 (hskp12),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[4002, 104, 3945, 3944, 3943, 3963, 3951, 3950, 3996])).
% 2.93/2.31 tff(4004,plain,
% 2.93/2.31 (~c3_1(a20)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[999, 4003])).
% 2.93/2.31 tff(4005,plain,
% 2.93/2.31 (~c1_1(a20)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[1005, 4003])).
% 2.93/2.31 tff(4006,plain,
% 2.93/2.31 (c2_1(a20)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[1016, 4003])).
% 2.93/2.31 tff(4007,plain,
% 2.93/2.31 ($false),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[2656, 104, 3979, 4006, 3978, 4005, 4004, 3930, 3929, 380, 3970, 3986])).
% 2.93/2.31 tff(4008,plain,((~hskp21) | c2_1(a58) | c0_1(a58) | hskp0 | c2_1(a2) | c3_1(a2) | c0_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.31 tff(4009,plain,
% 2.93/2.31 (~hskp21),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[4008, 37, 780, 11, 13, 12, 14])).
% 2.93/2.31 tff(4010,plain,
% 2.93/2.31 (c2_1(a13)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[2417, 811, 3168])).
% 2.93/2.31 tff(4011,plain,
% 2.93/2.31 (hskp5 | (~c2_1(a13))),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[299, 104, 240, 239, 14, 13, 12, 290])).
% 2.93/2.31 tff(4012,plain,
% 2.93/2.31 (hskp5),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[4011, 4010])).
% 2.93/2.31 tff(4013,plain,
% 2.93/2.31 (~c2_1(a11)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[306, 4012])).
% 2.93/2.31 tff(4014,plain,
% 2.93/2.31 (~c1_1(a11)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[312, 4012])).
% 2.93/2.31 tff(4015,plain,
% 2.93/2.31 (c3_1(a11)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[3621, 104, 811, 3168, 4014, 4013, 708])).
% 2.93/2.31 tff(4016,plain,
% 2.93/2.31 (hskp13),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[3880, 811])).
% 2.93/2.31 tff(4017,plain,
% 2.93/2.31 (~c3_1(a21)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[831, 4016])).
% 2.93/2.31 tff(4018,plain,
% 2.93/2.31 (c0_1(a11)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[323, 4012])).
% 2.93/2.31 tff(4019,plain,
% 2.93/2.31 (c2_1(a21)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[842, 4016])).
% 2.93/2.31 tff(4020,plain,
% 2.93/2.31 (c0_1(a21)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[853, 4016])).
% 2.93/2.31 tff(4021,plain,
% 2.93/2.31 ($false),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[3613, 104, 3168, 4020, 4019, 4018, 4017, 4014, 3150, 4015])).
% 2.93/2.31 tff(4022,plain,(hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.31 tff(4023,plain,
% 2.93/2.31 (hskp20),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[4022, 4009, 3929, 3928, 14, 13, 12])).
% 2.93/2.31 tff(4024,plain,
% 2.93/2.31 (~c0_1(a37)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[685, 4023])).
% 2.93/2.31 tff(4025,plain,
% 2.93/2.31 (c3_1(a37)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[555, 4023])).
% 2.93/2.31 tff(4026,plain,
% 2.93/2.31 (~c2_1(a37)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[693, 104, 11, 4025, 4024, 14, 13, 12, 24])).
% 2.93/2.31 tff(4027,plain,
% 2.93/2.31 ((~hskp20) | hskp0 | hskp3),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[3135, 3867])).
% 2.93/2.31 tff(4028,plain,
% 2.93/2.31 (hskp3),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[4027, 4023, 11])).
% 2.93/2.31 tff(4029,plain,
% 2.93/2.31 (~c2_1(a7)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[2959, 4028])).
% 2.93/2.31 tff(4030,plain,
% 2.93/2.31 (c3_1(a7)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[2972, 4028])).
% 2.93/2.31 tff(4031,plain,
% 2.93/2.31 (c0_1(a7)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[2983, 4028])).
% 2.93/2.31 tff(4032,plain,
% 2.93/2.31 (~c1_1(a7)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[3033, 104, 4031, 4030, 3930, 3929, 3928, 4029, 36])).
% 2.93/2.31 tff(4033,plain,
% 2.93/2.31 (c1_1(a37)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[566, 4023])).
% 2.93/2.31 tff(4034,plain,
% 2.93/2.31 (hskp28),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[697, 4023, 11, 12, 14, 13])).
% 2.93/2.31 tff(4035,plain,
% 2.93/2.31 (c3_1(a25)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[487, 4034])).
% 2.93/2.31 tff(4036,plain,
% 2.93/2.31 (c1_1(a25)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[498, 4034])).
% 2.93/2.31 tff(4037,plain,
% 2.93/2.31 (~c0_1(a25)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[3254, 104, 4036, 4035, 4033, 4025, 4030, 4029, 1772, 4032, 4026])).
% 2.93/2.31 tff(4038,plain,
% 2.93/2.31 (c2_1(a25)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[509, 4034])).
% 2.93/2.31 tff(4039,plain,
% 2.93/2.31 ($false),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[3102, 104, 11, 4038, 4035, 14, 13, 12, 24, 4037])).
% 2.93/2.31 tff(4040,plain,(c0_1(a58) | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | c2_1(a58)), inference(lemma,lemma(discharge,[]))).
% 2.93/2.31 tff(4041,plain,
% 2.93/2.31 (c0_1(a58)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[4040, 14, 11, 13, 12, 780])).
% 2.93/2.31 tff(4042,plain,
% 2.93/2.31 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0))),
% 2.93/2.31 inference(rewrite,[status(thm)],[])).
% 2.93/2.31 tff(4043,plain,
% 2.93/2.31 ((hskp24 | hskp6 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58))) <=> (hskp24 | hskp6 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0))),
% 2.93/2.31 inference(rewrite,[status(thm)],[])).
% 2.93/2.31 tff(4044,plain,
% 2.93/2.31 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0)))),
% 2.93/2.31 inference(monotonicity,[status(thm)],[4043])).
% 2.93/2.31 tff(4045,plain,
% 2.93/2.31 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0))),
% 2.93/2.31 inference(transitivity,[status(thm)],[4044, 4042])).
% 2.93/2.31 tff(4046,plain,
% 2.93/2.31 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)))),
% 2.93/2.31 inference(quant_inst,[status(thm)],[])).
% 2.93/2.31 tff(4047,plain,
% 2.93/2.31 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0)),
% 2.93/2.31 inference(modus_ponens,[status(thm)],[4046, 4045])).
% 2.93/2.31 tff(4048,plain,
% 2.93/2.31 (hskp6 | c2_1(a58) | (~c0_1(a58))),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[4047, 104, 3867, 3861, 1059])).
% 2.93/2.31 tff(4049,plain,
% 2.93/2.31 (hskp6),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[4048, 4041, 780])).
% 2.93/2.31 tff(4050,plain,
% 2.93/2.31 (~c3_1(a13)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[186, 4049])).
% 2.93/2.31 tff(4051,plain,
% 2.93/2.31 (~c1_1(a13)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[192, 4049])).
% 2.93/2.31 tff(4052,plain,
% 2.93/2.31 (~c0_1(a13)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[198, 4049])).
% 2.93/2.31 tff(4053,plain,
% 2.93/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a58)))),
% 2.93/2.31 inference(rewrite,[status(thm)],[])).
% 2.93/2.31 tff(4054,plain,
% 2.93/2.31 (((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a58)))),
% 2.93/2.31 inference(rewrite,[status(thm)],[])).
% 2.93/2.31 tff(4055,plain,
% 2.93/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a58))))),
% 2.93/2.31 inference(monotonicity,[status(thm)],[4054])).
% 2.93/2.31 tff(4056,plain,
% 2.93/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a58)))),
% 2.93/2.31 inference(transitivity,[status(thm)],[4055, 4053])).
% 2.93/2.31 tff(4057,plain,
% 2.93/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 2.93/2.31 inference(quant_inst,[status(thm)],[])).
% 2.93/2.31 tff(4058,plain,
% 2.93/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a58))),
% 2.93/2.31 inference(modus_ponens,[status(thm)],[4057, 4056])).
% 2.93/2.31 tff(4059,plain,
% 2.93/2.31 (~c3_1(a58)),
% 2.93/2.31 inference(unit_resolution,[status(thm)],[4058, 104, 780, 4041, 3861, 4052, 4051, 4050, 36])).
% 2.93/2.31 tff(4060,plain,
% 2.93/2.31 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 2.93/2.31 inference(rewrite,[status(thm)],[])).
% 2.93/2.31 tff(4061,plain,
% 2.93/2.31 ((hskp27 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp27 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 2.93/2.31 inference(rewrite,[status(thm)],[])).
% 3.03/2.31 tff(4062,plain,
% 3.03/2.31 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0)))),
% 3.03/2.31 inference(monotonicity,[status(thm)],[4061])).
% 3.03/2.31 tff(4063,plain,
% 3.03/2.31 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 3.03/2.31 inference(transitivity,[status(thm)],[4062, 4060])).
% 3.03/2.31 tff(4064,plain,
% 3.03/2.31 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 3.03/2.31 inference(quant_inst,[status(thm)],[])).
% 3.03/2.31 tff(4065,plain,
% 3.03/2.31 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0)),
% 3.03/2.31 inference(modus_ponens,[status(thm)],[4064, 4063])).
% 3.03/2.31 tff(4066,plain,
% 3.03/2.31 (hskp27 | (~c0_1(a58)) | c0_1(a2)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[4065, 104, 780, 3861, 13, 12, 668])).
% 3.03/2.31 tff(4067,plain,
% 3.03/2.31 (hskp27),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[4066, 4041, 14])).
% 3.03/2.31 tff(4068,plain,
% 3.03/2.31 (c3_1(a12)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[605, 4067])).
% 3.03/2.31 tff(4069,plain,
% 3.03/2.31 (c1_1(a12)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[616, 4067])).
% 3.03/2.31 tff(4070,plain,
% 3.03/2.31 (c0_1(a12)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[1192, 4067])).
% 3.03/2.31 tff(4071,plain,
% 3.03/2.31 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | c3_1(a58) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | c3_1(a58) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 3.03/2.31 inference(rewrite,[status(thm)],[])).
% 3.03/2.31 tff(4072,plain,
% 3.03/2.31 ((hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a58) | (~c0_1(a58)) | (~c1_1(a58))) <=> (hskp8 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | c3_1(a58) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 3.03/2.31 inference(rewrite,[status(thm)],[])).
% 3.03/2.31 tff(4073,plain,
% 3.03/2.31 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a58) | (~c0_1(a58)) | (~c1_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | c3_1(a58) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))))),
% 3.03/2.31 inference(monotonicity,[status(thm)],[4072])).
