TSTP Solution File: SYN436-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN436-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 23:55:22 EDT 2022
% Result : Unsatisfiable 1.61s 1.27s
% Output : Proof 2.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN436-1 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 03:35:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.61/1.27 % SZS status Unsatisfiable
% 1.61/1.27 % SZS output start Proof
% 1.61/1.27 tff(c1_1_type, type, (
% 1.61/1.27 c1_1: $i > $o)).
% 1.61/1.27 tff(a22_type, type, (
% 1.61/1.27 a22: $i)).
% 1.61/1.27 tff(a33_type, type, (
% 1.61/1.27 a33: $i)).
% 1.61/1.27 tff(c3_1_type, type, (
% 1.61/1.27 c3_1: $i > $o)).
% 1.61/1.27 tff(a31_type, type, (
% 1.61/1.27 a31: $i)).
% 1.61/1.27 tff(c2_1_type, type, (
% 1.61/1.27 c2_1: $i > $o)).
% 1.61/1.27 tff(hskp17_type, type, (
% 1.61/1.27 hskp17: $o)).
% 1.61/1.27 tff(c0_1_type, type, (
% 1.61/1.27 c0_1: $i > $o)).
% 1.61/1.27 tff(a3_type, type, (
% 1.61/1.27 a3: $i)).
% 1.61/1.27 tff(hskp11_type, type, (
% 1.61/1.27 hskp11: $o)).
% 1.61/1.27 tff(a24_type, type, (
% 1.61/1.27 a24: $i)).
% 1.61/1.27 tff(hskp14_type, type, (
% 1.61/1.27 hskp14: $o)).
% 1.61/1.27 tff(hskp8_type, type, (
% 1.61/1.27 hskp8: $o)).
% 1.61/1.27 tff(hskp9_type, type, (
% 1.61/1.27 hskp9: $o)).
% 1.61/1.27 tff(a16_type, type, (
% 1.61/1.27 a16: $i)).
% 1.61/1.27 tff(a4_type, type, (
% 1.61/1.27 a4: $i)).
% 1.61/1.27 tff(hskp4_type, type, (
% 1.61/1.27 hskp4: $o)).
% 1.61/1.27 tff(a5_type, type, (
% 1.61/1.27 a5: $i)).
% 1.61/1.27 tff(ndr1_0_type, type, (
% 1.61/1.27 ndr1_0: $o)).
% 1.61/1.27 tff(hskp3_type, type, (
% 1.61/1.27 hskp3: $o)).
% 1.61/1.27 tff(hskp2_type, type, (
% 1.61/1.27 hskp2: $o)).
% 1.61/1.27 tff(a37_type, type, (
% 1.61/1.27 a37: $i)).
% 1.61/1.27 tff(a30_type, type, (
% 1.61/1.27 a30: $i)).
% 1.61/1.27 tff(hskp16_type, type, (
% 1.61/1.27 hskp16: $o)).
% 1.61/1.27 tff(a25_type, type, (
% 1.61/1.27 a25: $i)).
% 1.61/1.27 tff(a32_type, type, (
% 1.61/1.27 a32: $i)).
% 1.61/1.27 tff(hskp18_type, type, (
% 1.61/1.27 hskp18: $o)).
% 1.61/1.27 tff(a6_type, type, (
% 1.61/1.27 a6: $i)).
% 1.61/1.27 tff(a15_type, type, (
% 1.61/1.27 a15: $i)).
% 1.61/1.27 tff(hskp24_type, type, (
% 1.61/1.27 hskp24: $o)).
% 1.61/1.27 tff(hskp13_type, type, (
% 1.61/1.27 hskp13: $o)).
% 1.61/1.27 tff(a10_type, type, (
% 1.61/1.27 a10: $i)).
% 1.61/1.27 tff(hskp26_type, type, (
% 1.61/1.27 hskp26: $o)).
% 1.61/1.27 tff(a14_type, type, (
% 1.61/1.27 a14: $i)).
% 1.61/1.27 tff(hskp7_type, type, (
% 1.61/1.27 hskp7: $o)).
% 1.61/1.27 tff(hskp0_type, type, (
% 1.61/1.27 hskp0: $o)).
% 1.61/1.27 tff(hskp25_type, type, (
% 1.61/1.27 hskp25: $o)).
% 1.61/1.27 tff(hskp21_type, type, (
% 1.61/1.27 hskp21: $o)).
% 1.61/1.27 tff(a1_type, type, (
% 1.61/1.27 a1: $i)).
% 1.61/1.27 tff(hskp23_type, type, (
% 1.61/1.27 hskp23: $o)).
% 1.61/1.27 tff(a53_type, type, (
% 1.61/1.27 a53: $i)).
% 1.61/1.27 tff(hskp27_type, type, (
% 1.61/1.27 hskp27: $o)).
% 1.61/1.27 tff(a11_type, type, (
% 1.61/1.27 a11: $i)).
% 1.61/1.27 tff(hskp19_type, type, (
% 1.61/1.27 hskp19: $o)).
% 1.61/1.27 tff(a42_type, type, (
% 1.61/1.27 a42: $i)).
% 1.61/1.27 tff(a9_type, type, (
% 1.61/1.27 a9: $i)).
% 1.61/1.27 tff(hskp6_type, type, (
% 1.61/1.27 hskp6: $o)).
% 1.61/1.27 tff(a19_type, type, (
% 1.61/1.27 a19: $i)).
% 1.61/1.27 tff(a18_type, type, (
% 1.61/1.27 a18: $i)).
% 1.61/1.27 tff(hskp10_type, type, (
% 1.61/1.27 hskp10: $o)).
% 1.61/1.27 tff(hskp20_type, type, (
% 1.61/1.27 hskp20: $o)).
% 1.61/1.27 tff(a8_type, type, (
% 1.61/1.27 a8: $i)).
% 1.61/1.27 tff(a2_type, type, (
% 1.61/1.27 a2: $i)).
% 1.61/1.27 tff(hskp1_type, type, (
% 1.61/1.27 hskp1: $o)).
% 1.61/1.27 tff(hskp5_type, type, (
% 1.61/1.27 hskp5: $o)).
% 1.61/1.27 tff(a7_type, type, (
% 1.61/1.27 a7: $i)).
% 1.61/1.27 tff(a21_type, type, (
% 1.61/1.27 a21: $i)).
% 1.61/1.27 tff(hskp12_type, type, (
% 1.61/1.27 hskp12: $o)).
% 1.61/1.27 tff(hskp15_type, type, (
% 1.61/1.27 hskp15: $o)).
% 1.61/1.27 tff(hskp22_type, type, (
% 1.61/1.27 hskp22: $o)).
% 1.61/1.27 tff(a45_type, type, (
% 1.61/1.27 a45: $i)).
% 1.61/1.27 tff(1,assumption,(~c0_1(a3)), introduced(assumption)).
% 1.61/1.27 tff(2,assumption,(~c3_1(a16)), introduced(assumption)).
% 1.61/1.27 tff(3,assumption,(~c1_1(a16)), introduced(assumption)).
% 1.61/1.27 tff(4,plain,
% 1.61/1.27 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.61/1.27 inference(bind,[status(th)],[])).
% 1.61/1.27 tff(5,plain,
% 1.61/1.27 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.61/1.27 inference(quant_intro,[status(thm)],[4])).
% 1.61/1.27 tff(6,plain,
% 1.61/1.27 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.61/1.27 inference(rewrite,[status(thm)],[])).
% 1.61/1.27 tff(7,plain,
% 1.61/1.27 (^[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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.61/1.27 inference(bind,[status(th)],[])).
% 1.61/1.27 tff(8,plain,
% 1.61/1.27 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.61/1.27 inference(quant_intro,[status(thm)],[7])).
% 1.61/1.27 tff(9,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 1.61/1.27 tff(10,plain,
% 1.61/1.27 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.61/1.27 inference(modus_ponens,[status(thm)],[9, 8])).
% 1.61/1.27 tff(11,plain,
% 1.61/1.27 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.61/1.27 inference(modus_ponens,[status(thm)],[10, 6])).
% 1.61/1.27 tff(12,plain,(
% 1.61/1.27 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.61/1.27 inference(skolemize,[status(sab)],[11])).
% 1.61/1.27 tff(13,plain,
% 1.61/1.27 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.61/1.27 inference(modus_ponens,[status(thm)],[12, 5])).
% 1.61/1.27 tff(14,plain,
% 1.61/1.27 (^[U: $i] : refl((hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) <=> (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)))),
% 1.61/1.27 inference(bind,[status(th)],[])).
% 1.61/1.27 tff(15,plain,
% 1.61/1.27 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.61/1.27 inference(quant_intro,[status(thm)],[14])).
% 1.61/1.27 tff(16,plain,
% 1.61/1.27 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.61/1.27 inference(rewrite,[status(thm)],[])).
% 1.61/1.27 tff(17,plain,
% 1.61/1.27 (^[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) | (~c2_1(U)) | c0_1(U))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3) <=> ((hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) | hskp3))), rewrite(((hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U)) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))))),
% 1.61/1.27 inference(bind,[status(th)],[])).
% 1.61/1.27 tff(18,plain,
% 1.61/1.27 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.61/1.27 inference(quant_intro,[status(thm)],[17])).
% 1.61/1.27 tff(19,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.61/1.27 tff(20,plain,
% 1.61/1.27 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.61/1.27 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.61/1.27 tff(21,plain,
% 1.61/1.27 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.61/1.27 inference(modus_ponens,[status(thm)],[20, 16])).
% 1.61/1.27 tff(22,plain,(
% 1.61/1.27 ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.61/1.27 inference(skolemize,[status(sab)],[21])).
% 1.61/1.27 tff(23,plain,
% 1.61/1.27 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.61/1.27 inference(modus_ponens,[status(thm)],[22, 15])).
% 1.61/1.27 tff(24,assumption,(~c2_1(a16)), introduced(assumption)).
% 1.61/1.28 tff(25,plain,
% 1.61/1.28 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 1.61/1.28 inference(bind,[status(th)],[])).
% 1.61/1.28 tff(26,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(quant_intro,[status(thm)],[25])).
% 1.61/1.28 tff(27,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(rewrite,[status(thm)],[])).
% 1.61/1.28 tff(28,plain,
% 1.61/1.28 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 1.61/1.28 inference(bind,[status(th)],[])).
% 1.61/1.28 tff(29,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(quant_intro,[status(thm)],[28])).
% 1.61/1.28 tff(30,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 1.61/1.28 tff(31,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[30, 29])).
% 1.61/1.28 tff(32,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[31, 27])).
% 1.61/1.28 tff(33,plain,(
% 1.61/1.28 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(skolemize,[status(sab)],[32])).
% 1.61/1.28 tff(34,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[33, 26])).
% 1.61/1.28 tff(35,assumption,(~c0_1(a16)), introduced(assumption)).
% 1.61/1.28 tff(36,plain,
% 1.61/1.28 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.61/1.28 inference(bind,[status(th)],[])).
% 1.61/1.28 tff(37,plain,
% 1.61/1.28 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.61/1.28 inference(quant_intro,[status(thm)],[36])).
% 1.61/1.28 tff(38,plain,
% 1.61/1.28 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.61/1.28 inference(rewrite,[status(thm)],[])).
% 1.61/1.28 tff(39,plain,
% 1.61/1.28 (^[V: $i, U: $i] : 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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.61/1.28 inference(bind,[status(th)],[])).
% 1.61/1.28 tff(40,plain,
% 1.61/1.28 (![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.61/1.28 inference(quant_intro,[status(thm)],[39])).
% 1.61/1.28 tff(41,axiom,(![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.61/1.28 tff(42,plain,
% 1.61/1.28 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.61/1.28 tff(43,plain,
% 1.61/1.28 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[42, 38])).
% 1.61/1.28 tff(44,plain,(
% 1.61/1.28 ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.61/1.28 inference(skolemize,[status(sab)],[43])).
% 1.61/1.28 tff(45,plain,
% 1.61/1.28 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[44, 37])).
% 1.61/1.28 tff(46,plain,
% 1.61/1.28 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.61/1.28 inference(bind,[status(th)],[])).
% 1.61/1.28 tff(47,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.61/1.28 inference(quant_intro,[status(thm)],[46])).
% 1.61/1.28 tff(48,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.61/1.28 inference(rewrite,[status(thm)],[])).
% 1.61/1.28 tff(49,plain,
% 1.61/1.28 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.61/1.28 inference(bind,[status(th)],[])).
% 1.61/1.28 tff(50,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.61/1.28 inference(quant_intro,[status(thm)],[49])).
% 1.61/1.28 tff(51,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 1.61/1.28 tff(52,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.61/1.28 tff(53,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.61/1.28 tff(54,plain,(
% 1.61/1.28 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.61/1.28 inference(skolemize,[status(sab)],[53])).
% 1.61/1.28 tff(55,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[54, 47])).
% 1.61/1.28 tff(56,plain,
% 1.61/1.28 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.61/1.28 inference(bind,[status(th)],[])).
% 1.61/1.28 tff(57,plain,
% 1.61/1.28 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.61/1.28 inference(quant_intro,[status(thm)],[56])).
% 1.61/1.28 tff(58,plain,
% 1.61/1.28 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.61/1.28 inference(rewrite,[status(thm)],[])).
% 1.61/1.28 tff(59,plain,
% 1.61/1.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | 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))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_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) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.61/1.28 inference(bind,[status(th)],[])).
% 1.61/1.28 tff(60,plain,
% 1.61/1.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.61/1.28 inference(quant_intro,[status(thm)],[59])).
% 1.61/1.28 tff(61,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.61/1.28 tff(62,plain,
% 1.61/1.28 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.61/1.28 tff(63,plain,
% 1.61/1.28 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[62, 58])).
% 1.61/1.28 tff(64,plain,(
% 1.61/1.28 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.61/1.28 inference(skolemize,[status(sab)],[63])).
% 1.61/1.28 tff(65,plain,
% 1.61/1.28 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[64, 57])).
% 1.61/1.28 tff(66,assumption,(hskp17), introduced(assumption)).
% 1.61/1.28 tff(67,plain,
% 1.61/1.28 (((~hskp17) | (~c1_1(a31))) <=> ((~hskp17) | (~c1_1(a31)))),
% 1.61/1.28 inference(rewrite,[status(thm)],[])).
% 1.61/1.28 tff(68,plain,
% 1.61/1.28 (((~c1_1(a31)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a31)))),
% 1.61/1.28 inference(rewrite,[status(thm)],[])).
% 1.61/1.28 tff(69,axiom,((~c1_1(a31)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.61/1.28 tff(70,plain,
% 1.61/1.28 ((~hskp17) | (~c1_1(a31))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[69, 68])).
% 1.61/1.28 tff(71,plain,
% 1.61/1.28 ((~hskp17) | (~c1_1(a31))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[70, 67])).
% 1.61/1.28 tff(72,plain,
% 1.61/1.28 (~c1_1(a31)),
% 1.61/1.28 inference(unit_resolution,[status(thm)],[71, 66])).
% 1.61/1.28 tff(73,assumption,(~hskp24), introduced(assumption)).
% 1.61/1.28 tff(74,plain,
% 1.61/1.28 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.61/1.28 inference(bind,[status(th)],[])).
% 1.61/1.28 tff(75,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(quant_intro,[status(thm)],[74])).
% 1.61/1.28 tff(76,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(rewrite,[status(thm)],[])).
% 1.61/1.28 tff(77,plain,
% 1.61/1.28 (^[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(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.61/1.28 inference(bind,[status(th)],[])).
% 1.61/1.28 tff(78,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(quant_intro,[status(thm)],[77])).
% 1.61/1.28 tff(79,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 1.61/1.28 tff(80,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.61/1.28 tff(81,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[80, 76])).
% 1.61/1.28 tff(82,plain,(
% 1.61/1.28 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(skolemize,[status(sab)],[81])).
% 1.61/1.28 tff(83,plain,
% 1.61/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[82, 75])).
% 1.61/1.28 tff(84,assumption,(~hskp26), introduced(assumption)).
% 1.61/1.28 tff(85,plain,
% 1.61/1.28 (^[U: $i] : refl((hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 1.61/1.28 inference(bind,[status(th)],[])).
% 1.61/1.28 tff(86,plain,
% 1.61/1.28 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.28 inference(quant_intro,[status(thm)],[85])).
% 1.61/1.28 tff(87,plain,
% 1.61/1.28 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.28 inference(rewrite,[status(thm)],[])).
% 1.61/1.28 tff(88,plain,
% 1.61/1.28 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp16) <=> ((hskp26 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp16))), rewrite(((hskp26 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp16) <=> (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp16) <=> (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 1.61/1.28 inference(bind,[status(th)],[])).
% 1.61/1.28 tff(89,plain,
% 1.61/1.28 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp16) <=> ![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.28 inference(quant_intro,[status(thm)],[88])).
% 1.61/1.28 tff(90,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.61/1.28 tff(91,plain,
% 1.61/1.28 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.61/1.28 tff(92,plain,
% 1.61/1.28 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[91, 87])).
% 1.61/1.28 tff(93,plain,(
% 1.61/1.28 ![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.28 inference(skolemize,[status(sab)],[92])).
% 1.61/1.28 tff(94,plain,
% 1.61/1.28 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[93, 86])).
% 1.61/1.28 tff(95,plain,
% 1.61/1.28 (^[U: $i] : refl((hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(96,plain,
% 1.61/1.29 (![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.61/1.29 inference(quant_intro,[status(thm)],[95])).
% 1.61/1.29 tff(97,plain,
% 1.61/1.29 (![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(98,plain,
% 1.61/1.29 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp24) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp24))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp24) <=> (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp24) <=> (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(99,plain,
% 1.61/1.29 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp24) <=> ![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.61/1.29 inference(quant_intro,[status(thm)],[98])).
% 1.61/1.29 tff(100,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.61/1.29 tff(101,plain,
% 1.61/1.29 (![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[100, 99])).
% 1.61/1.29 tff(102,plain,
% 1.61/1.29 (![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[101, 97])).
% 1.61/1.29 tff(103,plain,(
% 1.61/1.29 ![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.61/1.29 inference(skolemize,[status(sab)],[102])).
% 1.61/1.29 tff(104,plain,
% 1.61/1.29 (![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[103, 96])).
% 1.61/1.29 tff(105,assumption,(~hskp9), introduced(assumption)).
% 1.61/1.29 tff(106,assumption,(hskp4), introduced(assumption)).
% 1.61/1.29 tff(107,plain,
% 1.61/1.29 (((~hskp4) | (~c2_1(a6))) <=> ((~hskp4) | (~c2_1(a6)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(108,plain,
% 1.61/1.29 (((~c2_1(a6)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a6)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(109,axiom,((~c2_1(a6)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 1.61/1.29 tff(110,plain,
% 1.61/1.29 ((~hskp4) | (~c2_1(a6))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.61/1.29 tff(111,plain,
% 1.61/1.29 ((~hskp4) | (~c2_1(a6))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[110, 107])).
% 1.61/1.29 tff(112,plain,
% 1.61/1.29 (~c2_1(a6)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[111, 106])).
% 1.61/1.29 tff(113,plain,
% 1.61/1.29 (((~hskp4) | c3_1(a6)) <=> ((~hskp4) | c3_1(a6))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(114,axiom,((~hskp4) | c3_1(a6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.61/1.29 tff(115,plain,
% 1.61/1.29 ((~hskp4) | c3_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.61/1.29 tff(116,plain,
% 1.61/1.29 ((~hskp4) | c3_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[115, 113])).
% 1.61/1.29 tff(117,plain,
% 1.61/1.29 ((~hskp4) | c3_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[116, 113])).
% 1.61/1.29 tff(118,plain,
% 1.61/1.29 ((~hskp4) | c3_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[117, 113])).
% 1.61/1.29 tff(119,plain,
% 1.61/1.29 ((~hskp4) | c3_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[118, 113])).
% 1.61/1.29 tff(120,plain,
% 1.61/1.29 ((~hskp4) | c3_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[119, 113])).
% 1.61/1.29 tff(121,plain,
% 1.61/1.29 ((~hskp4) | c3_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[120, 113])).
% 1.61/1.29 tff(122,plain,
% 1.61/1.29 ((~hskp4) | c3_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[121, 113])).
% 1.61/1.29 tff(123,plain,
% 1.61/1.29 (c3_1(a6)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[122, 106])).
% 1.61/1.29 tff(124,plain,
% 1.61/1.29 (((~hskp4) | c1_1(a6)) <=> ((~hskp4) | c1_1(a6))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(125,axiom,((~hskp4) | c1_1(a6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.61/1.29 tff(126,plain,
% 1.61/1.29 ((~hskp4) | c1_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.61/1.29 tff(127,plain,
% 1.61/1.29 ((~hskp4) | c1_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[126, 124])).
% 1.61/1.29 tff(128,plain,
% 1.61/1.29 ((~hskp4) | c1_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[127, 124])).
% 1.61/1.29 tff(129,plain,
% 1.61/1.29 ((~hskp4) | c1_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[128, 124])).
% 1.61/1.29 tff(130,plain,
% 1.61/1.29 ((~hskp4) | c1_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[129, 124])).
% 1.61/1.29 tff(131,plain,
% 1.61/1.29 ((~hskp4) | c1_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[130, 124])).
% 1.61/1.29 tff(132,plain,
% 1.61/1.29 ((~hskp4) | c1_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[131, 124])).
% 1.61/1.29 tff(133,plain,
% 1.61/1.29 ((~hskp4) | c1_1(a6)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[132, 124])).
% 1.61/1.29 tff(134,plain,
% 1.61/1.29 (c1_1(a6)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[133, 106])).
% 1.61/1.29 tff(135,assumption,(~ndr1_0), introduced(assumption)).
% 1.61/1.29 tff(136,plain,
% 1.61/1.29 ((ndr1_0 | (~hskp17)) <=> (ndr1_0 | (~hskp17))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(137,plain,
% 1.61/1.29 (((~hskp17) | ndr1_0) <=> (ndr1_0 | (~hskp17))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(138,axiom,((~hskp17) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause11')).
% 1.61/1.29 tff(139,plain,
% 1.61/1.29 (ndr1_0 | (~hskp17)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[138, 137])).
% 1.61/1.29 tff(140,plain,
% 1.61/1.29 (ndr1_0 | (~hskp17)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[139, 136])).
% 1.61/1.29 tff(141,plain,
% 1.61/1.29 (~hskp17),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[140, 135])).
% 1.61/1.29 tff(142,plain,
% 1.61/1.29 ((ndr1_0 | (~hskp25)) <=> (ndr1_0 | (~hskp25))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(143,plain,
% 1.61/1.29 (((~hskp25) | ndr1_0) <=> (ndr1_0 | (~hskp25))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(144,axiom,((~hskp25) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 1.61/1.29 tff(145,plain,
% 1.61/1.29 (ndr1_0 | (~hskp25)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.61/1.29 tff(146,plain,
% 1.61/1.29 (ndr1_0 | (~hskp25)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[145, 142])).
% 1.61/1.29 tff(147,plain,
% 1.61/1.29 (~hskp25),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[146, 135])).
% 1.61/1.29 tff(148,plain,
% 1.61/1.29 ((ndr1_0 | (~hskp21)) <=> (ndr1_0 | (~hskp21))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(149,plain,
% 1.61/1.29 (((~hskp21) | ndr1_0) <=> (ndr1_0 | (~hskp21))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(150,axiom,((~hskp21) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause7')).
% 1.61/1.29 tff(151,plain,
% 1.61/1.29 (ndr1_0 | (~hskp21)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.61/1.29 tff(152,plain,
% 1.61/1.29 (ndr1_0 | (~hskp21)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[151, 148])).
% 1.61/1.29 tff(153,plain,
% 1.61/1.29 (~hskp21),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[152, 135])).
% 1.61/1.29 tff(154,plain,
% 1.61/1.29 ((hskp25 | hskp21 | hskp17) <=> (hskp25 | hskp21 | hskp17)),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(155,plain,
% 1.61/1.29 (((hskp25 | hskp17) | hskp21) <=> (hskp25 | hskp21 | hskp17)),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(156,plain,
% 1.61/1.29 ((hskp25 | hskp17) <=> (hskp25 | hskp17)),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(157,plain,
% 1.61/1.29 (((hskp25 | hskp17) | hskp21) <=> ((hskp25 | hskp17) | hskp21)),
% 1.61/1.29 inference(monotonicity,[status(thm)],[156])).
% 1.61/1.29 tff(158,plain,
% 1.61/1.29 (((hskp25 | hskp17) | hskp21) <=> (hskp25 | hskp21 | hskp17)),
% 1.61/1.29 inference(transitivity,[status(thm)],[157, 155])).
% 1.61/1.29 tff(159,axiom,((hskp25 | hskp17) | hskp21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause29')).
% 1.61/1.29 tff(160,plain,
% 1.61/1.29 (hskp25 | hskp21 | hskp17),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[159, 158])).
% 1.61/1.29 tff(161,plain,
% 1.61/1.29 (hskp25 | hskp21 | hskp17),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[160, 154])).
% 1.61/1.29 tff(162,plain,
% 1.61/1.29 (hskp25 | hskp21 | hskp17),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[161, 154])).
% 1.61/1.29 tff(163,plain,
% 1.61/1.29 (hskp25 | hskp21 | hskp17),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[162, 154])).
% 1.61/1.29 tff(164,plain,
% 1.61/1.29 (hskp25 | hskp21 | hskp17),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[163, 154])).
% 1.61/1.29 tff(165,plain,
% 1.61/1.29 (hskp25 | hskp21 | hskp17),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[164, 154])).
% 1.61/1.29 tff(166,plain,
% 1.61/1.29 (hskp25 | hskp21 | hskp17),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[165, 154])).
% 1.61/1.29 tff(167,plain,
% 1.61/1.29 (hskp25 | hskp21 | hskp17),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[166, 154])).
% 1.61/1.29 tff(168,plain,
% 1.61/1.29 ($false),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[167, 153, 147, 141])).
% 1.61/1.29 tff(169,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.61/1.29 tff(170,plain,
% 1.61/1.29 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(171,plain,
% 1.61/1.29 ((hskp24 | hskp9 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6))) <=> (hskp24 | hskp9 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(172,plain,
% 1.61/1.29 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6))))),
% 1.61/1.29 inference(monotonicity,[status(thm)],[171])).
% 1.61/1.29 tff(173,plain,
% 1.61/1.29 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.61/1.29 inference(transitivity,[status(thm)],[172, 170])).
% 1.61/1.29 tff(174,plain,
% 1.61/1.29 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.61/1.29 inference(quant_inst,[status(thm)],[])).
% 1.61/1.29 tff(175,plain,
% 1.61/1.29 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[174, 173])).
% 1.61/1.29 tff(176,plain,
% 1.61/1.29 ($false),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[175, 169, 73, 105, 134, 123, 112, 104])).
% 1.61/1.29 tff(177,plain,((~hskp4) | hskp24 | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.61/1.29 tff(178,plain,
% 1.61/1.29 (~hskp4),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[177, 105, 73])).
% 1.61/1.29 tff(179,assumption,(hskp8), introduced(assumption)).
% 1.61/1.29 tff(180,plain,
% 1.61/1.29 (((~hskp8) | (~c2_1(a15))) <=> ((~hskp8) | (~c2_1(a15)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(181,plain,
% 1.61/1.29 (((~c2_1(a15)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a15)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(182,axiom,((~c2_1(a15)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.61/1.29 tff(183,plain,
% 1.61/1.29 ((~hskp8) | (~c2_1(a15))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[182, 181])).
% 1.61/1.29 tff(184,plain,
% 1.61/1.29 ((~hskp8) | (~c2_1(a15))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[183, 180])).
% 1.61/1.29 tff(185,plain,
% 1.61/1.29 (~c2_1(a15)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[184, 179])).
% 1.61/1.29 tff(186,plain,
% 1.61/1.29 (((~hskp8) | c0_1(a15)) <=> ((~hskp8) | c0_1(a15))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(187,axiom,((~hskp8) | c0_1(a15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 1.61/1.29 tff(188,plain,
% 1.61/1.29 ((~hskp8) | c0_1(a15)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[187, 186])).
% 1.61/1.29 tff(189,plain,
% 1.61/1.29 ((~hskp8) | c0_1(a15)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[188, 186])).
% 1.61/1.29 tff(190,plain,
% 1.61/1.29 ((~hskp8) | c0_1(a15)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[189, 186])).
% 1.61/1.29 tff(191,plain,
% 1.61/1.29 ((~hskp8) | c0_1(a15)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[190, 186])).
% 1.61/1.29 tff(192,plain,
% 1.61/1.29 ((~hskp8) | c0_1(a15)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[191, 186])).
% 1.61/1.29 tff(193,plain,
% 1.61/1.29 ((~hskp8) | c0_1(a15)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[192, 186])).
% 1.61/1.29 tff(194,plain,
% 1.61/1.29 ((~hskp8) | c0_1(a15)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[193, 186])).
% 1.61/1.29 tff(195,plain,
% 1.61/1.29 ((~hskp8) | c0_1(a15)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[194, 186])).
% 1.61/1.29 tff(196,plain,
% 1.61/1.29 (c0_1(a15)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[195, 179])).
% 1.61/1.29 tff(197,plain,
% 1.61/1.29 (((~hskp8) | (~c1_1(a15))) <=> ((~hskp8) | (~c1_1(a15)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(198,plain,
% 1.61/1.29 (((~c1_1(a15)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a15)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(199,axiom,((~c1_1(a15)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.61/1.29 tff(200,plain,
% 1.61/1.29 ((~hskp8) | (~c1_1(a15))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.61/1.29 tff(201,plain,
% 1.61/1.29 ((~hskp8) | (~c1_1(a15))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[200, 197])).
% 1.61/1.29 tff(202,plain,
% 1.61/1.29 (~c1_1(a15)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[201, 179])).
% 1.61/1.29 tff(203,assumption,(~c2_1(a15)), introduced(assumption)).
% 1.61/1.29 tff(204,assumption,(c0_1(a15)), introduced(assumption)).
% 1.61/1.29 tff(205,assumption,(~hskp4), introduced(assumption)).
% 1.61/1.29 tff(206,assumption,(~c1_1(a15)), introduced(assumption)).
% 1.61/1.29 tff(207,assumption,(hskp23), introduced(assumption)).
% 1.61/1.29 tff(208,plain,
% 1.61/1.29 (((~hskp23) | (~c1_1(a53))) <=> ((~hskp23) | (~c1_1(a53)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(209,plain,
% 1.61/1.29 (((~c1_1(a53)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a53)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(210,axiom,((~c1_1(a53)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.61/1.29 tff(211,plain,
% 1.61/1.29 ((~hskp23) | (~c1_1(a53))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[210, 209])).
% 1.61/1.29 tff(212,plain,
% 1.61/1.29 ((~hskp23) | (~c1_1(a53))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[211, 208])).
% 1.61/1.29 tff(213,plain,
% 1.61/1.29 (~c1_1(a53)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[212, 207])).
% 1.61/1.29 tff(214,plain,
% 1.61/1.29 (((~hskp23) | (~c0_1(a53))) <=> ((~hskp23) | (~c0_1(a53)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(215,plain,
% 1.61/1.29 (((~c0_1(a53)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a53)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(216,axiom,((~c0_1(a53)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.61/1.29 tff(217,plain,
% 1.61/1.29 ((~hskp23) | (~c0_1(a53))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[216, 215])).
% 1.61/1.29 tff(218,plain,
% 1.61/1.29 ((~hskp23) | (~c0_1(a53))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[217, 214])).
% 1.61/1.29 tff(219,plain,
% 1.61/1.29 (~c0_1(a53)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[218, 207])).
% 1.61/1.29 tff(220,plain,
% 1.61/1.29 (((~hskp23) | c3_1(a53)) <=> ((~hskp23) | c3_1(a53))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(221,axiom,((~hskp23) | c3_1(a53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.61/1.29 tff(222,plain,
% 1.61/1.29 ((~hskp23) | c3_1(a53)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[221, 220])).
% 1.61/1.29 tff(223,plain,
% 1.61/1.29 ((~hskp23) | c3_1(a53)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[222, 220])).
% 1.61/1.29 tff(224,plain,
% 1.61/1.29 ((~hskp23) | c3_1(a53)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[223, 220])).
% 1.61/1.29 tff(225,plain,
% 1.61/1.29 ((~hskp23) | c3_1(a53)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[224, 220])).
% 1.61/1.29 tff(226,plain,
% 1.61/1.29 ((~hskp23) | c3_1(a53)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[225, 220])).
% 1.61/1.29 tff(227,plain,
% 1.61/1.29 ((~hskp23) | c3_1(a53)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[226, 220])).
% 1.61/1.29 tff(228,plain,
% 1.61/1.29 ((~hskp23) | c3_1(a53)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[227, 220])).
% 1.61/1.29 tff(229,plain,
% 1.61/1.29 ((~hskp23) | c3_1(a53)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[228, 220])).
% 1.61/1.29 tff(230,plain,
% 1.61/1.29 (c3_1(a53)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[229, 207])).
% 1.61/1.29 tff(231,plain,
% 1.61/1.29 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a53)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a53)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(232,plain,
% 1.61/1.29 ((hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53))) <=> (hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a53)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(233,plain,
% 1.61/1.29 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a53))))),
% 1.61/1.29 inference(monotonicity,[status(thm)],[232])).
% 1.61/1.29 tff(234,plain,
% 1.61/1.29 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a53)))),
% 1.61/1.29 inference(transitivity,[status(thm)],[233, 231])).
% 1.61/1.29 tff(235,plain,
% 1.61/1.29 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53)))),
% 1.61/1.29 inference(quant_inst,[status(thm)],[])).
% 1.61/1.29 tff(236,plain,
% 1.61/1.29 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a53))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[235, 234])).
% 1.61/1.29 tff(237,plain,
% 1.61/1.29 ($false),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[236, 169, 205, 230, 204, 219, 213, 206, 203, 65])).
% 1.61/1.29 tff(238,plain,((~hskp23) | hskp4 | (~c0_1(a15)) | c1_1(a15) | c2_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.29 tff(239,plain,
% 1.61/1.29 (~hskp23),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[238, 206, 205, 204, 203])).
% 1.61/1.29 tff(240,plain,
% 1.61/1.29 ((hskp24 | hskp23 | hskp0) <=> (hskp24 | hskp23 | hskp0)),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(241,plain,
% 1.61/1.29 (((hskp24 | hskp23) | hskp0) <=> (hskp24 | hskp23 | hskp0)),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(242,plain,
% 1.61/1.29 ((hskp24 | hskp23) <=> (hskp24 | hskp23)),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(243,plain,
% 1.61/1.29 (((hskp24 | hskp23) | hskp0) <=> ((hskp24 | hskp23) | hskp0)),
% 1.61/1.29 inference(monotonicity,[status(thm)],[242])).
% 1.61/1.29 tff(244,plain,
% 1.61/1.29 (((hskp24 | hskp23) | hskp0) <=> (hskp24 | hskp23 | hskp0)),
% 1.61/1.29 inference(transitivity,[status(thm)],[243, 241])).
% 1.61/1.29 tff(245,axiom,((hskp24 | hskp23) | hskp0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 1.61/1.29 tff(246,plain,
% 1.61/1.29 (hskp24 | hskp23 | hskp0),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[245, 244])).
% 1.61/1.29 tff(247,plain,
% 1.61/1.29 (hskp24 | hskp23 | hskp0),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[246, 240])).
% 1.61/1.29 tff(248,plain,
% 1.61/1.29 (hskp24 | hskp23 | hskp0),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[247, 240])).
% 1.61/1.29 tff(249,plain,
% 1.61/1.29 (hskp24 | hskp23 | hskp0),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[248, 240])).
% 1.61/1.29 tff(250,plain,
% 1.61/1.29 (hskp24 | hskp23 | hskp0),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[249, 240])).
% 1.61/1.29 tff(251,plain,
% 1.61/1.29 (hskp24 | hskp23 | hskp0),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[250, 240])).
% 1.61/1.29 tff(252,plain,
% 1.61/1.29 (hskp24 | hskp23 | hskp0),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[251, 240])).
% 1.61/1.29 tff(253,plain,
% 1.61/1.29 (hskp24 | hskp23 | hskp0),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[252, 240])).
% 1.61/1.29 tff(254,plain,
% 1.61/1.29 (hskp0),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[253, 73, 239])).
% 1.61/1.29 tff(255,plain,
% 1.61/1.29 (((~hskp0) | (~c2_1(a1))) <=> ((~hskp0) | (~c2_1(a1)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(256,plain,
% 1.61/1.29 (((~c2_1(a1)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(257,axiom,((~c2_1(a1)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.61/1.29 tff(258,plain,
% 1.61/1.29 ((~hskp0) | (~c2_1(a1))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[257, 256])).
% 1.61/1.29 tff(259,plain,
% 1.61/1.29 ((~hskp0) | (~c2_1(a1))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[258, 255])).
% 1.61/1.29 tff(260,plain,
% 1.61/1.29 (~c2_1(a1)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[259, 254])).
% 1.61/1.29 tff(261,plain,
% 1.61/1.29 (((~hskp0) | c3_1(a1)) <=> ((~hskp0) | c3_1(a1))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(262,axiom,((~hskp0) | c3_1(a1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.61/1.29 tff(263,plain,
% 1.61/1.29 ((~hskp0) | c3_1(a1)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[262, 261])).
% 1.61/1.29 tff(264,plain,
% 1.61/1.29 ((~hskp0) | c3_1(a1)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[263, 261])).
% 1.61/1.29 tff(265,plain,
% 1.61/1.29 ((~hskp0) | c3_1(a1)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[264, 261])).
% 1.61/1.29 tff(266,plain,
% 1.61/1.29 ((~hskp0) | c3_1(a1)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[265, 261])).
% 1.61/1.29 tff(267,plain,
% 1.61/1.29 ((~hskp0) | c3_1(a1)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[266, 261])).
% 1.61/1.29 tff(268,plain,
% 1.61/1.29 ((~hskp0) | c3_1(a1)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[267, 261])).
% 1.61/1.29 tff(269,plain,
% 1.61/1.29 ((~hskp0) | c3_1(a1)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[268, 261])).
% 1.61/1.29 tff(270,plain,
% 1.61/1.29 ((~hskp0) | c3_1(a1)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[269, 261])).
% 1.61/1.29 tff(271,plain,
% 1.61/1.29 (c3_1(a1)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[270, 254])).
% 1.61/1.29 tff(272,plain,
% 1.61/1.29 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(273,plain,
% 1.61/1.29 ((hskp24 | hskp9 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1))) <=> (hskp24 | hskp9 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(274,plain,
% 1.61/1.29 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1))))),
% 1.61/1.29 inference(monotonicity,[status(thm)],[273])).
% 1.61/1.29 tff(275,plain,
% 1.61/1.29 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)))),
% 1.61/1.29 inference(transitivity,[status(thm)],[274, 272])).
% 1.61/1.29 tff(276,plain,
% 1.61/1.29 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)))),
% 1.61/1.29 inference(quant_inst,[status(thm)],[])).
% 1.61/1.29 tff(277,plain,
% 1.61/1.29 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.61/1.29 tff(278,plain,
% 1.61/1.29 (~c1_1(a1)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[277, 169, 73, 105, 271, 260, 104])).
% 1.61/1.29 tff(279,plain,
% 1.61/1.29 (((~hskp0) | (~c0_1(a1))) <=> ((~hskp0) | (~c0_1(a1)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(280,plain,
% 1.61/1.29 (((~c0_1(a1)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a1)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(281,axiom,((~c0_1(a1)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.61/1.29 tff(282,plain,
% 1.61/1.29 ((~hskp0) | (~c0_1(a1))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[281, 280])).
% 1.61/1.29 tff(283,plain,
% 1.61/1.29 ((~hskp0) | (~c0_1(a1))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[282, 279])).
% 1.61/1.29 tff(284,plain,
% 1.61/1.29 (~c0_1(a1)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[283, 254])).