% 3.03/2.31 tff(4074,plain,
% 3.03/2.31 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a58) | (~c0_1(a58)) | (~c1_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | c3_1(a58) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 3.03/2.31 inference(transitivity,[status(thm)],[4073, 4071])).
% 3.03/2.31 tff(4075,plain,
% 3.03/2.31 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a58) | (~c0_1(a58)) | (~c1_1(a58)))),
% 3.03/2.31 inference(quant_inst,[status(thm)],[])).
% 3.03/2.31 tff(4076,plain,
% 3.03/2.31 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | c3_1(a58) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))),
% 3.03/2.31 inference(modus_ponens,[status(thm)],[4075, 4074])).
% 3.03/2.31 tff(4077,plain,
% 3.03/2.31 (hskp8),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[4076, 104, 4070, 4069, 4068, 4041, 3861, 2283, 4059])).
% 3.03/2.31 tff(4078,plain,
% 3.03/2.31 (~c3_1(a15)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[1394, 4077])).
% 3.03/2.31 tff(4079,plain,
% 3.03/2.31 (~c2_1(a15)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[2093, 4077])).
% 3.03/2.31 tff(4080,plain,
% 3.03/2.31 (~c1_1(a15)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[2184, 4077])).
% 3.03/2.31 tff(4081,plain,
% 3.03/2.31 (hskp22),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[3948, 104, 11, 4070, 4069, 4068, 3941])).
% 3.03/2.31 tff(4082,plain,
% 3.03/2.31 (~c1_1(a42)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[1475, 4081])).
% 3.03/2.31 tff(4083,plain,
% 3.03/2.31 (c2_1(a42)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[1487, 4081])).
% 3.03/2.31 tff(4084,plain,
% 3.03/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)))),
% 3.03/2.31 inference(rewrite,[status(thm)],[])).
% 3.03/2.31 tff(4085,plain,
% 3.03/2.31 (((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)))),
% 3.03/2.31 inference(rewrite,[status(thm)],[])).
% 3.03/2.31 tff(4086,plain,
% 3.03/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42))))),
% 3.03/2.31 inference(monotonicity,[status(thm)],[4085])).
% 3.03/2.31 tff(4087,plain,
% 3.03/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)))),
% 3.03/2.31 inference(transitivity,[status(thm)],[4086, 4084])).
% 3.03/2.31 tff(4088,plain,
% 3.03/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 3.03/2.31 inference(quant_inst,[status(thm)],[])).
% 3.03/2.31 tff(4089,plain,
% 3.03/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42))),
% 3.03/2.31 inference(modus_ponens,[status(thm)],[4088, 4087])).
% 3.03/2.31 tff(4090,plain,
% 3.03/2.31 (~c3_1(a42)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[4089, 104, 4083, 4082, 4080, 4079, 4078, 14, 13, 12, 362])).
% 3.03/2.31 tff(4091,plain,
% 3.03/2.31 (c0_1(a42)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[1498, 4081])).
% 3.03/2.31 tff(4092,plain,
% 3.03/2.31 (hskp12),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[4002, 104, 4070, 4069, 4068, 4091, 4083, 4082, 3996])).
% 3.03/2.31 tff(4093,plain,
% 3.03/2.31 (~c3_1(a20)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[999, 4092])).
% 3.03/2.31 tff(4094,plain,
% 3.03/2.31 (~c1_1(a20)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[1005, 4092])).
% 3.03/2.31 tff(4095,plain,
% 3.03/2.31 (c2_1(a20)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[1016, 4092])).
% 3.03/2.31 tff(4096,plain,
% 3.03/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | (~c1_1(a58)) | c1_1(a20) | c3_1(a20) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a20)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | (~c1_1(a58)) | c1_1(a20) | c3_1(a20) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a20)) | c3_1(a58))),
% 3.03/2.31 inference(rewrite,[status(thm)],[])).
% 3.03/2.31 tff(4097,plain,
% 3.03/2.31 (((~ndr1_0) | c3_1(a58) | c2_1(a58) | (~c1_1(a58)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a15) | c1_1(a15) | c0_1(a15)) <=> (c2_1(a58) | (~c1_1(a58)) | c1_1(a20) | c3_1(a20) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a20)) | c3_1(a58))),
% 3.03/2.31 inference(rewrite,[status(thm)],[])).
% 3.03/2.31 tff(4098,plain,
% 3.03/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a58) | c2_1(a58) | (~c1_1(a58)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | (~c1_1(a58)) | c1_1(a20) | c3_1(a20) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a20)) | c3_1(a58)))),
% 3.03/2.31 inference(monotonicity,[status(thm)],[4097])).
% 3.03/2.31 tff(4099,plain,
% 3.03/2.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a58) | c2_1(a58) | (~c1_1(a58)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | (~c1_1(a58)) | c1_1(a20) | c3_1(a20) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a20)) | c3_1(a58))),
% 3.03/2.31 inference(transitivity,[status(thm)],[4098, 4096])).
% 3.03/2.31 tff(4100,plain,
% 3.03/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a58) | c2_1(a58) | (~c1_1(a58)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a15) | c1_1(a15) | c0_1(a15))),
% 3.03/2.31 inference(quant_inst,[status(thm)],[])).
% 3.03/2.31 tff(4101,plain,
% 3.03/2.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | (~c1_1(a58)) | c1_1(a20) | c3_1(a20) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a20)) | c3_1(a58)),
% 3.03/2.31 inference(modus_ponens,[status(thm)],[4100, 4099])).
% 3.03/2.31 tff(4102,plain,
% 3.03/2.31 (c0_1(a15)),
% 3.03/2.31 inference(unit_resolution,[status(thm)],[4101, 104, 780, 4095, 3861, 4094, 4093, 4080, 4079, 380, 4059])).
% 3.03/2.31 tff(4103,plain,
% 3.03/2.31 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a42) | c1_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | c1_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 3.03/2.31 inference(rewrite,[status(thm)],[])).
% 3.03/2.31 tff(4104,plain,
% 3.03/2.31 ((hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15))) <=> (hskp18 | c1_1(a42) | c1_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 3.03/2.32 inference(rewrite,[status(thm)],[])).
% 3.03/2.32 tff(4105,plain,
% 3.03/2.32 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a42) | c1_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a42)) | (~c0_1(a42))))),
% 3.03/2.32 inference(monotonicity,[status(thm)],[4104])).
% 3.03/2.32 tff(4106,plain,
% 3.03/2.32 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | c1_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 3.03/2.32 inference(transitivity,[status(thm)],[4105, 4103])).
% 3.03/2.32 tff(4107,plain,
% 3.03/2.32 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)))),
% 3.03/2.32 inference(quant_inst,[status(thm)],[])).
% 3.03/2.32 tff(4108,plain,
% 3.03/2.32 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | c1_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a42)) | (~c0_1(a42))),
% 3.03/2.32 inference(modus_ponens,[status(thm)],[4107, 4106])).
% 3.03/2.32 tff(4109,plain,
% 3.03/2.32 (hskp18),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4108, 104, 4091, 4083, 4082, 4080, 4078, 2737, 4102])).
% 3.03/2.32 tff(4110,plain,
% 3.03/2.32 (~c3_1(a31)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[403, 4109])).
% 3.03/2.32 tff(4111,plain,
% 3.03/2.32 (~c0_1(a31)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[444, 4109])).
% 3.03/2.32 tff(4112,plain,
% 3.03/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a42) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a42) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a42) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a42) | (~c0_1(a42)))),
% 3.03/2.32 inference(rewrite,[status(thm)],[])).
% 3.03/2.32 tff(4113,plain,
% 3.03/2.32 (((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15)) <=> (c1_1(a42) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a42) | (~c0_1(a42)))),
% 3.03/2.32 inference(rewrite,[status(thm)],[])).
% 3.03/2.32 tff(4114,plain,
% 3.03/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a42) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a42) | (~c0_1(a42))))),
% 3.03/2.32 inference(monotonicity,[status(thm)],[4113])).
% 3.03/2.32 tff(4115,plain,
% 3.03/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a42) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a42) | (~c0_1(a42)))),
% 3.03/2.32 inference(transitivity,[status(thm)],[4114, 4112])).
% 3.03/2.32 tff(4116,plain,
% 3.03/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15))),
% 3.03/2.32 inference(quant_inst,[status(thm)],[])).
% 3.03/2.32 tff(4117,plain,
% 3.03/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a42) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a42) | (~c0_1(a42))),
% 3.03/2.32 inference(modus_ponens,[status(thm)],[4116, 4115])).
% 3.03/2.32 tff(4118,plain,
% 3.03/2.32 (~c2_1(a31)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4117, 104, 4091, 4082, 4111, 4110, 4080, 4079, 4078, 341, 4090])).
% 3.03/2.32 tff(4119,plain,
% 3.03/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | (~c0_1(a15)))),
% 3.03/2.32 inference(rewrite,[status(thm)],[])).
% 3.03/2.32 tff(4120,plain,
% 3.03/2.32 (((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15)) <=> (c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | (~c0_1(a15)))),
% 3.03/2.32 inference(rewrite,[status(thm)],[])).
% 3.03/2.32 tff(4121,plain,
% 3.03/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | (~c0_1(a15))))),
% 3.03/2.32 inference(monotonicity,[status(thm)],[4120])).
% 3.03/2.32 tff(4122,plain,
% 3.03/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | (~c0_1(a15)))),
% 3.03/2.32 inference(transitivity,[status(thm)],[4121, 4119])).
% 3.03/2.32 tff(4123,plain,
% 3.03/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15))),
% 3.03/2.32 inference(quant_inst,[status(thm)],[])).
% 3.03/2.32 tff(4124,plain,
% 3.03/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | (~c0_1(a15))),
% 3.03/2.32 inference(modus_ponens,[status(thm)],[4123, 4122])).
% 3.03/2.32 tff(4125,plain,
% 3.03/2.32 ((~c2_1(a13)) | (~c0_1(a15))),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4124, 104, 4080, 4079, 4078, 4052, 4050, 341])).
% 3.03/2.32 tff(4126,plain,
% 3.03/2.32 (~c2_1(a13)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4125, 4102])).
% 3.03/2.32 tff(4127,plain,
% 3.03/2.32 (c1_1(a31)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[414, 4109])).
% 3.03/2.32 tff(4128,plain,
% 3.03/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a42) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a42)) | c3_1(a42))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a42) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a42)) | c3_1(a42))),
% 3.03/2.32 inference(rewrite,[status(thm)],[])).
% 3.03/2.32 tff(4129,plain,
% 3.03/2.32 (((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)) | c2_1(a13) | c1_1(a13) | c0_1(a13)) <=> (c1_1(a42) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a42)) | c3_1(a42))),
% 3.03/2.32 inference(rewrite,[status(thm)],[])).
% 3.03/2.32 tff(4130,plain,
% 3.03/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a42) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a42)) | c3_1(a42)))),
% 3.03/2.32 inference(monotonicity,[status(thm)],[4129])).
% 3.03/2.32 tff(4131,plain,
% 3.03/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a42) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a42)) | c3_1(a42))),
% 3.03/2.32 inference(transitivity,[status(thm)],[4130, 4128])).
% 3.03/2.32 tff(4132,plain,
% 3.03/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)) | c2_1(a13) | c1_1(a13) | c0_1(a13))),
% 3.03/2.32 inference(quant_inst,[status(thm)],[])).
% 3.03/2.32 tff(4133,plain,
% 3.03/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a42) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a42)) | c3_1(a42)),
% 3.03/2.32 inference(modus_ponens,[status(thm)],[4132, 4131])).
% 3.03/2.32 tff(4134,plain,
% 3.03/2.32 ($false),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4133, 104, 4083, 4127, 4082, 4110, 4052, 4051, 380, 4126, 4118, 4090])).
% 3.03/2.32 tff(4135,plain,(c0_1(a2) | c2_1(a2) | c3_1(a2) | c2_1(a58) | hskp0), inference(lemma,lemma(discharge,[]))).
% 3.03/2.32 tff(4136,plain,
% 3.03/2.32 (c0_1(a2)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4135, 780, 12, 13, 11])).
% 3.03/2.32 tff(4137,plain,
% 3.03/2.32 (~hskp1),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[268, 4136])).
% 3.03/2.32 tff(4138,plain,
% 3.03/2.32 (~hskp6),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[3748, 4137, 11])).
% 3.03/2.32 tff(4139,plain,
% 3.03/2.32 (~hskp21),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[3868, 4138])).
% 3.03/2.32 tff(4140,plain,
% 3.03/2.32 (hskp13),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[3880, 4139])).
% 3.03/2.32 tff(4141,plain,
% 3.03/2.32 (c0_1(a21)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[853, 4140])).
% 3.03/2.32 tff(4142,plain,
% 3.03/2.32 (~c0_1(a58)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4048, 4138, 780])).
% 3.03/2.32 tff(4143,plain,
% 3.03/2.32 (c2_1(a21)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[842, 4140])).
% 3.03/2.32 tff(4144,plain,
% 3.03/2.32 (~c1_1(a21)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[3889, 104, 4138, 780, 4141, 4143, 4142, 3861, 3879])).
% 3.03/2.32 tff(4145,plain,
% 3.03/2.32 (~c3_1(a21)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[831, 4140])).
% 3.03/2.32 tff(4146,plain,
% 3.03/2.32 (hskp18),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[2743, 104, 4141, 4143, 4145, 2737, 4144])).
% 3.03/2.32 tff(4147,plain,
% 3.03/2.32 (c1_1(a31)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[414, 4146])).
% 3.03/2.32 tff(4148,plain,
% 3.03/2.32 (hskp10),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[3770, 104, 4137, 4143, 4145, 1882, 4144])).
% 3.03/2.32 tff(4149,plain,
% 3.03/2.32 (~c0_1(a18)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[943, 4148])).
% 3.03/2.32 tff(4150,plain,
% 3.03/2.32 (c3_1(a18)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[1037, 4148])).
% 3.03/2.32 tff(4151,plain,
% 3.03/2.32 (~c1_1(a18)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[937, 4148])).
% 3.03/2.32 tff(4152,plain,
% 3.03/2.32 (~c0_1(a31)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[444, 4146])).
% 3.03/2.32 tff(4153,plain,
% 3.03/2.32 (~c3_1(a31)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[403, 4146])).
% 3.03/2.32 tff(4154,plain,
% 3.03/2.32 ($false),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[3803, 4153, 4152, 4138, 4151, 4143, 4150, 4149, 4145, 11, 4147, 4141])).
% 3.03/2.32 tff(4155,plain,(c2_1(a58) | hskp0 | c3_1(a2) | c2_1(a2)), inference(lemma,lemma(discharge,[]))).
% 3.03/2.32 tff(4156,plain,
% 3.03/2.32 (c2_1(a58)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4155, 13, 12, 11])).
% 3.03/2.32 tff(4157,plain,
% 3.03/2.32 (~c3_1(a58)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[3065, 104, 11, 4156, 37, 14, 13, 12, 24])).
% 3.03/2.32 tff(4158,plain,
% 3.03/2.32 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 3.03/2.32 inference(rewrite,[status(thm)],[])).
% 3.03/2.32 tff(4159,plain,
% 3.03/2.32 ((hskp6 | (~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58))) <=> (hskp6 | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 3.03/2.32 inference(rewrite,[status(thm)],[])).
% 3.03/2.32 tff(4160,plain,
% 3.03/2.32 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)))),
% 3.03/2.32 inference(monotonicity,[status(thm)],[4159])).
% 3.03/2.32 tff(4161,plain,
% 3.03/2.32 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 3.03/2.32 inference(transitivity,[status(thm)],[4160, 4158])).
% 3.03/2.32 tff(4162,plain,
% 3.03/2.32 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)))),
% 3.03/2.32 inference(quant_inst,[status(thm)],[])).
% 3.03/2.32 tff(4163,plain,
% 3.03/2.32 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)),
% 3.03/2.32 inference(modus_ponens,[status(thm)],[4162, 4161])).
% 3.03/2.32 tff(4164,plain,
% 3.03/2.32 (hskp6),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4163, 104, 4156, 37, 3861, 171, 4157])).
% 3.03/2.32 tff(4165,plain,
% 3.03/2.32 (~c3_1(a13)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[186, 4164])).
% 3.03/2.32 tff(4166,plain,
% 3.03/2.32 (~c1_1(a13)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[192, 4164])).
% 3.03/2.32 tff(4167,plain,
% 3.03/2.32 (~c0_1(a13)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[198, 4164])).
% 3.03/2.32 tff(4168,plain,
% 3.03/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~c1_1(a58)) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (~c1_1(a58)) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c2_1(a58)) | c3_1(a58))),
% 3.03/2.32 inference(rewrite,[status(thm)],[])).
% 3.03/2.32 tff(4169,plain,
% 3.03/2.32 (((~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7))) <=> ((~c1_1(a58)) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c2_1(a58)) | c3_1(a58))),
% 3.03/2.32 inference(rewrite,[status(thm)],[])).
% 3.03/2.32 tff(4170,plain,
% 3.03/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~c1_1(a58)) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c2_1(a58)) | c3_1(a58)))),
% 3.03/2.32 inference(monotonicity,[status(thm)],[4169])).
% 3.03/2.32 tff(4171,plain,
% 3.03/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (~c1_1(a58)) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c2_1(a58)) | c3_1(a58))),
% 3.03/2.32 inference(transitivity,[status(thm)],[4170, 4168])).
% 3.03/2.32 tff(4172,plain,
% 3.03/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))),
% 3.03/2.32 inference(quant_inst,[status(thm)],[])).
% 3.03/2.32 tff(4173,plain,
% 3.03/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (~c1_1(a58)) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c2_1(a58)) | c3_1(a58)),
% 3.03/2.32 inference(modus_ponens,[status(thm)],[4172, 4171])).
% 3.03/2.32 tff(4174,plain,
% 3.03/2.32 (c1_1(a7)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4173, 104, 59, 3293, 3292, 3861, 3291, 279, 2265])).
% 3.03/2.32 tff(4175,plain,
% 3.03/2.32 ($false),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[3033, 104, 3293, 3292, 241, 240, 239, 3291, 36, 4174])).
% 3.03/2.32 tff(4176,plain,((~hskp3) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~c2_1(a58)) | c3_1(a58)), inference(lemma,lemma(discharge,[]))).
% 3.03/2.32 tff(4177,plain,
% 3.03/2.32 (~hskp3),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4176, 4167, 4166, 4165, 4156, 4157])).
% 3.03/2.32 tff(4178,plain,
% 3.03/2.32 (~hskp20),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4027, 4177, 11])).
% 3.03/2.32 tff(4179,plain,
% 3.03/2.32 (hskp21),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4022, 4178, 4166, 4165, 14, 13, 12])).
% 3.03/2.32 tff(4180,plain,
% 3.03/2.32 ((~hskp28) | hskp3),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[3130, 3867])).
% 3.03/2.32 tff(4181,plain,
% 3.03/2.32 (~hskp28),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4180, 4177])).
% 3.03/2.32 tff(4182,plain,
% 3.03/2.32 ((~hskp27) | hskp28 | hskp0 | hskp3),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[633, 3867])).
% 3.03/2.32 tff(4183,plain,
% 3.03/2.32 (~hskp27),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4182, 4181, 11, 4177])).
% 3.03/2.32 tff(4184,plain,
% 3.03/2.32 (c2_1(a38)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[678, 4183, 4179, 13, 12, 14])).
% 3.03/2.32 tff(4185,plain,
% 3.03/2.32 ($false),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[2495, 4184, 4179])).
% 3.03/2.32 tff(4186,plain,(c0_1(a58) | c2_1(a2) | c3_1(a2) | c0_1(a2) | hskp0), inference(lemma,lemma(discharge,[]))).
% 3.03/2.32 tff(4187,plain,
% 3.03/2.32 (c0_1(a58)),
% 3.03/2.32 inference(unit_resolution,[status(thm)],[4186, 14, 12, 13, 11])).
% 3.03/2.32 tff(4188,plain,
% 3.03/2.32 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a58)))),
% 3.03/2.33 inference(rewrite,[status(thm)],[])).
% 3.03/2.33 tff(4189,plain,
% 3.03/2.33 ((hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | (~c1_1(a2))) <=> (hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a58)))),
% 3.03/2.33 inference(rewrite,[status(thm)],[])).
% 3.03/2.33 tff(4190,plain,
% 3.03/2.33 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | (~c1_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a58))))),
% 3.03/2.33 inference(monotonicity,[status(thm)],[4189])).
% 3.03/2.33 tff(4191,plain,
% 3.03/2.33 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | (~c1_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a58)))),
% 3.03/2.33 inference(transitivity,[status(thm)],[4190, 4188])).
% 3.03/2.33 tff(4192,plain,
% 3.03/2.33 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | (~c1_1(a2)))),
% 3.03/2.33 inference(quant_inst,[status(thm)],[])).
% 3.03/2.33 tff(4193,plain,
% 3.03/2.33 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a58))),
% 3.03/2.33 inference(modus_ponens,[status(thm)],[4192, 4191])).
% 3.03/2.33 tff(4194,plain,
% 3.03/2.33 (hskp6 | (~c0_1(a58)) | c0_1(a2) | (~c1_1(a2))),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4193, 104, 4156, 3861, 13, 3879])).
% 3.03/2.33 tff(4195,plain,
% 3.03/2.33 (~c1_1(a2)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4194, 25, 14, 4187])).