% 1.61/1.29 tff(285,plain,
% 1.61/1.29 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c1_1(a15) | c2_1(a15) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a15) | c2_1(a15) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a15)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(286,plain,
% 1.61/1.29 ((hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1))) <=> (hskp4 | c1_1(a15) | c2_1(a15) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a15)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(287,plain,
% 1.61/1.29 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c1_1(a15) | c2_1(a15) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a15))))),
% 1.61/1.29 inference(monotonicity,[status(thm)],[286])).
% 1.61/1.29 tff(288,plain,
% 1.61/1.29 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a15) | c2_1(a15) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a15)))),
% 1.61/1.29 inference(transitivity,[status(thm)],[287, 285])).
% 1.61/1.29 tff(289,plain,
% 1.61/1.29 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1)))),
% 1.61/1.29 inference(quant_inst,[status(thm)],[])).
% 1.61/1.29 tff(290,plain,
% 1.61/1.29 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a15) | c2_1(a15) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a15))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[289, 288])).
% 1.61/1.29 tff(291,plain,
% 1.61/1.29 ($false),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[290, 169, 205, 204, 271, 206, 203, 284, 65, 278])).
% 1.61/1.29 tff(292,plain,(hskp24 | hskp4 | (~c0_1(a15)) | c1_1(a15) | c2_1(a15) | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.61/1.29 tff(293,plain,
% 1.61/1.29 ($false),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[292, 202, 196, 105, 73, 185, 178])).
% 1.61/1.29 tff(294,plain,((~hskp8) | hskp9 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.61/1.29 tff(295,plain,
% 1.61/1.29 (~hskp8),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[294, 105, 73])).
% 1.61/1.29 tff(296,plain,
% 1.61/1.29 ((hskp17 | hskp8 | hskp4) <=> (hskp17 | hskp8 | hskp4)),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(297,plain,
% 1.61/1.29 (((hskp17 | hskp8) | hskp4) <=> (hskp17 | hskp8 | hskp4)),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(298,axiom,((hskp17 | hskp8) | hskp4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause31')).
% 1.61/1.29 tff(299,plain,
% 1.61/1.29 (hskp17 | hskp8 | hskp4),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[298, 297])).
% 1.61/1.29 tff(300,plain,
% 1.61/1.29 (hskp17 | hskp8 | hskp4),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[299, 296])).
% 1.61/1.29 tff(301,plain,
% 1.61/1.29 (hskp17 | hskp8 | hskp4),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[300, 296])).
% 1.61/1.29 tff(302,plain,
% 1.61/1.29 (hskp17 | hskp8 | hskp4),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[301, 296])).
% 1.61/1.29 tff(303,plain,
% 1.61/1.30 (hskp17 | hskp8 | hskp4),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[302, 296])).
% 1.61/1.30 tff(304,plain,
% 1.61/1.30 (hskp17 | hskp8 | hskp4),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[303, 296])).
% 1.61/1.30 tff(305,plain,
% 1.61/1.30 (hskp17 | hskp8 | hskp4),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[304, 296])).
% 1.61/1.30 tff(306,plain,
% 1.61/1.30 (hskp17 | hskp8 | hskp4),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[305, 296])).
% 1.61/1.30 tff(307,plain,
% 1.61/1.30 (hskp17),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[306, 295, 178])).
% 1.61/1.30 tff(308,plain,
% 1.61/1.30 (((~hskp17) | c0_1(a31)) <=> ((~hskp17) | c0_1(a31))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(309,axiom,((~hskp17) | c0_1(a31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.61/1.30 tff(310,plain,
% 1.61/1.30 ((~hskp17) | c0_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[309, 308])).
% 1.61/1.30 tff(311,plain,
% 1.61/1.30 ((~hskp17) | c0_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[310, 308])).
% 1.61/1.30 tff(312,plain,
% 1.61/1.30 ((~hskp17) | c0_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[311, 308])).
% 1.61/1.30 tff(313,plain,
% 1.61/1.30 ((~hskp17) | c0_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[312, 308])).
% 1.61/1.30 tff(314,plain,
% 1.61/1.30 ((~hskp17) | c0_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[313, 308])).
% 1.61/1.30 tff(315,plain,
% 1.61/1.30 ((~hskp17) | c0_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[314, 308])).
% 1.61/1.30 tff(316,plain,
% 1.61/1.30 ((~hskp17) | c0_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[315, 308])).
% 1.61/1.30 tff(317,plain,
% 1.61/1.30 ((~hskp17) | c0_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[316, 308])).
% 1.61/1.30 tff(318,plain,
% 1.61/1.30 (c0_1(a31)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[317, 307])).
% 1.61/1.30 tff(319,plain,
% 1.61/1.30 (((~hskp17) | c2_1(a31)) <=> ((~hskp17) | c2_1(a31))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(320,axiom,((~hskp17) | c2_1(a31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.61/1.30 tff(321,plain,
% 1.61/1.30 ((~hskp17) | c2_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[320, 319])).
% 1.61/1.30 tff(322,plain,
% 1.61/1.30 ((~hskp17) | c2_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[321, 319])).
% 1.61/1.30 tff(323,plain,
% 1.61/1.30 ((~hskp17) | c2_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[322, 319])).
% 1.61/1.30 tff(324,plain,
% 1.61/1.30 ((~hskp17) | c2_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[323, 319])).
% 1.61/1.30 tff(325,plain,
% 1.61/1.30 ((~hskp17) | c2_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[324, 319])).
% 1.61/1.30 tff(326,plain,
% 1.61/1.30 ((~hskp17) | c2_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[325, 319])).
% 1.61/1.30 tff(327,plain,
% 1.61/1.30 ((~hskp17) | c2_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[326, 319])).
% 1.61/1.30 tff(328,plain,
% 1.61/1.30 ((~hskp17) | c2_1(a31)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[327, 319])).
% 1.61/1.30 tff(329,plain,
% 1.61/1.30 (c2_1(a31)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[328, 307])).
% 1.61/1.30 tff(330,plain,
% 1.61/1.30 (~c1_1(a31)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[71, 307])).
% 1.61/1.30 tff(331,assumption,(c0_1(a31)), introduced(assumption)).
% 1.61/1.30 tff(332,assumption,(c2_1(a31)), introduced(assumption)).
% 1.61/1.30 tff(333,plain,
% 1.61/1.30 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 1.61/1.30 inference(bind,[status(th)],[])).
% 1.61/1.30 tff(334,plain,
% 1.61/1.30 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 1.61/1.30 inference(quant_intro,[status(thm)],[333])).
% 1.61/1.30 tff(335,plain,
% 1.61/1.30 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(336,plain,
% 1.61/1.30 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 1.61/1.30 inference(bind,[status(th)],[])).
% 1.61/1.30 tff(337,plain,
% 1.61/1.30 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 1.61/1.30 inference(quant_intro,[status(thm)],[336])).
% 1.61/1.30 tff(338,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.61/1.30 tff(339,plain,
% 1.61/1.30 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[338, 337])).
% 1.61/1.30 tff(340,plain,
% 1.61/1.30 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[339, 335])).
% 1.61/1.30 tff(341,plain,(
% 1.61/1.30 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 1.61/1.30 inference(skolemize,[status(sab)],[340])).
% 1.61/1.30 tff(342,plain,
% 1.61/1.30 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[341, 334])).
% 1.61/1.30 tff(343,assumption,(~c1_1(a31)), introduced(assumption)).
% 1.61/1.30 tff(344,assumption,(~hskp0), introduced(assumption)).
% 1.61/1.30 tff(345,plain,
% 1.61/1.30 (hskp23),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[253, 344, 73])).
% 1.61/1.30 tff(346,plain,
% 1.61/1.30 (~c1_1(a53)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[212, 345])).
% 1.61/1.30 tff(347,plain,
% 1.61/1.30 (~c0_1(a53)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[218, 345])).
% 1.61/1.30 tff(348,plain,
% 1.61/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | c2_1(a53))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(349,plain,
% 1.61/1.30 ((hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | c2_1(a53)) <=> (hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | c2_1(a53))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(350,plain,
% 1.61/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | c2_1(a53)))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[349])).
% 1.61/1.30 tff(351,plain,
% 1.61/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | c2_1(a53))),
% 1.61/1.30 inference(transitivity,[status(thm)],[350, 348])).
% 1.61/1.30 tff(352,plain,
% 1.61/1.30 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | c2_1(a53))),
% 1.61/1.30 inference(quant_inst,[status(thm)],[])).
% 1.61/1.30 tff(353,plain,
% 1.61/1.30 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | c2_1(a53)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[352, 351])).
% 1.61/1.30 tff(354,plain,
% 1.61/1.30 (c2_1(a53)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[353, 169, 344, 331, 332, 347, 346, 343, 342])).
% 1.61/1.30 tff(355,plain,
% 1.61/1.30 (c3_1(a53)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[229, 345])).
% 1.61/1.30 tff(356,assumption,(hskp3), introduced(assumption)).
% 1.61/1.30 tff(357,plain,
% 1.61/1.30 (((~hskp3) | (~c2_1(a5))) <=> ((~hskp3) | (~c2_1(a5)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(358,plain,
% 1.61/1.30 (((~c2_1(a5)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a5)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(359,axiom,((~c2_1(a5)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 1.61/1.30 tff(360,plain,
% 1.61/1.30 ((~hskp3) | (~c2_1(a5))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.61/1.30 tff(361,plain,
% 1.61/1.30 ((~hskp3) | (~c2_1(a5))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[360, 357])).
% 1.61/1.30 tff(362,plain,
% 1.61/1.30 (~c2_1(a5)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[361, 356])).
% 1.61/1.30 tff(363,plain,
% 1.61/1.30 (((~hskp3) | (~c1_1(a5))) <=> ((~hskp3) | (~c1_1(a5)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(364,plain,
% 1.61/1.30 (((~c1_1(a5)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a5)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(365,axiom,((~c1_1(a5)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.61/1.30 tff(366,plain,
% 1.61/1.30 ((~hskp3) | (~c1_1(a5))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[365, 364])).
% 1.61/1.30 tff(367,plain,
% 1.61/1.30 ((~hskp3) | (~c1_1(a5))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[366, 363])).
% 1.61/1.30 tff(368,plain,
% 1.61/1.30 (~c1_1(a5)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[367, 356])).
% 1.61/1.30 tff(369,assumption,(~c1_1(a53)), introduced(assumption)).
% 1.61/1.30 tff(370,assumption,(~c0_1(a53)), introduced(assumption)).
% 1.61/1.30 tff(371,assumption,(c3_1(a53)), introduced(assumption)).
% 1.61/1.30 tff(372,plain,
% 1.61/1.30 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a53)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a53)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(373,plain,
% 1.61/1.30 ((hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53))) <=> (hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a53)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(374,plain,
% 1.61/1.30 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a53))))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[373])).
% 1.61/1.30 tff(375,plain,
% 1.61/1.30 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a53)))),
% 1.61/1.30 inference(transitivity,[status(thm)],[374, 372])).
% 1.61/1.30 tff(376,plain,
% 1.61/1.30 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a53) | c0_1(a53) | (~c3_1(a53)))),
% 1.61/1.30 inference(quant_inst,[status(thm)],[])).
% 1.61/1.30 tff(377,plain,
% 1.61/1.30 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a53) | c1_1(a53) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a53))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[376, 375])).
% 1.61/1.30 tff(378,plain,
% 1.61/1.30 (~c0_1(a5)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[377, 169, 205, 371, 370, 369, 368, 362, 65])).
% 1.61/1.30 tff(379,plain,
% 1.61/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a31)) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a31)) | (~c0_1(a31)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(380,plain,
% 1.61/1.30 ((hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a5) | c0_1(a5) | c2_1(a5)) <=> (hskp0 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a31)) | (~c0_1(a31)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(381,plain,
% 1.61/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a5) | c0_1(a5) | c2_1(a5))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a31)) | (~c0_1(a31))))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[380])).
% 1.61/1.30 tff(382,plain,
% 1.61/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a5) | c0_1(a5) | c2_1(a5))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a31)) | (~c0_1(a31)))),
% 1.61/1.30 inference(transitivity,[status(thm)],[381, 379])).
% 1.61/1.30 tff(383,plain,
% 1.61/1.30 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c1_1(a5) | c0_1(a5) | c2_1(a5))),
% 1.61/1.30 inference(quant_inst,[status(thm)],[])).
% 1.61/1.30 tff(384,plain,
% 1.61/1.30 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a31)) | (~c0_1(a31))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[383, 382])).
% 1.61/1.30 tff(385,plain,
% 1.61/1.30 ($false),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[384, 169, 344, 331, 332, 343, 368, 362, 342, 378])).
% 1.61/1.30 tff(386,plain,((~hskp3) | hskp0 | (~c0_1(a31)) | (~c2_1(a31)) | c1_1(a31) | hskp4 | (~c3_1(a53)) | c0_1(a53) | c1_1(a53)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.30 tff(387,plain,
% 1.61/1.30 (~hskp3),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[386, 344, 331, 332, 343, 205, 355, 347, 346])).
% 1.61/1.30 tff(388,plain,
% 1.61/1.30 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c2_1(a53)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c2_1(a53)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(389,plain,
% 1.61/1.30 ((hskp3 | hskp2 | (~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | c0_1(a53)) <=> (hskp3 | hskp2 | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c2_1(a53)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(390,plain,
% 1.61/1.30 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | c0_1(a53))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c2_1(a53))))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[389])).
% 1.61/1.30 tff(391,plain,
% 1.61/1.30 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | c0_1(a53))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c2_1(a53)))),
% 1.61/1.30 inference(transitivity,[status(thm)],[390, 388])).
% 1.61/1.30 tff(392,plain,
% 1.61/1.30 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | c0_1(a53))),
% 1.61/1.30 inference(quant_inst,[status(thm)],[])).
% 1.61/1.30 tff(393,plain,
% 1.61/1.30 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c2_1(a53))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[392, 391])).
% 1.61/1.30 tff(394,plain,
% 1.61/1.30 (hskp3 | hskp2 | (~c2_1(a53))),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[393, 169, 347, 346, 23])).
% 1.61/1.30 tff(395,plain,
% 1.61/1.30 (hskp2),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[394, 387, 354])).
% 1.61/1.30 tff(396,plain,
% 1.61/1.30 (((~hskp2) | (~c3_1(a4))) <=> ((~hskp2) | (~c3_1(a4)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(397,plain,
% 1.61/1.30 (((~c3_1(a4)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a4)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(398,axiom,((~c3_1(a4)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.61/1.30 tff(399,plain,
% 1.61/1.30 ((~hskp2) | (~c3_1(a4))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[398, 397])).
% 1.61/1.30 tff(400,plain,
% 1.61/1.30 ((~hskp2) | (~c3_1(a4))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[399, 396])).
% 1.61/1.30 tff(401,plain,
% 1.61/1.30 (~c3_1(a4)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[400, 395])).
% 1.61/1.30 tff(402,plain,
% 1.61/1.30 (((~hskp2) | c1_1(a4)) <=> ((~hskp2) | c1_1(a4))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(403,axiom,((~hskp2) | c1_1(a4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.61/1.30 tff(404,plain,
% 1.61/1.30 ((~hskp2) | c1_1(a4)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[403, 402])).
% 1.61/1.30 tff(405,plain,
% 1.61/1.30 ((~hskp2) | c1_1(a4)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[404, 402])).
% 1.61/1.30 tff(406,plain,
% 1.61/1.30 ((~hskp2) | c1_1(a4)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[405, 402])).
% 1.61/1.30 tff(407,plain,
% 1.61/1.30 ((~hskp2) | c1_1(a4)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[406, 402])).
% 1.61/1.30 tff(408,plain,
% 1.61/1.30 ((~hskp2) | c1_1(a4)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[407, 402])).
% 1.61/1.30 tff(409,plain,
% 1.61/1.30 ((~hskp2) | c1_1(a4)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[408, 402])).
% 1.61/1.30 tff(410,plain,
% 1.61/1.30 ((~hskp2) | c1_1(a4)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[409, 402])).
% 1.61/1.30 tff(411,plain,
% 1.61/1.30 ((~hskp2) | c1_1(a4)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[410, 402])).
% 1.61/1.30 tff(412,plain,
% 1.61/1.30 (c1_1(a4)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[411, 395])).
% 1.61/1.30 tff(413,plain,
% 1.61/1.30 (((~hskp2) | (~c2_1(a4))) <=> ((~hskp2) | (~c2_1(a4)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(414,plain,
% 1.61/1.30 (((~c2_1(a4)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a4)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(415,axiom,((~c2_1(a4)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.61/1.30 tff(416,plain,
% 1.61/1.30 ((~hskp2) | (~c2_1(a4))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[415, 414])).
% 1.61/1.30 tff(417,plain,
% 1.61/1.30 ((~hskp2) | (~c2_1(a4))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[416, 413])).
% 1.61/1.30 tff(418,plain,
% 1.61/1.30 (~c2_1(a4)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[417, 395])).
% 1.61/1.30 tff(419,assumption,(c2_1(a53)), introduced(assumption)).
% 1.61/1.30 tff(420,assumption,(~c3_1(a4)), introduced(assumption)).
% 1.61/1.30 tff(421,assumption,(c1_1(a4)), introduced(assumption)).
% 1.61/1.30 tff(422,plain,
% 1.61/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a53)) | (~c3_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(423,plain,
% 1.61/1.30 (((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a53) | c1_1(a53) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(424,plain,
% 1.61/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a53)) | (~c3_1(a53))))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[423])).
% 1.61/1.30 tff(425,plain,
% 1.61/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.61/1.30 inference(transitivity,[status(thm)],[424, 422])).
% 1.61/1.30 tff(426,plain,
% 1.61/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 1.61/1.30 inference(quant_inst,[status(thm)],[])).
% 1.61/1.30 tff(427,plain,
% 1.61/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a53)) | (~c3_1(a53))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[426, 425])).
% 1.61/1.30 tff(428,plain,
% 1.61/1.30 (c0_1(a4) | (~c2_1(a53))),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[427, 169, 371, 421, 370, 369, 420, 83])).
% 1.61/1.30 tff(429,plain,
% 1.61/1.30 (c0_1(a4)),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[428, 419])).
% 1.61/1.30 tff(430,plain,
% 1.61/1.30 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))))),
% 1.61/1.30 inference(bind,[status(th)],[])).
% 1.61/1.30 tff(431,plain,
% 1.61/1.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.61/1.30 inference(quant_intro,[status(thm)],[430])).
% 1.61/1.30 tff(432,plain,
% 1.61/1.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(433,plain,
% 1.61/1.30 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(U)) | (~c0_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) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))))),
% 1.61/1.31 inference(bind,[status(th)],[])).
% 1.61/1.31 tff(434,plain,
% 1.61/1.31 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.61/1.31 inference(quant_intro,[status(thm)],[433])).
% 1.61/1.31 tff(435,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 1.61/1.31 tff(436,plain,
% 1.61/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[435, 434])).
% 1.61/1.31 tff(437,plain,
% 1.61/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[436, 432])).
% 1.61/1.31 tff(438,plain,(
% 1.61/1.31 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.61/1.31 inference(skolemize,[status(sab)],[437])).
% 1.61/1.31 tff(439,plain,
% 1.61/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[438, 431])).
% 1.61/1.31 tff(440,assumption,(~c2_1(a4)), introduced(assumption)).
% 1.61/1.31 tff(441,plain,
% 1.61/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(442,plain,
% 1.61/1.31 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4))) <=> (c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(443,plain,
% 1.61/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.61/1.31 inference(monotonicity,[status(thm)],[442])).
% 1.61/1.31 tff(444,plain,
% 1.61/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.61/1.31 inference(transitivity,[status(thm)],[443, 441])).
% 1.61/1.31 tff(445,plain,
% 1.61/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4)))),
% 1.61/1.31 inference(quant_inst,[status(thm)],[])).
% 1.61/1.31 tff(446,plain,
% 1.61/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[445, 444])).
% 1.61/1.31 tff(447,plain,
% 1.61/1.31 ((~c0_1(a4)) | (~c3_1(a31))),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[446, 169, 331, 332, 421, 440, 420, 439])).
% 1.61/1.31 tff(448,plain,
% 1.61/1.31 (~c3_1(a31)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[447, 429])).
% 1.61/1.31 tff(449,plain,
% 1.61/1.31 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.61/1.31 inference(bind,[status(th)],[])).
% 1.61/1.31 tff(450,plain,
% 1.61/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.31 inference(quant_intro,[status(thm)],[449])).
% 1.61/1.31 tff(451,plain,
% 1.61/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(452,plain,
% 1.61/1.31 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | 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) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | 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) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | 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) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | 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) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | 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) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | 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) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.61/1.31 inference(bind,[status(th)],[])).
% 1.61/1.31 tff(453,plain,
% 1.61/1.31 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_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) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.31 inference(quant_intro,[status(thm)],[452])).
% 1.61/1.31 tff(454,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 1.61/1.31 tff(455,plain,
% 1.61/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[454, 453])).
% 1.61/1.31 tff(456,plain,
% 1.61/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[455, 451])).
% 1.61/1.31 tff(457,plain,(
% 1.61/1.31 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.31 inference(skolemize,[status(sab)],[456])).
% 1.61/1.31 tff(458,plain,
% 1.61/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[457, 450])).
% 1.61/1.31 tff(459,plain,
% 1.61/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a31) | (~c0_1(a31)) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a31) | (~c0_1(a31)) | (~c2_1(a53)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(460,plain,
% 1.61/1.31 (((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a31) | (~c0_1(a31)) | (~c2_1(a53)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(461,plain,
% 1.61/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a31) | (~c0_1(a31)) | (~c2_1(a53))))),
% 1.61/1.31 inference(monotonicity,[status(thm)],[460])).
% 1.61/1.31 tff(462,plain,
% 1.61/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a31) | (~c0_1(a31)) | (~c2_1(a53)))),
% 1.61/1.31 inference(transitivity,[status(thm)],[461, 459])).
% 1.61/1.31 tff(463,plain,
% 1.61/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 1.61/1.31 inference(quant_inst,[status(thm)],[])).
% 1.61/1.31 tff(464,plain,
% 1.61/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a31) | (~c0_1(a31)) | (~c2_1(a53))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[463, 462])).
% 1.61/1.31 tff(465,plain,
% 1.61/1.31 ($false),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[464, 169, 331, 421, 370, 369, 343, 440, 420, 458, 448, 419])).
% 1.61/1.31 tff(466,plain,((~c2_1(a53)) | (~c0_1(a31)) | (~c1_1(a4)) | c0_1(a53) | c1_1(a53) | c1_1(a31) | c2_1(a4) | c3_1(a4) | (~c2_1(a31)) | (~c3_1(a53))), inference(lemma,lemma(discharge,[]))).
% 1.61/1.31 tff(467,plain,
% 1.61/1.31 ($false),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[466, 418, 412, 355, 347, 346, 343, 354, 401, 332, 331])).
% 1.61/1.31 tff(468,plain,(hskp0 | c1_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | hskp4 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.61/1.31 tff(469,plain,
% 1.61/1.31 (hskp0),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[468, 330, 329, 318, 178, 73])).
% 1.61/1.31 tff(470,assumption,(hskp0), introduced(assumption)).
% 1.61/1.31 tff(471,plain,
% 1.61/1.31 (~c2_1(a1)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[259, 470])).
% 1.61/1.31 tff(472,plain,
% 1.61/1.31 (~c0_1(a1)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[283, 470])).
% 1.61/1.31 tff(473,assumption,(hskp13), introduced(assumption)).
% 1.61/1.31 tff(474,plain,
% 1.61/1.31 (c3_1(a1)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[270, 470])).
% 1.61/1.31 tff(475,assumption,(~c1_1(a1)), introduced(assumption)).
% 1.61/1.31 tff(476,assumption,(~c2_1(a1)), introduced(assumption)).
% 1.61/1.31 tff(477,assumption,(~c0_1(a1)), introduced(assumption)).
% 1.61/1.31 tff(478,plain,
% 1.61/1.31 (((~hskp13) | (~c3_1(a22))) <=> ((~hskp13) | (~c3_1(a22)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(479,plain,
% 1.61/1.31 (((~c3_1(a22)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a22)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(480,axiom,((~c3_1(a22)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.61/1.31 tff(481,plain,
% 1.61/1.31 ((~hskp13) | (~c3_1(a22))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[480, 479])).
% 1.61/1.31 tff(482,plain,
% 1.61/1.31 ((~hskp13) | (~c3_1(a22))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[481, 478])).
% 1.61/1.31 tff(483,plain,
% 1.61/1.31 (~c3_1(a22)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[482, 473])).
% 1.61/1.31 tff(484,plain,
% 1.61/1.31 (((~hskp13) | (~c2_1(a22))) <=> ((~hskp13) | (~c2_1(a22)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(485,plain,
% 1.61/1.31 (((~c2_1(a22)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a22)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(486,axiom,((~c2_1(a22)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 1.61/1.31 tff(487,plain,
% 1.61/1.31 ((~hskp13) | (~c2_1(a22))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[486, 485])).
% 1.61/1.31 tff(488,plain,
% 1.61/1.31 ((~hskp13) | (~c2_1(a22))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[487, 484])).
% 1.61/1.31 tff(489,plain,
% 1.61/1.31 (~c2_1(a22)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[488, 473])).
% 1.61/1.31 tff(490,plain,
% 1.61/1.31 (((~hskp13) | (~c0_1(a22))) <=> ((~hskp13) | (~c0_1(a22)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(491,plain,
% 1.61/1.31 (((~c0_1(a22)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a22)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(492,axiom,((~c0_1(a22)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.61/1.31 tff(493,plain,
% 1.61/1.31 ((~hskp13) | (~c0_1(a22))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[492, 491])).
% 1.61/1.31 tff(494,plain,
% 1.61/1.31 ((~hskp13) | (~c0_1(a22))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[493, 490])).
% 1.61/1.31 tff(495,plain,
% 1.61/1.31 (~c0_1(a22)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[494, 473])).
% 1.61/1.31 tff(496,assumption,(c3_1(a1)), introduced(assumption)).
% 1.61/1.31 tff(497,plain,
% 1.61/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(498,plain,
% 1.61/1.31 (((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a22) | c0_1(a22) | c2_1(a22) | c2_1(a1) | c1_1(a1) | c0_1(a1)) <=> (c0_1(a22) | c2_1(a22) | c3_1(a22) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(499,plain,
% 1.61/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a22) | c0_1(a22) | c2_1(a22) | c2_1(a1) | c1_1(a1) | c0_1(a1))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1))))),
% 1.61/1.31 inference(monotonicity,[status(thm)],[498])).
% 1.61/1.31 tff(500,plain,
% 1.61/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a22) | c0_1(a22) | c2_1(a22) | c2_1(a1) | c1_1(a1) | c0_1(a1))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)))),
% 1.61/1.31 inference(transitivity,[status(thm)],[499, 497])).
% 1.61/1.31 tff(501,plain,
% 1.61/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a22) | c0_1(a22) | c2_1(a22) | c2_1(a1) | c1_1(a1) | c0_1(a1))),
% 1.61/1.31 inference(quant_inst,[status(thm)],[])).
% 1.61/1.31 tff(502,plain,
% 1.61/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[501, 500])).
% 1.61/1.31 tff(503,plain,
% 1.61/1.31 ($false),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[502, 169, 496, 495, 489, 483, 477, 476, 55, 475])).
% 1.61/1.31 tff(504,plain,((~hskp13) | (~c3_1(a1)) | c0_1(a1) | c2_1(a1) | c1_1(a1)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.31 tff(505,plain,
% 1.61/1.31 (c1_1(a1)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[504, 474, 473, 472, 471])).
% 1.61/1.31 tff(506,plain,
% 1.61/1.31 ($false),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[277, 169, 73, 105, 474, 471, 104, 505])).
% 1.61/1.31 tff(507,plain,((~hskp0) | hskp24 | hskp9 | (~hskp13)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.31 tff(508,plain,
% 1.61/1.31 (~hskp13),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[507, 469, 73, 105])).
% 1.61/1.31 tff(509,plain,
% 1.61/1.31 ((hskp13 | hskp9 | hskp7) <=> (hskp13 | hskp9 | hskp7)),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(510,plain,
% 1.61/1.31 (((hskp7 | hskp9) | hskp13) <=> (hskp13 | hskp9 | hskp7)),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(511,axiom,((hskp7 | hskp9) | hskp13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 1.61/1.31 tff(512,plain,
% 1.61/1.31 (hskp13 | hskp9 | hskp7),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[511, 510])).
% 1.61/1.31 tff(513,plain,
% 1.61/1.31 (hskp13 | hskp9 | hskp7),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[512, 509])).
% 1.61/1.31 tff(514,plain,
% 1.61/1.31 (hskp13 | hskp9 | hskp7),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[513, 509])).
% 1.61/1.31 tff(515,plain,
% 1.61/1.31 (hskp13 | hskp9 | hskp7),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[514, 509])).
% 1.61/1.31 tff(516,plain,
% 1.61/1.31 (hskp13 | hskp9 | hskp7),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[515, 509])).
% 1.61/1.31 tff(517,plain,
% 1.61/1.31 (hskp13 | hskp9 | hskp7),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[516, 509])).
% 1.61/1.31 tff(518,plain,
% 1.61/1.31 (hskp13 | hskp9 | hskp7),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[517, 509])).
% 1.61/1.31 tff(519,plain,
% 1.61/1.31 (hskp13 | hskp9 | hskp7),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[518, 509])).
% 1.61/1.31 tff(520,plain,
% 1.61/1.31 (hskp7),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[519, 508, 105])).
% 1.61/1.31 tff(521,plain,
% 1.61/1.31 (((~hskp7) | (~c2_1(a14))) <=> ((~hskp7) | (~c2_1(a14)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(522,plain,
% 1.61/1.31 (((~c2_1(a14)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a14)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(523,axiom,((~c2_1(a14)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.61/1.31 tff(524,plain,
% 1.61/1.31 ((~hskp7) | (~c2_1(a14))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[523, 522])).
% 1.61/1.31 tff(525,plain,
% 1.61/1.31 ((~hskp7) | (~c2_1(a14))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[524, 521])).
% 1.61/1.31 tff(526,plain,
% 1.61/1.31 (~c2_1(a14)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[525, 520])).
% 1.61/1.31 tff(527,plain,
% 1.61/1.31 (((~hskp7) | c3_1(a14)) <=> ((~hskp7) | c3_1(a14))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(528,axiom,((~hskp7) | c3_1(a14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.61/1.31 tff(529,plain,
% 1.61/1.31 ((~hskp7) | c3_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[528, 527])).
% 1.61/1.31 tff(530,plain,
% 1.61/1.31 ((~hskp7) | c3_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[529, 527])).
% 1.61/1.31 tff(531,plain,
% 1.61/1.31 ((~hskp7) | c3_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[530, 527])).
% 1.61/1.31 tff(532,plain,
% 1.61/1.31 ((~hskp7) | c3_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[531, 527])).
% 1.61/1.31 tff(533,plain,
% 1.61/1.31 ((~hskp7) | c3_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[532, 527])).
% 1.61/1.31 tff(534,plain,
% 1.61/1.31 ((~hskp7) | c3_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[533, 527])).
% 1.61/1.31 tff(535,plain,
% 1.61/1.31 ((~hskp7) | c3_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[534, 527])).
% 1.61/1.31 tff(536,plain,
% 1.61/1.31 ((~hskp7) | c3_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[535, 527])).
% 1.61/1.31 tff(537,plain,
% 1.61/1.31 (c3_1(a14)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[536, 520])).
% 1.61/1.31 tff(538,plain,
% 1.61/1.31 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(539,plain,
% 1.61/1.31 ((hskp24 | hskp9 | (~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14))) <=> (hskp24 | hskp9 | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(540,plain,
% 1.61/1.31 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14))))),
% 1.61/1.31 inference(monotonicity,[status(thm)],[539])).
% 1.61/1.31 tff(541,plain,
% 1.61/1.31 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)))),
% 1.61/1.31 inference(transitivity,[status(thm)],[540, 538])).
% 1.61/1.31 tff(542,plain,
% 1.61/1.31 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)))),
% 1.61/1.31 inference(quant_inst,[status(thm)],[])).
% 1.61/1.31 tff(543,plain,
% 1.61/1.31 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[542, 541])).
% 1.61/1.31 tff(544,plain,
% 1.61/1.31 (~c1_1(a14)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[543, 169, 73, 105, 537, 526, 104])).
% 1.61/1.31 tff(545,plain,
% 1.61/1.31 (~c2_1(a1)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[259, 469])).
% 1.61/1.31 tff(546,plain,
% 1.61/1.31 (c3_1(a1)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[270, 469])).
% 1.61/1.31 tff(547,plain,
% 1.61/1.31 (~c1_1(a1)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[277, 169, 73, 105, 546, 545, 104])).
% 1.61/1.31 tff(548,plain,
% 1.61/1.31 (~c0_1(a1)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[283, 469])).
% 1.61/1.31 tff(549,plain,
% 1.61/1.31 (((~hskp7) | c0_1(a14)) <=> ((~hskp7) | c0_1(a14))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(550,axiom,((~hskp7) | c0_1(a14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.61/1.31 tff(551,plain,
% 1.61/1.31 ((~hskp7) | c0_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[550, 549])).
% 1.61/1.31 tff(552,plain,
% 1.61/1.31 ((~hskp7) | c0_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[551, 549])).
% 1.61/1.31 tff(553,plain,
% 1.61/1.31 ((~hskp7) | c0_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[552, 549])).
% 1.61/1.31 tff(554,plain,
% 1.61/1.31 ((~hskp7) | c0_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[553, 549])).
% 1.61/1.31 tff(555,plain,
% 1.61/1.31 ((~hskp7) | c0_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[554, 549])).
% 1.61/1.31 tff(556,plain,
% 1.61/1.31 ((~hskp7) | c0_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[555, 549])).
% 1.61/1.31 tff(557,plain,
% 1.61/1.31 ((~hskp7) | c0_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[556, 549])).
% 1.61/1.31 tff(558,plain,
% 1.61/1.31 ((~hskp7) | c0_1(a14)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[557, 549])).
% 1.61/1.31 tff(559,plain,
% 1.61/1.31 (c0_1(a14)),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[558, 520])).
% 1.61/1.31 tff(560,plain,
% 1.61/1.31 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a14) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c1_1(a14) | (~c0_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a14) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c1_1(a14) | (~c0_1(a14)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(561,plain,
% 1.61/1.31 ((hskp4 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1))) <=> (hskp4 | c2_1(a14) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c1_1(a14) | (~c0_1(a14)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(562,plain,
% 1.61/1.32 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a14) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c1_1(a14) | (~c0_1(a14))))),
% 1.61/1.32 inference(monotonicity,[status(thm)],[561])).
% 1.61/1.32 tff(563,plain,
% 1.61/1.32 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a14) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c1_1(a14) | (~c0_1(a14)))),
% 1.61/1.32 inference(transitivity,[status(thm)],[562, 560])).
% 1.61/1.32 tff(564,plain,
% 1.61/1.32 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)) | c1_1(a1) | c0_1(a1) | (~c3_1(a1)))),
% 1.61/1.32 inference(quant_inst,[status(thm)],[])).
% 1.61/1.32 tff(565,plain,
% 1.61/1.32 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a14) | c0_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c1_1(a14) | (~c0_1(a14))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[564, 563])).
% 1.61/1.32 tff(566,plain,
% 1.61/1.32 ($false),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[565, 169, 178, 559, 546, 526, 548, 65, 547, 544])).
% 1.61/1.32 tff(567,plain,(hskp9 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.61/1.32 tff(568,plain,
% 1.61/1.32 (hskp9),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[567, 73])).
% 1.61/1.32 tff(569,plain,
% 1.61/1.32 (((~hskp9) | (~c3_1(a16))) <=> ((~hskp9) | (~c3_1(a16)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(570,plain,
% 1.61/1.32 (((~c3_1(a16)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a16)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(571,axiom,((~c3_1(a16)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.61/1.32 tff(572,plain,
% 1.61/1.32 ((~hskp9) | (~c3_1(a16))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[571, 570])).
% 1.61/1.32 tff(573,plain,
% 1.61/1.32 ((~hskp9) | (~c3_1(a16))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[572, 569])).
% 1.61/1.32 tff(574,plain,
% 1.61/1.32 (~c3_1(a16)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[573, 568])).
% 1.61/1.32 tff(575,plain,
% 1.61/1.32 (((~hskp9) | (~c2_1(a16))) <=> ((~hskp9) | (~c2_1(a16)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(576,plain,
% 1.61/1.32 (((~c2_1(a16)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a16)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(577,axiom,((~c2_1(a16)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.61/1.32 tff(578,plain,
% 1.61/1.32 ((~hskp9) | (~c2_1(a16))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[577, 576])).
% 1.61/1.32 tff(579,plain,
% 1.61/1.32 ((~hskp9) | (~c2_1(a16))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[578, 575])).
% 1.61/1.32 tff(580,plain,
% 1.61/1.32 (~c2_1(a16)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[579, 568])).
% 1.61/1.32 tff(581,plain,
% 1.61/1.32 (((~hskp9) | c0_1(a16)) <=> ((~hskp9) | c0_1(a16))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(582,axiom,((~hskp9) | c0_1(a16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.61/1.32 tff(583,plain,
% 1.61/1.32 ((~hskp9) | c0_1(a16)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[582, 581])).
% 1.61/1.32 tff(584,plain,
% 1.61/1.32 ((~hskp9) | c0_1(a16)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[583, 581])).
% 1.61/1.32 tff(585,plain,
% 1.61/1.32 ((~hskp9) | c0_1(a16)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[584, 581])).
% 1.61/1.32 tff(586,plain,
% 1.61/1.32 ((~hskp9) | c0_1(a16)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[585, 581])).
% 1.61/1.32 tff(587,plain,
% 1.61/1.32 ((~hskp9) | c0_1(a16)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[586, 581])).
% 1.61/1.32 tff(588,plain,
% 1.61/1.32 ((~hskp9) | c0_1(a16)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[587, 581])).
% 1.61/1.32 tff(589,plain,
% 1.61/1.32 ((~hskp9) | c0_1(a16)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[588, 581])).
% 1.61/1.32 tff(590,plain,
% 1.61/1.32 ((~hskp9) | c0_1(a16)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[589, 581])).
% 1.61/1.32 tff(591,plain,
% 1.61/1.32 (c0_1(a16)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[590, 568])).
% 1.61/1.32 tff(592,plain,
% 1.61/1.32 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp26 | hskp16 | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(593,plain,
% 1.61/1.32 ((hskp26 | hskp16 | (~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c0_1(a16))) <=> (hskp26 | hskp16 | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(594,plain,
% 1.61/1.32 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16))))),
% 1.61/1.32 inference(monotonicity,[status(thm)],[593])).
% 1.61/1.32 tff(595,plain,
% 1.61/1.32 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp26 | hskp16 | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))),
% 1.61/1.32 inference(transitivity,[status(thm)],[594, 592])).
% 1.61/1.32 tff(596,plain,
% 1.61/1.32 ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c0_1(a16)))),
% 1.61/1.32 inference(quant_inst,[status(thm)],[])).
% 1.61/1.32 tff(597,plain,
% 1.61/1.32 ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp26 | hskp16 | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[596, 595])).
% 1.61/1.32 tff(598,plain,
% 1.61/1.32 (hskp26 | hskp16),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[597, 169, 591, 580, 574, 94])).
% 1.61/1.32 tff(599,plain,
% 1.61/1.32 (hskp16),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[598, 84])).
% 1.61/1.32 tff(600,plain,
% 1.61/1.32 (((~hskp16) | c1_1(a30)) <=> ((~hskp16) | c1_1(a30))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(601,axiom,((~hskp16) | c1_1(a30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.61/1.32 tff(602,plain,
% 1.61/1.32 ((~hskp16) | c1_1(a30)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[601, 600])).
% 1.61/1.32 tff(603,plain,
% 1.61/1.32 ((~hskp16) | c1_1(a30)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[602, 600])).
% 1.61/1.32 tff(604,plain,
% 1.61/1.32 ((~hskp16) | c1_1(a30)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[603, 600])).
% 1.61/1.32 tff(605,plain,
% 1.61/1.32 ((~hskp16) | c1_1(a30)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[604, 600])).
% 1.61/1.32 tff(606,plain,
% 1.61/1.32 ((~hskp16) | c1_1(a30)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[605, 600])).