% 3.03/2.33 tff(4196,plain,
% 3.03/2.33 (hskp20),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[715, 4195, 13, 3869])).
% 3.03/2.33 tff(4197,plain,
% 3.03/2.33 (~c0_1(a37)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[685, 4196])).
% 3.03/2.33 tff(4198,plain,
% 3.03/2.33 (c3_1(a37)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[555, 4196])).
% 3.03/2.33 tff(4199,plain,
% 3.03/2.33 (~c2_1(a37)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[693, 104, 11, 4198, 4197, 14, 13, 12, 24])).
% 3.03/2.33 tff(4200,plain,
% 3.03/2.33 (c1_1(a37)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[566, 4196])).
% 3.03/2.33 tff(4201,plain,
% 3.03/2.33 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a37) | (~ndr1_0) | c2_1(a37) | (~c1_1(a37)) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a37) | (~ndr1_0) | c2_1(a37) | (~c1_1(a37)) | (~c2_1(a58)))),
% 3.03/2.33 inference(rewrite,[status(thm)],[])).
% 3.03/2.33 tff(4202,plain,
% 3.03/2.33 ((hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a37) | c0_1(a37) | (~c1_1(a37))) <=> (hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a37) | (~ndr1_0) | c2_1(a37) | (~c1_1(a37)) | (~c2_1(a58)))),
% 3.03/2.33 inference(rewrite,[status(thm)],[])).
% 3.03/2.33 tff(4203,plain,
% 3.03/2.33 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a37) | c0_1(a37) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a37) | (~ndr1_0) | c2_1(a37) | (~c1_1(a37)) | (~c2_1(a58))))),
% 3.03/2.33 inference(monotonicity,[status(thm)],[4202])).
% 3.03/2.33 tff(4204,plain,
% 3.03/2.33 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a37) | c0_1(a37) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a37) | (~ndr1_0) | c2_1(a37) | (~c1_1(a37)) | (~c2_1(a58)))),
% 3.03/2.33 inference(transitivity,[status(thm)],[4203, 4201])).
% 3.03/2.33 tff(4205,plain,
% 3.03/2.33 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a37) | c0_1(a37) | (~c1_1(a37)))),
% 3.03/2.33 inference(quant_inst,[status(thm)],[])).
% 3.03/2.33 tff(4206,plain,
% 3.03/2.33 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a37) | (~ndr1_0) | c2_1(a37) | (~c1_1(a37)) | (~c2_1(a58))),
% 3.03/2.33 inference(modus_ponens,[status(thm)],[4205, 4204])).
% 3.03/2.33 tff(4207,plain,
% 3.03/2.33 ($false),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4206, 104, 25, 4156, 4200, 4187, 3861, 4197, 3879, 4199])).
% 3.03/2.33 tff(4208,plain,(hskp6 | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 3.03/2.33 tff(4209,plain,
% 3.03/2.33 (hskp6),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4208, 14, 11, 13, 12])).
% 3.03/2.33 tff(4210,plain,
% 3.03/2.33 (~c3_1(a13)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[186, 4209])).
% 3.03/2.33 tff(4211,plain,
% 3.03/2.33 (~c1_1(a13)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[192, 4209])).
% 3.03/2.33 tff(4212,plain,
% 3.03/2.33 (hskp20),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4022, 3869, 240, 239, 14, 13, 12])).
% 3.03/2.33 tff(4213,plain,
% 3.03/2.33 (~c0_1(a37)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[685, 4212])).
% 3.03/2.33 tff(4214,plain,
% 3.03/2.33 (c3_1(a37)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[555, 4212])).
% 3.03/2.33 tff(4215,plain,
% 3.03/2.33 (~c2_1(a37)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[693, 104, 11, 4214, 4213, 14, 13, 12, 24])).
% 3.03/2.33 tff(4216,plain,
% 3.03/2.33 (c1_1(a37)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[566, 4212])).
% 3.03/2.33 tff(4217,plain,
% 3.03/2.33 ($false),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4206, 104, 25, 4156, 4216, 4187, 3861, 4213, 3879, 4215])).
% 3.03/2.33 tff(4218,plain,(hskp6 | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | c1_1(a13) | c3_1(a13)), inference(lemma,lemma(discharge,[]))).
% 3.03/2.33 tff(4219,plain,
% 3.03/2.33 (hskp6),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4218, 240, 14, 13, 12, 11, 239])).
% 3.03/2.33 tff(4220,plain,
% 3.03/2.33 (~c0_1(a13)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[198, 4219])).
% 3.03/2.33 tff(4221,plain,
% 3.03/2.33 (hskp20),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4022, 811, 240, 239, 14, 13, 12])).
% 3.03/2.33 tff(4222,plain,
% 3.03/2.33 (hskp3),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4027, 4221, 11])).
% 3.03/2.33 tff(4223,plain,
% 3.03/2.33 (~c2_1(a7)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[2959, 4222])).
% 3.03/2.33 tff(4224,plain,
% 3.03/2.33 (c3_1(a7)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[2972, 4222])).
% 3.03/2.33 tff(4225,plain,
% 3.03/2.33 (c0_1(a7)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[2983, 4222])).
% 3.03/2.33 tff(4226,plain,
% 3.03/2.33 (~c1_1(a21)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[3000, 104, 4019, 4225, 4224, 4017, 4223, 279, 2962])).
% 3.03/2.33 tff(4227,plain,
% 3.03/2.33 (c3_1(a58)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4176, 4222, 240, 239, 4156, 4220])).
% 3.03/2.33 tff(4228,plain,
% 3.03/2.33 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp0 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c3_1(a58)))),
% 3.03/2.33 inference(rewrite,[status(thm)],[])).
% 3.03/2.33 tff(4229,plain,
% 3.03/2.33 ((hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a58)) | (~c1_1(a58)) | (~c0_1(a58))) <=> (hskp22 | hskp0 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c3_1(a58)))),
% 3.03/2.33 inference(rewrite,[status(thm)],[])).
% 3.03/2.33 tff(4230,plain,
% 3.03/2.33 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c3_1(a58))))),
% 3.03/2.33 inference(monotonicity,[status(thm)],[4229])).
% 3.03/2.33 tff(4231,plain,
% 3.03/2.33 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp0 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c3_1(a58)))),
% 3.03/2.33 inference(transitivity,[status(thm)],[4230, 4228])).
% 3.03/2.33 tff(4232,plain,
% 3.03/2.33 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)))),
% 3.03/2.33 inference(quant_inst,[status(thm)],[])).
% 3.03/2.33 tff(4233,plain,
% 3.03/2.33 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp0 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c3_1(a58))),
% 3.03/2.33 inference(modus_ponens,[status(thm)],[4232, 4231])).
% 3.03/2.33 tff(4234,plain,
% 3.03/2.33 (hskp22 | hskp0 | (~c0_1(a58)) | (~c3_1(a58))),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4233, 104, 3861, 3941])).
% 3.03/2.33 tff(4235,plain,
% 3.03/2.33 (hskp22),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4234, 4227, 11, 4187])).
% 3.03/2.33 tff(4236,plain,
% 3.03/2.33 (~c1_1(a42)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1475, 4235])).
% 3.03/2.33 tff(4237,plain,
% 3.03/2.33 (c2_1(a42)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1487, 4235])).
% 3.03/2.33 tff(4238,plain,
% 3.03/2.33 (c0_1(a42)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1498, 4235])).
% 3.03/2.33 tff(4239,plain,
% 3.03/2.33 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a42) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 3.03/2.33 inference(rewrite,[status(thm)],[])).
% 3.03/2.33 tff(4240,plain,
% 3.03/2.33 ((hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21))) <=> (hskp18 | c1_1(a42) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 3.03/2.33 inference(rewrite,[status(thm)],[])).
% 3.03/2.33 tff(4241,plain,
% 3.03/2.33 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a42) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a42)) | (~c0_1(a42))))),
% 3.03/2.33 inference(monotonicity,[status(thm)],[4240])).
% 3.03/2.33 tff(4242,plain,
% 3.03/2.33 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 3.03/2.33 inference(transitivity,[status(thm)],[4241, 4239])).
% 3.03/2.33 tff(4243,plain,
% 3.03/2.33 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))),
% 3.03/2.33 inference(quant_inst,[status(thm)],[])).
% 3.03/2.33 tff(4244,plain,
% 3.03/2.33 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a42)) | (~c0_1(a42))),
% 3.03/2.33 inference(modus_ponens,[status(thm)],[4243, 4242])).
% 3.03/2.33 tff(4245,plain,
% 3.03/2.33 (hskp18),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4244, 104, 4238, 4237, 4020, 4236, 4017, 2737, 4226])).
% 3.03/2.33 tff(4246,plain,
% 3.03/2.33 (~c0_1(a31)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[444, 4245])).
% 3.03/2.33 tff(4247,plain,
% 3.03/2.33 (~c3_1(a31)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[403, 4245])).
% 3.03/2.33 tff(4248,plain,
% 3.03/2.33 (c2_1(a31)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[3849, 4247, 11, 4221, 4224, 4223, 4225, 14, 13, 12, 4246])).
% 3.03/2.33 tff(4249,plain,
% 3.03/2.33 (c1_1(a31)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[414, 4245])).
% 3.03/2.33 tff(4250,plain,
% 3.03/2.33 ($false),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[3857, 104, 4249, 4020, 4019, 4247, 14, 13, 12, 1342, 4248, 4226])).
% 3.03/2.33 tff(4251,plain,(hskp21 | c0_1(a2) | c2_1(a2) | c3_1(a2) | hskp0 | c1_1(a7) | c1_1(a13) | c3_1(a13)), inference(lemma,lemma(discharge,[]))).
% 3.03/2.33 tff(4252,plain,
% 3.03/2.33 (hskp21),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4251, 240, 13, 12, 11, 2962, 14, 239])).
% 3.03/2.33 tff(4253,plain,
% 3.03/2.33 (~c2_1(a38)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[2495, 4252])).
% 3.03/2.33 tff(4254,plain,
% 3.03/2.33 (c1_1(a38)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[657, 4252])).
% 3.03/2.33 tff(4255,plain,
% 3.03/2.33 (c0_1(a38)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[646, 4252])).
% 3.03/2.33 tff(4256,plain,
% 3.03/2.33 (~c3_1(a38)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1076, 104, 4255, 4254, 4253, 4220, 240, 239, 36])).
% 3.03/2.33 tff(4257,plain,
% 3.03/2.33 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))))),
% 3.03/2.33 inference(bind,[status(th)],[])).
% 3.03/2.33 tff(4258,plain,
% 3.03/2.33 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 3.03/2.33 inference(quant_intro,[status(thm)],[4257])).
% 3.03/2.33 tff(4259,plain,
% 3.03/2.33 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 3.03/2.33 inference(rewrite,[status(thm)],[])).
% 3.03/2.33 tff(4260,plain,
% 3.03/2.33 (^[V: $i, U: $i] : 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)) | (~c0_1(V)) | (~c1_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))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp7) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))))),
% 3.03/2.33 inference(bind,[status(th)],[])).
% 3.03/2.33 tff(4261,plain,
% 3.03/2.33 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 3.03/2.33 inference(quant_intro,[status(thm)],[4260])).
% 3.03/2.33 tff(4262,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 3.03/2.33 tff(4263,plain,
% 3.03/2.33 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 3.03/2.33 inference(modus_ponens,[status(thm)],[4262, 4261])).
% 3.03/2.33 tff(4264,plain,
% 3.03/2.33 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 3.03/2.33 inference(modus_ponens,[status(thm)],[4263, 4259])).
% 3.03/2.33 tff(4265,plain,(
% 3.03/2.33 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 3.03/2.33 inference(skolemize,[status(sab)],[4264])).
% 3.03/2.33 tff(4266,plain,
% 3.03/2.33 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 3.03/2.33 inference(modus_ponens,[status(thm)],[4265, 4258])).
% 3.03/2.33 tff(4267,plain,
% 3.03/2.33 (hskp27),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[678, 4253, 4252, 13, 12, 14])).
% 3.03/2.33 tff(4268,plain,
% 3.03/2.33 (c3_1(a12)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[605, 4267])).
% 3.03/2.33 tff(4269,plain,
% 3.03/2.33 (c1_1(a12)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[616, 4267])).
% 3.03/2.33 tff(4270,plain,
% 3.03/2.33 (c0_1(a12)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1192, 4267])).
% 3.03/2.33 tff(4271,plain,
% 3.03/2.33 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | (hskp7 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | hskp7 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 3.03/2.33 inference(rewrite,[status(thm)],[])).
% 3.03/2.33 tff(4272,plain,
% 3.03/2.33 ((hskp7 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | (~c2_1(a58)) | (~c0_1(a58)) | (~c1_1(a58))) <=> (hskp7 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 3.03/2.33 inference(rewrite,[status(thm)],[])).
% 3.03/2.33 tff(4273,plain,
% 3.03/2.33 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | (~c2_1(a58)) | (~c0_1(a58)) | (~c1_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | (hskp7 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))))),
% 3.03/2.33 inference(monotonicity,[status(thm)],[4272])).
% 3.03/2.33 tff(4274,plain,
% 3.03/2.33 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | (~c2_1(a58)) | (~c0_1(a58)) | (~c1_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | hskp7 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 3.03/2.33 inference(transitivity,[status(thm)],[4273, 4271])).
% 3.03/2.33 tff(4275,plain,
% 3.03/2.33 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | (~c2_1(a58)) | (~c0_1(a58)) | (~c1_1(a58)))),
% 3.03/2.33 inference(quant_inst,[status(thm)],[])).
% 3.03/2.33 tff(4276,plain,
% 3.03/2.33 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | hskp7 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))),
% 3.03/2.33 inference(modus_ponens,[status(thm)],[4275, 4274])).
% 3.03/2.33 tff(4277,plain,
% 3.03/2.33 (hskp7),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4276, 104, 4270, 4269, 4268, 4156, 4187, 3861, 4266])).
% 3.03/2.33 tff(4278,plain,
% 3.03/2.33 (~c2_1(a14)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1408, 4277])).
% 3.03/2.33 tff(4279,plain,
% 3.03/2.33 (~c0_1(a14)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1433, 4277])).
% 3.03/2.33 tff(4280,plain,
% 3.03/2.33 (hskp22),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[3948, 104, 11, 4270, 4269, 4268, 3941])).
% 3.03/2.33 tff(4281,plain,
% 3.03/2.33 (~c1_1(a42)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1475, 4280])).
% 3.03/2.33 tff(4282,plain,
% 3.03/2.33 (c1_1(a14)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1419, 4277])).
% 3.03/2.33 tff(4283,plain,
% 3.03/2.33 (c2_1(a42)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1487, 4280])).
% 3.03/2.33 tff(4284,plain,
% 3.03/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a42) | c2_1(a38) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | c3_1(a38) | (~c0_1(a38)) | (~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)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a42) | c2_1(a38) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 3.03/2.33 inference(rewrite,[status(thm)],[])).
% 3.03/2.33 tff(4285,plain,
% 3.03/2.33 (((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14))) <=> (c1_1(a42) | c2_1(a38) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 3.03/2.33 inference(rewrite,[status(thm)],[])).
% 3.03/2.33 tff(4286,plain,
% 3.03/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a42) | c2_1(a38) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42))))),
% 3.03/2.33 inference(monotonicity,[status(thm)],[4285])).
% 3.03/2.33 tff(4287,plain,
% 3.03/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a42) | c2_1(a38) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 3.03/2.33 inference(transitivity,[status(thm)],[4286, 4284])).
% 3.03/2.33 tff(4288,plain,
% 3.03/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))),
% 3.03/2.33 inference(quant_inst,[status(thm)],[])).
% 3.03/2.33 tff(4289,plain,
% 3.03/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a42) | c2_1(a38) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42))),
% 3.03/2.33 inference(modus_ponens,[status(thm)],[4288, 4287])).
% 3.03/2.33 tff(4290,plain,
% 3.03/2.33 (~c3_1(a42)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4289, 104, 4283, 4255, 4282, 4281, 4253, 4279, 4278, 2061, 4256])).
% 3.03/2.33 tff(4291,plain,
% 3.03/2.33 (hskp8),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[2294, 104, 4270, 4269, 4268, 4255, 4254, 2283, 4256])).
% 3.03/2.33 tff(4292,plain,
% 3.03/2.33 (~c3_1(a15)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1394, 4291])).
% 3.03/2.33 tff(4293,plain,
% 3.03/2.33 (~c2_1(a15)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[2093, 4291])).
% 3.03/2.33 tff(4294,plain,
% 3.03/2.33 (~c1_1(a15)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[2184, 4291])).
% 3.03/2.33 tff(4295,plain,
% 3.03/2.33 (c0_1(a42)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1498, 4280])).
% 3.03/2.33 tff(4296,plain,
% 3.03/2.33 (~c2_1(a13)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[3969, 104, 4295, 4281, 4294, 4293, 4292, 4220, 239, 341, 4290])).
% 3.03/2.33 tff(4297,plain,
% 3.03/2.33 (hskp18),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[3976, 104, 4295, 4283, 4281, 2737, 4290])).
% 3.03/2.33 tff(4298,plain,
% 3.03/2.33 (~c3_1(a31)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[403, 4297])).
% 3.03/2.33 tff(4299,plain,
% 3.03/2.33 (c1_1(a31)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[414, 4297])).
% 3.03/2.33 tff(4300,plain,
% 3.03/2.33 (~c2_1(a31)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[3985, 104, 4295, 4283, 4299, 4281, 4298, 4220, 239, 1342, 4296])).
% 3.03/2.33 tff(4301,plain,
% 3.03/2.33 (hskp12),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4002, 104, 4270, 4269, 4268, 4295, 4283, 4281, 3996])).
% 3.03/2.33 tff(4302,plain,
% 3.03/2.33 (~c3_1(a20)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[999, 4301])).
% 3.03/2.33 tff(4303,plain,
% 3.03/2.33 (~c1_1(a20)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1005, 4301])).
% 3.03/2.33 tff(4304,plain,
% 3.03/2.33 (c2_1(a20)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[1016, 4301])).
% 3.03/2.33 tff(4305,plain,
% 3.03/2.33 ($false),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[2656, 104, 4299, 4304, 4298, 4303, 4302, 4220, 240, 380, 4296, 4300])).
% 3.03/2.33 tff(4306,plain,(c1_1(a13) | c3_1(a13) | hskp0 | c2_1(a2) | c3_1(a2) | c0_1(a2) | c1_1(a7)), inference(lemma,lemma(discharge,[]))).
% 3.03/2.33 tff(4307,plain,
% 3.03/2.33 (c1_1(a7)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4306, 4210, 11, 13, 12, 14, 4211])).
% 3.03/2.33 tff(4308,plain,
% 3.03/2.33 (~c0_1(a13)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[198, 4209])).
% 3.03/2.33 tff(4309,assumption,(c1_1(a7)), introduced(assumption)).
% 3.03/2.33 tff(4310,plain,
% 3.03/2.33 ($false),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[3033, 104, 3293, 3292, 241, 240, 239, 3291, 36, 4309])).
% 3.03/2.33 tff(4311,plain,((~hskp3) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~c1_1(a7))), inference(lemma,lemma(discharge,[]))).
% 3.03/2.33 tff(4312,plain,
% 3.03/2.33 (~hskp3),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4311, 4308, 4211, 4210, 4307])).
% 3.03/2.33 tff(4313,plain,
% 3.03/2.33 (~hskp20),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4027, 4312, 11])).
% 3.03/2.33 tff(4314,plain,
% 3.03/2.33 (hskp21),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4022, 4313, 4211, 4210, 14, 13, 12])).
% 3.03/2.33 tff(4315,plain,
% 3.03/2.33 (~hskp28),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4180, 4312])).
% 3.03/2.33 tff(4316,plain,
% 3.03/2.33 (~hskp27),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4182, 4315, 11, 4312])).
% 3.03/2.33 tff(4317,plain,
% 3.03/2.33 (c2_1(a38)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[678, 4316, 4314, 13, 12, 14])).
% 3.03/2.33 tff(4318,plain,
% 3.03/2.33 ($false),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[2495, 4317, 4314])).
% 3.03/2.33 tff(4319,plain,(c0_1(a2) | c2_1(a2) | c3_1(a2) | hskp0), inference(lemma,lemma(discharge,[]))).
% 3.03/2.33 tff(4320,plain,
% 3.03/2.33 (c0_1(a2)),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[4319, 13, 12, 11])).
% 3.03/2.33 tff(4321,plain,
% 3.03/2.33 (~hskp1),
% 3.03/2.33 inference(unit_resolution,[status(thm)],[268, 4320])).
% 3.03/2.34 tff(4322,plain,
% 3.03/2.34 (~hskp6),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3748, 4321, 11])).
% 3.03/2.34 tff(4323,plain,
% 3.03/2.34 (~hskp21),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3868, 4322])).
% 3.03/2.34 tff(4324,plain,
% 3.03/2.34 (hskp13),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3880, 4323])).
% 3.03/2.34 tff(4325,plain,
% 3.03/2.34 (c0_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[853, 4324])).
% 3.03/2.34 tff(4326,plain,
% 3.03/2.34 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)))),
% 3.03/2.34 inference(rewrite,[status(thm)],[])).
% 3.03/2.34 tff(4327,plain,
% 3.03/2.34 ((hskp24 | hskp6 | (~ndr1_0) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2))) <=> (hskp24 | hskp6 | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)))),
% 3.03/2.34 inference(rewrite,[status(thm)],[])).