% 1.61/1.32 tff(607,plain,
% 1.61/1.32 ((~hskp16) | c1_1(a30)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[606, 600])).
% 1.61/1.32 tff(608,plain,
% 1.61/1.32 ((~hskp16) | c1_1(a30)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[607, 600])).
% 1.61/1.32 tff(609,plain,
% 1.61/1.32 ((~hskp16) | c1_1(a30)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[608, 600])).
% 1.61/1.32 tff(610,plain,
% 1.61/1.32 (c1_1(a30)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[609, 599])).
% 1.61/1.32 tff(611,plain,
% 1.61/1.32 (((~hskp16) | (~c2_1(a30))) <=> ((~hskp16) | (~c2_1(a30)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(612,plain,
% 1.61/1.32 (((~c2_1(a30)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a30)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(613,axiom,((~c2_1(a30)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.61/1.32 tff(614,plain,
% 1.61/1.32 ((~hskp16) | (~c2_1(a30))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[613, 612])).
% 1.61/1.32 tff(615,plain,
% 1.61/1.32 ((~hskp16) | (~c2_1(a30))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[614, 611])).
% 1.61/1.32 tff(616,plain,
% 1.61/1.32 (~c2_1(a30)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[615, 599])).
% 1.61/1.32 tff(617,plain,
% 1.61/1.32 (((~hskp16) | (~c0_1(a30))) <=> ((~hskp16) | (~c0_1(a30)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(618,plain,
% 1.61/1.32 (((~c0_1(a30)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a30)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(619,axiom,((~c0_1(a30)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.61/1.32 tff(620,plain,
% 1.61/1.32 ((~hskp16) | (~c0_1(a30))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[619, 618])).
% 1.61/1.32 tff(621,plain,
% 1.61/1.32 ((~hskp16) | (~c0_1(a30))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[620, 617])).
% 1.61/1.32 tff(622,plain,
% 1.61/1.32 (~c0_1(a30)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[621, 599])).
% 1.61/1.32 tff(623,plain,
% 1.61/1.32 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.61/1.32 inference(bind,[status(th)],[])).
% 1.61/1.32 tff(624,plain,
% 1.61/1.32 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.32 inference(quant_intro,[status(thm)],[623])).
% 1.61/1.32 tff(625,plain,
% 1.61/1.32 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(626,plain,
% 1.61/1.32 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.61/1.32 inference(bind,[status(th)],[])).
% 1.61/1.32 tff(627,plain,
% 1.61/1.32 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.32 inference(quant_intro,[status(thm)],[626])).
% 1.61/1.32 tff(628,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 1.61/1.32 tff(629,plain,
% 1.61/1.32 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[628, 627])).
% 1.61/1.32 tff(630,plain,
% 1.61/1.32 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[629, 625])).
% 1.61/1.32 tff(631,plain,(
% 1.61/1.32 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.32 inference(skolemize,[status(sab)],[630])).
% 1.61/1.32 tff(632,plain,
% 1.61/1.32 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[631, 624])).
% 1.61/1.32 tff(633,assumption,(~c0_1(a30)), introduced(assumption)).
% 1.61/1.32 tff(634,assumption,(c1_1(a30)), introduced(assumption)).
% 1.61/1.32 tff(635,plain,
% 1.61/1.32 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c0_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(636,plain,
% 1.61/1.32 ((hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30))) <=> (hskp4 | c0_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(637,plain,
% 1.61/1.32 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c0_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30))))),
% 1.61/1.32 inference(monotonicity,[status(thm)],[636])).
% 1.61/1.32 tff(638,plain,
% 1.61/1.32 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.61/1.32 inference(transitivity,[status(thm)],[637, 635])).
% 1.61/1.32 tff(639,plain,
% 1.61/1.32 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))),
% 1.61/1.32 inference(quant_inst,[status(thm)],[])).
% 1.61/1.32 tff(640,plain,
% 1.61/1.32 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[639, 638])).
% 1.61/1.32 tff(641,plain,
% 1.61/1.32 (hskp4 | (~c3_1(a30))),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[640, 169, 634, 591, 633, 574, 632, 3])).
% 1.61/1.32 tff(642,plain,
% 1.61/1.32 (~c3_1(a30)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[641, 205])).
% 1.61/1.32 tff(643,assumption,(~hskp17), introduced(assumption)).
% 1.61/1.32 tff(644,plain,
% 1.61/1.32 (hskp8),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[306, 205, 643])).
% 1.61/1.32 tff(645,plain,
% 1.61/1.32 (~c2_1(a15)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[184, 644])).
% 1.61/1.32 tff(646,plain,
% 1.61/1.32 (c0_1(a15)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[195, 644])).
% 1.61/1.32 tff(647,plain,
% 1.61/1.32 (~c1_1(a15)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[201, 644])).
% 1.61/1.32 tff(648,plain,
% 1.61/1.32 ($false),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[238, 647, 646, 205, 207, 645])).
% 1.61/1.32 tff(649,plain,(hskp4 | (~hskp23) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.61/1.32 tff(650,plain,
% 1.61/1.32 (hskp4),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[649, 345, 643])).
% 1.61/1.32 tff(651,plain,
% 1.61/1.32 (~c2_1(a6)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[111, 650])).
% 1.61/1.32 tff(652,plain,
% 1.61/1.32 (c3_1(a6)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[122, 650])).
% 1.61/1.32 tff(653,plain,
% 1.61/1.32 (c1_1(a6)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[133, 650])).
% 1.61/1.32 tff(654,assumption,(~hskp2), introduced(assumption)).
% 1.61/1.32 tff(655,assumption,(~hskp14), introduced(assumption)).
% 1.61/1.32 tff(656,assumption,(hskp26), introduced(assumption)).
% 1.61/1.32 tff(657,plain,
% 1.61/1.32 (((~hskp26) | c0_1(a10)) <=> ((~hskp26) | c0_1(a10))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(658,axiom,((~hskp26) | c0_1(a10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 1.61/1.32 tff(659,plain,
% 1.61/1.32 ((~hskp26) | c0_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[658, 657])).
% 1.61/1.32 tff(660,plain,
% 1.61/1.32 ((~hskp26) | c0_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[659, 657])).
% 1.61/1.32 tff(661,plain,
% 1.61/1.32 ((~hskp26) | c0_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[660, 657])).
% 1.61/1.32 tff(662,plain,
% 1.61/1.32 ((~hskp26) | c0_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[661, 657])).
% 1.61/1.32 tff(663,plain,
% 1.61/1.32 ((~hskp26) | c0_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[662, 657])).
% 1.61/1.32 tff(664,plain,
% 1.61/1.32 ((~hskp26) | c0_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[663, 657])).
% 1.61/1.32 tff(665,plain,
% 1.61/1.32 ((~hskp26) | c0_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[664, 657])).
% 1.61/1.32 tff(666,plain,
% 1.61/1.32 ((~hskp26) | c0_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[665, 657])).
% 1.61/1.32 tff(667,plain,
% 1.61/1.32 (c0_1(a10)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[666, 656])).
% 1.61/1.32 tff(668,assumption,(hskp9), introduced(assumption)).
% 1.61/1.32 tff(669,plain,
% 1.61/1.32 (((~hskp26) | c2_1(a10)) <=> ((~hskp26) | c2_1(a10))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(670,axiom,((~hskp26) | c2_1(a10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.61/1.32 tff(671,plain,
% 1.61/1.32 ((~hskp26) | c2_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[670, 669])).
% 1.61/1.32 tff(672,plain,
% 1.61/1.32 ((~hskp26) | c2_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[671, 669])).
% 1.61/1.32 tff(673,plain,
% 1.61/1.32 ((~hskp26) | c2_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[672, 669])).
% 1.61/1.32 tff(674,plain,
% 1.61/1.32 ((~hskp26) | c2_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[673, 669])).
% 1.61/1.32 tff(675,plain,
% 1.61/1.32 ((~hskp26) | c2_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[674, 669])).
% 1.61/1.32 tff(676,plain,
% 1.61/1.32 ((~hskp26) | c2_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[675, 669])).
% 1.61/1.32 tff(677,plain,
% 1.61/1.32 ((~hskp26) | c2_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[676, 669])).
% 1.61/1.32 tff(678,plain,
% 1.61/1.32 ((~hskp26) | c2_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[677, 669])).
% 1.61/1.32 tff(679,plain,
% 1.61/1.32 (c2_1(a10)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[678, 656])).
% 1.61/1.32 tff(680,plain,
% 1.61/1.32 (((~hskp26) | c3_1(a10)) <=> ((~hskp26) | c3_1(a10))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(681,axiom,((~hskp26) | c3_1(a10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 1.61/1.32 tff(682,plain,
% 1.61/1.32 ((~hskp26) | c3_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[681, 680])).
% 1.61/1.32 tff(683,plain,
% 1.61/1.32 ((~hskp26) | c3_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[682, 680])).
% 1.61/1.32 tff(684,plain,
% 1.61/1.32 ((~hskp26) | c3_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[683, 680])).
% 1.61/1.32 tff(685,plain,
% 1.61/1.32 ((~hskp26) | c3_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[684, 680])).
% 1.61/1.32 tff(686,plain,
% 1.61/1.32 ((~hskp26) | c3_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[685, 680])).
% 1.61/1.32 tff(687,plain,
% 1.61/1.32 ((~hskp26) | c3_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[686, 680])).
% 1.61/1.32 tff(688,plain,
% 1.61/1.32 ((~hskp26) | c3_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[687, 680])).
% 1.61/1.32 tff(689,plain,
% 1.61/1.32 ((~hskp26) | c3_1(a10)),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[688, 680])).
% 1.61/1.32 tff(690,plain,
% 1.61/1.32 (c3_1(a10)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[689, 656])).
% 1.61/1.32 tff(691,plain,
% 1.61/1.32 (^[U: $i] : refl((hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))),
% 1.61/1.32 inference(bind,[status(th)],[])).
% 1.61/1.32 tff(692,plain,
% 1.61/1.32 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.32 inference(quant_intro,[status(thm)],[691])).
% 1.61/1.32 tff(693,plain,
% 1.61/1.32 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(694,plain,
% 1.61/1.32 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp14) <=> ((hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp14))), rewrite(((hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp14) <=> (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp14) <=> (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))))),
% 1.61/1.32 inference(bind,[status(th)],[])).
% 1.61/1.32 tff(695,plain,
% 1.61/1.32 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp14) <=> ![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.32 inference(quant_intro,[status(thm)],[694])).
% 1.61/1.32 tff(696,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.61/1.32 tff(697,plain,
% 1.61/1.32 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[696, 695])).
% 1.61/1.32 tff(698,plain,
% 1.61/1.32 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[697, 693])).
% 1.61/1.32 tff(699,plain,(
% 1.61/1.32 ![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.32 inference(skolemize,[status(sab)],[698])).
% 1.61/1.32 tff(700,plain,
% 1.61/1.32 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[699, 692])).
% 1.61/1.32 tff(701,plain,
% 1.61/1.32 (~c2_1(a16)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[579, 668])).
% 1.61/1.32 tff(702,plain,
% 1.61/1.32 (c0_1(a16)),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[590, 668])).
% 1.61/1.32 tff(703,plain,
% 1.61/1.32 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(704,plain,
% 1.61/1.32 ((hskp14 | hskp2 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16))) <=> (hskp14 | hskp2 | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(705,plain,
% 1.61/1.32 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16))))),
% 1.61/1.32 inference(monotonicity,[status(thm)],[704])).
% 1.61/1.32 tff(706,plain,
% 1.61/1.32 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)))),
% 1.61/1.32 inference(transitivity,[status(thm)],[705, 703])).
% 1.61/1.32 tff(707,plain,
% 1.61/1.32 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)))),
% 1.61/1.33 inference(quant_inst,[status(thm)],[])).
% 1.61/1.33 tff(708,plain,
% 1.61/1.33 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16))),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[707, 706])).
% 1.61/1.33 tff(709,plain,
% 1.61/1.33 (c1_1(a16)),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[708, 169, 655, 654, 702, 701, 700])).
% 1.61/1.33 tff(710,plain,
% 1.61/1.33 (~c3_1(a16)),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[573, 668])).
% 1.61/1.33 tff(711,assumption,(c3_1(a10)), introduced(assumption)).
% 1.61/1.33 tff(712,assumption,(c2_1(a10)), introduced(assumption)).
% 1.61/1.33 tff(713,assumption,(c0_1(a10)), introduced(assumption)).
% 1.61/1.33 tff(714,plain,
% 1.61/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a16)) | (~c1_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(715,plain,
% 1.61/1.33 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(716,plain,
% 1.61/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a16)) | (~c1_1(a16))))),
% 1.61/1.33 inference(monotonicity,[status(thm)],[715])).
% 1.61/1.33 tff(717,plain,
% 1.61/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.61/1.33 inference(transitivity,[status(thm)],[716, 714])).
% 1.61/1.33 tff(718,plain,
% 1.61/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.61/1.33 inference(quant_inst,[status(thm)],[])).
% 1.61/1.33 tff(719,plain,
% 1.61/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a16)) | (~c1_1(a16))),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[718, 717])).
% 1.61/1.33 tff(720,plain,
% 1.61/1.33 ($false),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[719, 169, 713, 712, 711, 702, 701, 710, 439, 709])).
% 1.61/1.33 tff(721,plain,((~hskp9) | (~c0_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.61/1.33 tff(722,plain,
% 1.61/1.33 ($false),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[721, 690, 679, 668, 654, 655, 667])).
% 1.61/1.33 tff(723,plain,((~hskp26) | (~hskp9) | hskp2 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.61/1.33 tff(724,plain,
% 1.61/1.33 (~hskp26),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[723, 655, 654, 568])).
% 1.61/1.33 tff(725,assumption,(c0_1(a16)), introduced(assumption)).
% 1.61/1.33 tff(726,plain,
% 1.61/1.33 (hskp14 | hskp2 | c1_1(a16)),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[708, 169, 725, 24, 700])).
% 1.61/1.33 tff(727,plain,
% 1.61/1.33 (c1_1(a16)),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[726, 655, 654])).
% 1.61/1.33 tff(728,assumption,(~c2_1(a6)), introduced(assumption)).
% 1.61/1.33 tff(729,assumption,(c3_1(a6)), introduced(assumption)).
% 1.61/1.33 tff(730,assumption,(c1_1(a6)), introduced(assumption)).
% 1.61/1.33 tff(731,assumption,(~hskp18), introduced(assumption)).
% 1.61/1.33 tff(732,plain,
% 1.61/1.33 (^[U: $i] : refl((hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 1.61/1.33 inference(bind,[status(th)],[])).
% 1.61/1.33 tff(733,plain,
% 1.61/1.33 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.61/1.33 inference(quant_intro,[status(thm)],[732])).
% 1.61/1.33 tff(734,plain,
% 1.61/1.33 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(735,plain,
% 1.61/1.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp18) <=> ((hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp18))), rewrite(((hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp18) <=> (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp18) <=> (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 1.61/1.33 inference(bind,[status(th)],[])).
% 1.61/1.33 tff(736,plain,
% 1.61/1.33 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp18) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.61/1.33 inference(quant_intro,[status(thm)],[735])).
% 1.61/1.33 tff(737,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.61/1.33 tff(738,plain,
% 1.61/1.33 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[737, 736])).
% 1.61/1.33 tff(739,plain,
% 1.61/1.33 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[738, 734])).
% 1.61/1.33 tff(740,plain,(
% 1.61/1.33 ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.61/1.33 inference(skolemize,[status(sab)],[739])).
% 1.61/1.33 tff(741,plain,
% 1.61/1.33 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[740, 733])).
% 1.61/1.33 tff(742,assumption,(hskp27), introduced(assumption)).
% 1.61/1.33 tff(743,plain,
% 1.61/1.33 (((~hskp27) | c3_1(a11)) <=> ((~hskp27) | c3_1(a11))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(744,axiom,((~hskp27) | c3_1(a11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 1.61/1.33 tff(745,plain,
% 1.61/1.33 ((~hskp27) | c3_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[744, 743])).
% 1.61/1.33 tff(746,plain,
% 1.61/1.33 ((~hskp27) | c3_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[745, 743])).
% 1.61/1.33 tff(747,plain,
% 1.61/1.33 ((~hskp27) | c3_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[746, 743])).
% 1.61/1.33 tff(748,plain,
% 1.61/1.33 ((~hskp27) | c3_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[747, 743])).
% 1.61/1.33 tff(749,plain,
% 1.61/1.33 ((~hskp27) | c3_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[748, 743])).
% 1.61/1.33 tff(750,plain,
% 1.61/1.33 ((~hskp27) | c3_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[749, 743])).
% 1.61/1.33 tff(751,plain,
% 1.61/1.33 ((~hskp27) | c3_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[750, 743])).
% 1.61/1.33 tff(752,plain,
% 1.61/1.33 ((~hskp27) | c3_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[751, 743])).
% 1.61/1.33 tff(753,plain,
% 1.61/1.33 (c3_1(a11)),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[752, 742])).
% 1.61/1.33 tff(754,plain,
% 1.61/1.33 (((~hskp27) | c0_1(a11)) <=> ((~hskp27) | c0_1(a11))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(755,axiom,((~hskp27) | c0_1(a11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 1.61/1.33 tff(756,plain,
% 1.61/1.33 ((~hskp27) | c0_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[755, 754])).
% 1.61/1.33 tff(757,plain,
% 1.61/1.33 ((~hskp27) | c0_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[756, 754])).
% 1.61/1.33 tff(758,plain,
% 1.61/1.33 ((~hskp27) | c0_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[757, 754])).
% 1.61/1.33 tff(759,plain,
% 1.61/1.33 ((~hskp27) | c0_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[758, 754])).
% 1.61/1.33 tff(760,plain,
% 1.61/1.33 ((~hskp27) | c0_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[759, 754])).
% 1.61/1.33 tff(761,plain,
% 1.61/1.33 ((~hskp27) | c0_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[760, 754])).
% 1.61/1.33 tff(762,plain,
% 1.61/1.33 ((~hskp27) | c0_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[761, 754])).
% 1.61/1.33 tff(763,plain,
% 1.61/1.33 ((~hskp27) | c0_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[762, 754])).
% 1.61/1.33 tff(764,plain,
% 1.61/1.33 (c0_1(a11)),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[763, 742])).
% 1.61/1.33 tff(765,plain,
% 1.61/1.33 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a11)) | c2_1(a11))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a11)) | c2_1(a11))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(766,plain,
% 1.61/1.33 ((hskp18 | hskp17 | (~ndr1_0) | c2_1(a11) | (~c0_1(a11)) | (~c3_1(a11))) <=> (hskp18 | hskp17 | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a11)) | c2_1(a11))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(767,plain,
% 1.61/1.33 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a11) | (~c0_1(a11)) | (~c3_1(a11)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a11)) | c2_1(a11)))),
% 1.61/1.33 inference(monotonicity,[status(thm)],[766])).
% 1.61/1.33 tff(768,plain,
% 1.61/1.33 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a11) | (~c0_1(a11)) | (~c3_1(a11)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a11)) | c2_1(a11))),
% 1.61/1.33 inference(transitivity,[status(thm)],[767, 765])).
% 1.61/1.33 tff(769,plain,
% 1.61/1.33 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a11) | (~c0_1(a11)) | (~c3_1(a11)))),
% 1.61/1.33 inference(quant_inst,[status(thm)],[])).
% 1.61/1.33 tff(770,plain,
% 1.61/1.33 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a11)) | c2_1(a11)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[769, 768])).
% 1.61/1.33 tff(771,plain,
% 1.61/1.33 (c2_1(a11)),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[770, 169, 731, 643, 764, 753, 741])).
% 1.61/1.33 tff(772,assumption,(c1_1(a16)), introduced(assumption)).
% 1.61/1.33 tff(773,plain,
% 1.61/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(774,plain,
% 1.61/1.33 (((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(775,plain,
% 1.61/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16))))),
% 1.61/1.33 inference(monotonicity,[status(thm)],[774])).
% 1.61/1.33 tff(776,plain,
% 1.61/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))),
% 1.61/1.33 inference(transitivity,[status(thm)],[775, 773])).
% 1.61/1.33 tff(777,plain,
% 1.61/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.61/1.33 inference(quant_inst,[status(thm)],[])).
% 1.61/1.33 tff(778,plain,
% 1.61/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16))),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[777, 776])).
% 1.61/1.33 tff(779,plain,
% 1.61/1.33 ($false),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[778, 169, 764, 753, 725, 24, 2, 439, 772, 771])).
% 1.61/1.33 tff(780,plain,((~hskp27) | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16)) | hskp18 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.61/1.33 tff(781,plain,
% 1.61/1.33 (~hskp27),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[780, 731, 24, 2, 727, 725, 643])).
% 1.61/1.33 tff(782,plain,
% 1.61/1.33 (^[U: $i] : refl((hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))),
% 1.61/1.33 inference(bind,[status(th)],[])).
% 1.61/1.33 tff(783,plain,
% 1.61/1.33 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.61/1.33 inference(quant_intro,[status(thm)],[782])).
% 1.61/1.33 tff(784,plain,
% 1.61/1.33 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(785,plain,
% 1.61/1.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp26) <=> ((hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp26))), rewrite(((hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp26) <=> (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp26) <=> (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))))),
% 1.61/1.33 inference(bind,[status(th)],[])).
% 1.61/1.33 tff(786,plain,
% 1.61/1.33 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp26) <=> ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.61/1.33 inference(quant_intro,[status(thm)],[785])).
% 1.61/1.33 tff(787,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.61/1.33 tff(788,plain,
% 1.61/1.33 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[787, 786])).
% 1.61/1.33 tff(789,plain,
% 1.61/1.33 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[788, 784])).
% 1.61/1.33 tff(790,plain,(
% 1.61/1.33 ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.61/1.33 inference(skolemize,[status(sab)],[789])).
% 1.61/1.33 tff(791,plain,
% 1.61/1.33 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[790, 783])).
% 1.61/1.33 tff(792,assumption,(~hskp3), introduced(assumption)).
% 1.61/1.33 tff(793,assumption,(hskp21), introduced(assumption)).
% 1.61/1.33 tff(794,plain,
% 1.61/1.33 (((~hskp21) | c3_1(a42)) <=> ((~hskp21) | c3_1(a42))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(795,axiom,((~hskp21) | c3_1(a42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.61/1.33 tff(796,plain,
% 1.61/1.33 ((~hskp21) | c3_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[795, 794])).
% 1.61/1.33 tff(797,plain,
% 1.61/1.33 ((~hskp21) | c3_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[796, 794])).
% 1.61/1.33 tff(798,plain,
% 1.61/1.33 ((~hskp21) | c3_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[797, 794])).
% 1.61/1.33 tff(799,plain,
% 1.61/1.33 ((~hskp21) | c3_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[798, 794])).
% 1.61/1.33 tff(800,plain,
% 1.61/1.33 ((~hskp21) | c3_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[799, 794])).
% 1.61/1.33 tff(801,plain,
% 1.61/1.33 ((~hskp21) | c3_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[800, 794])).
% 1.61/1.33 tff(802,plain,
% 1.61/1.33 ((~hskp21) | c3_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[801, 794])).
% 1.61/1.33 tff(803,plain,
% 1.61/1.33 ((~hskp21) | c3_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[802, 794])).
% 1.61/1.33 tff(804,plain,
% 1.61/1.33 (c3_1(a42)),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[803, 793])).
% 1.61/1.33 tff(805,plain,
% 1.61/1.33 (((~hskp21) | c2_1(a42)) <=> ((~hskp21) | c2_1(a42))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(806,axiom,((~hskp21) | c2_1(a42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.61/1.33 tff(807,plain,
% 1.61/1.33 ((~hskp21) | c2_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[806, 805])).
% 1.61/1.33 tff(808,plain,
% 1.61/1.33 ((~hskp21) | c2_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[807, 805])).
% 1.61/1.33 tff(809,plain,
% 1.61/1.33 ((~hskp21) | c2_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[808, 805])).
% 1.61/1.33 tff(810,plain,
% 1.61/1.33 ((~hskp21) | c2_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[809, 805])).
% 1.61/1.33 tff(811,plain,
% 1.61/1.33 ((~hskp21) | c2_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[810, 805])).
% 1.61/1.33 tff(812,plain,
% 1.61/1.33 ((~hskp21) | c2_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[811, 805])).
% 1.61/1.33 tff(813,plain,
% 1.61/1.33 ((~hskp21) | c2_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[812, 805])).
% 1.61/1.33 tff(814,plain,
% 1.61/1.33 ((~hskp21) | c2_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[813, 805])).
% 1.61/1.33 tff(815,plain,
% 1.61/1.33 (c2_1(a42)),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[814, 793])).
% 1.61/1.33 tff(816,plain,
% 1.61/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(817,plain,
% 1.61/1.33 (((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(818,plain,
% 1.61/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42))))),
% 1.61/1.33 inference(monotonicity,[status(thm)],[817])).
% 1.61/1.33 tff(819,plain,
% 1.61/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))),
% 1.61/1.33 inference(transitivity,[status(thm)],[818, 816])).
% 1.61/1.33 tff(820,plain,
% 1.61/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.61/1.33 inference(quant_inst,[status(thm)],[])).
% 1.61/1.33 tff(821,plain,
% 1.61/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42))),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[820, 819])).
% 1.61/1.33 tff(822,plain,
% 1.61/1.33 (~c0_1(a42)),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[821, 169, 815, 804, 725, 24, 2, 439, 772])).
% 1.61/1.33 tff(823,plain,
% 1.61/1.33 (((~hskp21) | (~c1_1(a42))) <=> ((~hskp21) | (~c1_1(a42)))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(824,plain,
% 1.61/1.33 (((~c1_1(a42)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a42)))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(825,axiom,((~c1_1(a42)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.61/1.33 tff(826,plain,
% 1.61/1.33 ((~hskp21) | (~c1_1(a42))),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[825, 824])).
% 1.61/1.33 tff(827,plain,
% 1.61/1.33 ((~hskp21) | (~c1_1(a42))),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[826, 823])).
% 1.61/1.33 tff(828,plain,
% 1.61/1.33 (~c1_1(a42)),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[827, 793])).
% 1.61/1.33 tff(829,plain,
% 1.61/1.33 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(830,plain,
% 1.61/1.33 ((hskp3 | hskp2 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | c0_1(a42)) <=> (hskp3 | hskp2 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(831,plain,
% 1.61/1.33 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | c0_1(a42))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42)))),
% 1.61/1.33 inference(monotonicity,[status(thm)],[830])).
% 1.61/1.33 tff(832,plain,
% 1.61/1.33 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | c0_1(a42))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42))),
% 1.61/1.33 inference(transitivity,[status(thm)],[831, 829])).
% 1.61/1.33 tff(833,plain,
% 1.61/1.33 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | c0_1(a42))),
% 1.61/1.33 inference(quant_inst,[status(thm)],[])).
% 1.61/1.33 tff(834,plain,
% 1.61/1.33 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42)),
% 1.61/1.33 inference(modus_ponens,[status(thm)],[833, 832])).
% 1.61/1.33 tff(835,plain,
% 1.61/1.33 ($false),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[834, 169, 792, 654, 815, 828, 23, 822])).
% 1.61/1.33 tff(836,plain,((~hskp21) | hskp3 | hskp2 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16))), inference(lemma,lemma(discharge,[]))).
% 1.61/1.33 tff(837,plain,
% 1.61/1.33 (~hskp21),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[836, 792, 654, 725, 24, 2, 772])).
% 1.61/1.33 tff(838,plain,
% 1.61/1.33 (hskp25),
% 1.61/1.33 inference(unit_resolution,[status(thm)],[167, 837, 643])).
% 1.61/1.33 tff(839,plain,
% 1.61/1.33 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.61/1.33 inference(bind,[status(th)],[])).
% 1.61/1.33 tff(840,plain,
% 1.61/1.33 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.33 inference(quant_intro,[status(thm)],[839])).
% 1.61/1.33 tff(841,plain,
% 1.61/1.33 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.33 inference(rewrite,[status(thm)],[])).
% 1.61/1.33 tff(842,plain,
% 1.61/1.33 (^[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)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp19) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp19))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.61/1.34 inference(bind,[status(th)],[])).
% 1.61/1.34 tff(843,plain,
% 1.61/1.34 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.34 inference(quant_intro,[status(thm)],[842])).
% 1.61/1.34 tff(844,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.61/1.34 tff(845,plain,
% 1.61/1.34 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.34 inference(modus_ponens,[status(thm)],[844, 843])).
% 1.61/1.34 tff(846,plain,
% 1.61/1.34 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.34 inference(modus_ponens,[status(thm)],[845, 841])).
% 1.61/1.34 tff(847,plain,(
% 1.61/1.34 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.34 inference(skolemize,[status(sab)],[846])).
% 1.61/1.34 tff(848,plain,
% 1.61/1.34 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.61/1.34 inference(modus_ponens,[status(thm)],[847, 840])).
% 1.61/1.34 tff(849,assumption,(hskp25), introduced(assumption)).
% 1.61/1.34 tff(850,plain,
% 1.61/1.34 (((~hskp25) | c2_1(a9)) <=> ((~hskp25) | c2_1(a9))),
% 1.61/1.34 inference(rewrite,[status(thm)],[])).
% 1.61/1.34 tff(851,axiom,((~hskp25) | c2_1(a9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.61/1.34 tff(852,plain,
% 1.61/1.34 ((~hskp25) | c2_1(a9)),
% 1.61/1.34 inference(modus_ponens,[status(thm)],[851, 850])).
% 1.61/1.34 tff(853,plain,
% 1.61/1.34 ((~hskp25) | c2_1(a9)),
% 1.61/1.34 inference(modus_ponens,[status(thm)],[852, 850])).
% 1.61/1.34 tff(854,plain,
% 1.68/1.34 ((~hskp25) | c2_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[853, 850])).
% 1.68/1.34 tff(855,plain,
% 1.68/1.34 ((~hskp25) | c2_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[854, 850])).
% 1.68/1.34 tff(856,plain,
% 1.68/1.34 ((~hskp25) | c2_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[855, 850])).
% 1.68/1.34 tff(857,plain,
% 1.68/1.34 ((~hskp25) | c2_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[856, 850])).
% 1.68/1.34 tff(858,plain,
% 1.68/1.34 ((~hskp25) | c2_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[857, 850])).
% 1.68/1.34 tff(859,plain,
% 1.68/1.34 ((~hskp25) | c2_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[858, 850])).
% 1.68/1.34 tff(860,plain,
% 1.68/1.34 (c2_1(a9)),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[859, 849])).
% 1.68/1.34 tff(861,plain,
% 1.68/1.34 (((~hskp25) | c1_1(a9)) <=> ((~hskp25) | c1_1(a9))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(862,axiom,((~hskp25) | c1_1(a9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.68/1.34 tff(863,plain,
% 1.68/1.34 ((~hskp25) | c1_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[862, 861])).
% 1.68/1.34 tff(864,plain,
% 1.68/1.34 ((~hskp25) | c1_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[863, 861])).
% 1.68/1.34 tff(865,plain,
% 1.68/1.34 ((~hskp25) | c1_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[864, 861])).
% 1.68/1.34 tff(866,plain,
% 1.68/1.34 ((~hskp25) | c1_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[865, 861])).
% 1.68/1.34 tff(867,plain,
% 1.68/1.34 ((~hskp25) | c1_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[866, 861])).
% 1.68/1.34 tff(868,plain,
% 1.68/1.34 ((~hskp25) | c1_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[867, 861])).
% 1.68/1.34 tff(869,plain,
% 1.68/1.34 ((~hskp25) | c1_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[868, 861])).
% 1.68/1.34 tff(870,plain,
% 1.68/1.34 ((~hskp25) | c1_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[869, 861])).
% 1.68/1.34 tff(871,plain,
% 1.68/1.34 (c1_1(a9)),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[870, 849])).
% 1.68/1.34 tff(872,plain,
% 1.68/1.34 (((~hskp25) | c0_1(a9)) <=> ((~hskp25) | c0_1(a9))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(873,axiom,((~hskp25) | c0_1(a9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.68/1.34 tff(874,plain,
% 1.68/1.34 ((~hskp25) | c0_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[873, 872])).
% 1.68/1.34 tff(875,plain,
% 1.68/1.34 ((~hskp25) | c0_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[874, 872])).
% 1.68/1.34 tff(876,plain,
% 1.68/1.34 ((~hskp25) | c0_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[875, 872])).
% 1.68/1.34 tff(877,plain,
% 1.68/1.34 ((~hskp25) | c0_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[876, 872])).
% 1.68/1.34 tff(878,plain,
% 1.68/1.34 ((~hskp25) | c0_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[877, 872])).
% 1.68/1.34 tff(879,plain,
% 1.68/1.34 ((~hskp25) | c0_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[878, 872])).
% 1.68/1.34 tff(880,plain,
% 1.68/1.34 ((~hskp25) | c0_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[879, 872])).
% 1.68/1.34 tff(881,plain,
% 1.68/1.34 ((~hskp25) | c0_1(a9)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[880, 872])).
% 1.68/1.34 tff(882,plain,
% 1.68/1.34 (c0_1(a9)),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[881, 849])).
% 1.68/1.34 tff(883,assumption,(~hskp19), introduced(assumption)).
% 1.68/1.34 tff(884,plain,
% 1.68/1.34 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(885,plain,
% 1.68/1.34 ((hskp19 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6))) <=> (hskp19 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(886,plain,
% 1.68/1.34 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))))),
% 1.68/1.34 inference(monotonicity,[status(thm)],[885])).
% 1.68/1.34 tff(887,plain,
% 1.68/1.34 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.68/1.34 inference(transitivity,[status(thm)],[886, 884])).
% 1.68/1.34 tff(888,plain,
% 1.68/1.34 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))),
% 1.68/1.34 inference(quant_inst,[status(thm)],[])).
% 1.68/1.34 tff(889,plain,
% 1.68/1.34 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[888, 887])).
% 1.68/1.34 tff(890,plain,
% 1.68/1.34 ($false),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[889, 169, 883, 882, 871, 860, 730, 729, 728, 848])).
% 1.68/1.34 tff(891,plain,((~hskp25) | hskp19 | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.34 tff(892,plain,
% 1.68/1.34 (hskp19),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[891, 838, 730, 729, 728])).
% 1.68/1.34 tff(893,plain,
% 1.68/1.34 (((~hskp19) | (~c0_1(a33))) <=> ((~hskp19) | (~c0_1(a33)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(894,plain,
% 1.68/1.34 (((~c0_1(a33)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a33)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(895,axiom,((~c0_1(a33)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.68/1.34 tff(896,plain,
% 1.68/1.34 ((~hskp19) | (~c0_1(a33))),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[895, 894])).
% 1.68/1.34 tff(897,plain,
% 1.68/1.34 ((~hskp19) | (~c0_1(a33))),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[896, 893])).
% 1.68/1.34 tff(898,plain,
% 1.68/1.34 (~c0_1(a33)),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[897, 892])).
% 1.68/1.34 tff(899,plain,
% 1.68/1.34 (((~hskp19) | c2_1(a33)) <=> ((~hskp19) | c2_1(a33))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(900,axiom,((~hskp19) | c2_1(a33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.68/1.34 tff(901,plain,
% 1.68/1.34 ((~hskp19) | c2_1(a33)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[900, 899])).
% 1.68/1.34 tff(902,plain,
% 1.68/1.34 ((~hskp19) | c2_1(a33)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[901, 899])).
% 1.68/1.34 tff(903,plain,
% 1.68/1.34 ((~hskp19) | c2_1(a33)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[902, 899])).
% 1.68/1.34 tff(904,plain,
% 1.68/1.34 ((~hskp19) | c2_1(a33)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[903, 899])).
% 1.68/1.34 tff(905,plain,
% 1.68/1.34 ((~hskp19) | c2_1(a33)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[904, 899])).
% 1.68/1.34 tff(906,plain,
% 1.68/1.34 ((~hskp19) | c2_1(a33)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[905, 899])).
% 1.68/1.34 tff(907,plain,
% 1.68/1.34 ((~hskp19) | c2_1(a33)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[906, 899])).
% 1.68/1.34 tff(908,plain,
% 1.68/1.34 ((~hskp19) | c2_1(a33)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[907, 899])).
% 1.68/1.34 tff(909,plain,
% 1.68/1.34 (c2_1(a33)),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[908, 892])).
% 1.68/1.34 tff(910,assumption,(~hskp27), introduced(assumption)).
% 1.68/1.34 tff(911,plain,
% 1.68/1.34 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(912,plain,
% 1.68/1.34 ((hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33))) <=> (hskp27 | hskp26 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(913,plain,
% 1.68/1.34 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33))))),
% 1.68/1.34 inference(monotonicity,[status(thm)],[912])).
% 1.68/1.34 tff(914,plain,
% 1.68/1.34 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 1.68/1.34 inference(transitivity,[status(thm)],[913, 911])).
% 1.68/1.34 tff(915,plain,
% 1.68/1.34 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)))),
% 1.68/1.34 inference(quant_inst,[status(thm)],[])).
% 1.68/1.34 tff(916,plain,
% 1.68/1.34 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33))),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[915, 914])).
% 1.68/1.34 tff(917,plain,
% 1.68/1.34 (~c1_1(a33)),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[916, 910, 169, 84, 909, 898, 791])).
% 1.68/1.34 tff(918,plain,
% 1.68/1.34 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | c1_1(a33))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(919,plain,
% 1.68/1.34 ((hskp3 | hskp2 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | c0_1(a33)) <=> (hskp3 | hskp2 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | c1_1(a33))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(920,plain,
% 1.68/1.34 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | c0_1(a33))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | c1_1(a33)))),
% 1.68/1.34 inference(monotonicity,[status(thm)],[919])).
% 1.68/1.34 tff(921,plain,
% 1.68/1.34 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | c0_1(a33))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | c1_1(a33))),
% 1.68/1.34 inference(transitivity,[status(thm)],[920, 918])).
% 1.68/1.34 tff(922,plain,
% 1.68/1.34 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | c0_1(a33))),
% 1.68/1.34 inference(quant_inst,[status(thm)],[])).
% 1.68/1.34 tff(923,plain,
% 1.68/1.34 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | c1_1(a33)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[922, 921])).
% 1.68/1.34 tff(924,plain,
% 1.68/1.34 ($false),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[923, 169, 792, 654, 909, 898, 23, 917])).
% 1.68/1.34 tff(925,plain,(hskp3 | hskp2 | hskp27 | hskp26 | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6) | hskp17 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.34 tff(926,plain,
% 1.68/1.34 (hskp3),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[925, 781, 654, 84, 730, 729, 728, 643, 725, 24, 2, 727])).
% 1.68/1.34 tff(927,plain,
% 1.68/1.34 (~c2_1(a5)),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[361, 926])).
% 1.68/1.34 tff(928,plain,
% 1.68/1.34 (~c1_1(a5)),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[367, 926])).
% 1.68/1.34 tff(929,plain,
% 1.68/1.34 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(930,plain,
% 1.68/1.34 ((hskp14 | hskp2 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5))) <=> (hskp14 | hskp2 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(931,plain,
% 1.68/1.34 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5))))),
% 1.68/1.34 inference(monotonicity,[status(thm)],[930])).
% 1.68/1.34 tff(932,plain,
% 1.68/1.34 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)))),
% 1.68/1.34 inference(transitivity,[status(thm)],[931, 929])).
% 1.68/1.34 tff(933,plain,
% 1.68/1.34 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))),
% 1.68/1.34 inference(quant_inst,[status(thm)],[])).
% 1.68/1.34 tff(934,plain,
% 1.68/1.34 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5))),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[933, 932])).
% 1.68/1.34 tff(935,plain,
% 1.68/1.34 (~c0_1(a5)),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[934, 169, 655, 654, 928, 927, 700])).
% 1.68/1.34 tff(936,plain,
% 1.68/1.34 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | (~c0_1(a6)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(937,plain,
% 1.68/1.34 ((hskp18 | hskp17 | (~ndr1_0) | c2_1(a6) | (~c0_1(a6)) | (~c3_1(a6))) <=> (hskp18 | hskp17 | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | (~c0_1(a6)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(938,plain,
% 1.68/1.34 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a6) | (~c0_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | (~c0_1(a6))))),
% 1.68/1.34 inference(monotonicity,[status(thm)],[937])).