% 3.03/2.34 tff(4328,plain,
% 3.03/2.34 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2))))),
% 3.03/2.34 inference(monotonicity,[status(thm)],[4327])).
% 3.03/2.34 tff(4329,plain,
% 3.03/2.34 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)))),
% 3.03/2.34 inference(transitivity,[status(thm)],[4328, 4326])).
% 3.03/2.34 tff(4330,plain,
% 3.03/2.34 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)))),
% 3.03/2.34 inference(quant_inst,[status(thm)],[])).
% 3.03/2.34 tff(4331,plain,
% 3.03/2.34 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2))),
% 3.03/2.34 inference(modus_ponens,[status(thm)],[4330, 4329])).
% 3.03/2.34 tff(4332,plain,
% 3.03/2.34 (hskp6 | (~c0_1(a2)) | (~c1_1(a2))),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4331, 104, 3867, 13, 1059])).
% 3.03/2.34 tff(4333,plain,
% 3.03/2.34 (~c1_1(a2)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4332, 4322, 4320])).
% 3.03/2.34 tff(4334,plain,
% 3.03/2.34 (hskp20),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[715, 4333, 13, 4323])).
% 3.03/2.34 tff(4335,plain,
% 3.03/2.34 (hskp3),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4027, 4334, 11])).
% 3.03/2.34 tff(4336,plain,
% 3.03/2.34 (~c2_1(a7)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[2959, 4335])).
% 3.03/2.34 tff(4337,plain,
% 3.03/2.34 (c0_1(a7)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[2983, 4335])).
% 3.03/2.34 tff(4338,plain,
% 3.03/2.34 (~c1_1(a7)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3021, 104, 3867, 4322, 4337, 4336, 1059])).
% 3.03/2.34 tff(4339,plain,
% 3.03/2.34 (~c3_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[831, 4324])).
% 3.03/2.34 tff(4340,plain,
% 3.03/2.34 (c3_1(a7)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[2972, 4335])).
% 3.03/2.34 tff(4341,plain,
% 3.03/2.34 (c2_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[842, 4324])).
% 3.03/2.34 tff(4342,plain,
% 3.03/2.34 (~c1_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3000, 104, 4341, 4337, 4340, 4339, 4336, 279, 4338])).
% 3.03/2.34 tff(4343,plain,
% 3.03/2.34 (hskp18),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[2743, 104, 4325, 4341, 4339, 2737, 4342])).
% 3.03/2.34 tff(4344,plain,
% 3.03/2.34 (c1_1(a31)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[414, 4343])).
% 3.03/2.34 tff(4345,plain,
% 3.03/2.34 (hskp10 | c1_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3770, 104, 4321, 4341, 4339, 1882])).
% 3.03/2.34 tff(4346,plain,
% 3.03/2.34 (hskp10),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4345, 4342])).
% 3.03/2.34 tff(4347,plain,
% 3.03/2.34 (~c0_1(a18)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[943, 4346])).
% 3.03/2.34 tff(4348,plain,
% 3.03/2.34 (c3_1(a18)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1037, 4346])).
% 3.03/2.34 tff(4349,plain,
% 3.03/2.34 (~c1_1(a18)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[937, 4346])).
% 3.03/2.34 tff(4350,plain,
% 3.03/2.34 (~c0_1(a31)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[444, 4343])).
% 3.03/2.34 tff(4351,plain,
% 3.03/2.34 (~c3_1(a31)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[403, 4343])).
% 3.03/2.34 tff(4352,plain,
% 3.03/2.34 ($false),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3803, 4351, 4350, 4322, 4349, 4341, 4348, 4347, 4339, 11, 4344, 4325])).
% 3.03/2.34 tff(4353,plain,(c2_1(a2) | hskp0 | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 3.03/2.34 tff(4354,plain,
% 3.03/2.34 (c2_1(a2)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4353, 11, 12])).
% 3.03/2.34 tff(4355,plain,
% 3.03/2.34 (~hskp1),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[262, 4354])).
% 3.03/2.34 tff(4356,plain,
% 3.03/2.34 (~hskp6),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3748, 4355, 11])).
% 3.03/2.34 tff(4357,plain,
% 3.03/2.34 (~hskp21),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3868, 4356])).
% 3.03/2.34 tff(4358,plain,
% 3.03/2.34 (hskp13),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3880, 4357])).
% 3.03/2.34 tff(4359,plain,
% 3.03/2.34 (c0_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[853, 4358])).
% 3.03/2.34 tff(4360,plain,
% 3.03/2.34 (~c3_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[831, 4358])).
% 3.03/2.34 tff(4361,plain,
% 3.03/2.34 (c2_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[842, 4358])).
% 3.03/2.34 tff(4362,plain,
% 3.03/2.34 (~c1_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[2519, 104, 4356, 4359, 4361, 4360, 150])).
% 3.03/2.34 tff(4363,plain,
% 3.03/2.34 (hskp18),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[2743, 104, 4359, 4361, 4360, 2737, 4362])).
% 3.03/2.34 tff(4364,plain,
% 3.03/2.34 (c1_1(a31)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[414, 4363])).
% 3.03/2.34 tff(4365,plain,
% 3.03/2.34 (hskp10 | c1_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3770, 104, 4355, 4361, 4360, 1882])).
% 3.03/2.34 tff(4366,plain,
% 3.03/2.34 (hskp10),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4365, 4362])).
% 3.03/2.34 tff(4367,plain,
% 3.03/2.34 (~c0_1(a18)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[943, 4366])).
% 3.03/2.34 tff(4368,plain,
% 3.03/2.34 (c3_1(a18)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1037, 4366])).
% 3.03/2.34 tff(4369,plain,
% 3.03/2.34 (~c1_1(a18)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[937, 4366])).
% 3.03/2.34 tff(4370,plain,
% 3.03/2.34 (~c0_1(a31)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[444, 4363])).
% 3.03/2.34 tff(4371,plain,
% 3.03/2.34 (~c3_1(a31)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[403, 4363])).
% 3.03/2.34 tff(4372,plain,
% 3.03/2.34 ($false),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3803, 4371, 4370, 4356, 4369, 4361, 4368, 4367, 4360, 11, 4364, 4359])).
% 3.03/2.34 tff(4373,plain,(hskp0 | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 3.03/2.34 tff(4374,plain,
% 3.03/2.34 (hskp0),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4373, 12])).
% 3.03/2.34 tff(4375,plain,
% 3.03/2.34 ($false),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3744, 3292, 3293, 2553, 3291])).
% 3.03/2.34 tff(4376,plain,((~hskp3) | (~hskp0)), inference(lemma,lemma(discharge,[]))).
% 3.03/2.34 tff(4377,plain,
% 3.03/2.34 (~hskp3),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4376, 4374])).
% 3.03/2.34 tff(4378,plain,
% 3.03/2.34 (~hskp28),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4180, 4377])).
% 3.03/2.34 tff(4379,plain,
% 3.03/2.34 (c1_1(a1)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[139, 4374])).
% 3.03/2.34 tff(4380,plain,
% 3.03/2.34 (~c3_1(a1)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[117, 4374])).
% 3.03/2.34 tff(4381,plain,
% 3.03/2.34 (c2_1(a1)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[128, 4374])).
% 3.03/2.34 tff(4382,plain,
% 3.03/2.34 (~c2_1(a13)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[350, 14, 4381, 4380, 4379, 13, 12])).
% 3.03/2.34 tff(4383,plain,
% 3.03/2.34 (hskp6),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[180, 4381, 4379, 4380])).
% 3.03/2.34 tff(4384,plain,
% 3.03/2.34 (~c3_1(a13)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[186, 4383])).
% 3.03/2.34 tff(4385,plain,
% 3.03/2.34 (~c1_1(a13)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[192, 4383])).
% 3.03/2.34 tff(4386,assumption,(~c2_1(a37)), introduced(assumption)).
% 3.03/2.34 tff(4387,plain,
% 3.03/2.34 (hskp20),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4022, 811, 4385, 4384, 14, 13, 12])).
% 3.03/2.34 tff(4388,plain,
% 3.03/2.34 (c3_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[555, 4387])).
% 3.03/2.34 tff(4389,plain,
% 3.03/2.34 (c1_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[566, 4387])).
% 3.03/2.34 tff(4390,plain,
% 3.03/2.34 (hskp9),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[896, 104, 4389, 4388, 4379, 4381, 4380, 890, 4386])).
% 3.03/2.34 tff(4391,plain,
% 3.03/2.34 (~c3_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[902, 4390])).
% 3.03/2.34 tff(4392,plain,
% 3.03/2.34 (c1_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[913, 4390])).
% 3.03/2.34 tff(4393,plain,
% 3.03/2.34 (c0_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[924, 4390])).
% 3.03/2.34 tff(4394,plain,
% 3.03/2.34 (hskp10),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[931, 104, 811, 4393, 4392, 4391, 876])).
% 3.03/2.34 tff(4395,plain,
% 3.03/2.34 (~c1_1(a18)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[937, 4394])).
% 3.03/2.34 tff(4396,plain,
% 3.03/2.34 (c3_1(a18)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1037, 4394])).
% 3.03/2.34 tff(4397,plain,
% 3.03/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a18) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a18) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)))),
% 3.03/2.34 inference(rewrite,[status(thm)],[])).
% 3.03/2.34 tff(4398,plain,
% 3.03/2.34 (((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a18) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)))),
% 3.03/2.34 inference(rewrite,[status(thm)],[])).
% 3.03/2.34 tff(4399,plain,
% 3.03/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a18) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18))))),
% 3.03/2.34 inference(monotonicity,[status(thm)],[4398])).
% 3.03/2.34 tff(4400,plain,
% 3.03/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a18) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)))),
% 3.03/2.34 inference(transitivity,[status(thm)],[4399, 4397])).
% 3.03/2.34 tff(4401,plain,
% 3.03/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 3.03/2.34 inference(quant_inst,[status(thm)],[])).
% 3.03/2.34 tff(4402,plain,
% 3.03/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a18) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18))),
% 3.03/2.34 inference(modus_ponens,[status(thm)],[4401, 4400])).
% 3.03/2.34 tff(4403,plain,
% 3.03/2.34 (~c2_1(a18)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4402, 104, 4396, 4395, 4385, 4384, 14, 13, 12, 362, 4382])).
% 3.03/2.34 tff(4404,plain,
% 3.03/2.34 (~c0_1(a13)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[198, 4383])).
% 3.03/2.34 tff(4405,plain,
% 3.03/2.34 (~c0_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[685, 4387])).
% 3.03/2.34 tff(4406,plain,
% 3.03/2.34 (hskp12),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1154, 104, 4388, 4393, 4392, 4405, 4391, 987, 4386])).