% 1.68/1.34 tff(939,plain,
% 1.68/1.34 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a6) | (~c0_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | (~c0_1(a6)))),
% 1.68/1.34 inference(transitivity,[status(thm)],[938, 936])).
% 1.68/1.34 tff(940,plain,
% 1.68/1.34 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a6) | (~c0_1(a6)) | (~c3_1(a6)))),
% 1.68/1.34 inference(quant_inst,[status(thm)],[])).
% 1.68/1.34 tff(941,plain,
% 1.68/1.34 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | (~c0_1(a6))),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[940, 939])).
% 1.68/1.34 tff(942,plain,
% 1.68/1.34 (hskp18 | (~c0_1(a6))),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[941, 169, 643, 729, 728, 741])).
% 1.68/1.34 tff(943,plain,
% 1.68/1.34 (~c0_1(a6)),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[942, 731])).
% 1.68/1.34 tff(944,plain,
% 1.68/1.34 (((~hskp3) | (~c3_1(a5))) <=> ((~hskp3) | (~c3_1(a5)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(945,plain,
% 1.68/1.34 (((~c3_1(a5)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a5)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(946,axiom,((~c3_1(a5)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.68/1.34 tff(947,plain,
% 1.68/1.34 ((~hskp3) | (~c3_1(a5))),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[946, 945])).
% 1.68/1.34 tff(948,plain,
% 1.68/1.34 ((~hskp3) | (~c3_1(a5))),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[947, 944])).
% 1.68/1.34 tff(949,plain,
% 1.68/1.34 (~c3_1(a5)),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[948, 926])).
% 1.68/1.34 tff(950,plain,
% 1.68/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a6) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c3_1(a6)) | c0_1(a6))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a6) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c3_1(a6)) | c0_1(a6))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(951,plain,
% 1.68/1.34 (((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5)) <=> (c2_1(a6) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c3_1(a6)) | c0_1(a6))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(952,plain,
% 1.68/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a6) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c3_1(a6)) | c0_1(a6)))),
% 1.68/1.34 inference(monotonicity,[status(thm)],[951])).
% 1.68/1.34 tff(953,plain,
% 1.68/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a6) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c3_1(a6)) | c0_1(a6))),
% 1.68/1.34 inference(transitivity,[status(thm)],[952, 950])).
% 1.68/1.34 tff(954,plain,
% 1.68/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5))),
% 1.68/1.34 inference(quant_inst,[status(thm)],[])).
% 1.68/1.34 tff(955,plain,
% 1.68/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a6) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c3_1(a6)) | c0_1(a6)),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[954, 953])).
% 1.68/1.34 tff(956,plain,
% 1.68/1.34 ($false),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[955, 169, 729, 728, 928, 927, 949, 55, 943, 935])).
% 1.68/1.34 tff(957,plain,(hskp18 | (~c3_1(a6)) | c2_1(a6) | hskp14 | hskp2 | hskp26 | (~c1_1(a6)) | hskp17 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.34 tff(958,plain,
% 1.68/1.34 (hskp18),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[957, 655, 651, 652, 654, 724, 653, 643, 591, 580, 574])).
% 1.68/1.34 tff(959,plain,
% 1.68/1.34 (((~hskp18) | (~c1_1(a32))) <=> ((~hskp18) | (~c1_1(a32)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(960,plain,
% 1.68/1.34 (((~c1_1(a32)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a32)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(961,axiom,((~c1_1(a32)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.68/1.34 tff(962,plain,
% 1.68/1.34 ((~hskp18) | (~c1_1(a32))),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[961, 960])).
% 1.68/1.34 tff(963,plain,
% 1.68/1.34 ((~hskp18) | (~c1_1(a32))),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[962, 959])).
% 1.68/1.34 tff(964,plain,
% 1.68/1.34 (~c1_1(a32)),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[963, 958])).
% 1.68/1.34 tff(965,plain,
% 1.68/1.34 (((~hskp18) | (~c3_1(a32))) <=> ((~hskp18) | (~c3_1(a32)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(966,plain,
% 1.68/1.34 (((~c3_1(a32)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a32)))),
% 1.68/1.34 inference(rewrite,[status(thm)],[])).
% 1.68/1.34 tff(967,axiom,((~c3_1(a32)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.68/1.34 tff(968,plain,
% 1.68/1.34 ((~hskp18) | (~c3_1(a32))),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[967, 966])).
% 1.68/1.34 tff(969,plain,
% 1.68/1.34 ((~hskp18) | (~c3_1(a32))),
% 1.68/1.34 inference(modus_ponens,[status(thm)],[968, 965])).
% 1.68/1.34 tff(970,plain,
% 1.68/1.34 (~c3_1(a32)),
% 1.68/1.34 inference(unit_resolution,[status(thm)],[969, 958])).
% 1.68/1.35 tff(971,plain,
% 1.68/1.35 (hskp14 | hskp2 | c1_1(a16)),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[708, 169, 591, 580, 700])).
% 1.68/1.35 tff(972,plain,
% 1.68/1.35 (c1_1(a16)),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[971, 655, 654])).
% 1.68/1.35 tff(973,plain,
% 1.68/1.35 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.68/1.35 inference(bind,[status(th)],[])).
% 1.68/1.35 tff(974,plain,
% 1.68/1.35 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.68/1.35 inference(quant_intro,[status(thm)],[973])).
% 1.68/1.35 tff(975,plain,
% 1.68/1.35 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(976,plain,
% 1.68/1.35 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp24) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp24))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.68/1.35 inference(bind,[status(th)],[])).
% 1.68/1.35 tff(977,plain,
% 1.68/1.35 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.68/1.35 inference(quant_intro,[status(thm)],[976])).
% 1.68/1.35 tff(978,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.68/1.35 tff(979,plain,
% 1.68/1.35 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[978, 977])).
% 1.68/1.35 tff(980,plain,
% 1.68/1.35 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[979, 975])).
% 1.68/1.35 tff(981,plain,(
% 1.68/1.35 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.68/1.35 inference(skolemize,[status(sab)],[980])).
% 1.68/1.35 tff(982,plain,
% 1.68/1.35 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[981, 974])).
% 1.68/1.35 tff(983,assumption,(~c3_1(a32)), introduced(assumption)).
% 1.68/1.35 tff(984,assumption,(~c1_1(a32)), introduced(assumption)).
% 1.68/1.35 tff(985,plain,
% 1.68/1.35 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(986,plain,
% 1.68/1.35 ((hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(987,plain,
% 1.68/1.35 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16))))),
% 1.68/1.35 inference(monotonicity,[status(thm)],[986])).
% 1.68/1.35 tff(988,plain,
% 1.68/1.35 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.68/1.35 inference(transitivity,[status(thm)],[987, 985])).
% 1.68/1.35 tff(989,plain,
% 1.68/1.35 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 1.68/1.35 inference(quant_inst,[status(thm)],[])).
% 1.68/1.35 tff(990,plain,
% 1.68/1.35 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16))),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[989, 988])).
% 1.68/1.35 tff(991,plain,
% 1.68/1.35 (c0_1(a32)),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[990, 169, 73, 591, 984, 983, 574, 982, 972])).
% 1.68/1.35 tff(992,plain,
% 1.68/1.35 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | c2_1(a32))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | c2_1(a32))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(993,plain,
% 1.68/1.35 ((hskp14 | hskp2 | (~ndr1_0) | c1_1(a32) | c2_1(a32) | (~c0_1(a32))) <=> (hskp14 | hskp2 | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | c2_1(a32))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(994,plain,
% 1.68/1.35 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a32) | c2_1(a32) | (~c0_1(a32)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | c2_1(a32)))),
% 1.68/1.35 inference(monotonicity,[status(thm)],[993])).
% 1.68/1.35 tff(995,plain,
% 1.68/1.35 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a32) | c2_1(a32) | (~c0_1(a32)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | c2_1(a32))),
% 1.68/1.35 inference(transitivity,[status(thm)],[994, 992])).
% 1.68/1.35 tff(996,plain,
% 1.68/1.35 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a32) | c2_1(a32) | (~c0_1(a32)))),
% 1.68/1.35 inference(quant_inst,[status(thm)],[])).
% 1.68/1.35 tff(997,plain,
% 1.68/1.35 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | c2_1(a32)),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[996, 995])).
% 1.68/1.35 tff(998,plain,
% 1.68/1.35 ((~c0_1(a32)) | c2_1(a32)),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[997, 169, 655, 654, 984, 700])).
% 1.68/1.35 tff(999,plain,
% 1.68/1.35 (c2_1(a32)),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[998, 991])).
% 1.68/1.35 tff(1000,plain,
% 1.68/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a53)))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(1001,plain,
% 1.68/1.35 (((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a53)))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(1002,plain,
% 1.68/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a53))))),
% 1.68/1.35 inference(monotonicity,[status(thm)],[1001])).
% 1.68/1.35 tff(1003,plain,
% 1.68/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a53)))),
% 1.68/1.35 inference(transitivity,[status(thm)],[1002, 1000])).
% 1.68/1.35 tff(1004,plain,
% 1.68/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 1.68/1.35 inference(quant_inst,[status(thm)],[])).
% 1.68/1.35 tff(1005,plain,
% 1.68/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a53))),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 1.68/1.35 tff(1006,plain,
% 1.68/1.35 ((~c0_1(a32)) | (~c2_1(a53))),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[1005, 169, 347, 346, 984, 983, 580, 574, 458, 972])).
% 1.68/1.35 tff(1007,plain,
% 1.68/1.35 (~c2_1(a53)),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[1006, 991])).
% 1.68/1.35 tff(1008,plain,
% 1.68/1.35 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | (~c2_1(a32)) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | (~c2_1(a32)) | c2_1(a53))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(1009,plain,
% 1.68/1.35 ((hskp0 | (~ndr1_0) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | c2_1(a53)) <=> (hskp0 | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | (~c2_1(a32)) | c2_1(a53))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(1010,plain,
% 1.68/1.35 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | (~c2_1(a32)) | c2_1(a53)))),
% 1.68/1.35 inference(monotonicity,[status(thm)],[1009])).
% 1.68/1.35 tff(1011,plain,
% 1.68/1.35 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | (~c2_1(a32)) | c2_1(a53))),
% 1.68/1.35 inference(transitivity,[status(thm)],[1010, 1008])).
% 1.68/1.35 tff(1012,plain,
% 1.68/1.35 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)) | c1_1(a53) | c0_1(a53) | c2_1(a53))),
% 1.68/1.35 inference(quant_inst,[status(thm)],[])).
% 1.68/1.35 tff(1013,plain,
% 1.68/1.35 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | (~c0_1(a32)) | c1_1(a32) | (~ndr1_0) | (~c2_1(a32)) | c2_1(a53)),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 1.68/1.35 tff(1014,plain,
% 1.68/1.35 ((~c0_1(a32)) | (~c2_1(a32)) | c2_1(a53)),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[1013, 169, 344, 347, 346, 984, 342])).
% 1.68/1.35 tff(1015,plain,
% 1.68/1.35 ($false),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[1014, 1007, 999, 991])).
% 1.68/1.35 tff(1016,plain,(c3_1(a32) | hskp0 | c1_1(a32) | hskp14 | hskp2 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.68/1.35 tff(1017,plain,
% 1.68/1.35 ($false),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[1016, 970, 964, 344, 655, 654, 73])).
% 1.68/1.35 tff(1018,plain,(hskp14 | hskp0 | hskp2 | hskp24 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.68/1.35 tff(1019,plain,
% 1.68/1.35 (hskp14),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[1018, 654, 344, 73, 643])).
% 1.68/1.35 tff(1020,plain,
% 1.68/1.35 (((~hskp14) | (~c1_1(a24))) <=> ((~hskp14) | (~c1_1(a24)))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(1021,plain,
% 1.68/1.35 (((~c1_1(a24)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a24)))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(1022,axiom,((~c1_1(a24)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.68/1.35 tff(1023,plain,
% 1.68/1.35 ((~hskp14) | (~c1_1(a24))),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 1.68/1.35 tff(1024,plain,
% 1.68/1.35 ((~hskp14) | (~c1_1(a24))),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1023, 1020])).
% 1.68/1.35 tff(1025,plain,
% 1.68/1.35 (~c1_1(a24)),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[1024, 1019])).
% 1.68/1.35 tff(1026,plain,
% 1.68/1.35 (((~hskp14) | (~c0_1(a24))) <=> ((~hskp14) | (~c0_1(a24)))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(1027,plain,
% 1.68/1.35 (((~c0_1(a24)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a24)))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(1028,axiom,((~c0_1(a24)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.68/1.35 tff(1029,plain,
% 1.68/1.35 ((~hskp14) | (~c0_1(a24))),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 1.68/1.35 tff(1030,plain,
% 1.68/1.35 ((~hskp14) | (~c0_1(a24))),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1029, 1026])).
% 1.68/1.35 tff(1031,plain,
% 1.68/1.35 (~c0_1(a24)),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[1030, 1019])).
% 1.68/1.35 tff(1032,plain,
% 1.68/1.35 (((~hskp14) | c2_1(a24)) <=> ((~hskp14) | c2_1(a24))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(1033,axiom,((~hskp14) | c2_1(a24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.68/1.35 tff(1034,plain,
% 1.68/1.35 ((~hskp14) | c2_1(a24)),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1033, 1032])).
% 1.68/1.35 tff(1035,plain,
% 1.68/1.35 ((~hskp14) | c2_1(a24)),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1034, 1032])).
% 1.68/1.35 tff(1036,plain,
% 1.68/1.35 ((~hskp14) | c2_1(a24)),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1035, 1032])).
% 1.68/1.35 tff(1037,plain,
% 1.68/1.35 ((~hskp14) | c2_1(a24)),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1036, 1032])).
% 1.68/1.35 tff(1038,plain,
% 1.68/1.35 ((~hskp14) | c2_1(a24)),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1037, 1032])).
% 1.68/1.35 tff(1039,plain,
% 1.68/1.35 ((~hskp14) | c2_1(a24)),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1038, 1032])).
% 1.68/1.35 tff(1040,plain,
% 1.68/1.35 ((~hskp14) | c2_1(a24)),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1039, 1032])).
% 1.68/1.35 tff(1041,plain,
% 1.68/1.35 ((~hskp14) | c2_1(a24)),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1040, 1032])).
% 1.68/1.35 tff(1042,plain,
% 1.68/1.35 (c2_1(a24)),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[1041, 1019])).
% 1.68/1.35 tff(1043,plain,
% 1.68/1.35 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(1044,plain,
% 1.68/1.35 ((hskp3 | hskp2 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | c0_1(a24)) <=> (hskp3 | hskp2 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)))),
% 1.68/1.35 inference(rewrite,[status(thm)],[])).
% 1.68/1.35 tff(1045,plain,
% 1.68/1.35 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | c0_1(a24))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24))))),
% 1.68/1.35 inference(monotonicity,[status(thm)],[1044])).
% 1.68/1.35 tff(1046,plain,
% 1.68/1.35 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | c0_1(a24))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)))),
% 1.68/1.35 inference(transitivity,[status(thm)],[1045, 1043])).
% 1.68/1.35 tff(1047,plain,
% 1.68/1.35 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | c0_1(a24))),
% 1.68/1.35 inference(quant_inst,[status(thm)],[])).
% 1.68/1.35 tff(1048,plain,
% 1.68/1.35 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c0_1(U))) | hskp3 | hskp2 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24))),
% 1.68/1.35 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 1.68/1.35 tff(1049,plain,
% 1.68/1.35 (hskp3),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[1048, 169, 654, 1042, 1031, 1025, 23])).
% 1.68/1.35 tff(1050,plain,
% 1.68/1.35 (~c3_1(a5)),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[948, 1049])).
% 1.68/1.35 tff(1051,plain,
% 1.68/1.35 (~c1_1(a5)),
% 1.68/1.35 inference(unit_resolution,[status(thm)],[367, 1049])).
% 1.68/1.35 tff(1052,assumption,(~c3_1(a5)), introduced(assumption)).
% 1.68/1.35 tff(1053,assumption,(~c1_1(a5)), introduced(assumption)).
% 1.68/1.35 tff(1054,assumption,(~c1_1(a24)), introduced(assumption)).
% 1.68/1.35 tff(1055,assumption,(~c0_1(a24)), introduced(assumption)).
% 1.68/1.35 tff(1056,assumption,(c2_1(a24)), introduced(assumption)).
% 1.68/1.35 tff(1057,plain,
% 1.68/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a24) | c1_1(a24) | c2_1(a16) | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a16)) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c2_1(a16) | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a16)) | (~c2_1(a24)))),
% 1.68/1.36 inference(rewrite,[status(thm)],[])).
% 1.68/1.36 tff(1058,plain,
% 1.68/1.36 (((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24))) <=> (c0_1(a24) | c1_1(a24) | c2_1(a16) | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a16)) | (~c2_1(a24)))),
% 1.68/1.36 inference(rewrite,[status(thm)],[])).
% 1.68/1.36 tff(1059,plain,
% 1.68/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a24) | c1_1(a24) | c2_1(a16) | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a16)) | (~c2_1(a24))))),
% 1.68/1.36 inference(monotonicity,[status(thm)],[1058])).
% 1.68/1.36 tff(1060,plain,
% 1.68/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c2_1(a16) | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a16)) | (~c2_1(a24)))),
% 1.68/1.36 inference(transitivity,[status(thm)],[1059, 1057])).
% 1.68/1.36 tff(1061,plain,
% 1.68/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))),
% 1.68/1.36 inference(quant_inst,[status(thm)],[])).
% 1.68/1.36 tff(1062,plain,
% 1.68/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c2_1(a16) | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a16)) | (~c2_1(a24))),
% 1.68/1.36 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 1.68/1.36 tff(1063,plain,
% 1.68/1.36 ((~c0_1(a5)) | (~c1_1(a16))),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[1062, 169, 1056, 1055, 1054, 580, 574, 1053, 1052, 458])).
% 1.68/1.36 tff(1064,plain,
% 1.68/1.36 (~c0_1(a5)),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[1063, 772])).
% 1.68/1.36 tff(1065,plain,
% 1.68/1.36 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c0_1(a16)) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.68/1.36 inference(rewrite,[status(thm)],[])).
% 1.68/1.36 tff(1066,plain,
% 1.68/1.36 ((hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | c0_1(a5)) <=> (hskp24 | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.68/1.36 inference(rewrite,[status(thm)],[])).
% 1.68/1.36 tff(1067,plain,
% 1.68/1.36 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c0_1(a16)) | (~c1_1(a16))))),
% 1.68/1.36 inference(monotonicity,[status(thm)],[1066])).
% 1.68/1.36 tff(1068,plain,
% 1.68/1.36 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.68/1.36 inference(transitivity,[status(thm)],[1067, 1065])).
% 1.68/1.36 tff(1069,plain,
% 1.68/1.36 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a5) | c1_1(a5) | c0_1(a5))),
% 1.68/1.36 inference(quant_inst,[status(thm)],[])).
% 1.68/1.36 tff(1070,plain,
% 1.68/1.36 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c3_1(a16) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c0_1(a16)) | (~c1_1(a16))),
% 1.68/1.36 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 1.68/1.36 tff(1071,plain,
% 1.68/1.36 (c0_1(a5) | (~c1_1(a16))),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[1070, 169, 73, 591, 574, 1053, 1052, 982])).
% 1.68/1.36 tff(1072,plain,
% 1.68/1.36 ($false),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[1071, 1064, 772])).
% 1.68/1.36 tff(1073,plain,((~c1_1(a16)) | hskp24 | c1_1(a5) | c3_1(a5) | (~c2_1(a24)) | c0_1(a24) | c1_1(a24)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.36 tff(1074,plain,
% 1.68/1.36 (~c1_1(a16)),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[1073, 1051, 73, 1050, 1042, 1031, 1025])).
% 1.68/1.36 tff(1075,plain,
% 1.68/1.36 (~c2_1(a5)),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[361, 1049])).
% 1.68/1.36 tff(1076,plain,
% 1.68/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a16) | c2_1(a6) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a16) | c2_1(a6) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))),
% 1.68/1.36 inference(rewrite,[status(thm)],[])).
% 1.68/1.36 tff(1077,plain,
% 1.68/1.36 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a5) | c0_1(a5) | c3_1(a5)) <=> (c3_1(a16) | c2_1(a6) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))),
% 1.68/1.36 inference(rewrite,[status(thm)],[])).
% 1.68/1.36 tff(1078,plain,
% 1.68/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a5) | c0_1(a5) | c3_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a16) | c2_1(a6) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16))))),
% 1.68/1.36 inference(monotonicity,[status(thm)],[1077])).
% 1.68/1.36 tff(1079,plain,
% 1.68/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a5) | c0_1(a5) | c3_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a16) | c2_1(a6) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))),
% 1.68/1.36 inference(transitivity,[status(thm)],[1078, 1076])).
% 1.68/1.36 tff(1080,plain,
% 1.68/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a5) | c0_1(a5) | c3_1(a5))),
% 1.68/1.36 inference(quant_inst,[status(thm)],[])).
% 1.68/1.36 tff(1081,plain,
% 1.68/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a16) | c2_1(a6) | c2_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16))),
% 1.68/1.36 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 1.68/1.36 tff(1082,plain,
% 1.68/1.36 (c0_1(a5) | c1_1(a16)),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[1081, 169, 591, 653, 652, 574, 651, 1075, 1050, 13])).
% 1.68/1.36 tff(1083,plain,
% 1.68/1.36 (c0_1(a5)),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[1082, 1074])).
% 1.68/1.36 tff(1084,plain,
% 1.68/1.36 (hskp26 | hskp16),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[597, 169, 725, 24, 2, 94])).
% 1.68/1.36 tff(1085,plain,
% 1.68/1.36 (hskp16),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[1084, 84])).
% 1.68/1.36 tff(1086,plain,
% 1.68/1.36 (~c2_1(a30)),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[615, 1085])).
% 1.68/1.36 tff(1087,plain,
% 1.68/1.36 (c1_1(a30)),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[609, 1085])).
% 1.68/1.36 tff(1088,plain,
% 1.68/1.36 (~c0_1(a30)),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[621, 1085])).
% 1.68/1.36 tff(1089,assumption,(~c2_1(a30)), introduced(assumption)).
% 1.68/1.36 tff(1090,plain,
% 1.68/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a30) | c2_1(a30) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a30) | c2_1(a30) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c3_1(a30))),
% 1.68/1.36 inference(rewrite,[status(thm)],[])).
% 1.68/1.36 tff(1091,plain,
% 1.68/1.36 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a30) | c0_1(a30) | c3_1(a30)) <=> (c0_1(a30) | c2_1(a30) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c3_1(a30))),
% 1.68/1.36 inference(rewrite,[status(thm)],[])).
% 1.68/1.36 tff(1092,plain,
% 1.68/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a30) | c2_1(a30) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c3_1(a30)))),
% 1.68/1.36 inference(monotonicity,[status(thm)],[1091])).
% 1.68/1.36 tff(1093,plain,
% 1.68/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a30) | c2_1(a30) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c3_1(a30))),
% 1.68/1.36 inference(transitivity,[status(thm)],[1092, 1090])).
% 1.68/1.36 tff(1094,plain,
% 1.68/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a30) | c0_1(a30) | c3_1(a30))),
% 1.68/1.36 inference(quant_inst,[status(thm)],[])).
% 1.68/1.36 tff(1095,plain,
% 1.68/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a30) | c2_1(a30) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c3_1(a30)),
% 1.68/1.36 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.68/1.36 tff(1096,plain,
% 1.68/1.36 (c1_1(a16) | c3_1(a30)),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[1095, 169, 725, 730, 729, 633, 1089, 2, 728, 13])).
% 1.68/1.36 tff(1097,plain,
% 1.68/1.36 (c3_1(a30)),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[1096, 3])).
% 1.68/1.36 tff(1098,plain,
% 1.68/1.36 (^[U: $i] : refl((hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) <=> (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)))),
% 1.68/1.36 inference(bind,[status(th)],[])).
% 1.68/1.36 tff(1099,plain,
% 1.68/1.36 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.68/1.36 inference(quant_intro,[status(thm)],[1098])).
% 1.68/1.36 tff(1100,plain,
% 1.68/1.36 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.68/1.36 inference(rewrite,[status(thm)],[])).
% 1.68/1.36 tff(1101,plain,
% 1.68/1.36 (^[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) | (~c2_1(U)) | c0_1(U))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp25) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) | hskp25))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp25) | hskp26) <=> ((hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) | hskp26))), rewrite(((hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U)) | hskp26) <=> (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp25) | hskp26) <=> (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))))),
% 1.68/1.36 inference(bind,[status(th)],[])).
% 1.68/1.36 tff(1102,plain,
% 1.68/1.36 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp25) | hskp26) <=> ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.68/1.36 inference(quant_intro,[status(thm)],[1101])).
% 1.68/1.36 tff(1103,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp25) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.68/1.36 tff(1104,plain,
% 1.68/1.36 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.68/1.36 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 1.68/1.36 tff(1105,plain,
% 1.68/1.36 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.68/1.36 inference(modus_ponens,[status(thm)],[1104, 1100])).
% 1.68/1.36 tff(1106,plain,(
% 1.68/1.36 ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.68/1.36 inference(skolemize,[status(sab)],[1105])).
% 1.68/1.36 tff(1107,plain,
% 1.68/1.36 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))),
% 1.68/1.36 inference(modus_ponens,[status(thm)],[1106, 1099])).
% 1.68/1.36 tff(1108,assumption,(~hskp25), introduced(assumption)).
% 1.68/1.36 tff(1109,plain,
% 1.68/1.36 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))),
% 1.68/1.36 inference(rewrite,[status(thm)],[])).
% 1.68/1.36 tff(1110,plain,
% 1.68/1.36 ((hskp26 | hskp25 | (~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24)) <=> (hskp26 | hskp25 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))),
% 1.68/1.36 inference(rewrite,[status(thm)],[])).
% 1.68/1.36 tff(1111,plain,
% 1.68/1.36 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24)))),
% 1.68/1.36 inference(monotonicity,[status(thm)],[1110])).
% 1.68/1.36 tff(1112,plain,
% 1.68/1.36 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))),
% 1.68/1.36 inference(transitivity,[status(thm)],[1111, 1109])).
% 1.68/1.36 tff(1113,plain,
% 1.68/1.36 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24))),
% 1.68/1.36 inference(quant_inst,[status(thm)],[])).
% 1.68/1.36 tff(1114,plain,
% 1.68/1.36 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24)),
% 1.68/1.36 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 1.68/1.36 tff(1115,plain,
% 1.68/1.36 (hskp26 | hskp25 | c3_1(a24)),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[1114, 169, 1056, 1055, 1107])).
% 1.68/1.36 tff(1116,plain,
% 1.68/1.36 (c3_1(a24)),
% 1.68/1.36 inference(unit_resolution,[status(thm)],[1115, 1108, 84])).
% 1.68/1.36 tff(1117,plain,
% 1.68/1.36 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.68/1.36 inference(bind,[status(th)],[])).
% 1.68/1.36 tff(1118,plain,
% 1.68/1.36 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.68/1.36 inference(quant_intro,[status(thm)],[1117])).
% 1.68/1.36 tff(1119,plain,
% 1.68/1.36 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.68/1.36 inference(rewrite,[status(thm)],[])).
% 1.68/1.36 tff(1120,plain,
% 1.68/1.36 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.68/1.36 inference(bind,[status(th)],[])).
% 1.68/1.36 tff(1121,plain,
% 1.68/1.36 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.68/1.36 inference(quant_intro,[status(thm)],[1120])).
% 1.68/1.36 tff(1122,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 1.68/1.36 tff(1123,plain,
% 1.68/1.36 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.68/1.36 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 1.68/1.36 tff(1124,plain,
% 1.68/1.36 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.68/1.36 inference(modus_ponens,[status(thm)],[1123, 1119])).
% 1.68/1.36 tff(1125,plain,(
% 1.68/1.36 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.68/1.36 inference(skolemize,[status(sab)],[1124])).
% 1.68/1.36 tff(1126,plain,
% 1.68/1.36 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.68/1.36 inference(modus_ponens,[status(thm)],[1125, 1118])).
% 1.68/1.36 tff(1127,assumption,(c3_1(a30)), introduced(assumption)).
% 1.68/1.36 tff(1128,plain,
% 1.68/1.36 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.68/1.36 inference(bind,[status(th)],[])).
% 1.68/1.36 tff(1129,plain,
% 1.68/1.36 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.36 inference(quant_intro,[status(thm)],[1128])).
% 1.68/1.36 tff(1130,plain,
% 1.68/1.36 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.36 inference(rewrite,[status(thm)],[])).
% 1.68/1.36 tff(1131,plain,
% 1.68/1.36 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.68/1.37 inference(bind,[status(th)],[])).
% 1.68/1.37 tff(1132,plain,
% 1.68/1.37 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.37 inference(quant_intro,[status(thm)],[1131])).
% 1.68/1.37 tff(1133,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 1.68/1.37 tff(1134,plain,
% 1.68/1.37 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 1.68/1.37 tff(1135,plain,
% 1.68/1.37 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1134, 1130])).
% 1.68/1.37 tff(1136,plain,(
% 1.68/1.37 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.37 inference(skolemize,[status(sab)],[1135])).
% 1.68/1.37 tff(1137,plain,
% 1.68/1.37 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1136, 1129])).
% 1.68/1.37 tff(1138,plain,
% 1.68/1.37 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c0_1(a30) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a30) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.68/1.37 inference(rewrite,[status(thm)],[])).
% 1.68/1.37 tff(1139,plain,
% 1.68/1.37 ((hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30))) <=> (hskp10 | c0_1(a30) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.68/1.37 inference(rewrite,[status(thm)],[])).
% 1.68/1.37 tff(1140,plain,
% 1.68/1.37 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c0_1(a30) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a30)) | (~c3_1(a30))))),
% 1.68/1.37 inference(monotonicity,[status(thm)],[1139])).
% 1.68/1.37 tff(1141,plain,
% 1.68/1.37 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a30) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.68/1.37 inference(transitivity,[status(thm)],[1140, 1138])).
% 1.68/1.37 tff(1142,plain,
% 1.68/1.37 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))),
% 1.68/1.37 inference(quant_inst,[status(thm)],[])).
% 1.68/1.37 tff(1143,plain,
% 1.68/1.37 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a30) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a30)) | (~c3_1(a30))),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 1.68/1.37 tff(1144,plain,
% 1.68/1.37 (hskp10 | (~c3_1(a24)) | (~c3_1(a30))),
% 1.68/1.37 inference(unit_resolution,[status(thm)],[1143, 169, 634, 1056, 633, 1054, 1137])).
% 1.68/1.37 tff(1145,plain,
% 1.68/1.37 (hskp10),
% 1.68/1.37 inference(unit_resolution,[status(thm)],[1144, 1116, 1127])).
% 1.68/1.37 tff(1146,plain,
% 1.68/1.37 (((~hskp10) | (~c3_1(a18))) <=> ((~hskp10) | (~c3_1(a18)))),
% 1.68/1.37 inference(rewrite,[status(thm)],[])).
% 1.68/1.37 tff(1147,plain,
% 1.68/1.37 (((~c3_1(a18)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a18)))),
% 1.68/1.37 inference(rewrite,[status(thm)],[])).
% 1.68/1.37 tff(1148,axiom,((~c3_1(a18)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 1.68/1.37 tff(1149,plain,
% 1.68/1.37 ((~hskp10) | (~c3_1(a18))),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 1.68/1.37 tff(1150,plain,
% 1.68/1.37 ((~hskp10) | (~c3_1(a18))),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1149, 1146])).
% 1.68/1.37 tff(1151,plain,
% 1.68/1.37 (~c3_1(a18)),
% 1.68/1.37 inference(unit_resolution,[status(thm)],[1150, 1145])).
% 1.68/1.37 tff(1152,plain,
% 1.68/1.37 (((~hskp10) | c2_1(a18)) <=> ((~hskp10) | c2_1(a18))),
% 1.68/1.37 inference(rewrite,[status(thm)],[])).
% 1.68/1.37 tff(1153,axiom,((~hskp10) | c2_1(a18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.68/1.37 tff(1154,plain,
% 1.68/1.37 ((~hskp10) | c2_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 1.68/1.37 tff(1155,plain,
% 1.68/1.37 ((~hskp10) | c2_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1154, 1152])).
% 1.68/1.37 tff(1156,plain,
% 1.68/1.37 ((~hskp10) | c2_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1155, 1152])).
% 1.68/1.37 tff(1157,plain,
% 1.68/1.37 ((~hskp10) | c2_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1156, 1152])).
% 1.68/1.37 tff(1158,plain,
% 1.68/1.37 ((~hskp10) | c2_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1157, 1152])).
% 1.68/1.37 tff(1159,plain,
% 1.68/1.37 ((~hskp10) | c2_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1158, 1152])).
% 1.68/1.37 tff(1160,plain,
% 1.68/1.37 ((~hskp10) | c2_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1159, 1152])).
% 1.68/1.37 tff(1161,plain,
% 1.68/1.37 ((~hskp10) | c2_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1160, 1152])).
% 1.68/1.37 tff(1162,plain,
% 1.68/1.37 (c2_1(a18)),
% 1.68/1.37 inference(unit_resolution,[status(thm)],[1161, 1145])).
% 1.68/1.37 tff(1163,plain,
% 1.68/1.37 (((~hskp10) | c0_1(a18)) <=> ((~hskp10) | c0_1(a18))),
% 1.68/1.37 inference(rewrite,[status(thm)],[])).
% 1.68/1.37 tff(1164,axiom,((~hskp10) | c0_1(a18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.68/1.37 tff(1165,plain,
% 1.68/1.37 ((~hskp10) | c0_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 1.68/1.37 tff(1166,plain,
% 1.68/1.37 ((~hskp10) | c0_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1165, 1163])).
% 1.68/1.37 tff(1167,plain,
% 1.68/1.37 ((~hskp10) | c0_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1166, 1163])).
% 1.68/1.37 tff(1168,plain,
% 1.68/1.37 ((~hskp10) | c0_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1167, 1163])).
% 1.68/1.37 tff(1169,plain,
% 1.68/1.37 ((~hskp10) | c0_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1168, 1163])).
% 1.68/1.37 tff(1170,plain,
% 1.68/1.37 ((~hskp10) | c0_1(a18)),
% 1.68/1.37 inference(modus_ponens,[status(thm)],[1169, 1163])).
% 1.71/1.37 tff(1171,plain,
% 1.71/1.37 ((~hskp10) | c0_1(a18)),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1170, 1163])).
% 1.71/1.37 tff(1172,plain,
% 1.71/1.37 ((~hskp10) | c0_1(a18)),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1171, 1163])).
% 1.71/1.37 tff(1173,plain,
% 1.71/1.37 (c0_1(a18)),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[1172, 1145])).
% 1.71/1.37 tff(1174,plain,
% 1.71/1.37 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a24) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a24)) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1175,plain,
% 1.71/1.37 ((hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24))) <=> (hskp11 | c0_1(a24) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1176,plain,
% 1.71/1.37 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a24) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a24)) | (~c3_1(a24))))),
% 1.71/1.37 inference(monotonicity,[status(thm)],[1175])).
% 1.71/1.37 tff(1177,plain,
% 1.71/1.37 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.71/1.37 inference(transitivity,[status(thm)],[1176, 1174])).
% 1.71/1.37 tff(1178,plain,
% 1.71/1.37 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))),
% 1.71/1.37 inference(quant_inst,[status(thm)],[])).
% 1.71/1.37 tff(1179,plain,
% 1.71/1.37 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a24)) | (~c3_1(a24))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 1.71/1.37 tff(1180,plain,
% 1.71/1.37 (hskp11),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[1179, 169, 1056, 1173, 1162, 1055, 1151, 1126, 1116])).
% 1.71/1.37 tff(1181,plain,
% 1.71/1.37 (((~hskp11) | (~c3_1(a19))) <=> ((~hskp11) | (~c3_1(a19)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1182,plain,
% 1.71/1.37 (((~c3_1(a19)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a19)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1183,axiom,((~c3_1(a19)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.71/1.37 tff(1184,plain,
% 1.71/1.37 ((~hskp11) | (~c3_1(a19))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 1.71/1.37 tff(1185,plain,
% 1.71/1.37 ((~hskp11) | (~c3_1(a19))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1184, 1181])).
% 1.71/1.37 tff(1186,plain,
% 1.71/1.37 (~c3_1(a19)),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[1185, 1180])).
% 1.71/1.37 tff(1187,plain,
% 1.71/1.37 (((~hskp11) | c2_1(a19)) <=> ((~hskp11) | c2_1(a19))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1188,axiom,((~hskp11) | c2_1(a19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 1.71/1.37 tff(1189,plain,
% 1.71/1.37 ((~hskp11) | c2_1(a19)),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 1.71/1.37 tff(1190,plain,
% 1.71/1.37 ((~hskp11) | c2_1(a19)),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1189, 1187])).
% 1.71/1.37 tff(1191,plain,
% 1.71/1.37 ((~hskp11) | c2_1(a19)),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1190, 1187])).
% 1.71/1.37 tff(1192,plain,
% 1.71/1.37 ((~hskp11) | c2_1(a19)),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1191, 1187])).
% 1.71/1.37 tff(1193,plain,
% 1.71/1.37 ((~hskp11) | c2_1(a19)),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1192, 1187])).
% 1.71/1.37 tff(1194,plain,
% 1.71/1.37 ((~hskp11) | c2_1(a19)),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1193, 1187])).
% 1.71/1.37 tff(1195,plain,
% 1.71/1.37 ((~hskp11) | c2_1(a19)),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1194, 1187])).
% 1.71/1.37 tff(1196,plain,
% 1.71/1.37 ((~hskp11) | c2_1(a19)),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1195, 1187])).
% 1.71/1.37 tff(1197,plain,
% 1.71/1.37 (c2_1(a19)),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[1196, 1180])).
% 1.71/1.37 tff(1198,plain,
% 1.71/1.37 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c3_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c3_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1199,plain,
% 1.71/1.37 ((hskp26 | hskp25 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | c0_1(a19)) <=> (hskp26 | hskp25 | c3_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1200,plain,
% 1.71/1.37 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | c0_1(a19))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c3_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19))))),
% 1.71/1.37 inference(monotonicity,[status(thm)],[1199])).
% 1.71/1.37 tff(1201,plain,
% 1.71/1.37 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | c0_1(a19))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c3_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)))),
% 1.71/1.37 inference(transitivity,[status(thm)],[1200, 1198])).
% 1.71/1.37 tff(1202,plain,
% 1.71/1.37 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | c0_1(a19))),
% 1.71/1.37 inference(quant_inst,[status(thm)],[])).
% 1.71/1.37 tff(1203,plain,
% 1.71/1.37 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c3_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 1.71/1.37 tff(1204,plain,
% 1.71/1.37 (c0_1(a19)),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[1203, 169, 84, 1108, 1197, 1186, 1107])).
% 1.71/1.37 tff(1205,plain,
% 1.71/1.37 (((~hskp11) | (~c1_1(a19))) <=> ((~hskp11) | (~c1_1(a19)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1206,plain,
% 1.71/1.37 (((~c1_1(a19)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a19)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1207,axiom,((~c1_1(a19)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.71/1.37 tff(1208,plain,
% 1.71/1.37 ((~hskp11) | (~c1_1(a19))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 1.71/1.37 tff(1209,plain,
% 1.71/1.37 ((~hskp11) | (~c1_1(a19))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1208, 1205])).
% 1.71/1.37 tff(1210,plain,
% 1.71/1.37 (~c1_1(a19)),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[1209, 1180])).
% 1.71/1.37 tff(1211,plain,
% 1.71/1.37 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)) | c2_1(a53))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1212,plain,
% 1.71/1.37 ((hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a53) | c0_1(a53) | c2_1(a53)) <=> (hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)) | c2_1(a53))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1213,plain,
% 1.71/1.37 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a53) | c0_1(a53) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)) | c2_1(a53)))),
% 1.71/1.37 inference(monotonicity,[status(thm)],[1212])).
% 1.71/1.37 tff(1214,plain,
% 1.71/1.37 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a53) | c0_1(a53) | c2_1(a53))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)) | c2_1(a53))),
% 1.71/1.37 inference(transitivity,[status(thm)],[1213, 1211])).
% 1.71/1.37 tff(1215,plain,
% 1.71/1.37 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a53) | c0_1(a53) | c2_1(a53))),
% 1.71/1.37 inference(quant_inst,[status(thm)],[])).
% 1.71/1.37 tff(1216,plain,
% 1.71/1.37 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a53) | c1_1(a53) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)) | c2_1(a53)),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 1.71/1.37 tff(1217,plain,
% 1.71/1.37 (c2_1(a53)),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[1216, 169, 344, 1197, 370, 369, 1210, 342, 1204])).
% 1.71/1.37 tff(1218,plain,
% 1.71/1.37 (^[U: $i] : refl((hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.71/1.37 inference(bind,[status(th)],[])).
% 1.71/1.37 tff(1219,plain,
% 1.71/1.37 (![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.37 inference(quant_intro,[status(thm)],[1218])).
% 1.71/1.37 tff(1220,plain,
% 1.71/1.37 (![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1221,plain,
% 1.71/1.37 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) | hskp20) <=> ((hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20))), rewrite(((hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) | hskp20) <=> (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.71/1.37 inference(bind,[status(th)],[])).
% 1.71/1.37 tff(1222,plain,
% 1.71/1.37 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) | hskp20) <=> ![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.37 inference(quant_intro,[status(thm)],[1221])).
% 1.71/1.37 tff(1223,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp26) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.71/1.37 tff(1224,plain,
% 1.71/1.37 (![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 1.71/1.37 tff(1225,plain,
% 1.71/1.37 (![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1224, 1220])).
% 1.71/1.37 tff(1226,plain,(
% 1.71/1.37 ![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.37 inference(skolemize,[status(sab)],[1225])).
% 1.71/1.37 tff(1227,plain,
% 1.71/1.37 (![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1226, 1219])).
% 1.71/1.37 tff(1228,plain,
% 1.71/1.37 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1229,plain,
% 1.71/1.37 ((hskp26 | hskp20 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18))) <=> (hskp26 | hskp20 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1230,plain,
% 1.71/1.37 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18))))),
% 1.71/1.37 inference(monotonicity,[status(thm)],[1229])).
% 1.71/1.37 tff(1231,plain,
% 1.71/1.37 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)))),
% 1.71/1.37 inference(transitivity,[status(thm)],[1230, 1228])).
% 1.71/1.37 tff(1232,plain,
% 1.71/1.37 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)))),
% 1.71/1.37 inference(quant_inst,[status(thm)],[])).
% 1.71/1.37 tff(1233,plain,
% 1.71/1.37 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 1.71/1.37 tff(1234,plain,
% 1.71/1.37 (hskp20),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[1233, 169, 84, 1173, 1162, 1151, 1227])).
% 1.71/1.37 tff(1235,plain,
% 1.71/1.37 (((~hskp20) | (~c3_1(a37))) <=> ((~hskp20) | (~c3_1(a37)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1236,plain,
% 1.71/1.37 (((~c3_1(a37)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a37)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1237,axiom,((~c3_1(a37)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.71/1.37 tff(1238,plain,
% 1.71/1.37 ((~hskp20) | (~c3_1(a37))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 1.71/1.37 tff(1239,plain,
% 1.71/1.37 ((~hskp20) | (~c3_1(a37))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1238, 1235])).
% 1.71/1.37 tff(1240,plain,
% 1.71/1.37 (~c3_1(a37)),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[1239, 1234])).
% 1.71/1.37 tff(1241,plain,
% 1.71/1.37 (((~hskp20) | (~c0_1(a37))) <=> ((~hskp20) | (~c0_1(a37)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1242,plain,
% 1.71/1.37 (((~c0_1(a37)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a37)))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1243,axiom,((~c0_1(a37)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.71/1.37 tff(1244,plain,
% 1.71/1.37 ((~hskp20) | (~c0_1(a37))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1243, 1242])).
% 1.71/1.37 tff(1245,plain,
% 1.71/1.37 ((~hskp20) | (~c0_1(a37))),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1244, 1241])).
% 1.71/1.37 tff(1246,plain,
% 1.71/1.37 (~c0_1(a37)),
% 1.71/1.37 inference(unit_resolution,[status(thm)],[1245, 1234])).
% 1.71/1.37 tff(1247,plain,
% 1.71/1.37 (((~hskp20) | c1_1(a37)) <=> ((~hskp20) | c1_1(a37))),
% 1.71/1.37 inference(rewrite,[status(thm)],[])).
% 1.71/1.37 tff(1248,axiom,((~hskp20) | c1_1(a37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 1.71/1.37 tff(1249,plain,
% 1.71/1.37 ((~hskp20) | c1_1(a37)),
% 1.71/1.37 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 1.71/1.37 tff(1250,plain,
% 1.71/1.38 ((~hskp20) | c1_1(a37)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1249, 1247])).
% 1.71/1.38 tff(1251,plain,
% 1.71/1.38 ((~hskp20) | c1_1(a37)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1250, 1247])).
% 1.71/1.38 tff(1252,plain,
% 1.71/1.38 ((~hskp20) | c1_1(a37)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1251, 1247])).
% 1.71/1.38 tff(1253,plain,
% 1.71/1.38 ((~hskp20) | c1_1(a37)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1252, 1247])).
% 1.71/1.38 tff(1254,plain,
% 1.71/1.38 ((~hskp20) | c1_1(a37)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1253, 1247])).
% 1.71/1.38 tff(1255,plain,
% 1.71/1.38 ((~hskp20) | c1_1(a37)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1254, 1247])).
% 1.71/1.38 tff(1256,plain,
% 1.71/1.38 ((~hskp20) | c1_1(a37)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1255, 1247])).
% 1.71/1.38 tff(1257,plain,
% 1.71/1.38 (c1_1(a37)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1256, 1234])).
% 1.71/1.38 tff(1258,plain,
% 1.71/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a53)) | (~c3_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1259,plain,
% 1.71/1.38 (((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1260,plain,
% 1.71/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a53)) | (~c3_1(a53))))),
% 1.71/1.38 inference(monotonicity,[status(thm)],[1259])).
% 1.71/1.38 tff(1261,plain,
% 1.71/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.71/1.38 inference(transitivity,[status(thm)],[1260, 1258])).
% 1.71/1.38 tff(1262,plain,
% 1.71/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 1.71/1.38 inference(quant_inst,[status(thm)],[])).
% 1.71/1.38 tff(1263,plain,
% 1.71/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a53)) | (~c3_1(a53))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 1.71/1.38 tff(1264,plain,
% 1.71/1.38 ($false),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1263, 169, 371, 1257, 370, 369, 1246, 1240, 83, 1217])).
% 1.71/1.38 tff(1265,plain,(hskp25 | (~c3_1(a53)) | c0_1(a53) | c1_1(a53) | hskp0 | hskp26 | (~c2_1(a24)) | c0_1(a24) | (~c3_1(a30)) | (~c1_1(a30)) | c0_1(a30) | c1_1(a24)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.38 tff(1266,plain,
% 1.71/1.38 (hskp25),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1265, 1097, 370, 369, 344, 84, 1056, 1055, 371, 634, 633, 1054])).
% 1.71/1.38 tff(1267,plain,
% 1.71/1.38 (c1_1(a9)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[870, 1266])).
% 1.71/1.38 tff(1268,plain,
% 1.71/1.38 (c2_1(a9)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[859, 1266])).
% 1.71/1.38 tff(1269,plain,
% 1.71/1.38 (c0_1(a9)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[881, 1266])).
% 1.71/1.38 tff(1270,assumption,(~hskp6), introduced(assumption)).
% 1.71/1.38 tff(1271,plain,
% 1.71/1.38 (^[U: $i] : refl((hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 1.71/1.38 inference(bind,[status(th)],[])).
% 1.71/1.38 tff(1272,plain,
% 1.71/1.38 (![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.71/1.38 inference(quant_intro,[status(thm)],[1271])).
% 1.71/1.38 tff(1273,plain,
% 1.71/1.38 (![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1274,plain,
% 1.71/1.38 (^[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)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp26) <=> ((hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp26))), rewrite(((hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp26) <=> (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp26) <=> (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 1.71/1.38 inference(bind,[status(th)],[])).
% 1.71/1.38 tff(1275,plain,
% 1.71/1.38 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp26) <=> ![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.71/1.38 inference(quant_intro,[status(thm)],[1274])).
% 1.71/1.38 tff(1276,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.71/1.38 tff(1277,plain,
% 1.71/1.38 (![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 1.71/1.38 tff(1278,plain,
% 1.71/1.38 (![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1277, 1273])).
% 1.71/1.38 tff(1279,plain,(
% 1.71/1.38 ![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.71/1.38 inference(skolemize,[status(sab)],[1278])).
% 1.71/1.38 tff(1280,plain,
% 1.71/1.38 (![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1279, 1272])).
% 1.71/1.38 tff(1281,plain,
% 1.71/1.38 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1282,plain,
% 1.71/1.38 ((hskp26 | hskp6 | (~ndr1_0) | c3_1(a24) | c1_1(a24) | (~c2_1(a24))) <=> (hskp26 | hskp6 | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1283,plain,
% 1.71/1.38 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24)))),
% 1.71/1.38 inference(monotonicity,[status(thm)],[1282])).
% 1.71/1.38 tff(1284,plain,
% 1.71/1.38 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24))),
% 1.71/1.38 inference(transitivity,[status(thm)],[1283, 1281])).
% 1.71/1.38 tff(1285,plain,
% 1.71/1.38 ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))),
% 1.71/1.38 inference(quant_inst,[status(thm)],[])).
% 1.71/1.38 tff(1286,plain,
% 1.71/1.38 ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | c3_1(a24)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 1.71/1.38 tff(1287,plain,
% 1.71/1.38 (hskp26 | hskp6 | c3_1(a24)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1286, 169, 1056, 1054, 1280])).
% 1.71/1.38 tff(1288,plain,
% 1.71/1.38 (c3_1(a24)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1287, 1270, 84])).
% 1.71/1.38 tff(1289,plain,
% 1.71/1.38 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.71/1.38 inference(bind,[status(th)],[])).
% 1.71/1.38 tff(1290,plain,
% 1.71/1.38 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.71/1.38 inference(quant_intro,[status(thm)],[1289])).
% 1.71/1.38 tff(1291,plain,
% 1.71/1.38 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1292,plain,
% 1.71/1.38 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp6))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.71/1.38 inference(bind,[status(th)],[])).
% 1.71/1.38 tff(1293,plain,
% 1.71/1.38 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.71/1.38 inference(quant_intro,[status(thm)],[1292])).
% 1.71/1.38 tff(1294,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.71/1.38 tff(1295,plain,
% 1.71/1.38 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 1.71/1.38 tff(1296,plain,
% 1.71/1.38 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1295, 1291])).
% 1.71/1.38 tff(1297,plain,(
% 1.71/1.38 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.71/1.38 inference(skolemize,[status(sab)],[1296])).
% 1.71/1.38 tff(1298,plain,
% 1.71/1.38 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1297, 1290])).
% 1.71/1.38 tff(1299,assumption,(c2_1(a9)), introduced(assumption)).
% 1.71/1.38 tff(1300,assumption,(c1_1(a9)), introduced(assumption)).
% 1.71/1.38 tff(1301,plain,
% 1.71/1.38 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | (~c2_1(a9)) | (~c3_1(a9)) | (~c1_1(a9)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | (~c2_1(a9)) | (~c3_1(a9)) | (~c1_1(a9)))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1302,plain,
% 1.71/1.38 ((hskp6 | (~ndr1_0) | (~c2_1(a9)) | (~c1_1(a9)) | (~c3_1(a9)) | c0_1(a30) | c2_1(a30) | (~c3_1(a30))) <=> (hskp6 | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | (~c2_1(a9)) | (~c3_1(a9)) | (~c1_1(a9)))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1303,plain,
% 1.71/1.38 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a9)) | (~c1_1(a9)) | (~c3_1(a9)) | c0_1(a30) | c2_1(a30) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | (~c2_1(a9)) | (~c3_1(a9)) | (~c1_1(a9))))),
% 1.71/1.38 inference(monotonicity,[status(thm)],[1302])).
% 1.71/1.38 tff(1304,plain,
% 1.71/1.38 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a9)) | (~c1_1(a9)) | (~c3_1(a9)) | c0_1(a30) | c2_1(a30) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | (~c2_1(a9)) | (~c3_1(a9)) | (~c1_1(a9)))),
% 1.71/1.38 inference(transitivity,[status(thm)],[1303, 1301])).
% 1.71/1.38 tff(1305,plain,
% 1.71/1.38 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a9)) | (~c1_1(a9)) | (~c3_1(a9)) | c0_1(a30) | c2_1(a30) | (~c3_1(a30)))),
% 1.71/1.38 inference(quant_inst,[status(thm)],[])).
% 1.71/1.38 tff(1306,plain,
% 1.71/1.38 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | (~c2_1(a9)) | (~c3_1(a9)) | (~c1_1(a9))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 1.71/1.38 tff(1307,plain,
% 1.71/1.38 (hskp6 | (~c3_1(a9))),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1306, 169, 1300, 1299, 633, 1089, 1298, 1127])).
% 1.71/1.38 tff(1308,plain,
% 1.71/1.38 (~c3_1(a9)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1307, 1270])).
% 1.71/1.38 tff(1309,assumption,(c0_1(a9)), introduced(assumption)).
% 1.71/1.38 tff(1310,plain,
% 1.71/1.38 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | c3_1(a9))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | c3_1(a9))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1311,plain,
% 1.71/1.38 ((hskp26 | hskp20 | (~ndr1_0) | c3_1(a9) | (~c2_1(a9)) | (~c0_1(a9))) <=> (hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | c3_1(a9))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1312,plain,
% 1.71/1.38 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a9) | (~c2_1(a9)) | (~c0_1(a9)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | c3_1(a9)))),
% 1.71/1.38 inference(monotonicity,[status(thm)],[1311])).
% 1.71/1.38 tff(1313,plain,
% 1.71/1.38 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a9) | (~c2_1(a9)) | (~c0_1(a9)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | c3_1(a9))),
% 1.71/1.38 inference(transitivity,[status(thm)],[1312, 1310])).
% 1.71/1.38 tff(1314,plain,
% 1.71/1.38 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a9) | (~c2_1(a9)) | (~c0_1(a9)))),
% 1.71/1.38 inference(quant_inst,[status(thm)],[])).
% 1.71/1.38 tff(1315,plain,
% 1.71/1.38 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | c3_1(a9)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 1.71/1.38 tff(1316,plain,
% 1.71/1.38 (hskp20 | c3_1(a9)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1315, 169, 84, 1309, 1299, 1227])).
% 1.71/1.38 tff(1317,plain,
% 1.71/1.38 (hskp20),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1316, 1308])).
% 1.71/1.38 tff(1318,plain,
% 1.71/1.38 (~c3_1(a37)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1239, 1317])).
% 1.71/1.38 tff(1319,plain,
% 1.71/1.38 (~c0_1(a37)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1245, 1317])).
% 1.71/1.38 tff(1320,plain,
% 1.71/1.38 (c1_1(a37)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1256, 1317])).
% 1.71/1.38 tff(1321,plain,
% 1.71/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a37)))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1322,plain,
% 1.71/1.38 (((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24))) <=> (c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a37)))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1323,plain,
% 1.71/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a37))))),
% 1.71/1.38 inference(monotonicity,[status(thm)],[1322])).
% 1.71/1.38 tff(1324,plain,
% 1.71/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a37)))),
% 1.71/1.38 inference(transitivity,[status(thm)],[1323, 1321])).
% 1.71/1.38 tff(1325,plain,
% 1.71/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))),
% 1.71/1.38 inference(quant_inst,[status(thm)],[])).
% 1.71/1.38 tff(1326,plain,
% 1.71/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c1_1(a37))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 1.71/1.38 tff(1327,plain,
% 1.71/1.38 ($false),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1326, 169, 1320, 1056, 1319, 1318, 1055, 1054, 83, 1288])).
% 1.71/1.38 tff(1328,plain,(hskp6 | (~c2_1(a24)) | c0_1(a24) | c1_1(a24) | hskp26 | (~c0_1(a9)) | (~c2_1(a9)) | (~c1_1(a9)) | c0_1(a30) | c2_1(a30) | (~c3_1(a30))), inference(lemma,lemma(discharge,[]))).
% 1.71/1.38 tff(1329,plain,
% 1.71/1.38 (hskp6),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1328, 1269, 1055, 1054, 84, 1056, 1268, 1267, 633, 1089, 1097])).
% 1.71/1.38 tff(1330,assumption,(hskp6), introduced(assumption)).
% 1.71/1.38 tff(1331,plain,
% 1.71/1.38 (((~hskp6) | (~c2_1(a8))) <=> ((~hskp6) | (~c2_1(a8)))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1332,plain,
% 1.71/1.38 (((~c2_1(a8)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a8)))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1333,axiom,((~c2_1(a8)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.71/1.38 tff(1334,plain,
% 1.71/1.38 ((~hskp6) | (~c2_1(a8))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 1.71/1.38 tff(1335,plain,
% 1.71/1.38 ((~hskp6) | (~c2_1(a8))),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1334, 1331])).
% 1.71/1.38 tff(1336,plain,
% 1.71/1.38 (~c2_1(a8)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1335, 1330])).
% 1.71/1.38 tff(1337,plain,
% 1.71/1.38 (((~hskp6) | c1_1(a8)) <=> ((~hskp6) | c1_1(a8))),
% 1.71/1.38 inference(rewrite,[status(thm)],[])).
% 1.71/1.38 tff(1338,axiom,((~hskp6) | c1_1(a8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.71/1.38 tff(1339,plain,
% 1.71/1.38 ((~hskp6) | c1_1(a8)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 1.71/1.38 tff(1340,plain,
% 1.71/1.38 ((~hskp6) | c1_1(a8)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1339, 1337])).
% 1.71/1.38 tff(1341,plain,
% 1.71/1.38 ((~hskp6) | c1_1(a8)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1340, 1337])).
% 1.71/1.38 tff(1342,plain,
% 1.71/1.38 ((~hskp6) | c1_1(a8)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1341, 1337])).
% 1.71/1.38 tff(1343,plain,
% 1.71/1.38 ((~hskp6) | c1_1(a8)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1342, 1337])).
% 1.71/1.38 tff(1344,plain,
% 1.71/1.38 ((~hskp6) | c1_1(a8)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1343, 1337])).
% 1.71/1.38 tff(1345,plain,
% 1.71/1.38 ((~hskp6) | c1_1(a8)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1344, 1337])).
% 1.71/1.38 tff(1346,plain,
% 1.71/1.38 ((~hskp6) | c1_1(a8)),
% 1.71/1.38 inference(modus_ponens,[status(thm)],[1345, 1337])).
% 1.71/1.38 tff(1347,plain,
% 1.71/1.38 (c1_1(a8)),
% 1.71/1.38 inference(unit_resolution,[status(thm)],[1346, 1330])).
% 1.71/1.38 tff(1348,assumption,(~c3_1(a8)), introduced(assumption)).
% 1.71/1.39 tff(1349,assumption,(~c2_1(a8)), introduced(assumption)).
% 1.71/1.39 tff(1350,assumption,(c1_1(a8)), introduced(assumption)).
% 1.71/1.39 tff(1351,plain,
% 1.71/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a24)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1352,plain,
% 1.71/1.39 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24))) <=> (c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a24)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1353,plain,
% 1.71/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a24))))),
% 1.71/1.39 inference(monotonicity,[status(thm)],[1352])).
% 1.71/1.39 tff(1354,plain,
% 1.71/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a24)))),
% 1.71/1.39 inference(transitivity,[status(thm)],[1353, 1351])).
% 1.71/1.39 tff(1355,plain,
% 1.71/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))),
% 1.71/1.39 inference(quant_inst,[status(thm)],[])).
% 1.71/1.39 tff(1356,plain,
% 1.71/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a24))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 1.71/1.39 tff(1357,plain,
% 1.71/1.39 ($false),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1356, 169, 1056, 725, 1350, 1055, 1054, 2, 1349, 458, 3, 1348])).
% 1.71/1.39 tff(1358,plain,(c3_1(a8) | (~c2_1(a24)) | (~c0_1(a16)) | (~c1_1(a8)) | c0_1(a24) | c1_1(a24) | c3_1(a16) | c2_1(a8) | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.39 tff(1359,plain,
% 1.71/1.39 (c3_1(a8)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1358, 1347, 725, 3, 1055, 1054, 2, 1336, 1056])).
% 1.71/1.39 tff(1360,plain,
% 1.71/1.39 (((~hskp6) | c0_1(a8)) <=> ((~hskp6) | c0_1(a8))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1361,axiom,((~hskp6) | c0_1(a8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.71/1.39 tff(1362,plain,
% 1.71/1.39 ((~hskp6) | c0_1(a8)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 1.71/1.39 tff(1363,plain,
% 1.71/1.39 ((~hskp6) | c0_1(a8)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1362, 1360])).
% 1.71/1.39 tff(1364,plain,
% 1.71/1.39 ((~hskp6) | c0_1(a8)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1363, 1360])).
% 1.71/1.39 tff(1365,plain,
% 1.71/1.39 ((~hskp6) | c0_1(a8)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1364, 1360])).
% 1.71/1.39 tff(1366,plain,
% 1.71/1.39 ((~hskp6) | c0_1(a8)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1365, 1360])).
% 1.71/1.39 tff(1367,plain,
% 1.71/1.39 ((~hskp6) | c0_1(a8)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1366, 1360])).
% 1.71/1.39 tff(1368,plain,
% 1.71/1.39 ((~hskp6) | c0_1(a8)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1367, 1360])).
% 1.71/1.39 tff(1369,plain,
% 1.71/1.39 ((~hskp6) | c0_1(a8)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1368, 1360])).
% 1.71/1.39 tff(1370,plain,
% 1.71/1.39 (c0_1(a8)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1369, 1330])).
% 1.71/1.39 tff(1371,plain,
% 1.71/1.39 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a8) | (~ndr1_0) | (~c3_1(a8)) | (~c0_1(a8)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a8) | (~ndr1_0) | (~c3_1(a8)) | (~c0_1(a8)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1372,plain,
% 1.71/1.39 ((hskp18 | hskp17 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8))) <=> (hskp18 | hskp17 | c2_1(a8) | (~ndr1_0) | (~c3_1(a8)) | (~c0_1(a8)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1373,plain,
% 1.71/1.39 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a8) | (~ndr1_0) | (~c3_1(a8)) | (~c0_1(a8))))),
% 1.71/1.39 inference(monotonicity,[status(thm)],[1372])).
% 1.71/1.39 tff(1374,plain,
% 1.71/1.39 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a8) | (~ndr1_0) | (~c3_1(a8)) | (~c0_1(a8)))),
% 1.71/1.39 inference(transitivity,[status(thm)],[1373, 1371])).
% 1.71/1.39 tff(1375,plain,
% 1.71/1.39 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)))),
% 1.71/1.39 inference(quant_inst,[status(thm)],[])).
% 1.71/1.39 tff(1376,plain,
% 1.71/1.39 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a8) | (~ndr1_0) | (~c3_1(a8)) | (~c0_1(a8))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 1.71/1.39 tff(1377,plain,
% 1.71/1.39 ($false),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1376, 169, 731, 643, 1370, 1336, 741, 1359])).
% 1.71/1.39 tff(1378,plain,((~hskp6) | hskp18 | hskp17 | (~c0_1(a16)) | c1_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~c2_1(a24))), inference(lemma,lemma(discharge,[]))).
% 1.71/1.39 tff(1379,plain,
% 1.71/1.39 (hskp18),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1378, 1329, 643, 725, 3, 1055, 1054, 2, 1056])).
% 1.71/1.39 tff(1380,plain,
% 1.71/1.39 (~c1_1(a32)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[963, 1379])).
% 1.71/1.39 tff(1381,plain,
% 1.71/1.39 (((~hskp18) | (~c0_1(a32))) <=> ((~hskp18) | (~c0_1(a32)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1382,plain,
% 1.71/1.39 (((~c0_1(a32)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a32)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1383,axiom,((~c0_1(a32)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.71/1.39 tff(1384,plain,
% 1.71/1.39 ((~hskp18) | (~c0_1(a32))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 1.71/1.39 tff(1385,plain,
% 1.71/1.39 ((~hskp18) | (~c0_1(a32))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1384, 1381])).
% 1.71/1.39 tff(1386,plain,
% 1.71/1.39 (~c0_1(a32)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1385, 1379])).
% 1.71/1.39 tff(1387,plain,
% 1.71/1.39 (~c3_1(a32)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[969, 1379])).
% 1.71/1.39 tff(1388,assumption,(~c0_1(a32)), introduced(assumption)).
% 1.71/1.39 tff(1389,plain,
% 1.71/1.39 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a32)))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a32)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1390,plain,
% 1.71/1.39 ((hskp26 | hskp25 | (~ndr1_0) | c3_1(a32) | (~c2_1(a32)) | c0_1(a32)) <=> (hskp26 | hskp25 | c0_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a32)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1391,plain,
% 1.71/1.39 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a32) | (~c2_1(a32)) | c0_1(a32))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a32))))),
% 1.71/1.39 inference(monotonicity,[status(thm)],[1390])).
% 1.71/1.39 tff(1392,plain,
% 1.71/1.39 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a32) | (~c2_1(a32)) | c0_1(a32))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a32)))),
% 1.71/1.39 inference(transitivity,[status(thm)],[1391, 1389])).
% 1.71/1.39 tff(1393,plain,
% 1.71/1.39 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a32) | (~c2_1(a32)) | c0_1(a32))),
% 1.71/1.39 inference(quant_inst,[status(thm)],[])).
% 1.71/1.39 tff(1394,plain,
% 1.71/1.39 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a32))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 1.71/1.39 tff(1395,plain,
% 1.71/1.39 (hskp25 | c0_1(a32) | (~c2_1(a32))),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1394, 169, 84, 983, 1107])).
% 1.71/1.39 tff(1396,plain,
% 1.71/1.39 (~c2_1(a32)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1395, 1108, 1388])).
% 1.71/1.39 tff(1397,plain,
% 1.71/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a32) | c3_1(a32) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c0_1(a18)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c3_1(a32) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c0_1(a18)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a32))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1398,plain,
% 1.71/1.39 (((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a32) | c0_1(a32) | c3_1(a32)) <=> (c0_1(a32) | c3_1(a32) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c0_1(a18)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a32))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1399,plain,
% 1.71/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a32) | c0_1(a32) | c3_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a32) | c3_1(a32) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c0_1(a18)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a32)))),
% 1.71/1.39 inference(monotonicity,[status(thm)],[1398])).
% 1.71/1.39 tff(1400,plain,
% 1.71/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a32) | c0_1(a32) | c3_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c3_1(a32) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c0_1(a18)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a32))),
% 1.71/1.39 inference(transitivity,[status(thm)],[1399, 1397])).
% 1.71/1.39 tff(1401,plain,
% 1.71/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a32) | c0_1(a32) | c3_1(a32))),
% 1.71/1.39 inference(quant_inst,[status(thm)],[])).
% 1.71/1.39 tff(1402,plain,
% 1.71/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c3_1(a32) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c0_1(a18)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a32)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 1.71/1.39 tff(1403,plain,
% 1.71/1.39 (c1_1(a18)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1402, 169, 634, 1173, 1388, 983, 1089, 1151, 13, 1396, 1127])).
% 1.71/1.39 tff(1404,plain,
% 1.71/1.39 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.71/1.39 inference(bind,[status(th)],[])).
% 1.71/1.39 tff(1405,plain,
% 1.71/1.39 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.71/1.39 inference(quant_intro,[status(thm)],[1404])).
% 1.71/1.39 tff(1406,plain,
% 1.71/1.39 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1407,plain,
% 1.71/1.39 (^[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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.71/1.39 inference(bind,[status(th)],[])).
% 1.71/1.39 tff(1408,plain,
% 1.71/1.39 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.71/1.39 inference(quant_intro,[status(thm)],[1407])).
% 1.71/1.39 tff(1409,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.71/1.39 tff(1410,plain,
% 1.71/1.39 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1409, 1408])).
% 1.71/1.39 tff(1411,plain,
% 1.71/1.39 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1410, 1406])).
% 1.71/1.39 tff(1412,plain,(
% 1.71/1.39 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.71/1.39 inference(skolemize,[status(sab)],[1411])).
% 1.71/1.39 tff(1413,plain,
% 1.71/1.39 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1412, 1405])).
% 1.71/1.39 tff(1414,assumption,(hskp5), introduced(assumption)).
% 1.71/1.39 tff(1415,plain,
% 1.71/1.39 (((~hskp5) | (~c0_1(a7))) <=> ((~hskp5) | (~c0_1(a7)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1416,plain,
% 1.71/1.39 (((~c0_1(a7)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a7)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1417,axiom,((~c0_1(a7)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.71/1.39 tff(1418,plain,
% 1.71/1.39 ((~hskp5) | (~c0_1(a7))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 1.71/1.39 tff(1419,plain,
% 1.71/1.39 ((~hskp5) | (~c0_1(a7))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1418, 1415])).
% 1.71/1.39 tff(1420,plain,
% 1.71/1.39 (~c0_1(a7)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1419, 1414])).
% 1.71/1.39 tff(1421,plain,
% 1.71/1.39 (((~hskp5) | c1_1(a7)) <=> ((~hskp5) | c1_1(a7))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1422,axiom,((~hskp5) | c1_1(a7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.71/1.39 tff(1423,plain,
% 1.71/1.39 ((~hskp5) | c1_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1422, 1421])).
% 1.71/1.39 tff(1424,plain,
% 1.71/1.39 ((~hskp5) | c1_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1423, 1421])).
% 1.71/1.39 tff(1425,plain,
% 1.71/1.39 ((~hskp5) | c1_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1424, 1421])).
% 1.71/1.39 tff(1426,plain,
% 1.71/1.39 ((~hskp5) | c1_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1425, 1421])).
% 1.71/1.39 tff(1427,plain,
% 1.71/1.39 ((~hskp5) | c1_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1426, 1421])).
% 1.71/1.39 tff(1428,plain,
% 1.71/1.39 ((~hskp5) | c1_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1427, 1421])).
% 1.71/1.39 tff(1429,plain,
% 1.71/1.39 ((~hskp5) | c1_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1428, 1421])).
% 1.71/1.39 tff(1430,plain,
% 1.71/1.39 ((~hskp5) | c1_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1429, 1421])).
% 1.71/1.39 tff(1431,plain,
% 1.71/1.39 (c1_1(a7)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1430, 1414])).
% 1.71/1.39 tff(1432,assumption,(c2_1(a7)), introduced(assumption)).
% 1.71/1.39 tff(1433,assumption,(~c0_1(a7)), introduced(assumption)).
% 1.71/1.39 tff(1434,assumption,(c1_1(a7)), introduced(assumption)).
% 1.71/1.39 tff(1435,plain,
% 1.71/1.39 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1436,plain,
% 1.71/1.39 (((~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1437,plain,
% 1.71/1.39 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7))))),
% 1.71/1.39 inference(monotonicity,[status(thm)],[1436])).
% 1.71/1.39 tff(1438,plain,
% 1.71/1.39 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))),
% 1.71/1.39 inference(transitivity,[status(thm)],[1437, 1435])).
% 1.71/1.39 tff(1439,plain,
% 1.71/1.39 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 1.71/1.39 inference(quant_inst,[status(thm)],[])).
% 1.71/1.39 tff(1440,plain,
% 1.71/1.39 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7))),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 1.71/1.39 tff(1441,plain,
% 1.71/1.39 ($false),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1440, 169, 1434, 1388, 984, 983, 1433, 45, 1432])).
% 1.71/1.39 tff(1442,plain,((~c2_1(a7)) | (~c1_1(a7)) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.39 tff(1443,plain,
% 1.71/1.39 (~c2_1(a7)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1442, 1431, 1388, 984, 983, 1420])).
% 1.71/1.39 tff(1444,assumption,(~c2_1(a32)), introduced(assumption)).
% 1.71/1.39 tff(1445,plain,
% 1.71/1.39 (((~hskp5) | c3_1(a7)) <=> ((~hskp5) | c3_1(a7))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1446,axiom,((~hskp5) | c3_1(a7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.71/1.39 tff(1447,plain,
% 1.71/1.39 ((~hskp5) | c3_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 1.71/1.39 tff(1448,plain,
% 1.71/1.39 ((~hskp5) | c3_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1447, 1445])).
% 1.71/1.39 tff(1449,plain,
% 1.71/1.39 ((~hskp5) | c3_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1448, 1445])).
% 1.71/1.39 tff(1450,plain,
% 1.71/1.39 ((~hskp5) | c3_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1449, 1445])).
% 1.71/1.39 tff(1451,plain,
% 1.71/1.39 ((~hskp5) | c3_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1450, 1445])).
% 1.71/1.39 tff(1452,plain,
% 1.71/1.39 ((~hskp5) | c3_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1451, 1445])).
% 1.71/1.39 tff(1453,plain,
% 1.71/1.39 ((~hskp5) | c3_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1452, 1445])).
% 1.71/1.39 tff(1454,plain,
% 1.71/1.39 ((~hskp5) | c3_1(a7)),
% 1.71/1.39 inference(modus_ponens,[status(thm)],[1453, 1445])).
% 1.71/1.39 tff(1455,plain,
% 1.71/1.39 (c3_1(a7)),
% 1.71/1.39 inference(unit_resolution,[status(thm)],[1454, 1414])).
% 1.71/1.39 tff(1456,plain,
% 1.71/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c2_1(a7) | c2_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c2_1(a7) | c2_1(a32))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1457,plain,
% 1.71/1.39 (((~ndr1_0) | c2_1(a7) | c0_1(a7) | (~c3_1(a7)) | c3_1(a32) | c0_1(a32) | c2_1(a32) | c2_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c2_1(a7) | c2_1(a32))),
% 1.71/1.39 inference(rewrite,[status(thm)],[])).
% 1.71/1.39 tff(1458,plain,
% 1.71/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a7) | c0_1(a7) | (~c3_1(a7)) | c3_1(a32) | c0_1(a32) | c2_1(a32) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c2_1(a7) | c2_1(a32)))),
% 1.71/1.39 inference(monotonicity,[status(thm)],[1457])).
% 1.71/1.39 tff(1459,plain,
% 1.71/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a7) | c0_1(a7) | (~c3_1(a7)) | c3_1(a32) | c0_1(a32) | c2_1(a32) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c2_1(a7) | c2_1(a32))),
% 1.71/1.40 inference(transitivity,[status(thm)],[1458, 1456])).
% 1.71/1.40 tff(1460,plain,
% 1.71/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a7) | c0_1(a7) | (~c3_1(a7)) | c3_1(a32) | c0_1(a32) | c2_1(a32) | c2_1(a32) | c1_1(a32) | c0_1(a32))),
% 1.71/1.40 inference(quant_inst,[status(thm)],[])).
% 1.71/1.40 tff(1461,plain,
% 1.71/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c2_1(a7) | c2_1(a32)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1460, 1459])).
% 1.71/1.40 tff(1462,plain,
% 1.71/1.40 ($false),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1461, 169, 1455, 1388, 984, 983, 1420, 55, 1444, 1443])).
% 1.71/1.40 tff(1463,plain,((~hskp5) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c2_1(a32)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.40 tff(1464,plain,
% 1.71/1.40 (~hskp5),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1463, 1396, 983, 984, 1388])).
% 1.71/1.40 tff(1465,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a30) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a30) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a30)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1466,plain,
% 1.71/1.40 ((hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a30) | c2_1(a30) | (~c1_1(a30))) <=> (hskp5 | c0_1(a30) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a30)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1467,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a30) | c2_1(a30) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a30) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a30))))),
% 1.71/1.40 inference(monotonicity,[status(thm)],[1466])).
% 1.71/1.40 tff(1468,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a30) | c2_1(a30) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a30) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a30)))),
% 1.71/1.40 inference(transitivity,[status(thm)],[1467, 1465])).
% 1.71/1.40 tff(1469,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a30) | c2_1(a30) | (~c1_1(a30)))),
% 1.71/1.40 inference(quant_inst,[status(thm)],[])).
% 1.71/1.40 tff(1470,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a30) | c2_1(a30) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a30))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1469, 1468])).
% 1.71/1.40 tff(1471,plain,
% 1.71/1.40 ($false),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1470, 169, 1464, 634, 1162, 633, 1089, 1151, 1413, 1403])).
% 1.71/1.40 tff(1472,plain,(hskp25 | (~c1_1(a30)) | c0_1(a30) | c2_1(a30) | c0_1(a32) | c3_1(a32) | (~c3_1(a30)) | c1_1(a32) | (~c2_1(a24)) | c1_1(a24) | hskp26 | c0_1(a24)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.40 tff(1473,plain,
% 1.71/1.40 (hskp25),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1472, 1388, 633, 1089, 634, 983, 1127, 984, 1056, 1054, 84, 1055])).
% 1.71/1.40 tff(1474,plain,
% 1.71/1.40 (hskp19),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[891, 1473, 730, 729, 728])).
% 1.71/1.40 tff(1475,plain,
% 1.71/1.40 (~c0_1(a33)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[897, 1474])).
% 1.71/1.40 tff(1476,plain,
% 1.71/1.40 (c2_1(a33)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[908, 1474])).
% 1.71/1.40 tff(1477,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a33) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a33) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1478,plain,
% 1.71/1.40 (((~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c0_1(a33) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1479,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a33) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33))))),
% 1.71/1.40 inference(monotonicity,[status(thm)],[1478])).
% 1.71/1.40 tff(1480,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a33) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 1.71/1.40 inference(transitivity,[status(thm)],[1479, 1477])).
% 1.71/1.40 tff(1481,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 1.71/1.40 inference(quant_inst,[status(thm)],[])).
% 1.71/1.40 tff(1482,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a33) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 1.71/1.40 tff(1483,plain,
% 1.71/1.40 (~c1_1(a33)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1482, 169, 1476, 1475, 1388, 984, 983, 45])).
% 1.71/1.40 tff(1484,plain,
% 1.71/1.40 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.71/1.40 inference(bind,[status(th)],[])).
% 1.71/1.40 tff(1485,plain,
% 1.71/1.40 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.40 inference(quant_intro,[status(thm)],[1484])).
% 1.71/1.40 tff(1486,plain,
% 1.71/1.40 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1487,plain,
% 1.71/1.40 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~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)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.71/1.40 inference(bind,[status(th)],[])).
% 1.71/1.40 tff(1488,plain,
% 1.71/1.40 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.40 inference(quant_intro,[status(thm)],[1487])).
% 1.71/1.40 tff(1489,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.71/1.40 tff(1490,plain,
% 1.71/1.40 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1489, 1488])).
% 1.71/1.40 tff(1491,plain,
% 1.71/1.40 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1490, 1486])).
% 1.71/1.40 tff(1492,plain,(
% 1.71/1.40 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.40 inference(skolemize,[status(sab)],[1491])).
% 1.71/1.40 tff(1493,plain,
% 1.71/1.40 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1492, 1485])).
% 1.71/1.40 tff(1494,plain,
% 1.71/1.40 (((~hskp19) | c3_1(a33)) <=> ((~hskp19) | c3_1(a33))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1495,axiom,((~hskp19) | c3_1(a33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 1.71/1.40 tff(1496,plain,
% 1.71/1.40 ((~hskp19) | c3_1(a33)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 1.71/1.40 tff(1497,plain,
% 1.71/1.40 ((~hskp19) | c3_1(a33)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1496, 1494])).
% 1.71/1.40 tff(1498,plain,
% 1.71/1.40 ((~hskp19) | c3_1(a33)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1497, 1494])).
% 1.71/1.40 tff(1499,plain,
% 1.71/1.40 ((~hskp19) | c3_1(a33)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1498, 1494])).
% 1.71/1.40 tff(1500,plain,
% 1.71/1.40 ((~hskp19) | c3_1(a33)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1499, 1494])).