% 3.03/2.34 tff(4407,plain,
% 3.03/2.34 (~c3_1(a20)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[999, 4406])).
% 3.03/2.34 tff(4408,plain,
% 3.03/2.34 (~c1_1(a20)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1005, 4406])).
% 3.03/2.34 tff(4409,plain,
% 3.03/2.34 (c2_1(a20)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1016, 4406])).
% 3.03/2.34 tff(4410,plain,
% 3.03/2.34 (hskp5),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1023, 104, 4409, 4408, 4407, 4404, 4384, 290, 4382])).
% 3.03/2.34 tff(4411,plain,
% 3.03/2.34 (~c2_1(a11)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[306, 4410])).
% 3.03/2.34 tff(4412,plain,
% 3.03/2.34 (~c1_1(a11)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[312, 4410])).
% 3.03/2.34 tff(4413,plain,
% 3.03/2.34 (~c0_1(a18)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[943, 4394])).
% 3.03/2.34 tff(4414,plain,
% 3.03/2.34 (c0_1(a11)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[323, 4410])).
% 3.03/2.34 tff(4415,plain,
% 3.03/2.34 ($false),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1044, 104, 4396, 4414, 4413, 4395, 4412, 4411, 751, 4403])).
% 3.03/2.34 tff(4416,plain,(c2_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | hskp21), inference(lemma,lemma(discharge,[]))).
% 3.03/2.34 tff(4417,plain,
% 3.03/2.34 (c2_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4416, 811, 13, 12, 14])).
% 3.03/2.34 tff(4418,plain,
% 3.03/2.34 ($false),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[571, 104, 3867, 4377, 4389, 4388, 10, 4417])).
% 3.03/2.34 tff(4419,plain,(hskp21 | c2_1(a2) | c3_1(a2) | c0_1(a2)), inference(lemma,lemma(discharge,[]))).
% 3.03/2.34 tff(4420,plain,
% 3.03/2.34 (hskp21),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4419, 14, 12, 13])).
% 3.03/2.34 tff(4421,plain,
% 3.03/2.34 (~c2_1(a38)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[2495, 4420])).
% 3.03/2.34 tff(4422,plain,
% 3.03/2.34 (hskp27),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[678, 4421, 4420, 13, 12, 14])).
% 3.03/2.34 tff(4423,plain,
% 3.03/2.34 (c3_1(a12)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[605, 4422])).
% 3.03/2.34 tff(4424,plain,
% 3.03/2.34 (c1_1(a12)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[616, 4422])).
% 3.03/2.34 tff(4425,plain,
% 3.03/2.34 (~c2_1(a12)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[623, 104, 3867, 4377, 4424, 4423, 10])).
% 3.03/2.34 tff(4426,plain,
% 3.03/2.34 (c1_1(a38)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[657, 4420])).
% 3.03/2.34 tff(4427,plain,
% 3.03/2.34 (c0_1(a38)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[646, 4420])).
% 3.03/2.34 tff(4428,plain,
% 3.03/2.34 (~c3_1(a38)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1076, 104, 4427, 4426, 4421, 4404, 4385, 4384, 36])).
% 3.03/2.34 tff(4429,plain,
% 3.03/2.34 (c0_1(a12)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1192, 4422])).
% 3.03/2.34 tff(4430,plain,
% 3.03/2.34 ($false),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1199, 104, 4429, 4424, 4423, 4427, 4426, 970, 4428, 4425])).
% 3.03/2.34 tff(4431,plain,(c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 3.03/2.34 tff(4432,plain,
% 3.03/2.34 (c0_1(a2)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4431, 13, 12])).
% 3.03/2.34 tff(4433,plain,
% 3.03/2.34 (~hskp1),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[268, 4432])).
% 3.03/2.34 tff(4434,plain,
% 3.03/2.34 (hskp20),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[544, 4433, 4378])).
% 3.03/2.34 tff(4435,plain,
% 3.03/2.34 (c3_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[555, 4434])).
% 3.03/2.34 tff(4436,plain,
% 3.03/2.34 (c1_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[566, 4434])).
% 3.03/2.34 tff(4437,plain,
% 3.03/2.34 (~c2_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[571, 104, 3867, 4377, 4436, 4435, 10])).
% 3.03/2.34 tff(4438,plain,
% 3.03/2.34 (hskp2 | hskp1),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[247, 104, 4404, 4385, 4384, 47])).
% 3.03/2.34 tff(4439,plain,
% 3.03/2.34 (hskp2),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4438, 4433])).
% 3.03/2.34 tff(4440,plain,
% 3.03/2.34 (~c2_1(a3)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[206, 4439])).
% 3.03/2.34 tff(4441,plain,
% 3.03/2.34 (c3_1(a3)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[217, 4439])).
% 3.03/2.34 tff(4442,plain,
% 3.03/2.34 (c1_1(a3)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[228, 4439])).
% 3.03/2.34 tff(4443,plain,
% 3.03/2.34 (hskp9),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1296, 104, 4442, 4441, 4379, 4381, 4440, 4380, 890])).
% 3.03/2.34 tff(4444,plain,
% 3.03/2.34 (~c3_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[902, 4443])).
% 3.03/2.34 tff(4445,plain,
% 3.03/2.34 (~c0_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[685, 4434])).
% 3.03/2.34 tff(4446,plain,
% 3.03/2.34 (c1_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[913, 4443])).
% 3.03/2.34 tff(4447,plain,
% 3.03/2.34 (c2_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3335, 104, 4435, 4446, 4379, 4381, 4445, 4444, 4380, 734, 4437])).
% 3.03/2.34 tff(4448,plain,
% 3.03/2.34 (~c2_1(a13)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1331, 104, 4433, 4442, 4441, 4404, 4385, 4440, 58])).
% 3.03/2.34 tff(4449,plain,
% 3.03/2.34 (~c1_1(a2)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1901, 104, 4442, 4441, 4404, 4385, 4384, 4440, 4432, 13, 36])).
% 3.03/2.34 tff(4450,plain,
% 3.03/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~c0_1(a2)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c1_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c1_1(a2))),
% 3.03/2.34 inference(rewrite,[status(thm)],[])).
% 3.03/2.34 tff(4451,plain,
% 3.03/2.34 (((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a2) | c1_1(a2) | c3_1(a2)) <=> ((~c0_1(a2)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c1_1(a2))),
% 3.03/2.34 inference(rewrite,[status(thm)],[])).
% 3.03/2.34 tff(4452,plain,
% 3.03/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a2) | c1_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~c0_1(a2)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c1_1(a2)))),
% 3.03/2.34 inference(monotonicity,[status(thm)],[4451])).
% 3.03/2.34 tff(4453,plain,
% 3.03/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a2) | c1_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c1_1(a2))),
% 3.03/2.34 inference(transitivity,[status(thm)],[4452, 4450])).
% 3.03/2.34 tff(4454,plain,
% 3.03/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a2) | c1_1(a2) | c3_1(a2))),
% 3.03/2.34 inference(quant_inst,[status(thm)],[])).
% 3.03/2.34 tff(4455,plain,
% 3.03/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c1_1(a2)),
% 3.03/2.34 inference(modus_ponens,[status(thm)],[4454, 4453])).
% 3.03/2.34 tff(4456,plain,
% 3.03/2.34 ((~c0_1(a2)) | c0_1(a1) | c1_1(a2)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4455, 104, 4381, 13, 12, 4380, 341])).
% 3.03/2.34 tff(4457,plain,
% 3.03/2.34 (c0_1(a1)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4456, 4449, 4432])).
% 3.03/2.34 tff(4458,plain,
% 3.03/2.34 (~c0_1(a3)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[2050, 104, 4442, 4441, 4404, 4385, 4384, 4440, 36])).
% 3.03/2.34 tff(4459,plain,
% 3.03/2.34 (hskp12 | (~c0_1(a1))),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3356, 104, 4441, 4379, 4440, 4380, 987, 4458])).
% 3.03/2.34 tff(4460,plain,
% 3.03/2.34 (hskp12),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4459, 4457])).
% 3.03/2.34 tff(4461,plain,
% 3.03/2.34 (~c1_1(a20)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1005, 4460])).
% 3.03/2.34 tff(4462,plain,
% 3.03/2.34 (c2_1(a20)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1016, 4460])).
% 3.03/2.34 tff(4463,plain,
% 3.03/2.34 (~c0_1(a20)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1359, 104, 4462, 4446, 4461, 4444, 4404, 4384, 1342, 4448, 4447])).
% 3.03/2.34 tff(4464,plain,
% 3.03/2.34 (~c3_1(a20)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[999, 4460])).
% 3.03/2.34 tff(4465,plain,
% 3.03/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a20) | c1_1(a13) | c3_1(a13) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c2_1(a13) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a20) | c1_1(a13) | c3_1(a13) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c2_1(a13) | c0_1(a20) | (~c2_1(a20)))),
% 3.03/2.34 inference(rewrite,[status(thm)],[])).
% 3.03/2.34 tff(4466,plain,
% 3.03/2.34 (((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c3_1(a13)) <=> (c3_1(a20) | c1_1(a13) | c3_1(a13) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c2_1(a13) | c0_1(a20) | (~c2_1(a20)))),
% 3.03/2.34 inference(rewrite,[status(thm)],[])).
% 3.03/2.34 tff(4467,plain,
% 3.03/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a20) | c1_1(a13) | c3_1(a13) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c2_1(a13) | c0_1(a20) | (~c2_1(a20))))),
% 3.03/2.34 inference(monotonicity,[status(thm)],[4466])).
% 3.03/2.34 tff(4468,plain,
% 3.03/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a20) | c1_1(a13) | c3_1(a13) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c2_1(a13) | c0_1(a20) | (~c2_1(a20)))),
% 3.03/2.34 inference(transitivity,[status(thm)],[4467, 4465])).
% 3.03/2.34 tff(4469,plain,
% 3.03/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c3_1(a13))),
% 3.03/2.34 inference(quant_inst,[status(thm)],[])).
% 3.03/2.34 tff(4470,plain,
% 3.03/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a20) | c1_1(a13) | c3_1(a13) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c2_1(a13) | c0_1(a20) | (~c2_1(a20))),
% 3.03/2.34 inference(modus_ponens,[status(thm)],[4469, 4468])).
% 3.03/2.34 tff(4471,plain,
% 3.03/2.34 ($false),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4470, 104, 4462, 4464, 4385, 4384, 4432, 12, 341, 4448, 4449, 4463])).
% 3.03/2.34 tff(4472,plain,(c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 3.03/2.34 tff(4473,plain,
% 3.03/2.34 (c2_1(a2)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4472, 12])).
% 3.03/2.34 tff(4474,plain,
% 3.03/2.34 (~hskp1),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[262, 4473])).
% 3.03/2.34 tff(4475,plain,
% 3.03/2.34 (hskp20),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[544, 4474, 4378])).