% 1.71/1.40 tff(1501,plain,
% 1.71/1.40 ((~hskp19) | c3_1(a33)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1500, 1494])).
% 1.71/1.40 tff(1502,plain,
% 1.71/1.40 ((~hskp19) | c3_1(a33)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1501, 1494])).
% 1.71/1.40 tff(1503,plain,
% 1.71/1.40 ((~hskp19) | c3_1(a33)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1502, 1494])).
% 1.71/1.40 tff(1504,plain,
% 1.71/1.40 (c3_1(a33)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1503, 1474])).
% 1.71/1.40 tff(1505,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1506,plain,
% 1.71/1.40 ((hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (hskp1 | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1507,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33)))),
% 1.71/1.40 inference(monotonicity,[status(thm)],[1506])).
% 1.71/1.40 tff(1508,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 1.71/1.40 inference(transitivity,[status(thm)],[1507, 1505])).
% 1.71/1.40 tff(1509,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 1.71/1.40 inference(quant_inst,[status(thm)],[])).
% 1.71/1.40 tff(1510,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 1.71/1.40 tff(1511,plain,
% 1.71/1.40 (hskp1),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1510, 169, 1476, 1504, 1388, 984, 983, 1493, 1483])).
% 1.71/1.40 tff(1512,plain,
% 1.71/1.40 (((~hskp1) | (~c0_1(a2))) <=> ((~hskp1) | (~c0_1(a2)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1513,plain,
% 1.71/1.40 (((~c0_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a2)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1514,axiom,((~c0_1(a2)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.71/1.40 tff(1515,plain,
% 1.71/1.40 ((~hskp1) | (~c0_1(a2))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1514, 1513])).
% 1.71/1.40 tff(1516,plain,
% 1.71/1.40 ((~hskp1) | (~c0_1(a2))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1515, 1512])).
% 1.71/1.40 tff(1517,plain,
% 1.71/1.40 (~c0_1(a2)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1516, 1511])).
% 1.71/1.40 tff(1518,plain,
% 1.71/1.40 (((~hskp1) | c2_1(a2)) <=> ((~hskp1) | c2_1(a2))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1519,axiom,((~hskp1) | c2_1(a2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.71/1.40 tff(1520,plain,
% 1.71/1.40 ((~hskp1) | c2_1(a2)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1519, 1518])).
% 1.71/1.40 tff(1521,plain,
% 1.71/1.40 ((~hskp1) | c2_1(a2)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1520, 1518])).
% 1.71/1.40 tff(1522,plain,
% 1.71/1.40 ((~hskp1) | c2_1(a2)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1521, 1518])).
% 1.71/1.40 tff(1523,plain,
% 1.71/1.40 ((~hskp1) | c2_1(a2)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1522, 1518])).
% 1.71/1.40 tff(1524,plain,
% 1.71/1.40 ((~hskp1) | c2_1(a2)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1523, 1518])).
% 1.71/1.40 tff(1525,plain,
% 1.71/1.40 ((~hskp1) | c2_1(a2)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1524, 1518])).
% 1.71/1.40 tff(1526,plain,
% 1.71/1.40 ((~hskp1) | c2_1(a2)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1525, 1518])).
% 1.71/1.40 tff(1527,plain,
% 1.71/1.40 ((~hskp1) | c2_1(a2)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1526, 1518])).
% 1.71/1.40 tff(1528,plain,
% 1.71/1.40 (c2_1(a2)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1527, 1511])).
% 1.71/1.40 tff(1529,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1530,plain,
% 1.71/1.40 (((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1531,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2))))),
% 1.71/1.40 inference(monotonicity,[status(thm)],[1530])).
% 1.71/1.40 tff(1532,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)))),
% 1.71/1.40 inference(transitivity,[status(thm)],[1531, 1529])).
% 1.71/1.40 tff(1533,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 1.71/1.40 inference(quant_inst,[status(thm)],[])).
% 1.71/1.40 tff(1534,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 1.71/1.40 tff(1535,plain,
% 1.71/1.40 (~c1_1(a2)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1534, 169, 1528, 1388, 984, 983, 1517, 45])).
% 1.71/1.40 tff(1536,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1537,plain,
% 1.71/1.40 ((hskp10 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30))) <=> (hskp10 | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1538,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33)))),
% 1.71/1.40 inference(monotonicity,[status(thm)],[1537])).
% 1.71/1.40 tff(1539,plain,
% 1.71/1.40 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 1.71/1.40 inference(transitivity,[status(thm)],[1538, 1536])).
% 1.71/1.40 tff(1540,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))),
% 1.71/1.40 inference(quant_inst,[status(thm)],[])).
% 1.71/1.40 tff(1541,plain,
% 1.71/1.40 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33)),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 1.71/1.40 tff(1542,plain,
% 1.71/1.40 (hskp10),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1541, 169, 1476, 1504, 634, 633, 1137, 1127, 1483])).
% 1.71/1.40 tff(1543,plain,
% 1.71/1.40 (~c3_1(a18)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1150, 1542])).
% 1.71/1.40 tff(1544,plain,
% 1.71/1.40 (c2_1(a18)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1161, 1542])).
% 1.71/1.40 tff(1545,plain,
% 1.71/1.40 (c0_1(a18)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1172, 1542])).
% 1.71/1.40 tff(1546,plain,
% 1.71/1.40 (hskp20),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1233, 169, 84, 1545, 1544, 1543, 1227])).
% 1.71/1.40 tff(1547,plain,
% 1.71/1.40 (~c3_1(a37)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1239, 1546])).
% 1.71/1.40 tff(1548,plain,
% 1.71/1.40 (~c0_1(a37)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1245, 1546])).
% 1.71/1.40 tff(1549,plain,
% 1.71/1.40 (c1_1(a37)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1256, 1546])).
% 1.71/1.40 tff(1550,plain,
% 1.71/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c0_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1551,plain,
% 1.71/1.40 (((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a2) | c0_1(a2) | (~c2_1(a2))) <=> (c0_1(a37) | c3_1(a37) | c0_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1552,plain,
% 1.71/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a2) | c0_1(a2) | (~c2_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c0_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37))))),
% 1.71/1.40 inference(monotonicity,[status(thm)],[1551])).
% 1.71/1.40 tff(1553,plain,
% 1.71/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a2) | c0_1(a2) | (~c2_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))),
% 1.71/1.40 inference(transitivity,[status(thm)],[1552, 1550])).
% 1.71/1.40 tff(1554,plain,
% 1.71/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a2) | c0_1(a2) | (~c2_1(a2)))),
% 1.71/1.40 inference(quant_inst,[status(thm)],[])).
% 1.71/1.40 tff(1555,plain,
% 1.71/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37))),
% 1.71/1.40 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 1.71/1.40 tff(1556,plain,
% 1.71/1.40 ($false),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1555, 169, 1549, 1476, 1504, 1528, 1548, 1547, 1517, 83, 1483, 1535])).
% 1.71/1.40 tff(1557,plain,(c0_1(a32) | c1_1(a32) | c3_1(a32) | hskp26 | (~c1_1(a30)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6) | c2_1(a30) | (~c2_1(a24)) | c1_1(a24) | c0_1(a24)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.40 tff(1558,plain,
% 1.71/1.40 ($false),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1557, 1387, 1386, 1380, 84, 634, 633, 1097, 730, 729, 728, 1089, 1056, 1054, 1055])).
% 1.71/1.40 tff(1559,plain,(c1_1(a16) | hskp26 | (~c1_1(a30)) | c0_1(a30) | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6) | c2_1(a30) | (~c2_1(a24)) | c1_1(a24) | c0_1(a24) | hskp17 | (~c0_1(a16)) | c3_1(a16) | c0_1(a53) | c1_1(a53) | hskp0 | (~c3_1(a53))), inference(lemma,lemma(discharge,[]))).
% 1.71/1.40 tff(1560,plain,
% 1.71/1.40 ($false),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1559, 1088, 1087, 3, 84, 730, 729, 728, 1086, 1056, 1054, 1055, 643, 725, 2, 370, 369, 344, 371])).
% 1.71/1.40 tff(1561,plain,(hskp26 | c1_1(a16) | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6) | (~c2_1(a24)) | c1_1(a24) | c0_1(a24) | hskp17 | (~c0_1(a16)) | c3_1(a16) | c0_1(a53) | c1_1(a53) | hskp0 | (~c3_1(a53)) | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.40 tff(1562,plain,
% 1.71/1.40 (hskp26),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[1561, 1074, 653, 652, 651, 1042, 1025, 1031, 643, 591, 574, 347, 346, 344, 355, 580])).
% 1.71/1.40 tff(1563,plain,
% 1.71/1.40 (c3_1(a10)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[689, 1562])).
% 1.71/1.40 tff(1564,plain,
% 1.71/1.40 (c0_1(a10)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[666, 1562])).
% 1.71/1.40 tff(1565,plain,
% 1.71/1.40 (c2_1(a10)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[678, 1562])).
% 1.71/1.40 tff(1566,assumption,(c0_1(a5)), introduced(assumption)).
% 1.71/1.40 tff(1567,assumption,(~c2_1(a5)), introduced(assumption)).
% 1.71/1.40 tff(1568,assumption,(hskp18), introduced(assumption)).
% 1.71/1.40 tff(1569,plain,
% 1.71/1.40 (~c1_1(a32)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[963, 1568])).
% 1.71/1.40 tff(1570,plain,
% 1.71/1.40 (~c3_1(a32)),
% 1.71/1.40 inference(unit_resolution,[status(thm)],[969, 1568])).
% 1.71/1.40 tff(1571,plain,
% 1.71/1.40 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.71/1.40 inference(bind,[status(th)],[])).
% 1.71/1.40 tff(1572,plain,
% 1.71/1.40 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.71/1.40 inference(quant_intro,[status(thm)],[1571])).
% 1.71/1.40 tff(1573,plain,
% 1.71/1.40 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.71/1.40 inference(rewrite,[status(thm)],[])).
% 1.71/1.40 tff(1574,plain,
% 1.71/1.40 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.71/1.41 inference(bind,[status(th)],[])).
% 1.71/1.41 tff(1575,plain,
% 1.71/1.41 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.71/1.41 inference(quant_intro,[status(thm)],[1574])).
% 1.71/1.41 tff(1576,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 1.71/1.41 tff(1577,plain,
% 1.71/1.41 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 1.71/1.41 tff(1578,plain,
% 1.71/1.41 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[1577, 1573])).
% 1.71/1.41 tff(1579,plain,(
% 1.71/1.41 ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.71/1.41 inference(skolemize,[status(sab)],[1578])).
% 1.71/1.41 tff(1580,plain,
% 1.71/1.41 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[1579, 1572])).
% 1.71/1.41 tff(1581,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a32)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a32)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(1582,plain,
% 1.71/1.41 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32))) <=> (c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a32)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(1583,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a32))))),
% 1.71/1.41 inference(monotonicity,[status(thm)],[1582])).
% 1.71/1.41 tff(1584,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a32)))),
% 1.71/1.41 inference(transitivity,[status(thm)],[1583, 1581])).
% 1.71/1.41 tff(1585,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32)))),
% 1.71/1.41 inference(quant_inst,[status(thm)],[])).
% 1.71/1.41 tff(1586,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a32))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[1585, 1584])).
% 1.71/1.41 tff(1587,plain,
% 1.71/1.41 (c1_1(a32) | (~c2_1(a32))),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1586, 169, 713, 712, 711, 983, 1580])).
% 1.71/1.41 tff(1588,plain,
% 1.71/1.41 (~c2_1(a32)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1587, 984])).
% 1.71/1.41 tff(1589,plain,
% 1.71/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a32) | c3_1(a32) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c3_1(a32) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(1590,plain,
% 1.71/1.41 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32) | c0_1(a32) | c3_1(a32)) <=> (c0_1(a32) | c3_1(a32) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(1591,plain,
% 1.71/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32) | c0_1(a32) | c3_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a32) | c3_1(a32) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32)))),
% 1.71/1.41 inference(monotonicity,[status(thm)],[1590])).
% 1.71/1.41 tff(1592,plain,
% 1.71/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32) | c0_1(a32) | c3_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c3_1(a32) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32))),
% 1.71/1.41 inference(transitivity,[status(thm)],[1591, 1589])).
% 1.71/1.41 tff(1593,plain,
% 1.71/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32) | c0_1(a32) | c3_1(a32))),
% 1.71/1.41 inference(quant_inst,[status(thm)],[])).
% 1.71/1.41 tff(1594,plain,
% 1.71/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c3_1(a32) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)) | c2_1(a32)),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[1593, 1592])).
% 1.71/1.41 tff(1595,plain,
% 1.71/1.41 (c0_1(a32)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1594, 169, 725, 730, 729, 983, 2, 728, 13, 3, 1588])).
% 1.71/1.41 tff(1596,plain,
% 1.71/1.41 (~hskp18),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1385, 1595])).
% 1.71/1.41 tff(1597,plain,
% 1.71/1.41 (~c0_1(a6)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[942, 1596])).
% 1.71/1.41 tff(1598,plain,
% 1.71/1.41 (~hskp6),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1378, 1596, 643, 725, 3, 1055, 1054, 2, 1056])).
% 1.71/1.41 tff(1599,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c3_1(a6)) | c0_1(a6))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c3_1(a6)) | c0_1(a6))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(1600,plain,
% 1.71/1.41 ((hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6))) <=> (hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c3_1(a6)) | c0_1(a6))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(1601,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c3_1(a6)) | c0_1(a6)))),
% 1.71/1.41 inference(monotonicity,[status(thm)],[1600])).
% 1.71/1.41 tff(1602,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c3_1(a6)) | c0_1(a6))),
% 1.71/1.41 inference(transitivity,[status(thm)],[1601, 1599])).
% 1.71/1.41 tff(1603,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6)))),
% 1.71/1.41 inference(quant_inst,[status(thm)],[])).
% 1.71/1.41 tff(1604,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c3_1(a6)) | c0_1(a6)),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 1.71/1.41 tff(1605,plain,
% 1.71/1.41 (~c1_1(a10)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1604, 169, 1598, 712, 711, 729, 728, 1298, 1597])).
% 1.71/1.41 tff(1606,assumption,(~c1_1(a10)), introduced(assumption)).
% 1.71/1.41 tff(1607,plain,
% 1.71/1.41 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.71/1.41 inference(bind,[status(th)],[])).
% 1.71/1.41 tff(1608,plain,
% 1.71/1.41 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.71/1.41 inference(quant_intro,[status(thm)],[1607])).
% 1.71/1.41 tff(1609,plain,
% 1.71/1.41 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(1610,plain,
% 1.71/1.41 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.71/1.41 inference(bind,[status(th)],[])).
% 1.71/1.41 tff(1611,plain,
% 1.71/1.41 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.71/1.41 inference(quant_intro,[status(thm)],[1610])).
% 1.71/1.41 tff(1612,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 1.71/1.41 tff(1613,plain,
% 1.71/1.41 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[1612, 1611])).
% 1.71/1.41 tff(1614,plain,
% 1.71/1.41 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[1613, 1609])).
% 1.71/1.41 tff(1615,plain,(
% 1.71/1.41 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.71/1.41 inference(skolemize,[status(sab)],[1614])).
% 1.71/1.41 tff(1616,plain,
% 1.71/1.41 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[1615, 1608])).
% 1.71/1.41 tff(1617,assumption,(~hskp13), introduced(assumption)).
% 1.71/1.41 tff(1618,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a10)) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a10)) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a5)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(1619,plain,
% 1.71/1.41 ((hskp13 | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5))) <=> (hskp13 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a10)) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a5)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(1620,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a10)) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a5))))),
% 1.71/1.41 inference(monotonicity,[status(thm)],[1619])).
% 1.71/1.41 tff(1621,plain,
% 1.71/1.41 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a10)) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a5)))),
% 1.71/1.41 inference(transitivity,[status(thm)],[1620, 1618])).
% 1.71/1.41 tff(1622,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))),
% 1.71/1.41 inference(quant_inst,[status(thm)],[])).
% 1.71/1.41 tff(1623,plain,
% 1.71/1.41 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a10)) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a5))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 1.71/1.41 tff(1624,plain,
% 1.71/1.41 ($false),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1623, 169, 1617, 713, 711, 1053, 1567, 1616, 1566, 1606])).
% 1.71/1.41 tff(1625,plain,(c1_1(a10) | hskp13 | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5))), inference(lemma,lemma(discharge,[]))).
% 1.71/1.41 tff(1626,plain,
% 1.71/1.41 (hskp13),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1625, 1605, 713, 711, 1053, 1567, 1566])).
% 1.71/1.41 tff(1627,plain,
% 1.71/1.41 (~c3_1(a22)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[482, 1626])).
% 1.71/1.41 tff(1628,plain,
% 1.71/1.41 (~c2_1(a22)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[488, 1626])).
% 1.71/1.41 tff(1629,plain,
% 1.71/1.41 (~c0_1(a22)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[494, 1626])).
% 1.71/1.41 tff(1630,plain,
% 1.71/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(1631,plain,
% 1.71/1.41 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c2_1(a22) | c0_1(a22) | c3_1(a22)) <=> ((~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(1632,plain,
% 1.71/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6))))),
% 1.71/1.41 inference(monotonicity,[status(thm)],[1631])).
% 1.71/1.41 tff(1633,plain,
% 1.71/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.71/1.41 inference(transitivity,[status(thm)],[1632, 1630])).
% 1.71/1.41 tff(1634,plain,
% 1.71/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a32) | c1_1(a32) | (~c0_1(a32)) | c2_1(a22) | c0_1(a22) | c3_1(a22))),
% 1.71/1.41 inference(quant_inst,[status(thm)],[])).
% 1.71/1.41 tff(1635,plain,
% 1.71/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a32)) | c1_1(a32) | c3_1(a32) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6))),
% 1.71/1.41 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 1.71/1.41 tff(1636,plain,
% 1.71/1.41 ($false),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1635, 169, 730, 729, 1595, 984, 983, 1629, 1628, 1627, 728, 13])).
% 1.71/1.41 tff(1637,plain,(c1_1(a32) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a32) | c2_1(a6) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | (~c2_1(a10)) | hskp17 | (~c0_1(a16)) | c1_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~c2_1(a24))), inference(lemma,lemma(discharge,[]))).
% 1.71/1.41 tff(1638,plain,
% 1.71/1.41 ($false),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1637, 1570, 1569, 729, 730, 728, 713, 711, 1053, 1567, 1566, 712, 643, 725, 3, 1055, 1054, 2, 1056])).
% 1.71/1.41 tff(1639,plain,((~hskp18) | (~c3_1(a6)) | (~c1_1(a6)) | c2_1(a6) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | (~c2_1(a10)) | hskp17 | (~c0_1(a16)) | c1_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~c2_1(a24))), inference(lemma,lemma(discharge,[]))).
% 1.71/1.41 tff(1640,plain,
% 1.71/1.41 (~hskp18),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1639, 1564, 653, 651, 652, 1563, 1051, 1075, 1083, 1565, 643, 591, 1074, 1031, 1025, 574, 1042])).
% 1.71/1.41 tff(1641,plain,
% 1.71/1.41 (hskp18 | (~c0_1(a6))),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[941, 169, 643, 652, 651, 741])).
% 1.71/1.41 tff(1642,plain,
% 1.71/1.41 (~c0_1(a6)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1641, 1640])).
% 1.71/1.41 tff(1643,plain,
% 1.71/1.41 (~hskp6),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1378, 1640, 643, 591, 1074, 1031, 1025, 574, 1042])).
% 1.71/1.41 tff(1644,plain,
% 1.71/1.41 (~c1_1(a10)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1604, 169, 1643, 1565, 1563, 652, 651, 1298, 1642])).
% 1.71/1.41 tff(1645,plain,
% 1.71/1.41 (hskp13),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[1625, 1644, 1564, 1563, 1051, 1075, 1083])).
% 1.71/1.41 tff(1646,plain,
% 1.71/1.41 (~c3_1(a22)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[482, 1645])).
% 1.71/1.41 tff(1647,plain,
% 1.71/1.41 (~c2_1(a22)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[488, 1645])).
% 1.71/1.41 tff(1648,plain,
% 1.71/1.41 (~c0_1(a22)),
% 1.71/1.41 inference(unit_resolution,[status(thm)],[494, 1645])).
% 1.71/1.41 tff(1649,plain,
% 1.71/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(1650,plain,
% 1.71/1.41 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22)) <=> (c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))),
% 1.71/1.41 inference(rewrite,[status(thm)],[])).
% 1.71/1.41 tff(1651,plain,
% 1.71/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16))))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[1650])).
% 1.71/1.42 tff(1652,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16)))),
% 1.71/1.42 inference(transitivity,[status(thm)],[1651, 1649])).
% 1.71/1.42 tff(1653,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(1654,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a16) | (~c0_1(a16))),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[1653, 1652])).
% 1.71/1.42 tff(1655,plain,
% 1.71/1.42 ($false),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1654, 169, 591, 653, 652, 1648, 1647, 1646, 574, 651, 13, 1074])).
% 1.71/1.42 tff(1656,plain,(hskp2 | hskp17 | hskp0 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.71/1.42 tff(1657,plain,
% 1.71/1.42 (hskp2),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1656, 344, 643, 73])).
% 1.71/1.42 tff(1658,plain,
% 1.71/1.42 (~c3_1(a4)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[400, 1657])).
% 1.71/1.42 tff(1659,plain,
% 1.71/1.42 (~c2_1(a4)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[417, 1657])).
% 1.71/1.42 tff(1660,plain,
% 1.71/1.42 (c1_1(a4)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[411, 1657])).
% 1.71/1.42 tff(1661,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | (~c0_1(a16)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(1662,plain,
% 1.71/1.42 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | (~c0_1(a16)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(1663,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | (~c0_1(a16))))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[1662])).
% 1.71/1.42 tff(1664,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | (~c0_1(a16)))),
% 1.71/1.42 inference(transitivity,[status(thm)],[1663, 1661])).
% 1.71/1.42 tff(1665,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(1666,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | (~c0_1(a16))),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 1.71/1.42 tff(1667,plain,
% 1.71/1.42 ($false),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1666, 169, 667, 679, 690, 725, 421, 24, 2, 440, 420, 439])).
% 1.71/1.42 tff(1668,plain,((~hskp26) | (~c0_1(a16)) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.42 tff(1669,plain,
% 1.71/1.42 (~hskp26),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1668, 440, 725, 24, 2, 421, 420])).
% 1.71/1.42 tff(1670,plain,
% 1.71/1.42 (hskp16),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1084, 1669])).
% 1.71/1.42 tff(1671,plain,
% 1.71/1.42 (~c2_1(a30)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[615, 1670])).
% 1.71/1.42 tff(1672,plain,
% 1.71/1.42 (~c0_1(a30)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[621, 1670])).
% 1.71/1.42 tff(1673,plain,
% 1.71/1.42 (c1_1(a16) | c3_1(a30)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1095, 169, 725, 730, 729, 1672, 1671, 2, 728, 13])).
% 1.71/1.42 tff(1674,plain,
% 1.71/1.42 (c3_1(a30)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1673, 3])).
% 1.71/1.42 tff(1675,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a53)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(1676,plain,
% 1.71/1.42 (((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a53) | c1_1(a53) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a53)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(1677,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a53) | c1_1(a53) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a53))))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[1676])).
% 1.71/1.42 tff(1678,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a53)))),
% 1.71/1.42 inference(transitivity,[status(thm)],[1677, 1675])).
% 1.71/1.42 tff(1679,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(1680,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a53) | c1_1(a53) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a53))),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 1.71/1.42 tff(1681,plain,
% 1.71/1.42 (c1_1(a16) | (~c2_1(a53))),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1680, 169, 725, 421, 370, 369, 2, 440, 420, 458])).
% 1.71/1.42 tff(1682,plain,
% 1.71/1.42 (~c2_1(a53)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1681, 3])).
% 1.71/1.42 tff(1683,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(1684,plain,
% 1.71/1.42 (((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(1685,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42))))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[1684])).
% 1.71/1.42 tff(1686,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42)))),
% 1.71/1.42 inference(transitivity,[status(thm)],[1685, 1683])).
% 1.71/1.42 tff(1687,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a42)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(1688,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c0_1(a42))),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[1687, 1686])).
% 1.71/1.42 tff(1689,plain,
% 1.71/1.42 (~c0_1(a42)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1688, 169, 815, 804, 725, 421, 24, 2, 440, 420, 439])).
% 1.71/1.42 tff(1690,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a42) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a42)) | c0_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) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a42)) | c0_1(a42))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(1691,plain,
% 1.71/1.42 (((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a42) | c0_1(a42) | (~c2_1(a42))) <=> (c1_1(a42) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a42)) | c0_1(a42))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(1692,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a42) | c0_1(a42) | (~c2_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) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a42) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a42)) | c0_1(a42)))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[1691])).
% 1.71/1.42 tff(1693,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a42) | c0_1(a42) | (~c2_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) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a42)) | c0_1(a42))),
% 1.71/1.42 inference(transitivity,[status(thm)],[1692, 1690])).
% 1.71/1.42 tff(1694,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c1_1(a42) | c0_1(a42) | (~c2_1(a42)))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(1695,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c1_1(a16) | (~c0_1(a16)) | (~c2_1(a42)) | c0_1(a42)),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[1694, 1693])).
% 1.71/1.42 tff(1696,plain,
% 1.71/1.42 ($false),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1695, 169, 815, 725, 421, 828, 2, 440, 420, 458, 3, 1689])).
% 1.71/1.42 tff(1697,plain,((~hskp21) | (~c0_1(a16)) | (~c1_1(a4)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | c1_1(a16) | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.71/1.42 tff(1698,plain,
% 1.71/1.42 (~hskp21),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1697, 3, 421, 2, 440, 420, 725, 24])).
% 1.71/1.42 tff(1699,plain,
% 1.71/1.42 (hskp25),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[167, 1698, 643])).
% 1.71/1.42 tff(1700,plain,
% 1.71/1.42 (c2_1(a9)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[859, 1699])).
% 1.71/1.42 tff(1701,plain,
% 1.71/1.42 (c0_1(a9)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[881, 1699])).
% 1.71/1.42 tff(1702,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(1703,plain,
% 1.71/1.42 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(1704,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9))))),
% 1.71/1.42 inference(monotonicity,[status(thm)],[1703])).
% 1.71/1.42 tff(1705,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.71/1.42 inference(transitivity,[status(thm)],[1704, 1702])).
% 1.71/1.42 tff(1706,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.71/1.42 inference(quant_inst,[status(thm)],[])).
% 1.71/1.42 tff(1707,plain,
% 1.71/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9))),
% 1.71/1.42 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 1.71/1.42 tff(1708,plain,
% 1.71/1.42 (~c3_1(a9)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1707, 169, 1701, 1700, 725, 421, 24, 2, 440, 420, 439])).
% 1.71/1.42 tff(1709,plain,
% 1.71/1.42 (hskp20 | c3_1(a9)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1315, 169, 1669, 1701, 1700, 1227])).
% 1.71/1.42 tff(1710,plain,
% 1.71/1.42 (hskp20),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1709, 1708])).
% 1.71/1.42 tff(1711,plain,
% 1.71/1.42 (~c3_1(a37)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1239, 1710])).
% 1.71/1.42 tff(1712,plain,
% 1.71/1.42 (~c0_1(a37)),
% 1.71/1.42 inference(unit_resolution,[status(thm)],[1245, 1710])).
% 1.71/1.42 tff(1713,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | c2_1(a37) | c2_1(a53))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | c2_1(a37) | c2_1(a53))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(1714,plain,
% 1.71/1.42 (((~ndr1_0) | c2_1(a30) | c0_1(a30) | (~c3_1(a30)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a53) | c1_1(a53) | c0_1(a53)) <=> (c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | c2_1(a37) | c2_1(a53))),
% 1.71/1.42 inference(rewrite,[status(thm)],[])).
% 1.71/1.42 tff(1715,plain,
% 1.71/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a30) | c0_1(a30) | (~c3_1(a30)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a53) | c1_1(a53) | c0_1(a53))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | c2_1(a37) | c2_1(a53)))),
% 1.71/1.43 inference(monotonicity,[status(thm)],[1714])).
% 1.71/1.43 tff(1716,plain,
% 1.71/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a30) | c0_1(a30) | (~c3_1(a30)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a53) | c1_1(a53) | c0_1(a53))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | c2_1(a37) | c2_1(a53))),
% 1.71/1.43 inference(transitivity,[status(thm)],[1715, 1713])).
% 1.71/1.43 tff(1717,plain,
% 1.71/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a30) | c0_1(a30) | (~c3_1(a30)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a53) | c1_1(a53) | c0_1(a53))),
% 1.71/1.43 inference(quant_inst,[status(thm)],[])).
% 1.71/1.43 tff(1718,plain,
% 1.71/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a53) | c1_1(a53) | c0_1(a37) | c3_1(a37) | c0_1(a30) | c2_1(a30) | (~ndr1_0) | (~c3_1(a30)) | c2_1(a37) | c2_1(a53)),
% 1.71/1.43 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 1.71/1.43 tff(1719,plain,
% 1.71/1.43 (c2_1(a37)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[1718, 169, 370, 369, 1712, 1711, 1672, 1671, 55, 1682, 1674])).
% 1.71/1.43 tff(1720,plain,
% 1.71/1.43 (c1_1(a9)),
% 1.71/1.43 inference(unit_resolution,[status(thm)],[870, 1699])).
% 1.71/1.43 tff(1721,plain,
% 1.71/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(1722,plain,
% 1.71/1.43 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37))) <=> (c0_1(a37) | c3_1(a37) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.71/1.43 inference(rewrite,[status(thm)],[])).
% 1.71/1.43 tff(1723,plain,
% 1.71/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))))),
% 1.71/1.43 inference(monotonicity,[status(thm)],[1722])).
% 1.71/1.43 tff(1724,plain,
% 1.71/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.77/1.43 inference(transitivity,[status(thm)],[1723, 1721])).
% 1.77/1.43 tff(1725,plain,
% 1.77/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))),
% 1.77/1.43 inference(quant_inst,[status(thm)],[])).
% 1.77/1.43 tff(1726,plain,
% 1.77/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))),
% 1.77/1.43 inference(modus_ponens,[status(thm)],[1725, 1724])).
% 1.77/1.43 tff(1727,plain,
% 1.77/1.43 ($false),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1726, 169, 1701, 1720, 1700, 421, 1712, 1711, 440, 420, 34, 1719])).
% 1.77/1.43 tff(1728,plain,(c1_1(a16) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | c0_1(a53) | c1_1(a53) | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | hskp17 | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.43 tff(1729,plain,
% 1.77/1.43 (c1_1(a16)),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1728, 1660, 1659, 1658, 347, 346, 591, 580, 574, 643, 653, 652, 651])).
% 1.77/1.43 tff(1730,plain,
% 1.77/1.43 (~hskp26),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1668, 1659, 591, 580, 574, 1660, 1658])).
% 1.77/1.43 tff(1731,plain,
% 1.77/1.43 (~hskp27),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[780, 731, 24, 2, 772, 725, 643])).
% 1.77/1.43 tff(1732,assumption,(~c0_1(a6)), introduced(assumption)).
% 1.77/1.43 tff(1733,plain,
% 1.77/1.43 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a42) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a42) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.77/1.43 inference(rewrite,[status(thm)],[])).
% 1.77/1.43 tff(1734,plain,
% 1.77/1.43 ((hskp10 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a6) | (~c3_1(a6)) | (~c1_1(a6))) <=> (hskp10 | c1_1(a42) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.77/1.43 inference(rewrite,[status(thm)],[])).
% 1.77/1.43 tff(1735,plain,
% 1.77/1.43 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a42) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | (~c2_1(a42)) | (~c3_1(a42))))),
% 1.77/1.43 inference(monotonicity,[status(thm)],[1734])).
% 1.77/1.43 tff(1736,plain,
% 1.77/1.43 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a42) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.77/1.43 inference(transitivity,[status(thm)],[1735, 1733])).
% 1.77/1.43 tff(1737,plain,
% 1.77/1.43 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))),
% 1.77/1.43 inference(quant_inst,[status(thm)],[])).
% 1.77/1.43 tff(1738,plain,
% 1.77/1.43 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a42) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | (~c2_1(a42)) | (~c3_1(a42))),
% 1.77/1.43 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 1.77/1.43 tff(1739,plain,
% 1.77/1.43 (hskp10),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1738, 169, 815, 804, 730, 729, 828, 1137, 1732])).
% 1.77/1.43 tff(1740,plain,
% 1.77/1.43 (~c3_1(a18)),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1150, 1739])).
% 1.77/1.43 tff(1741,plain,
% 1.77/1.43 (c2_1(a18)),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1161, 1739])).
% 1.77/1.43 tff(1742,plain,
% 1.77/1.43 (c0_1(a18)),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1172, 1739])).
% 1.77/1.43 tff(1743,plain,
% 1.77/1.43 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))),
% 1.77/1.43 inference(rewrite,[status(thm)],[])).
% 1.77/1.43 tff(1744,plain,
% 1.77/1.43 ((hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a42) | (~c3_1(a42)) | (~c2_1(a42))) <=> (hskp11 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))),
% 1.77/1.43 inference(rewrite,[status(thm)],[])).
% 1.77/1.43 tff(1745,plain,
% 1.77/1.43 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a42) | (~c3_1(a42)) | (~c2_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42)))),
% 1.77/1.43 inference(monotonicity,[status(thm)],[1744])).
% 1.77/1.43 tff(1746,plain,
% 1.77/1.43 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a42) | (~c3_1(a42)) | (~c2_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))),
% 1.77/1.43 inference(transitivity,[status(thm)],[1745, 1743])).
% 1.77/1.43 tff(1747,plain,
% 1.77/1.43 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a42) | (~c3_1(a42)) | (~c2_1(a42)))),
% 1.77/1.43 inference(quant_inst,[status(thm)],[])).
% 1.77/1.43 tff(1748,plain,
% 1.77/1.43 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42)),
% 1.77/1.43 inference(modus_ponens,[status(thm)],[1747, 1746])).
% 1.77/1.43 tff(1749,plain,
% 1.77/1.43 (hskp11),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1748, 169, 815, 804, 1742, 1741, 1740, 1126, 822])).
% 1.77/1.43 tff(1750,plain,
% 1.77/1.43 (~c1_1(a19)),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1209, 1749])).
% 1.77/1.43 tff(1751,plain,
% 1.77/1.43 (hskp20),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1233, 169, 84, 1742, 1741, 1740, 1227])).
% 1.77/1.43 tff(1752,plain,
% 1.77/1.43 (~c3_1(a37)),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1239, 1751])).
% 1.77/1.43 tff(1753,plain,
% 1.77/1.43 (~c0_1(a37)),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1245, 1751])).
% 1.77/1.43 tff(1754,plain,
% 1.77/1.43 (c2_1(a19)),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1196, 1749])).
% 1.77/1.43 tff(1755,plain,
% 1.77/1.43 (c1_1(a37)),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1256, 1751])).
% 1.77/1.43 tff(1756,plain,
% 1.77/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a42) | c0_1(a37) | c3_1(a37) | c1_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c1_1(a37)) | (~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) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c0_1(a37) | c3_1(a37) | c1_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c1_1(a37)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.77/1.43 inference(rewrite,[status(thm)],[])).
% 1.77/1.43 tff(1757,plain,
% 1.77/1.43 (((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a19) | c0_1(a19) | (~c2_1(a19))) <=> (c1_1(a42) | c0_1(a37) | c3_1(a37) | c1_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c1_1(a37)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.77/1.43 inference(rewrite,[status(thm)],[])).
% 1.77/1.43 tff(1758,plain,
% 1.77/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a19) | c0_1(a19) | (~c2_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a42) | c0_1(a37) | c3_1(a37) | c1_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c1_1(a37)) | (~c2_1(a42)) | (~c3_1(a42))))),
% 1.77/1.43 inference(monotonicity,[status(thm)],[1757])).
% 1.77/1.43 tff(1759,plain,
% 1.77/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a19) | c0_1(a19) | (~c2_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c0_1(a37) | c3_1(a37) | c1_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c1_1(a37)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.77/1.43 inference(transitivity,[status(thm)],[1758, 1756])).
% 1.77/1.43 tff(1760,plain,
% 1.77/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a19) | c0_1(a19) | (~c2_1(a19)))),
% 1.77/1.43 inference(quant_inst,[status(thm)],[])).
% 1.77/1.43 tff(1761,plain,
% 1.77/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c0_1(a37) | c3_1(a37) | c1_1(a19) | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c1_1(a37)) | (~c2_1(a42)) | (~c3_1(a42))),
% 1.77/1.43 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 1.77/1.43 tff(1762,plain,
% 1.77/1.43 (c0_1(a19)),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1761, 169, 815, 804, 1755, 1754, 828, 1753, 1752, 1750, 83])).
% 1.77/1.43 tff(1763,plain,
% 1.77/1.43 (^[U: $i] : refl((hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))) <=> (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))))),
% 1.77/1.43 inference(bind,[status(th)],[])).
% 1.77/1.43 tff(1764,plain,
% 1.77/1.43 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.43 inference(quant_intro,[status(thm)],[1763])).
% 1.77/1.43 tff(1765,plain,
% 1.77/1.43 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.43 inference(rewrite,[status(thm)],[])).
% 1.77/1.43 tff(1766,plain,
% 1.77/1.43 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp12) <=> ((hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))) | hskp12))), rewrite(((hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U))) | hskp12) <=> (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp12) <=> (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))))),
% 1.77/1.43 inference(bind,[status(th)],[])).
% 1.77/1.43 tff(1767,plain,
% 1.77/1.43 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp12) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.43 inference(quant_intro,[status(thm)],[1766])).
% 1.77/1.43 tff(1768,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.77/1.43 tff(1769,plain,
% 1.77/1.43 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.43 inference(modus_ponens,[status(thm)],[1768, 1767])).
% 1.77/1.43 tff(1770,plain,
% 1.77/1.43 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.43 inference(modus_ponens,[status(thm)],[1769, 1765])).
% 1.77/1.43 tff(1771,plain,(
% 1.77/1.43 ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.43 inference(skolemize,[status(sab)],[1770])).
% 1.77/1.43 tff(1772,plain,
% 1.77/1.43 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))),
% 1.77/1.43 inference(modus_ponens,[status(thm)],[1771, 1764])).
% 1.77/1.43 tff(1773,plain,
% 1.77/1.43 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))),
% 1.77/1.43 inference(rewrite,[status(thm)],[])).
% 1.77/1.43 tff(1774,plain,
% 1.77/1.43 ((hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42) | (~c3_1(a42))) <=> (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))),
% 1.77/1.43 inference(rewrite,[status(thm)],[])).
% 1.77/1.43 tff(1775,plain,
% 1.77/1.43 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42) | (~c3_1(a42)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42)))),
% 1.77/1.43 inference(monotonicity,[status(thm)],[1774])).
% 1.77/1.43 tff(1776,plain,
% 1.77/1.43 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42) | (~c3_1(a42)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42))),
% 1.77/1.43 inference(transitivity,[status(thm)],[1775, 1773])).
% 1.77/1.43 tff(1777,plain,
% 1.77/1.43 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | c0_1(a42) | (~c3_1(a42)))),
% 1.77/1.43 inference(quant_inst,[status(thm)],[])).
% 1.77/1.43 tff(1778,plain,
% 1.77/1.43 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c3_1(U)))) | hskp27 | hskp12 | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | c0_1(a42)),
% 1.77/1.43 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 1.77/1.43 tff(1779,plain,
% 1.77/1.43 (hskp12),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1778, 910, 169, 815, 804, 1772, 822])).
% 1.77/1.43 tff(1780,plain,
% 1.77/1.43 (((~hskp12) | (~c2_1(a21))) <=> ((~hskp12) | (~c2_1(a21)))),
% 1.77/1.43 inference(rewrite,[status(thm)],[])).
% 1.77/1.43 tff(1781,plain,
% 1.77/1.43 (((~c2_1(a21)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a21)))),
% 1.77/1.43 inference(rewrite,[status(thm)],[])).
% 1.77/1.43 tff(1782,axiom,((~c2_1(a21)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 1.77/1.43 tff(1783,plain,
% 1.77/1.43 ((~hskp12) | (~c2_1(a21))),
% 1.77/1.43 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 1.77/1.43 tff(1784,plain,
% 1.77/1.43 ((~hskp12) | (~c2_1(a21))),
% 1.77/1.43 inference(modus_ponens,[status(thm)],[1783, 1780])).
% 1.77/1.43 tff(1785,plain,
% 1.77/1.43 (~c2_1(a21)),
% 1.77/1.43 inference(unit_resolution,[status(thm)],[1784, 1779])).
% 1.77/1.43 tff(1786,plain,
% 1.77/1.43 (((~hskp12) | (~c1_1(a21))) <=> ((~hskp12) | (~c1_1(a21)))),
% 1.77/1.43 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1787,plain,
% 1.77/1.44 (((~c1_1(a21)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a21)))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1788,axiom,((~c1_1(a21)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.77/1.44 tff(1789,plain,
% 1.77/1.44 ((~hskp12) | (~c1_1(a21))),
% 1.77/1.44 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 1.77/1.44 tff(1790,plain,
% 1.77/1.44 ((~hskp12) | (~c1_1(a21))),
% 1.77/1.44 inference(modus_ponens,[status(thm)],[1789, 1786])).
% 1.77/1.44 tff(1791,plain,
% 1.77/1.44 (~c1_1(a21)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1790, 1779])).
% 1.77/1.44 tff(1792,plain,
% 1.77/1.44 (((~hskp12) | (~c0_1(a21))) <=> ((~hskp12) | (~c0_1(a21)))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1793,plain,
% 1.77/1.44 (((~c0_1(a21)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a21)))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1794,axiom,((~c0_1(a21)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.77/1.44 tff(1795,plain,
% 1.77/1.44 ((~hskp12) | (~c0_1(a21))),
% 1.77/1.44 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 1.77/1.44 tff(1796,plain,
% 1.77/1.44 ((~hskp12) | (~c0_1(a21))),
% 1.77/1.44 inference(modus_ponens,[status(thm)],[1795, 1792])).
% 1.77/1.44 tff(1797,plain,
% 1.77/1.44 (~c0_1(a21)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1796, 1779])).
% 1.77/1.44 tff(1798,plain,
% 1.77/1.44 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a21) | c1_1(a21) | c2_1(a21) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a21) | c1_1(a21) | c2_1(a21) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1799,plain,
% 1.77/1.44 ((hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a21) | c0_1(a21) | c2_1(a21)) <=> (hskp0 | c0_1(a21) | c1_1(a21) | c2_1(a21) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1800,plain,
% 1.77/1.44 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a21) | c0_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a21) | c1_1(a21) | c2_1(a21) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19))))),
% 1.77/1.44 inference(monotonicity,[status(thm)],[1799])).
% 1.77/1.44 tff(1801,plain,
% 1.77/1.44 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a21) | c0_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a21) | c1_1(a21) | c2_1(a21) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19)))),
% 1.77/1.44 inference(transitivity,[status(thm)],[1800, 1798])).
% 1.77/1.44 tff(1802,plain,
% 1.77/1.44 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a21) | c0_1(a21) | c2_1(a21))),
% 1.77/1.44 inference(quant_inst,[status(thm)],[])).
% 1.77/1.44 tff(1803,plain,
% 1.77/1.44 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a21) | c1_1(a21) | c2_1(a21) | c1_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c2_1(a19))),
% 1.77/1.44 inference(modus_ponens,[status(thm)],[1802, 1801])).
% 1.77/1.44 tff(1804,plain,
% 1.77/1.44 ($false),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1803, 169, 344, 1754, 1797, 1791, 1785, 1750, 342, 1762])).
% 1.77/1.44 tff(1805,plain,((~hskp21) | hskp0 | hskp26 | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a6) | hskp27 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.44 tff(1806,plain,
% 1.77/1.44 (~hskp21),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1805, 943, 84, 730, 729, 344, 1731, 725, 24, 2, 772])).
% 1.77/1.44 tff(1807,plain,
% 1.77/1.44 (hskp25),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[167, 1806, 643])).
% 1.77/1.44 tff(1808,plain,
% 1.77/1.44 (hskp19),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[891, 1807, 730, 729, 728])).
% 1.77/1.44 tff(1809,plain,
% 1.77/1.44 (~c0_1(a33)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[897, 1808])).
% 1.77/1.44 tff(1810,plain,
% 1.77/1.44 (c2_1(a33)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[908, 1808])).
% 1.77/1.44 tff(1811,plain,
% 1.77/1.44 (~c1_1(a33)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[916, 1731, 169, 84, 1810, 1809, 791])).
% 1.77/1.44 tff(1812,plain,
% 1.77/1.44 (c2_1(a9)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[859, 1807])).
% 1.77/1.44 tff(1813,plain,
% 1.77/1.44 (c0_1(a9)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[881, 1807])).
% 1.77/1.44 tff(1814,plain,
% 1.77/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1815,plain,
% 1.77/1.44 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1816,plain,
% 1.77/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9))))),
% 1.77/1.44 inference(monotonicity,[status(thm)],[1815])).
% 1.77/1.44 tff(1817,plain,
% 1.77/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.77/1.44 inference(transitivity,[status(thm)],[1816, 1814])).
% 1.77/1.44 tff(1818,plain,
% 1.77/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.77/1.44 inference(quant_inst,[status(thm)],[])).
% 1.77/1.44 tff(1819,plain,
% 1.77/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9))),
% 1.77/1.44 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 1.77/1.44 tff(1820,plain,
% 1.77/1.44 (~c3_1(a9)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1819, 169, 1813, 1812, 725, 24, 2, 439, 772])).
% 1.77/1.44 tff(1821,plain,
% 1.77/1.44 (hskp20 | c3_1(a9)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1315, 169, 84, 1813, 1812, 1227])).
% 1.77/1.44 tff(1822,plain,
% 1.77/1.44 (hskp20),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1821, 1820])).
% 1.77/1.44 tff(1823,plain,
% 1.77/1.44 (~c3_1(a37)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1239, 1822])).
% 1.77/1.44 tff(1824,plain,
% 1.77/1.44 (~c0_1(a37)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1245, 1822])).
% 1.77/1.44 tff(1825,plain,
% 1.77/1.44 (c3_1(a33)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1503, 1808])).
% 1.77/1.44 tff(1826,plain,
% 1.77/1.44 (c1_1(a37)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1256, 1822])).
% 1.77/1.44 tff(1827,plain,
% 1.77/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1828,plain,
% 1.77/1.44 (((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33))) <=> (c0_1(a37) | c3_1(a37) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1829,plain,
% 1.77/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37))))),
% 1.77/1.44 inference(monotonicity,[status(thm)],[1828])).
% 1.77/1.44 tff(1830,plain,
% 1.77/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37)))),
% 1.77/1.44 inference(transitivity,[status(thm)],[1829, 1827])).
% 1.77/1.44 tff(1831,plain,
% 1.77/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a37) | c0_1(a37) | (~c1_1(a37)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))),
% 1.77/1.44 inference(quant_inst,[status(thm)],[])).
% 1.77/1.44 tff(1832,plain,
% 1.77/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c1_1(a37))),
% 1.77/1.44 inference(modus_ponens,[status(thm)],[1831, 1830])).
% 1.77/1.44 tff(1833,plain,
% 1.77/1.44 ($false),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1832, 169, 1826, 1810, 1825, 1824, 1823, 1809, 83, 1811])).
% 1.77/1.44 tff(1834,plain,(hskp18 | hskp26 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16)) | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6) | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.77/1.44 tff(1835,plain,
% 1.77/1.44 (hskp18),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1834, 1730, 591, 580, 574, 1729, 653, 652, 651, 643, 344])).
% 1.77/1.44 tff(1836,plain,
% 1.77/1.44 (~c3_1(a32)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[969, 1835])).
% 1.77/1.44 tff(1837,plain,
% 1.77/1.44 (~c1_1(a32)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[963, 1835])).
% 1.77/1.44 tff(1838,plain,
% 1.77/1.44 (~c0_1(a32)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1385, 1835])).
% 1.77/1.44 tff(1839,plain,
% 1.77/1.44 ($false),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[990, 169, 73, 591, 1838, 1837, 1836, 574, 982, 1729])).
% 1.77/1.44 tff(1840,plain,(hskp0 | hskp24 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.77/1.44 tff(1841,plain,
% 1.77/1.44 (hskp0),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1840, 643, 73])).
% 1.77/1.44 tff(1842,plain,
% 1.77/1.44 (~c2_1(a1)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[259, 1841])).
% 1.77/1.44 tff(1843,plain,
% 1.77/1.44 (~c0_1(a1)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[283, 1841])).
% 1.77/1.44 tff(1844,plain,
% 1.77/1.44 (c3_1(a1)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[270, 1841])).
% 1.77/1.44 tff(1845,plain,
% 1.77/1.44 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c3_1(a16) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a16) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c3_1(a16) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a16) | (~c0_1(a16)))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1846,plain,
% 1.77/1.44 ((hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1))) <=> (hskp4 | c3_1(a16) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a16) | (~c0_1(a16)))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1847,plain,
% 1.77/1.44 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c3_1(a16) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a16) | (~c0_1(a16))))),
% 1.77/1.44 inference(monotonicity,[status(thm)],[1846])).
% 1.77/1.44 tff(1848,plain,
% 1.77/1.44 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c3_1(a16) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a16) | (~c0_1(a16)))),
% 1.77/1.44 inference(transitivity,[status(thm)],[1847, 1845])).
% 1.77/1.44 tff(1849,plain,
% 1.77/1.44 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))),
% 1.77/1.44 inference(quant_inst,[status(thm)],[])).
% 1.77/1.44 tff(1850,plain,
% 1.77/1.44 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c3_1(a16) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a16) | (~c0_1(a16))),
% 1.77/1.44 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 1.77/1.44 tff(1851,plain,
% 1.77/1.44 (hskp4 | (~c1_1(a1)) | c1_1(a16)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1850, 169, 725, 496, 2, 477, 632])).
% 1.77/1.44 tff(1852,plain,
% 1.77/1.44 (~c1_1(a1)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1851, 205, 3])).
% 1.77/1.44 tff(1853,plain,
% 1.77/1.44 ($false),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[290, 169, 205, 646, 496, 647, 645, 477, 65, 1852])).
% 1.77/1.44 tff(1854,plain,(hskp4 | (~c3_1(a1)) | c0_1(a1) | c1_1(a16) | (~c0_1(a16)) | c3_1(a16) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.77/1.44 tff(1855,plain,
% 1.77/1.44 (hskp4),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1854, 3, 477, 496, 725, 2, 643])).
% 1.77/1.44 tff(1856,plain,
% 1.77/1.44 (~c2_1(a6)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[111, 1855])).
% 1.77/1.44 tff(1857,plain,
% 1.77/1.44 (c3_1(a6)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[122, 1855])).
% 1.77/1.44 tff(1858,plain,
% 1.77/1.44 (c1_1(a6)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[133, 1855])).
% 1.77/1.44 tff(1859,plain,
% 1.77/1.44 (c3_1(a30)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1095, 169, 725, 730, 729, 1088, 1086, 2, 728, 13, 3])).
% 1.77/1.44 tff(1860,assumption,(hskp2), introduced(assumption)).
% 1.77/1.44 tff(1861,plain,
% 1.77/1.44 (~c3_1(a4)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[400, 1860])).
% 1.77/1.44 tff(1862,plain,
% 1.77/1.44 (~c2_1(a4)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[417, 1860])).
% 1.77/1.44 tff(1863,plain,
% 1.77/1.44 (c1_1(a4)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[411, 1860])).
% 1.77/1.44 tff(1864,plain,
% 1.77/1.44 (~hskp21),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1697, 1863, 3, 2, 1862, 1861, 725, 24])).
% 1.77/1.44 tff(1865,plain,
% 1.77/1.44 (hskp25),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[167, 1864, 643])).
% 1.77/1.44 tff(1866,plain,
% 1.77/1.44 (c2_1(a9)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[859, 1865])).
% 1.77/1.44 tff(1867,plain,
% 1.77/1.44 (c0_1(a9)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[881, 1865])).
% 1.77/1.44 tff(1868,plain,
% 1.77/1.44 (~c3_1(a9)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1707, 169, 1867, 1866, 725, 1863, 24, 2, 1862, 1861, 439])).
% 1.77/1.44 tff(1869,plain,
% 1.77/1.44 (hskp20 | c3_1(a9)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1315, 169, 84, 1867, 1866, 1227])).
% 1.77/1.44 tff(1870,plain,
% 1.77/1.44 (hskp20),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1869, 1868])).
% 1.77/1.44 tff(1871,plain,
% 1.77/1.44 (~c3_1(a37)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1239, 1870])).
% 1.77/1.44 tff(1872,plain,
% 1.77/1.44 (~c0_1(a37)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1245, 1870])).
% 1.77/1.44 tff(1873,plain,
% 1.77/1.44 (c1_1(a9)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[870, 1865])).
% 1.77/1.44 tff(1874,plain,
% 1.77/1.44 (~c2_1(a37)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1726, 169, 1867, 1873, 1866, 1863, 1872, 1871, 1862, 1861, 34])).
% 1.77/1.44 tff(1875,plain,
% 1.77/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1876,plain,
% 1.77/1.44 (((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37)) <=> (c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1877,plain,
% 1.77/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37)))),
% 1.77/1.44 inference(monotonicity,[status(thm)],[1876])).
% 1.77/1.44 tff(1878,plain,
% 1.77/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))),
% 1.77/1.44 inference(transitivity,[status(thm)],[1877, 1875])).
% 1.77/1.44 tff(1879,plain,
% 1.77/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37))),
% 1.77/1.44 inference(quant_inst,[status(thm)],[])).
% 1.77/1.44 tff(1880,plain,
% 1.77/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37)),
% 1.77/1.44 inference(modus_ponens,[status(thm)],[1879, 1878])).
% 1.77/1.44 tff(1881,plain,
% 1.77/1.44 ($false),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1880, 169, 1087, 725, 1872, 1871, 1086, 2, 13, 1874, 3, 1127])).
% 1.77/1.44 tff(1882,plain,((~hskp2) | (~c0_1(a16)) | c3_1(a16) | c1_1(a16) | (~c3_1(a30)) | hskp26 | c2_1(a16) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.77/1.44 tff(1883,plain,
% 1.77/1.44 (~hskp2),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1882, 1859, 2, 3, 725, 84, 24, 643])).
% 1.77/1.44 tff(1884,plain,
% 1.77/1.44 (hskp14),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[726, 1883, 3])).
% 1.77/1.44 tff(1885,plain,
% 1.77/1.44 (~c0_1(a24)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1030, 1884])).
% 1.77/1.44 tff(1886,assumption,(~c2_1(a24)), introduced(assumption)).
% 1.77/1.44 tff(1887,plain,
% 1.77/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a24) | c2_1(a30) | c0_1(a24) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | c3_1(a24) | (~c1_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a24) | c2_1(a30) | c0_1(a24) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | c3_1(a24) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1888,plain,
% 1.77/1.44 (((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a24) | c0_1(a24) | c3_1(a24)) <=> (c2_1(a24) | c2_1(a30) | c0_1(a24) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | c3_1(a24) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.77/1.44 inference(rewrite,[status(thm)],[])).
% 1.77/1.44 tff(1889,plain,
% 1.77/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a24) | c0_1(a24) | c3_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a24) | c2_1(a30) | c0_1(a24) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | c3_1(a24) | (~c1_1(a30)) | (~c3_1(a30))))),
% 1.77/1.44 inference(monotonicity,[status(thm)],[1888])).
% 1.77/1.44 tff(1890,plain,
% 1.77/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a24) | c0_1(a24) | c3_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a24) | c2_1(a30) | c0_1(a24) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | c3_1(a24) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.77/1.44 inference(transitivity,[status(thm)],[1889, 1887])).
% 1.77/1.44 tff(1891,plain,
% 1.77/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a24) | c0_1(a24) | c3_1(a24))),
% 1.77/1.44 inference(quant_inst,[status(thm)],[])).
% 1.77/1.44 tff(1892,plain,
% 1.77/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a24) | c2_1(a30) | c0_1(a24) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | c3_1(a24) | (~c1_1(a30)) | (~c3_1(a30))),
% 1.77/1.44 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 1.77/1.44 tff(1893,plain,
% 1.77/1.44 (c3_1(a24)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1892, 169, 1087, 1886, 725, 1086, 1055, 2, 13, 3, 1127])).
% 1.77/1.44 tff(1894,plain,
% 1.77/1.44 (~hskp14),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1041, 1886])).
% 1.77/1.44 tff(1895,plain,
% 1.77/1.44 (hskp2),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[726, 1894, 3])).
% 1.77/1.44 tff(1896,plain,
% 1.77/1.44 (~c3_1(a4)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[400, 1895])).
% 1.77/1.44 tff(1897,plain,
% 1.77/1.44 (~c2_1(a4)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[417, 1895])).
% 1.77/1.44 tff(1898,plain,
% 1.77/1.44 (c1_1(a4)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[411, 1895])).
% 1.77/1.44 tff(1899,plain,
% 1.77/1.44 (~hskp21),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1697, 1898, 3, 2, 1897, 1896, 725, 24])).
% 1.77/1.44 tff(1900,plain,
% 1.77/1.44 (hskp25),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[167, 1899, 643])).
% 1.77/1.44 tff(1901,plain,
% 1.77/1.44 (c2_1(a9)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[859, 1900])).
% 1.77/1.44 tff(1902,plain,
% 1.77/1.44 (c0_1(a9)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[881, 1900])).
% 1.77/1.44 tff(1903,plain,
% 1.77/1.44 (~c3_1(a9)),
% 1.77/1.44 inference(unit_resolution,[status(thm)],[1707, 169, 1902, 1901, 725, 1898, 24, 2, 1897, 1896, 439])).
% 1.77/1.45 tff(1904,plain,
% 1.77/1.45 (hskp20 | c3_1(a9)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1315, 169, 84, 1902, 1901, 1227])).
% 1.77/1.45 tff(1905,plain,
% 1.77/1.45 (hskp20),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1904, 1903])).
% 1.77/1.45 tff(1906,plain,
% 1.77/1.45 (~c3_1(a37)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1239, 1905])).
% 1.77/1.45 tff(1907,plain,
% 1.77/1.45 (~c0_1(a37)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1245, 1905])).
% 1.77/1.45 tff(1908,plain,
% 1.77/1.45 (c1_1(a9)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[870, 1900])).
% 1.77/1.45 tff(1909,plain,
% 1.77/1.45 (~c2_1(a37)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1726, 169, 1902, 1908, 1901, 1898, 1907, 1906, 1897, 1896, 34])).
% 1.77/1.45 tff(1910,plain,
% 1.77/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a24) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a24) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c2_1(a37))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(1911,plain,
% 1.77/1.45 (((~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a24) | c1_1(a24) | c0_1(a24)) <=> (c2_1(a24) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c2_1(a37))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(1912,plain,
% 1.77/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a24) | c1_1(a24) | c0_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a24) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c2_1(a37)))),
% 1.77/1.45 inference(monotonicity,[status(thm)],[1911])).
% 1.77/1.45 tff(1913,plain,
% 1.77/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a24) | c1_1(a24) | c0_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a24) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c2_1(a37))),
% 1.77/1.45 inference(transitivity,[status(thm)],[1912, 1910])).
% 1.77/1.45 tff(1914,plain,
% 1.77/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a24) | c1_1(a24) | c0_1(a24))),
% 1.77/1.45 inference(quant_inst,[status(thm)],[])).
% 1.77/1.45 tff(1915,plain,
% 1.77/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a24) | c0_1(a37) | c3_1(a37) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c2_1(a37)),
% 1.77/1.45 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 1.77/1.45 tff(1916,plain,
% 1.77/1.45 (c1_1(a24) | c2_1(a37)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1915, 169, 1886, 1907, 1906, 1055, 55, 1893])).
% 1.77/1.45 tff(1917,plain,
% 1.77/1.45 (c1_1(a24)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1916, 1909])).
% 1.77/1.45 tff(1918,plain,
% 1.77/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a24) | c0_1(a37) | c3_1(a37) | (~c1_1(a24)) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a24) | c0_1(a37) | c3_1(a37) | (~c1_1(a24)) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)) | c2_1(a37))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(1919,plain,
% 1.77/1.45 (((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37)) <=> (c2_1(a24) | c0_1(a37) | c3_1(a37) | (~c1_1(a24)) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)) | c2_1(a37))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(1920,plain,
% 1.77/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a24) | c0_1(a37) | c3_1(a37) | (~c1_1(a24)) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)) | c2_1(a37)))),
% 1.77/1.45 inference(monotonicity,[status(thm)],[1919])).
% 1.77/1.45 tff(1921,plain,
% 1.77/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a24) | c0_1(a37) | c3_1(a37) | (~c1_1(a24)) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)) | c2_1(a37))),
% 1.77/1.45 inference(transitivity,[status(thm)],[1920, 1918])).
% 1.77/1.45 tff(1922,plain,
% 1.77/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | c3_1(a37))),
% 1.77/1.45 inference(quant_inst,[status(thm)],[])).
% 1.77/1.45 tff(1923,plain,
% 1.77/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a24) | c0_1(a37) | c3_1(a37) | (~c1_1(a24)) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)) | c2_1(a37)),
% 1.77/1.45 inference(modus_ponens,[status(thm)],[1922, 1921])).
% 1.77/1.45 tff(1924,plain,
% 1.77/1.45 ($false),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1923, 169, 1886, 725, 1907, 1906, 1917, 2, 13, 1909, 3, 1893])).
% 1.77/1.45 tff(1925,plain,(c2_1(a24) | (~c0_1(a16)) | c3_1(a16) | c1_1(a16) | c0_1(a24) | hskp26 | (~c3_1(a30)) | c2_1(a16) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.77/1.45 tff(1926,plain,
% 1.77/1.45 (c2_1(a24)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1925, 1055, 2, 3, 725, 84, 1127, 24, 643])).
% 1.77/1.45 tff(1927,plain,
% 1.77/1.45 (~hskp6),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1378, 1054, 643, 725, 3, 731, 1056, 2, 1055])).
% 1.77/1.45 tff(1928,plain,
% 1.77/1.45 (hskp6 | c1_1(a24) | c3_1(a24)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1286, 169, 84, 1056, 1280])).
% 1.77/1.45 tff(1929,plain,
% 1.77/1.45 (c3_1(a24)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1928, 1927, 1054])).
% 1.77/1.45 tff(1930,plain,
% 1.77/1.45 (hskp10),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1143, 169, 634, 1056, 633, 1054, 1137, 1127, 1929])).
% 1.77/1.45 tff(1931,plain,
% 1.77/1.45 (~c3_1(a18)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1150, 1930])).
% 1.77/1.45 tff(1932,plain,
% 1.77/1.45 (c2_1(a18)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1161, 1930])).
% 1.77/1.45 tff(1933,plain,
% 1.77/1.45 (c0_1(a18)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1172, 1930])).
% 1.77/1.45 tff(1934,plain,
% 1.77/1.45 (hskp11),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1179, 169, 1056, 1933, 1932, 1055, 1931, 1126, 1929])).
% 1.77/1.45 tff(1935,plain,
% 1.77/1.45 (~c3_1(a19)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1185, 1934])).
% 1.77/1.45 tff(1936,plain,
% 1.77/1.45 (~c1_1(a19)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1209, 1934])).
% 1.77/1.45 tff(1937,plain,
% 1.77/1.45 (c2_1(a19)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1196, 1934])).
% 1.77/1.45 tff(1938,plain,
% 1.77/1.45 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(1939,plain,
% 1.77/1.45 ((hskp26 | hskp6 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c2_1(a19))) <=> (hskp26 | hskp6 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(1940,plain,
% 1.77/1.45 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19))))),
% 1.77/1.45 inference(monotonicity,[status(thm)],[1939])).
% 1.77/1.45 tff(1941,plain,
% 1.77/1.45 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)))),
% 1.77/1.45 inference(transitivity,[status(thm)],[1940, 1938])).
% 1.77/1.45 tff(1942,plain,
% 1.77/1.45 ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))),
% 1.77/1.45 inference(quant_inst,[status(thm)],[])).
% 1.77/1.45 tff(1943,plain,
% 1.77/1.45 ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19))),
% 1.77/1.45 inference(modus_ponens,[status(thm)],[1942, 1941])).
% 1.77/1.45 tff(1944,plain,
% 1.77/1.45 ($false),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1943, 169, 84, 1927, 1937, 1936, 1935, 1280])).
% 1.77/1.45 tff(1945,plain,(c1_1(a24) | hskp26 | (~c2_1(a24)) | c0_1(a24) | (~c1_1(a30)) | c0_1(a30) | (~c3_1(a30)) | hskp17 | (~c0_1(a16)) | c1_1(a16) | hskp18 | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.45 tff(1946,plain,
% 1.77/1.45 (c1_1(a24)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1945, 1926, 84, 1055, 1087, 1088, 1127, 643, 725, 3, 731, 2])).
% 1.77/1.45 tff(1947,plain,
% 1.77/1.45 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | c0_1(a24) | (~c1_1(a24)) | (~ndr1_0) | (~c2_1(a24)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a24) | (~c1_1(a24)) | (~ndr1_0) | (~c2_1(a24)))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(1948,plain,
% 1.77/1.45 ((hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a24)) | c0_1(a24) | (~c1_1(a24))) <=> (hskp27 | hskp26 | c0_1(a24) | (~c1_1(a24)) | (~ndr1_0) | (~c2_1(a24)))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(1949,plain,
% 1.77/1.45 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a24)) | c0_1(a24) | (~c1_1(a24)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | c0_1(a24) | (~c1_1(a24)) | (~ndr1_0) | (~c2_1(a24))))),
% 1.77/1.45 inference(monotonicity,[status(thm)],[1948])).
% 1.77/1.45 tff(1950,plain,
% 1.77/1.45 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a24)) | c0_1(a24) | (~c1_1(a24)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a24) | (~c1_1(a24)) | (~ndr1_0) | (~c2_1(a24)))),
% 1.77/1.45 inference(transitivity,[status(thm)],[1949, 1947])).
% 1.77/1.45 tff(1951,plain,
% 1.77/1.45 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a24)) | c0_1(a24) | (~c1_1(a24)))),
% 1.77/1.45 inference(quant_inst,[status(thm)],[])).
% 1.77/1.45 tff(1952,plain,
% 1.77/1.45 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a24) | (~c1_1(a24)) | (~ndr1_0) | (~c2_1(a24))),
% 1.77/1.45 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 1.77/1.45 tff(1953,plain,
% 1.77/1.45 (hskp27 | (~c1_1(a24)) | (~c2_1(a24))),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1952, 169, 84, 1055, 791])).
% 1.77/1.45 tff(1954,plain,
% 1.77/1.45 (hskp27),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1953, 1946, 1926])).
% 1.77/1.45 tff(1955,plain,
% 1.77/1.45 (c3_1(a11)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[752, 1954])).
% 1.77/1.45 tff(1956,plain,
% 1.77/1.45 (c0_1(a11)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[763, 1954])).
% 1.77/1.45 tff(1957,plain,
% 1.77/1.45 (c2_1(a11)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[770, 169, 731, 643, 1956, 1955, 741])).
% 1.77/1.45 tff(1958,plain,
% 1.77/1.45 (~hskp14),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1024, 1946])).
% 1.77/1.45 tff(1959,plain,
% 1.77/1.45 (hskp2),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[726, 1958, 3])).
% 1.77/1.45 tff(1960,plain,
% 1.77/1.45 (~c3_1(a4)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[400, 1959])).
% 1.77/1.45 tff(1961,plain,
% 1.77/1.45 (~c2_1(a4)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[417, 1959])).
% 1.77/1.45 tff(1962,plain,
% 1.77/1.45 (c1_1(a4)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[411, 1959])).
% 1.77/1.45 tff(1963,plain,
% 1.77/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(1964,plain,
% 1.77/1.45 (((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(1965,plain,
% 1.77/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11))))),
% 1.77/1.45 inference(monotonicity,[status(thm)],[1964])).
% 1.77/1.45 tff(1966,plain,
% 1.77/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))),
% 1.77/1.45 inference(transitivity,[status(thm)],[1965, 1963])).
% 1.77/1.45 tff(1967,plain,
% 1.77/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.77/1.45 inference(quant_inst,[status(thm)],[])).
% 1.77/1.45 tff(1968,plain,
% 1.77/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11))),
% 1.77/1.45 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 1.77/1.45 tff(1969,plain,
% 1.77/1.45 ($false),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1968, 169, 1956, 1955, 725, 1962, 24, 2, 1961, 1960, 439, 1957])).
% 1.77/1.45 tff(1970,plain,(c0_1(a24) | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | hskp18 | hskp17 | c1_1(a16) | hskp26 | (~c3_1(a30))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.45 tff(1971,plain,
% 1.77/1.45 (hskp18),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1970, 1885, 24, 2, 725, 643, 3, 84, 1859])).
% 1.77/1.45 tff(1972,plain,
% 1.77/1.45 (~c1_1(a32)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[963, 1971])).
% 1.77/1.45 tff(1973,plain,
% 1.77/1.45 (~c1_1(a24)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1024, 1884])).
% 1.77/1.45 tff(1974,plain,
% 1.77/1.45 (c2_1(a24)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1041, 1884])).
% 1.77/1.45 tff(1975,plain,
% 1.77/1.45 (~c0_1(a32)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1385, 1971])).
% 1.77/1.45 tff(1976,plain,
% 1.77/1.45 (~c3_1(a32)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[969, 1971])).
% 1.77/1.45 tff(1977,plain,
% 1.77/1.45 ($false),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1557, 1976, 1975, 1885, 84, 1087, 1088, 1859, 730, 729, 728, 1086, 1974, 1973, 1972])).
% 1.77/1.45 tff(1978,plain,(hskp26 | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)) | hskp17 | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.45 tff(1979,plain,
% 1.77/1.45 (hskp26),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1978, 1858, 1857, 1856, 24, 2, 725, 643, 3])).
% 1.77/1.45 tff(1980,plain,
% 1.77/1.45 ($false),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1668, 1862, 1863, 725, 24, 2, 656, 1861])).
% 1.77/1.45 tff(1981,plain,((~hskp2) | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~hskp26)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.45 tff(1982,plain,
% 1.77/1.45 (~hskp2),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1981, 1979, 24, 2, 725])).
% 1.77/1.45 tff(1983,plain,
% 1.77/1.45 (hskp14),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[726, 1982, 3])).
% 1.77/1.45 tff(1984,plain,
% 1.77/1.45 (~c1_1(a24)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1024, 1983])).
% 1.77/1.45 tff(1985,plain,
% 1.77/1.45 (~c0_1(a24)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1030, 1983])).
% 1.77/1.45 tff(1986,plain,
% 1.77/1.45 (c2_1(a24)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1041, 1983])).
% 1.77/1.45 tff(1987,plain,
% 1.77/1.45 (hskp3),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1048, 169, 1982, 1986, 1985, 1984, 23])).
% 1.77/1.45 tff(1988,plain,
% 1.77/1.45 (~c3_1(a5)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[948, 1987])).
% 1.77/1.45 tff(1989,plain,
% 1.77/1.45 (~c2_1(a5)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[361, 1987])).
% 1.77/1.45 tff(1990,plain,
% 1.77/1.45 (c0_1(a5)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1081, 169, 725, 1858, 1857, 2, 1856, 1989, 1988, 13, 3])).
% 1.77/1.45 tff(1991,plain,
% 1.77/1.45 (~c1_1(a5)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[367, 1987])).
% 1.77/1.45 tff(1992,plain,
% 1.77/1.45 (c3_1(a10)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[689, 1979])).
% 1.77/1.45 tff(1993,plain,
% 1.77/1.45 (c0_1(a10)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[666, 1979])).
% 1.77/1.45 tff(1994,plain,
% 1.77/1.45 (c2_1(a10)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[678, 1979])).
% 1.77/1.45 tff(1995,plain,
% 1.77/1.45 (~hskp18),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1639, 1990, 1858, 1856, 1993, 1992, 1986, 1989, 1991, 1994, 643, 725, 3, 1985, 1984, 2, 1857])).
% 1.77/1.45 tff(1996,plain,
% 1.77/1.45 (~hskp6),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1378, 1995, 643, 725, 3, 1984, 1986, 2, 1985])).
% 1.77/1.45 tff(1997,plain,
% 1.77/1.45 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(1998,plain,
% 1.77/1.45 ((hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1))) <=> (hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(1999,plain,
% 1.77/1.45 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10))))),
% 1.77/1.45 inference(monotonicity,[status(thm)],[1998])).
% 1.77/1.45 tff(2000,plain,
% 1.77/1.45 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)))),
% 1.77/1.45 inference(transitivity,[status(thm)],[1999, 1997])).
% 1.77/1.45 tff(2001,plain,
% 1.77/1.45 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1)))),
% 1.77/1.45 inference(quant_inst,[status(thm)],[])).
% 1.77/1.45 tff(2002,plain,
% 1.77/1.45 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a10)) | (~c1_1(a10)) | (~c3_1(a10))),
% 1.77/1.45 inference(modus_ponens,[status(thm)],[2001, 2000])).
% 1.77/1.45 tff(2003,plain,
% 1.77/1.45 (hskp6 | (~c1_1(a10))),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[2002, 169, 1994, 1992, 496, 477, 476, 1298])).
% 1.77/1.45 tff(2004,plain,
% 1.77/1.45 (~c1_1(a10)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[2003, 1996])).
% 1.77/1.45 tff(2005,plain,
% 1.77/1.45 (hskp13),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1625, 2004, 1993, 1992, 1991, 1989, 1990])).
% 1.77/1.45 tff(2006,plain,
% 1.77/1.45 (~c3_1(a22)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[482, 2005])).
% 1.77/1.45 tff(2007,plain,
% 1.77/1.45 (~c2_1(a22)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[488, 2005])).
% 1.77/1.45 tff(2008,plain,
% 1.77/1.45 (~c0_1(a22)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[494, 2005])).
% 1.77/1.45 tff(2009,plain,
% 1.77/1.45 ($false),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1654, 169, 725, 1858, 1857, 2008, 2007, 2006, 2, 1856, 13, 3])).
% 1.77/1.45 tff(2010,plain,(c1_1(a16) | (~c0_1(a16)) | c3_1(a16) | (~c3_1(a1)) | c0_1(a1) | c2_1(a1) | hskp17 | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.77/1.45 tff(2011,plain,
% 1.77/1.45 (c1_1(a16)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[2010, 1844, 574, 591, 1843, 1842, 643, 580])).
% 1.77/1.45 tff(2012,plain,
% 1.77/1.45 (~c0_1(a32)),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[1385, 1568])).
% 1.77/1.45 tff(2013,plain,
% 1.77/1.45 ($false),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[990, 169, 73, 591, 2012, 1569, 1570, 574, 982, 772])).
% 1.77/1.45 tff(2014,plain,((~hskp18) | hskp24 | (~c1_1(a16))), inference(lemma,lemma(discharge,[]))).
% 1.77/1.45 tff(2015,plain,
% 1.77/1.45 (~hskp18),
% 1.77/1.45 inference(unit_resolution,[status(thm)],[2014, 2011, 73])).
% 1.77/1.45 tff(2016,assumption,(~c3_1(a15)), introduced(assumption)).
% 1.77/1.45 tff(2017,plain,
% 1.77/1.45 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c0_1(a30) | c1_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c1_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a30) | c1_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(2018,plain,
% 1.77/1.45 ((hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30))) <=> (hskp4 | c0_1(a30) | c1_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.77/1.45 inference(rewrite,[status(thm)],[])).
% 1.77/1.45 tff(2019,plain,
% 1.77/1.45 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c0_1(a30) | c1_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c1_1(a30)) | (~c3_1(a30))))),
% 1.77/1.45 inference(monotonicity,[status(thm)],[2018])).
% 1.77/1.45 tff(2020,plain,
% 1.77/1.45 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a30) | c1_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.80/1.46 inference(transitivity,[status(thm)],[2019, 2017])).
% 1.80/1.46 tff(2021,plain,
% 1.80/1.46 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))),
% 1.80/1.46 inference(quant_inst,[status(thm)],[])).
% 1.80/1.46 tff(2022,plain,
% 1.80/1.46 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a30) | c1_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c1_1(a30)) | (~c3_1(a30))),
% 1.80/1.46 inference(modus_ponens,[status(thm)],[2021, 2020])).
% 1.80/1.46 tff(2023,plain,
% 1.80/1.46 (~c3_1(a30)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2022, 169, 205, 634, 204, 633, 206, 632, 2016])).
% 1.80/1.46 tff(2024,plain,
% 1.80/1.46 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a15) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a15) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a15) | (~c0_1(a15)))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2025,plain,
% 1.80/1.46 ((hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1))) <=> (hskp4 | c1_1(a15) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a15) | (~c0_1(a15)))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2026,plain,
% 1.80/1.46 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a15) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a15) | (~c0_1(a15))))),
% 1.80/1.46 inference(monotonicity,[status(thm)],[2025])).
% 1.80/1.46 tff(2027,plain,
% 1.80/1.46 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a15) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a15) | (~c0_1(a15)))),
% 1.80/1.46 inference(transitivity,[status(thm)],[2026, 2024])).
% 1.80/1.46 tff(2028,plain,
% 1.80/1.46 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))),
% 1.80/1.46 inference(quant_inst,[status(thm)],[])).
% 1.80/1.46 tff(2029,plain,
% 1.80/1.46 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a15) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a15) | (~c0_1(a15))),
% 1.80/1.46 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 1.80/1.46 tff(2030,plain,
% 1.80/1.46 (~c1_1(a1)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2029, 169, 205, 204, 496, 206, 477, 632, 2016])).
% 1.80/1.46 tff(2031,plain,
% 1.80/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c3_1(a30))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2032,plain,
% 1.80/1.46 (((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a30) | c0_1(a30) | c2_1(a30) | c2_1(a1) | c1_1(a1) | c0_1(a1)) <=> (c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c3_1(a30))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2033,plain,
% 1.80/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a30) | c0_1(a30) | c2_1(a30) | c2_1(a1) | c1_1(a1) | c0_1(a1))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c3_1(a30)))),
% 1.80/1.46 inference(monotonicity,[status(thm)],[2032])).
% 1.80/1.46 tff(2034,plain,
% 1.80/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a30) | c0_1(a30) | c2_1(a30) | c2_1(a1) | c1_1(a1) | c0_1(a1))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c3_1(a30))),
% 1.80/1.46 inference(transitivity,[status(thm)],[2033, 2031])).
% 1.80/1.46 tff(2035,plain,
% 1.80/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a30) | c0_1(a30) | c2_1(a30) | c2_1(a1) | c1_1(a1) | c0_1(a1))),
% 1.80/1.46 inference(quant_inst,[status(thm)],[])).
% 1.80/1.46 tff(2036,plain,
% 1.80/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c3_1(a30)),
% 1.80/1.46 inference(modus_ponens,[status(thm)],[2035, 2034])).
% 1.80/1.46 tff(2037,plain,
% 1.80/1.46 ($false),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2036, 169, 496, 633, 1089, 477, 476, 55, 2030, 2023])).
% 1.80/1.46 tff(2038,plain,(c3_1(a15) | (~c3_1(a1)) | c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | hskp4 | (~c0_1(a15)) | c1_1(a15) | (~c1_1(a30))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.46 tff(2039,plain,
% 1.80/1.46 (c3_1(a15)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2038, 646, 633, 1089, 477, 476, 634, 205, 647, 496])).
% 1.80/1.46 tff(2040,plain,
% 1.80/1.46 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2041,plain,
% 1.80/1.46 ((hskp18 | hskp17 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15))) <=> (hskp18 | hskp17 | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2042,plain,
% 1.80/1.46 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15))))),
% 1.80/1.46 inference(monotonicity,[status(thm)],[2041])).
% 1.80/1.46 tff(2043,plain,
% 1.80/1.46 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.80/1.46 inference(transitivity,[status(thm)],[2042, 2040])).