% 3.03/2.34 tff(4476,plain,
% 3.03/2.34 (c3_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[555, 4475])).
% 3.03/2.34 tff(4477,plain,
% 3.03/2.34 (c1_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[566, 4475])).
% 3.03/2.34 tff(4478,plain,
% 3.03/2.34 (~c2_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[571, 104, 3867, 4377, 4477, 4476, 10])).
% 3.03/2.34 tff(4479,plain,
% 3.03/2.34 (hskp2),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4438, 4474])).
% 3.03/2.34 tff(4480,plain,
% 3.03/2.34 (~c2_1(a3)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[206, 4479])).
% 3.03/2.34 tff(4481,plain,
% 3.03/2.34 (c3_1(a3)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[217, 4479])).
% 3.03/2.34 tff(4482,plain,
% 3.03/2.34 (c1_1(a3)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[228, 4479])).
% 3.03/2.34 tff(4483,plain,
% 3.03/2.34 (hskp9),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1296, 104, 4482, 4481, 4379, 4381, 4480, 4380, 890])).
% 3.03/2.34 tff(4484,plain,
% 3.03/2.34 (~c3_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[902, 4483])).
% 3.03/2.34 tff(4485,plain,
% 3.03/2.34 (~c0_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[685, 4475])).
% 3.03/2.34 tff(4486,plain,
% 3.03/2.34 (c1_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[913, 4483])).
% 3.03/2.34 tff(4487,plain,
% 3.03/2.34 (c2_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3335, 104, 4476, 4486, 4379, 4381, 4485, 4484, 4380, 734, 4478])).
% 3.03/2.34 tff(4488,plain,
% 3.03/2.34 (~c2_1(a13)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1331, 104, 4474, 4482, 4481, 4404, 4385, 4480, 58])).
% 3.03/2.34 tff(4489,plain,
% 3.03/2.34 (c0_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[924, 4483])).
% 3.03/2.34 tff(4490,plain,
% 3.03/2.34 (hskp12),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1154, 104, 4476, 4489, 4486, 4485, 4484, 987, 4478])).
% 3.03/2.34 tff(4491,plain,
% 3.03/2.34 (~c1_1(a20)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1005, 4490])).
% 3.03/2.34 tff(4492,plain,
% 3.03/2.34 (c2_1(a20)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1016, 4490])).
% 3.03/2.34 tff(4493,plain,
% 3.03/2.34 (~c0_1(a20)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1359, 104, 4492, 4486, 4491, 4484, 4404, 4384, 1342, 4488, 4487])).
% 3.03/2.34 tff(4494,plain,
% 3.03/2.34 ($false),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1366, 104, 4474, 4492, 4482, 4481, 4491, 4480, 58, 4493])).
% 3.03/2.34 tff(4495,plain,(c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 3.03/2.34 tff(4496,plain,
% 3.03/2.34 (~hskp1),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[256, 4495])).
% 3.03/2.34 tff(4497,plain,
% 3.03/2.34 ((~hskp6) | hskp0),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3748, 4496])).
% 3.03/2.34 tff(4498,plain,
% 3.03/2.34 (~hskp6),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4497, 11])).
% 3.03/2.34 tff(4499,plain,
% 3.03/2.34 (~hskp21),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3868, 4498])).
% 3.03/2.34 tff(4500,plain,
% 3.03/2.34 (hskp13),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3880, 4499])).
% 3.03/2.34 tff(4501,plain,
% 3.03/2.34 (c0_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[853, 4500])).
% 3.03/2.34 tff(4502,plain,
% 3.03/2.34 (~c3_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[831, 4500])).
% 3.03/2.34 tff(4503,plain,
% 3.03/2.34 (c2_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[842, 4500])).
% 3.03/2.34 tff(4504,plain,
% 3.03/2.34 (~c1_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[2519, 104, 4498, 4501, 4503, 4502, 150])).
% 3.03/2.34 tff(4505,plain,
% 3.03/2.34 (hskp18),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[2743, 104, 4501, 4503, 4502, 2737, 4504])).
% 3.03/2.34 tff(4506,plain,
% 3.03/2.34 (c1_1(a31)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[414, 4505])).
% 3.03/2.34 tff(4507,plain,
% 3.03/2.34 (hskp10 | c1_1(a21)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3770, 104, 4496, 4503, 4502, 1882])).
% 3.03/2.34 tff(4508,plain,
% 3.03/2.34 (hskp10),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4507, 4504])).
% 3.03/2.34 tff(4509,plain,
% 3.03/2.34 (~c0_1(a18)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[943, 4508])).
% 3.03/2.34 tff(4510,plain,
% 3.03/2.34 (c3_1(a18)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[1037, 4508])).
% 3.03/2.34 tff(4511,plain,
% 3.03/2.34 (~c1_1(a18)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[937, 4508])).
% 3.03/2.34 tff(4512,plain,
% 3.03/2.34 (~c0_1(a31)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[444, 4505])).
% 3.03/2.34 tff(4513,plain,
% 3.03/2.34 (~c3_1(a31)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[403, 4505])).
% 3.03/2.34 tff(4514,plain,
% 3.03/2.34 ($false),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[3803, 4513, 4512, 4498, 4511, 4503, 4510, 4509, 4502, 11, 4506, 4501])).
% 3.03/2.34 tff(4515,plain,(hskp0), inference(lemma,lemma(discharge,[]))).
% 3.03/2.34 tff(4516,plain,
% 3.03/2.34 (~hskp3),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4376, 4515])).
% 3.03/2.34 tff(4517,plain,
% 3.03/2.34 (~hskp28),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4180, 4516])).
% 3.03/2.34 tff(4518,plain,
% 3.03/2.34 (hskp28 | hskp20),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[544, 4496])).
% 3.03/2.34 tff(4519,plain,
% 3.03/2.34 (hskp20),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4518, 4517])).
% 3.03/2.34 tff(4520,plain,
% 3.03/2.34 (c3_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[555, 4519])).
% 3.03/2.34 tff(4521,plain,
% 3.03/2.34 (c1_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[566, 4519])).
% 3.03/2.34 tff(4522,plain,
% 3.03/2.34 (~c2_1(a37)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[571, 104, 3867, 4516, 4521, 4520, 10])).
% 3.03/2.34 tff(4523,plain,
% 3.03/2.34 (~c3_1(a1)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[117, 4515])).
% 3.03/2.34 tff(4524,plain,
% 3.03/2.34 (c1_1(a1)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[139, 4515])).
% 3.03/2.34 tff(4525,plain,
% 3.03/2.34 (c2_1(a1)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[128, 4515])).
% 3.03/2.34 tff(4526,plain,
% 3.03/2.34 (hskp6),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[180, 4525, 4524, 4523])).
% 3.03/2.34 tff(4527,plain,
% 3.03/2.34 (~c3_1(a13)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[186, 4526])).
% 3.03/2.34 tff(4528,plain,
% 3.03/2.34 (~c1_1(a13)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[192, 4526])).
% 3.03/2.34 tff(4529,plain,
% 3.03/2.34 (~c0_1(a13)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[198, 4526])).
% 3.03/2.34 tff(4530,plain,
% 3.03/2.34 (hskp2),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[247, 104, 4496, 4529, 4528, 4527, 47])).
% 3.03/2.34 tff(4531,plain,
% 3.03/2.34 (~c2_1(a3)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[206, 4530])).
% 3.03/2.34 tff(4532,plain,
% 3.03/2.34 (c1_1(a3)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[228, 4530])).
% 3.03/2.34 tff(4533,plain,
% 3.03/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 3.03/2.34 inference(rewrite,[status(thm)],[])).
% 3.03/2.34 tff(4534,plain,
% 3.03/2.34 (((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 3.03/2.34 inference(rewrite,[status(thm)],[])).
% 3.03/2.34 tff(4535,plain,
% 3.03/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))))),
% 3.03/2.34 inference(monotonicity,[status(thm)],[4534])).
% 3.03/2.34 tff(4536,plain,
% 3.03/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 3.03/2.34 inference(transitivity,[status(thm)],[4535, 4533])).
% 3.03/2.34 tff(4537,plain,
% 3.03/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 3.03/2.34 inference(quant_inst,[status(thm)],[])).
% 3.03/2.34 tff(4538,plain,
% 3.03/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 3.03/2.34 inference(modus_ponens,[status(thm)],[4537, 4536])).
% 3.03/2.34 tff(4539,plain,
% 3.03/2.34 (~c0_1(a3)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[4538, 104, 4521, 4520, 4532, 4529, 4528, 4527, 4531, 36, 4522])).
% 3.03/2.34 tff(4540,plain,
% 3.03/2.34 (hskp9),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[896, 104, 4521, 4520, 4524, 4525, 4523, 890, 4522])).
% 3.03/2.34 tff(4541,plain,
% 3.03/2.34 (~c3_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[902, 4540])).
% 3.03/2.34 tff(4542,plain,
% 3.03/2.34 (c3_1(a3)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[217, 4530])).
% 3.03/2.34 tff(4543,plain,
% 3.03/2.34 (c1_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[913, 4540])).
% 3.03/2.34 tff(4544,plain,
% 3.03/2.34 (c2_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[2944, 104, 4543, 4542, 4524, 4525, 4541, 4531, 4523, 734, 4539])).
% 3.03/2.34 tff(4545,plain,
% 3.03/2.34 (~c2_1(a13)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[959, 104, 4496, 4521, 4520, 4529, 4528, 58, 4522])).
% 3.03/2.34 tff(4546,plain,
% 3.03/2.34 (c0_1(a16)),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[924, 4540])).
% 3.03/2.34 tff(4547,plain,
% 3.03/2.34 (hskp12),
% 3.03/2.34 inference(unit_resolution,[status(thm)],[993, 104, 4546, 4543, 4542, 4541, 4531, 987, 4539])).
% 3.03/2.35 tff(4548,plain,
% 3.03/2.35 (~c1_1(a20)),
% 3.03/2.35 inference(unit_resolution,[status(thm)],[1005, 4547])).
% 3.03/2.35 tff(4549,plain,
% 3.03/2.35 (c2_1(a20)),
% 3.03/2.35 inference(unit_resolution,[status(thm)],[1016, 4547])).
% 3.03/2.35 tff(4550,plain,
% 3.03/2.35 (~c0_1(a20)),
% 3.03/2.35 inference(unit_resolution,[status(thm)],[1359, 104, 4549, 4543, 4548, 4541, 4529, 4527, 1342, 4545, 4544])).
% 3.03/2.35 tff(4551,plain,
% 3.03/2.35 ($false),
% 3.03/2.35 inference(unit_resolution,[status(thm)],[1366, 104, 4496, 4549, 4532, 4542, 4548, 4531, 58, 4550])).
% 3.03/2.35 % SZS output end Proof
%------------------------------------------------------------------------------