% 1.80/1.46 tff(2044,plain,
% 1.80/1.46 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)))),
% 1.80/1.46 inference(quant_inst,[status(thm)],[])).
% 1.80/1.46 tff(2045,plain,
% 1.80/1.46 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15))),
% 1.80/1.46 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 1.80/1.46 tff(2046,plain,
% 1.80/1.46 ($false),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2045, 169, 731, 643, 646, 645, 741, 2039])).
% 1.80/1.46 tff(2047,plain,(hskp4 | hskp18 | hskp17 | c0_1(a30) | c2_1(a30) | c0_1(a1) | c2_1(a1) | (~c1_1(a30)) | (~c3_1(a1))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.46 tff(2048,plain,
% 1.80/1.46 (hskp4),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2047, 1088, 643, 731, 1086, 477, 476, 1087, 496])).
% 1.80/1.46 tff(2049,plain,
% 1.80/1.46 (~c2_1(a6)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[111, 2048])).
% 1.80/1.46 tff(2050,plain,
% 1.80/1.46 (c1_1(a16)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2010, 496, 2, 725, 477, 476, 643, 24])).
% 1.80/1.46 tff(2051,plain,
% 1.80/1.46 (c1_1(a6)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[133, 2048])).
% 1.80/1.46 tff(2052,plain,
% 1.80/1.46 (c3_1(a6)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[122, 2048])).
% 1.80/1.46 tff(2053,plain,
% 1.80/1.46 (hskp19),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[891, 849, 730, 729, 728])).
% 1.80/1.46 tff(2054,plain,
% 1.80/1.46 (~c0_1(a33)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[897, 2053])).
% 1.80/1.46 tff(2055,plain,
% 1.80/1.46 (c2_1(a33)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[908, 2053])).
% 1.80/1.46 tff(2056,plain,
% 1.80/1.46 (~c1_1(a33)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[916, 910, 169, 84, 2055, 2054, 791])).
% 1.80/1.46 tff(2057,plain,
% 1.80/1.46 (~c3_1(a9)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1819, 169, 882, 860, 725, 24, 2, 439, 772])).
% 1.80/1.46 tff(2058,plain,
% 1.80/1.46 (hskp20 | c3_1(a9)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1315, 169, 84, 882, 860, 1227])).
% 1.80/1.46 tff(2059,plain,
% 1.80/1.46 (hskp20),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2058, 2057])).
% 1.80/1.46 tff(2060,plain,
% 1.80/1.46 (~c3_1(a37)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1239, 2059])).
% 1.80/1.46 tff(2061,plain,
% 1.80/1.46 (~c0_1(a37)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1245, 2059])).
% 1.80/1.46 tff(2062,plain,
% 1.80/1.46 (c3_1(a33)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1503, 2053])).
% 1.80/1.46 tff(2063,plain,
% 1.80/1.46 (c1_1(a37)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1256, 2059])).
% 1.80/1.46 tff(2064,plain,
% 1.80/1.46 ($false),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1832, 169, 2063, 2055, 2062, 2061, 2060, 2054, 83, 2056])).
% 1.80/1.46 tff(2065,plain,((~hskp25) | hskp26 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16)) | hskp27 | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 1.80/1.46 tff(2066,plain,
% 1.80/1.46 (~hskp25),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2065, 1731, 725, 24, 2, 772, 84, 730, 729, 728])).
% 1.80/1.46 tff(2067,plain,
% 1.80/1.46 (hskp21),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[167, 2066, 643])).
% 1.80/1.46 tff(2068,plain,
% 1.80/1.46 (c3_1(a42)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[803, 2067])).
% 1.80/1.46 tff(2069,plain,
% 1.80/1.46 (c2_1(a42)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[814, 2067])).
% 1.80/1.46 tff(2070,plain,
% 1.80/1.46 (~c0_1(a42)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[821, 169, 2069, 2068, 725, 24, 2, 439, 772])).
% 1.80/1.46 tff(2071,plain,
% 1.80/1.46 (~c1_1(a42)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[827, 2067])).
% 1.80/1.46 tff(2072,plain,
% 1.80/1.46 (hskp10),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1738, 169, 2069, 2068, 730, 729, 2071, 1137, 943])).
% 1.80/1.46 tff(2073,plain,
% 1.80/1.46 (~c3_1(a18)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1150, 2072])).
% 1.80/1.46 tff(2074,plain,
% 1.80/1.46 (c2_1(a18)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1161, 2072])).
% 1.80/1.46 tff(2075,plain,
% 1.80/1.46 (c0_1(a18)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1172, 2072])).
% 1.80/1.46 tff(2076,plain,
% 1.80/1.46 (hskp11),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1748, 169, 2069, 2068, 2075, 2074, 2073, 1126, 2070])).
% 1.80/1.46 tff(2077,plain,
% 1.80/1.46 (~c1_1(a19)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1209, 2076])).
% 1.80/1.46 tff(2078,plain,
% 1.80/1.46 (hskp20),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1233, 169, 84, 2075, 2074, 2073, 1227])).
% 1.80/1.46 tff(2079,plain,
% 1.80/1.46 (~c3_1(a37)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1239, 2078])).
% 1.80/1.46 tff(2080,plain,
% 1.80/1.46 (~c0_1(a37)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1245, 2078])).
% 1.80/1.46 tff(2081,plain,
% 1.80/1.46 (c2_1(a19)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1196, 2076])).
% 1.80/1.46 tff(2082,plain,
% 1.80/1.46 (c1_1(a37)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1256, 2078])).
% 1.80/1.46 tff(2083,plain,
% 1.80/1.46 (c0_1(a19)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1761, 169, 2069, 2068, 2082, 2081, 2071, 2080, 2079, 2077, 83])).
% 1.80/1.46 tff(2084,plain,
% 1.80/1.46 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | c0_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a37)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a37)))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2085,plain,
% 1.80/1.46 ((hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a37)) | c0_1(a37) | (~c1_1(a37))) <=> (hskp27 | hskp26 | c0_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a37)))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2086,plain,
% 1.80/1.46 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a37)) | c0_1(a37) | (~c1_1(a37)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | c0_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a37))))),
% 1.80/1.46 inference(monotonicity,[status(thm)],[2085])).
% 1.80/1.46 tff(2087,plain,
% 1.80/1.46 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a37)) | c0_1(a37) | (~c1_1(a37)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a37)))),
% 1.80/1.46 inference(transitivity,[status(thm)],[2086, 2084])).
% 1.80/1.46 tff(2088,plain,
% 1.80/1.46 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a37)) | c0_1(a37) | (~c1_1(a37)))),
% 1.80/1.46 inference(quant_inst,[status(thm)],[])).
% 1.80/1.46 tff(2089,plain,
% 1.80/1.46 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | c0_1(a37) | (~ndr1_0) | (~c1_1(a37)) | (~c2_1(a37))),
% 1.80/1.46 inference(modus_ponens,[status(thm)],[2088, 2087])).
% 1.80/1.46 tff(2090,plain,
% 1.80/1.46 (~c2_1(a37)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2089, 1731, 169, 84, 2082, 2080, 791])).
% 1.80/1.46 tff(2091,plain,
% 1.80/1.46 (~c3_1(a19)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1185, 2076])).
% 1.80/1.46 tff(2092,plain,
% 1.80/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a42) | c3_1(a37) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a37)) | c2_1(a37) | (~c2_1(a42)) | c0_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) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c3_1(a37) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a37)) | c2_1(a37) | (~c2_1(a42)) | c0_1(a42))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2093,plain,
% 1.80/1.46 (((~ndr1_0) | c3_1(a37) | c2_1(a37) | (~c1_1(a37)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c1_1(a42) | c0_1(a42) | (~c2_1(a42))) <=> (c1_1(a42) | c3_1(a37) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a37)) | c2_1(a37) | (~c2_1(a42)) | c0_1(a42))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2094,plain,
% 1.80/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a37) | c2_1(a37) | (~c1_1(a37)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c1_1(a42) | c0_1(a42) | (~c2_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) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a42) | c3_1(a37) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a37)) | c2_1(a37) | (~c2_1(a42)) | c0_1(a42)))),
% 1.80/1.46 inference(monotonicity,[status(thm)],[2093])).
% 1.80/1.46 tff(2095,plain,
% 1.80/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a37) | c2_1(a37) | (~c1_1(a37)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c1_1(a42) | c0_1(a42) | (~c2_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) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c3_1(a37) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a37)) | c2_1(a37) | (~c2_1(a42)) | c0_1(a42))),
% 1.80/1.46 inference(transitivity,[status(thm)],[2094, 2092])).
% 1.80/1.46 tff(2096,plain,
% 1.80/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a37) | c2_1(a37) | (~c1_1(a37)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c1_1(a42) | c0_1(a42) | (~c2_1(a42)))),
% 1.80/1.46 inference(quant_inst,[status(thm)],[])).
% 1.80/1.46 tff(2097,plain,
% 1.80/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a42) | c3_1(a37) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a37)) | c2_1(a37) | (~c2_1(a42)) | c0_1(a42)),
% 1.80/1.46 inference(modus_ponens,[status(thm)],[2096, 2095])).
% 1.80/1.46 tff(2098,plain,
% 1.80/1.46 ($false),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2097, 169, 2069, 2082, 2071, 2079, 2077, 2091, 458, 2090, 2070, 2083])).
% 1.80/1.46 tff(2099,plain,(hskp18 | hskp26 | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | (~c1_1(a16)) | hskp17 | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 1.80/1.46 tff(2100,plain,
% 1.80/1.46 ($false),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2099, 2052, 2051, 731, 84, 725, 24, 2, 2050, 643, 2049])).
% 1.80/1.46 tff(2101,plain,(hskp26 | hskp18 | (~c0_1(a16)) | c2_1(a16) | c3_1(a16) | hskp17 | c0_1(a1) | c2_1(a1) | (~c3_1(a1))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.46 tff(2102,plain,
% 1.80/1.46 (hskp26),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2101, 2015, 591, 580, 574, 643, 1843, 1842, 1844])).
% 1.80/1.46 tff(2103,plain,
% 1.80/1.46 (c3_1(a10)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[689, 2102])).
% 1.80/1.46 tff(2104,plain,
% 1.80/1.46 (c2_1(a10)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[678, 2102])).
% 1.80/1.46 tff(2105,plain,
% 1.80/1.46 (c0_1(a10)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[666, 2102])).
% 1.80/1.46 tff(2106,plain,
% 1.80/1.46 ($false),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[719, 169, 2105, 2104, 2103, 591, 580, 574, 439, 2011])).
% 1.80/1.46 tff(2107,plain,(hskp17 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.80/1.46 tff(2108,plain,
% 1.80/1.46 (hskp17),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2107, 73])).
% 1.80/1.46 tff(2109,plain,
% 1.80/1.46 (c2_1(a31)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[328, 2108])).
% 1.80/1.46 tff(2110,plain,
% 1.80/1.46 (c0_1(a31)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[317, 2108])).
% 1.80/1.46 tff(2111,plain,
% 1.80/1.46 (~c1_1(a31)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[71, 2108])).
% 1.80/1.46 tff(2112,plain,
% 1.80/1.46 (hskp0),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[468, 205, 2111, 2110, 2109, 73])).
% 1.80/1.46 tff(2113,plain,
% 1.80/1.46 (~c2_1(a1)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[259, 2112])).
% 1.80/1.46 tff(2114,plain,
% 1.80/1.46 (~c0_1(a1)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[283, 2112])).
% 1.80/1.46 tff(2115,plain,
% 1.80/1.46 (c3_1(a1)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[270, 2112])).
% 1.80/1.46 tff(2116,plain,
% 1.80/1.46 (c1_1(a1)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2036, 169, 2115, 633, 1089, 2114, 2113, 55, 642])).
% 1.80/1.46 tff(2117,plain,
% 1.80/1.46 ($false),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1850, 169, 205, 591, 2115, 574, 2114, 632, 2116, 3])).
% 1.80/1.46 tff(2118,plain,(hskp4 | c1_1(a16) | c0_1(a30) | c2_1(a30) | (~c1_1(a30)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.80/1.46 tff(2119,plain,
% 1.80/1.46 (hskp4),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2118, 622, 3, 616, 610, 73])).
% 1.80/1.46 tff(2120,plain,
% 1.80/1.46 (~c2_1(a6)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[111, 2119])).
% 1.80/1.46 tff(2121,plain,
% 1.80/1.46 (c3_1(a6)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[122, 2119])).
% 1.80/1.46 tff(2122,plain,
% 1.80/1.46 (c1_1(a6)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[133, 2119])).
% 1.80/1.46 tff(2123,plain,
% 1.80/1.46 (c3_1(a30)),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[1095, 169, 591, 2122, 2121, 622, 616, 574, 2120, 13, 3])).
% 1.80/1.46 tff(2124,plain,
% 1.80/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a30) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a30) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2125,plain,
% 1.80/1.46 (((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22)) <=> (c2_1(a30) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2126,plain,
% 1.80/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a30) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30))))),
% 1.80/1.46 inference(monotonicity,[status(thm)],[2125])).
% 1.80/1.46 tff(2127,plain,
% 1.80/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a30) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30)))),
% 1.80/1.46 inference(transitivity,[status(thm)],[2126, 2124])).
% 1.80/1.46 tff(2128,plain,
% 1.80/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c2_1(a22) | c0_1(a22) | c3_1(a22))),
% 1.80/1.46 inference(quant_inst,[status(thm)],[])).
% 1.80/1.46 tff(2129,plain,
% 1.80/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a30) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c1_1(a30)) | (~c3_1(a30))),
% 1.80/1.46 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 1.80/1.46 tff(2130,plain,
% 1.80/1.46 ($false),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2129, 169, 634, 725, 1089, 495, 489, 483, 2, 13, 3, 1127])).
% 1.80/1.46 tff(2131,plain,((~hskp13) | (~c1_1(a30)) | (~c0_1(a16)) | c2_1(a30) | c3_1(a16) | c1_1(a16) | (~c3_1(a30))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.46 tff(2132,plain,
% 1.80/1.46 (~hskp13),
% 1.80/1.46 inference(unit_resolution,[status(thm)],[2131, 2123, 591, 616, 574, 3, 610])).
% 1.80/1.46 tff(2133,plain,
% 1.80/1.46 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a31) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2134,plain,
% 1.80/1.46 ((hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a16) | c2_1(a16) | (~c0_1(a16))) <=> (hskp13 | c1_1(a31) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.46 inference(rewrite,[status(thm)],[])).
% 1.80/1.46 tff(2135,plain,
% 1.80/1.46 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a31) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.80/1.47 inference(monotonicity,[status(thm)],[2134])).
% 1.80/1.47 tff(2136,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.47 inference(transitivity,[status(thm)],[2135, 2133])).
% 1.80/1.47 tff(2137,plain,
% 1.80/1.47 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)))),
% 1.80/1.47 inference(quant_inst,[status(thm)],[])).
% 1.80/1.47 tff(2138,plain,
% 1.80/1.47 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.80/1.47 inference(modus_ponens,[status(thm)],[2137, 2136])).
% 1.80/1.47 tff(2139,plain,
% 1.80/1.47 (hskp13 | (~c3_1(a31))),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2138, 169, 2110, 591, 2111, 580, 1616, 3])).
% 1.80/1.47 tff(2140,plain,
% 1.80/1.47 (~c3_1(a31)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2139, 2132])).
% 1.80/1.47 tff(2141,plain,
% 1.80/1.47 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2142,plain,
% 1.80/1.47 ((hskp26 | hskp20 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31))) <=> (hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2143,plain,
% 1.80/1.47 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31))))),
% 1.80/1.47 inference(monotonicity,[status(thm)],[2142])).
% 1.80/1.47 tff(2144,plain,
% 1.80/1.47 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.47 inference(transitivity,[status(thm)],[2143, 2141])).
% 1.80/1.47 tff(2145,plain,
% 1.80/1.47 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)))),
% 1.80/1.47 inference(quant_inst,[status(thm)],[])).
% 1.80/1.47 tff(2146,plain,
% 1.80/1.47 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31))),
% 1.80/1.47 inference(modus_ponens,[status(thm)],[2145, 2144])).
% 1.80/1.47 tff(2147,plain,
% 1.80/1.47 (hskp26 | hskp20 | c3_1(a31)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2146, 169, 2110, 2109, 1227])).
% 1.80/1.47 tff(2148,plain,
% 1.80/1.47 (hskp20),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2147, 2140, 84])).
% 1.80/1.47 tff(2149,plain,
% 1.80/1.47 (~c3_1(a37)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1239, 2148])).
% 1.80/1.47 tff(2150,plain,
% 1.80/1.47 (~c0_1(a37)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1245, 2148])).
% 1.80/1.47 tff(2151,assumption,(~c2_1(a37)), introduced(assumption)).
% 1.80/1.47 tff(2152,assumption,(~c3_1(a37)), introduced(assumption)).
% 1.80/1.47 tff(2153,assumption,(~c0_1(a37)), introduced(assumption)).
% 1.80/1.47 tff(2154,plain,
% 1.80/1.47 ($false),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1880, 169, 634, 725, 2153, 2152, 1089, 2, 13, 2151, 3, 1127])).
% 1.80/1.47 tff(2155,plain,(c2_1(a37) | (~c1_1(a30)) | (~c0_1(a16)) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c3_1(a16) | c1_1(a16) | (~c3_1(a30))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.47 tff(2156,plain,
% 1.80/1.47 (c2_1(a37)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2155, 610, 591, 2150, 2149, 616, 574, 3, 2123])).
% 1.80/1.47 tff(2157,plain,
% 1.80/1.47 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c2_1(a37)))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c2_1(a37)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2158,plain,
% 1.80/1.47 ((hskp26 | hskp25 | (~ndr1_0) | c3_1(a37) | (~c2_1(a37)) | c0_1(a37)) <=> (hskp26 | hskp25 | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c2_1(a37)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2159,plain,
% 1.80/1.47 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a37) | (~c2_1(a37)) | c0_1(a37))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c2_1(a37))))),
% 1.80/1.47 inference(monotonicity,[status(thm)],[2158])).
% 1.80/1.47 tff(2160,plain,
% 1.80/1.47 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a37) | (~c2_1(a37)) | c0_1(a37))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c2_1(a37)))),
% 1.80/1.47 inference(transitivity,[status(thm)],[2159, 2157])).
% 1.80/1.47 tff(2161,plain,
% 1.80/1.47 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a37) | (~c2_1(a37)) | c0_1(a37))),
% 1.80/1.47 inference(quant_inst,[status(thm)],[])).
% 1.80/1.47 tff(2162,plain,
% 1.80/1.47 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a37) | c3_1(a37) | (~ndr1_0) | (~c2_1(a37))),
% 1.80/1.47 inference(modus_ponens,[status(thm)],[2161, 2160])).
% 1.80/1.47 tff(2163,plain,
% 1.80/1.47 (hskp25 | (~c2_1(a37))),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2162, 169, 84, 2150, 2149, 1107])).
% 1.80/1.47 tff(2164,plain,
% 1.80/1.47 (hskp25),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2163, 2156])).
% 1.80/1.47 tff(2165,plain,
% 1.80/1.47 (c2_1(a9)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[859, 2164])).
% 1.80/1.47 tff(2166,plain,
% 1.80/1.47 (c1_1(a9)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[870, 2164])).
% 1.80/1.47 tff(2167,plain,
% 1.80/1.47 (c0_1(a9)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[881, 2164])).
% 1.80/1.47 tff(2168,assumption,(c2_1(a37)), introduced(assumption)).
% 1.80/1.47 tff(2169,plain,
% 1.80/1.47 ($false),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1726, 169, 1309, 1300, 1299, 1863, 2153, 2152, 1862, 1861, 34, 2168])).
% 1.80/1.47 tff(2170,plain,((~hskp2) | (~c0_1(a9)) | (~c1_1(a9)) | (~c2_1(a9)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.47 tff(2171,plain,
% 1.80/1.47 (~hskp2),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2170, 2167, 2166, 2165, 2150, 2149, 2156])).
% 1.80/1.47 tff(2172,plain,
% 1.80/1.47 (hskp14),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[971, 2171, 3])).
% 1.80/1.47 tff(2173,plain,
% 1.80/1.47 (~c1_1(a24)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1024, 2172])).
% 1.80/1.47 tff(2174,plain,
% 1.80/1.47 (~c0_1(a24)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1030, 2172])).
% 1.80/1.47 tff(2175,plain,
% 1.80/1.47 (c2_1(a24)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1041, 2172])).
% 1.80/1.47 tff(2176,plain,
% 1.80/1.47 (c1_1(a37)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1256, 2148])).
% 1.80/1.47 tff(2177,plain,
% 1.80/1.47 (~c3_1(a24)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1326, 169, 2176, 2175, 2150, 2149, 2174, 2173, 83])).
% 1.80/1.47 tff(2178,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2179,plain,
% 1.80/1.47 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31))) <=> (c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2180,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9))))),
% 1.80/1.47 inference(monotonicity,[status(thm)],[2179])).
% 1.80/1.47 tff(2181,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)))),
% 1.80/1.47 inference(transitivity,[status(thm)],[2180, 2178])).
% 1.80/1.47 tff(2182,plain,
% 1.80/1.47 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))),
% 1.80/1.47 inference(quant_inst,[status(thm)],[])).
% 1.80/1.47 tff(2183,plain,
% 1.80/1.47 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c2_1(a9)) | (~c0_1(a9)) | (~c3_1(a9))),
% 1.80/1.47 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 1.80/1.47 tff(2184,plain,
% 1.80/1.47 (~c3_1(a9)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2183, 169, 2167, 2165, 2109, 2111, 1580, 2140])).
% 1.80/1.47 tff(2185,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | c3_1(a24) | (~c0_1(a9)) | c3_1(a9) | (~c1_1(a9)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | c3_1(a24) | (~c0_1(a9)) | c3_1(a9) | (~c1_1(a9)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2186,plain,
% 1.80/1.47 ((hskp24 | (~ndr1_0) | c3_1(a9) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a24) | c1_1(a24) | c0_1(a24)) <=> (hskp24 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | c3_1(a24) | (~c0_1(a9)) | c3_1(a9) | (~c1_1(a9)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2187,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a9) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a24) | c1_1(a24) | c0_1(a24))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | c3_1(a24) | (~c0_1(a9)) | c3_1(a9) | (~c1_1(a9))))),
% 1.80/1.47 inference(monotonicity,[status(thm)],[2186])).
% 1.80/1.47 tff(2188,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a9) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a24) | c1_1(a24) | c0_1(a24))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | c3_1(a24) | (~c0_1(a9)) | c3_1(a9) | (~c1_1(a9)))),
% 1.80/1.47 inference(transitivity,[status(thm)],[2187, 2185])).
% 1.80/1.47 tff(2189,plain,
% 1.80/1.47 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a9) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a24) | c1_1(a24) | c0_1(a24))),
% 1.80/1.47 inference(quant_inst,[status(thm)],[])).
% 1.80/1.47 tff(2190,plain,
% 1.80/1.47 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a24) | c1_1(a24) | (~ndr1_0) | c3_1(a24) | (~c0_1(a9)) | c3_1(a9) | (~c1_1(a9))),
% 1.80/1.47 inference(modus_ponens,[status(thm)],[2189, 2188])).
% 1.80/1.47 tff(2191,plain,
% 1.80/1.47 ($false),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2190, 169, 73, 2167, 2166, 2174, 2173, 982, 2184, 2177])).
% 1.80/1.47 tff(2192,plain,(hskp26 | hskp24 | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.80/1.47 tff(2193,plain,
% 1.80/1.47 (hskp26),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2192, 3, 73])).
% 1.80/1.47 tff(2194,plain,
% 1.80/1.47 (c0_1(a10)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[666, 2193])).
% 1.80/1.47 tff(2195,plain,
% 1.80/1.47 (c2_1(a10)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[678, 2193])).
% 1.80/1.47 tff(2196,plain,
% 1.80/1.47 (~hskp2),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1981, 2193, 580, 574, 591])).
% 1.80/1.47 tff(2197,plain,
% 1.80/1.47 (c3_1(a10)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[689, 2193])).
% 1.80/1.47 tff(2198,plain,
% 1.80/1.47 (hskp14),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[721, 2197, 568, 2196, 2195, 2194])).
% 1.80/1.47 tff(2199,plain,
% 1.80/1.47 (~c1_1(a24)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1024, 2198])).
% 1.80/1.47 tff(2200,plain,
% 1.80/1.47 (c2_1(a24)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1041, 2198])).
% 1.80/1.47 tff(2201,assumption,(~c3_1(a24)), introduced(assumption)).
% 1.80/1.47 tff(2202,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a24) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c3_1(a24))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a24) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c3_1(a24))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2203,plain,
% 1.80/1.47 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24))) <=> (c1_1(a24) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c3_1(a24))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2204,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a24) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c3_1(a24)))),
% 1.80/1.47 inference(monotonicity,[status(thm)],[2203])).
% 1.80/1.47 tff(2205,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a24) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c3_1(a24))),
% 1.80/1.47 inference(transitivity,[status(thm)],[2204, 2202])).
% 1.80/1.47 tff(2206,plain,
% 1.80/1.47 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))),
% 1.80/1.47 inference(quant_inst,[status(thm)],[])).
% 1.80/1.47 tff(2207,plain,
% 1.80/1.47 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a24) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c3_1(a24)),
% 1.80/1.47 inference(modus_ponens,[status(thm)],[2206, 2205])).
% 1.80/1.47 tff(2208,plain,
% 1.80/1.47 ($false),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2207, 169, 713, 712, 711, 1056, 1054, 1580, 2201])).
% 1.80/1.47 tff(2209,plain,(c3_1(a24) | (~c0_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c2_1(a24)) | c1_1(a24)), inference(lemma,lemma(discharge,[]))).
% 1.80/1.47 tff(2210,plain,
% 1.80/1.47 (c3_1(a24)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2209, 2194, 2195, 2197, 2200, 2199])).
% 1.80/1.47 tff(2211,plain,
% 1.80/1.47 (~c0_1(a24)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1030, 2198])).
% 1.80/1.47 tff(2212,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a24) | c1_1(a24) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2213,plain,
% 1.80/1.47 ((hskp4 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24))) <=> (hskp4 | c0_1(a24) | c1_1(a24) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2214,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a24) | c1_1(a24) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24))))),
% 1.80/1.47 inference(monotonicity,[status(thm)],[2213])).
% 1.80/1.47 tff(2215,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24)))),
% 1.80/1.47 inference(transitivity,[status(thm)],[2214, 2212])).
% 1.80/1.47 tff(2216,plain,
% 1.80/1.47 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a16) | c2_1(a16) | (~c0_1(a16)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))),
% 1.80/1.47 inference(quant_inst,[status(thm)],[])).
% 1.80/1.47 tff(2217,plain,
% 1.80/1.47 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c2_1(a16) | (~ndr1_0) | c1_1(a16) | (~c0_1(a16)) | (~c3_1(a24))),
% 1.80/1.47 inference(modus_ponens,[status(thm)],[2216, 2215])).
% 1.80/1.47 tff(2218,plain,
% 1.80/1.47 (hskp4 | (~c3_1(a24))),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2217, 169, 591, 2211, 2199, 580, 65, 3])).
% 1.80/1.47 tff(2219,plain,
% 1.80/1.47 (hskp4),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2218, 2210])).
% 1.80/1.47 tff(2220,plain,
% 1.80/1.47 (~c2_1(a6)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[111, 2219])).
% 1.80/1.47 tff(2221,plain,
% 1.80/1.47 (c3_1(a6)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[122, 2219])).
% 1.80/1.47 tff(2222,plain,
% 1.80/1.47 (c1_1(a6)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[133, 2219])).
% 1.80/1.47 tff(2223,plain,
% 1.80/1.47 ($false),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1654, 169, 725, 730, 729, 495, 489, 483, 2, 728, 13, 3])).
% 1.80/1.47 tff(2224,plain,((~hskp13) | (~c0_1(a16)) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a16) | c2_1(a6) | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.80/1.47 tff(2225,plain,
% 1.80/1.47 (~hskp13),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2224, 2222, 591, 2221, 574, 2220, 3])).
% 1.80/1.47 tff(2226,plain,
% 1.80/1.47 (~c3_1(a31)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2139, 2225])).
% 1.80/1.47 tff(2227,plain,
% 1.80/1.47 (hskp3),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1048, 169, 2196, 2200, 2211, 2199, 23])).
% 1.80/1.47 tff(2228,plain,
% 1.80/1.47 (~c3_1(a5)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[948, 2227])).
% 1.80/1.47 tff(2229,plain,
% 1.80/1.47 (~c2_1(a5)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[361, 2227])).
% 1.80/1.47 tff(2230,plain,
% 1.80/1.47 (c0_1(a5)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1081, 169, 591, 2222, 2221, 574, 2220, 2229, 2228, 13, 3])).
% 1.80/1.47 tff(2231,plain,
% 1.80/1.47 (~c1_1(a5)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[367, 2227])).
% 1.80/1.47 tff(2232,plain,
% 1.80/1.47 (c1_1(a10)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1625, 2225, 2194, 2197, 2231, 2229, 2230])).
% 1.80/1.47 tff(2233,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2234,plain,
% 1.80/1.47 ((hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6))) <=> (hskp19 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2235,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c1_1(a6)) | (~c3_1(a6))))),
% 1.80/1.47 inference(monotonicity,[status(thm)],[2234])).
% 1.80/1.47 tff(2236,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.80/1.47 inference(transitivity,[status(thm)],[2235, 2233])).
% 1.80/1.47 tff(2237,plain,
% 1.80/1.47 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))),
% 1.80/1.47 inference(quant_inst,[status(thm)],[])).
% 1.80/1.47 tff(2238,plain,
% 1.80/1.47 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c1_1(a6)) | (~c3_1(a6))),
% 1.80/1.47 inference(modus_ponens,[status(thm)],[2237, 2236])).
% 1.80/1.47 tff(2239,plain,
% 1.80/1.47 (hskp19 | (~c1_1(a10))),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2238, 169, 2194, 2195, 2222, 2221, 2220, 848])).
% 1.80/1.47 tff(2240,plain,
% 1.80/1.47 (hskp19),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[2239, 2232])).
% 1.80/1.47 tff(2241,plain,
% 1.80/1.47 (~c0_1(a33)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[897, 2240])).
% 1.80/1.47 tff(2242,plain,
% 1.80/1.47 (c3_1(a33)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1503, 2240])).
% 1.80/1.47 tff(2243,plain,
% 1.80/1.47 (c2_1(a33)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[908, 2240])).
% 1.80/1.47 tff(2244,assumption,(hskp11), introduced(assumption)).
% 1.80/1.47 tff(2245,plain,
% 1.80/1.47 (~c3_1(a19)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1185, 2244])).
% 1.80/1.47 tff(2246,plain,
% 1.80/1.47 (~c1_1(a19)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1209, 2244])).
% 1.80/1.47 tff(2247,plain,
% 1.80/1.47 (c2_1(a19)),
% 1.80/1.47 inference(unit_resolution,[status(thm)],[1196, 2244])).
% 1.80/1.47 tff(2248,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a19)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2249,plain,
% 1.80/1.47 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19))) <=> (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a19)))),
% 1.80/1.47 inference(rewrite,[status(thm)],[])).
% 1.80/1.47 tff(2250,plain,
% 1.80/1.47 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a19))))),
% 1.80/1.47 inference(monotonicity,[status(thm)],[2249])).
% 1.80/1.48 tff(2251,plain,
% 1.80/1.48 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a19)))),
% 1.80/1.48 inference(transitivity,[status(thm)],[2250, 2248])).
% 1.80/1.48 tff(2252,plain,
% 1.80/1.48 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))),
% 1.80/1.48 inference(quant_inst,[status(thm)],[])).
% 1.80/1.48 tff(2253,plain,
% 1.80/1.48 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a19))),
% 1.80/1.48 inference(modus_ponens,[status(thm)],[2252, 2251])).
% 1.80/1.48 tff(2254,plain,
% 1.80/1.48 ($false),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2253, 169, 713, 712, 711, 2247, 2246, 2245, 1580])).
% 1.80/1.48 tff(2255,plain,((~hskp11) | (~c0_1(a10)) | (~c2_1(a10)) | (~c3_1(a10))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.48 tff(2256,plain,
% 1.80/1.48 (~hskp11),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2255, 2194, 2195, 2197])).
% 1.80/1.48 tff(2257,plain,
% 1.80/1.48 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2258,plain,
% 1.80/1.48 ((hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp11 | c0_1(a33) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2259,plain,
% 1.80/1.48 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)) | (~c3_1(a33)) | (~c2_1(a33))))),
% 1.80/1.48 inference(monotonicity,[status(thm)],[2258])).
% 1.80/1.48 tff(2260,plain,
% 1.80/1.48 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.80/1.48 inference(transitivity,[status(thm)],[2259, 2257])).
% 1.80/1.48 tff(2261,plain,
% 1.80/1.48 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.80/1.48 inference(quant_inst,[status(thm)],[])).
% 1.80/1.48 tff(2262,plain,
% 1.80/1.48 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)) | (~c3_1(a33)) | (~c2_1(a33))),
% 1.80/1.48 inference(modus_ponens,[status(thm)],[2261, 2260])).
% 1.80/1.48 tff(2263,plain,
% 1.80/1.48 ($false),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2262, 169, 2256, 2243, 2242, 2110, 2109, 2241, 1126, 2226])).
% 1.80/1.48 tff(2264,plain,(c1_1(a16) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.80/1.48 tff(2265,plain,
% 1.80/1.48 (c1_1(a16)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2264, 73])).
% 1.80/1.48 tff(2266,plain,
% 1.80/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2267,plain,
% 1.80/1.48 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2268,plain,
% 1.80/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.80/1.48 inference(monotonicity,[status(thm)],[2267])).
% 1.80/1.48 tff(2269,plain,
% 1.80/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.48 inference(transitivity,[status(thm)],[2268, 2266])).
% 1.80/1.48 tff(2270,plain,
% 1.80/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.80/1.48 inference(quant_inst,[status(thm)],[])).
% 1.80/1.48 tff(2271,plain,
% 1.80/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.80/1.48 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 1.80/1.48 tff(2272,plain,
% 1.80/1.48 ((~c1_1(a16)) | (~c3_1(a31))),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2271, 169, 2110, 2109, 591, 580, 574, 439])).
% 1.80/1.48 tff(2273,plain,
% 1.80/1.48 (~c3_1(a31)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2272, 2265])).
% 1.80/1.48 tff(2274,plain,
% 1.80/1.48 (~hskp2),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[1981, 656, 701, 710, 702])).
% 1.80/1.48 tff(2275,plain,
% 1.80/1.48 (hskp14),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[723, 656, 2274, 668])).
% 1.80/1.48 tff(2276,plain,
% 1.80/1.48 (c2_1(a24)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[1041, 2275])).
% 1.80/1.48 tff(2277,plain,
% 1.80/1.48 (~c1_1(a24)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[1024, 2275])).
% 1.80/1.48 tff(2278,plain,
% 1.80/1.48 (c3_1(a24)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2209, 2277, 679, 690, 2276, 667])).
% 1.80/1.48 tff(2279,assumption,(~c3_1(a31)), introduced(assumption)).
% 1.80/1.48 tff(2280,plain,
% 1.80/1.48 (~c0_1(a24)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[1030, 2275])).
% 1.80/1.48 tff(2281,plain,
% 1.80/1.48 (~hskp11),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2255, 667, 679, 690])).
% 1.80/1.48 tff(2282,plain,
% 1.80/1.48 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2283,plain,
% 1.80/1.48 ((hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24))) <=> (hskp11 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2284,plain,
% 1.80/1.48 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31))))),
% 1.80/1.48 inference(monotonicity,[status(thm)],[2283])).
% 1.80/1.48 tff(2285,plain,
% 1.80/1.48 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.48 inference(transitivity,[status(thm)],[2284, 2282])).
% 1.80/1.48 tff(2286,plain,
% 1.80/1.48 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))),
% 1.80/1.48 inference(quant_inst,[status(thm)],[])).
% 1.80/1.48 tff(2287,plain,
% 1.80/1.48 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | (~ndr1_0) | (~c2_1(a24)) | (~c3_1(a24)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31))),
% 1.80/1.48 inference(modus_ponens,[status(thm)],[2286, 2285])).
% 1.80/1.48 tff(2288,plain,
% 1.80/1.48 ($false),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2287, 169, 2281, 331, 332, 2276, 2280, 1126, 2279, 2278])).
% 1.80/1.48 tff(2289,plain,((~hskp26) | (~c0_1(a31)) | (~c2_1(a31)) | c3_1(a31) | (~hskp9)), inference(lemma,lemma(discharge,[]))).
% 1.80/1.48 tff(2290,plain,
% 1.80/1.48 (~hskp26),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2289, 2110, 2109, 2273, 568])).
% 1.80/1.48 tff(2291,plain,
% 1.80/1.48 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a31) | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2292,plain,
% 1.80/1.48 ((hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30))) <=> (hskp4 | c1_1(a31) | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2293,plain,
% 1.80/1.48 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a31) | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31))))),
% 1.80/1.48 inference(monotonicity,[status(thm)],[2292])).
% 1.80/1.48 tff(2294,plain,
% 1.80/1.48 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.48 inference(transitivity,[status(thm)],[2293, 2291])).
% 1.80/1.48 tff(2295,plain,
% 1.80/1.48 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a30) | (~c3_1(a30)) | (~c1_1(a30)))),
% 1.80/1.48 inference(quant_inst,[status(thm)],[])).
% 1.80/1.48 tff(2296,plain,
% 1.80/1.48 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | c0_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31))),
% 1.80/1.48 inference(modus_ponens,[status(thm)],[2295, 2294])).
% 1.80/1.48 tff(2297,plain,
% 1.80/1.48 (~c3_1(a30)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2296, 169, 205, 331, 1087, 343, 1088, 632, 2279])).
% 1.80/1.48 tff(2298,plain,
% 1.80/1.48 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2299,plain,
% 1.80/1.48 ((hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1))) <=> (hskp4 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2300,plain,
% 1.80/1.48 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a31) | (~c0_1(a31))))),
% 1.80/1.48 inference(monotonicity,[status(thm)],[2299])).
% 1.80/1.48 tff(2301,plain,
% 1.80/1.48 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.48 inference(transitivity,[status(thm)],[2300, 2298])).
% 1.80/1.48 tff(2302,plain,
% 1.80/1.48 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))),
% 1.80/1.48 inference(quant_inst,[status(thm)],[])).
% 1.80/1.48 tff(2303,plain,
% 1.80/1.48 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c3_1(a31) | (~c0_1(a31))),
% 1.80/1.48 inference(modus_ponens,[status(thm)],[2302, 2301])).
% 1.80/1.48 tff(2304,plain,
% 1.80/1.48 (~c1_1(a1)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2303, 169, 205, 331, 496, 343, 477, 632, 2279])).
% 1.80/1.48 tff(2305,plain,
% 1.80/1.48 (hskp26 | hskp20 | c3_1(a31)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2146, 169, 331, 332, 1227])).
% 1.80/1.48 tff(2306,plain,
% 1.80/1.48 (hskp20),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2305, 84, 2279])).
% 1.80/1.48 tff(2307,plain,
% 1.80/1.48 (~c3_1(a37)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[1239, 2306])).
% 1.80/1.48 tff(2308,plain,
% 1.80/1.48 (~c0_1(a37)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[1245, 2306])).
% 1.80/1.48 tff(2309,plain,
% 1.80/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a37) | c3_1(a37) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a37) | c3_1(a37) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c2_1(a37))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2310,plain,
% 1.80/1.48 (((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a1) | c1_1(a1) | c0_1(a1)) <=> (c0_1(a37) | c3_1(a37) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c2_1(a37))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2311,plain,
% 1.80/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a1) | c1_1(a1) | c0_1(a1))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a37) | c3_1(a37) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c2_1(a37)))),
% 1.80/1.48 inference(monotonicity,[status(thm)],[2310])).
% 1.80/1.48 tff(2312,plain,
% 1.80/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a1) | c1_1(a1) | c0_1(a1))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a37) | c3_1(a37) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c2_1(a37))),
% 1.80/1.48 inference(transitivity,[status(thm)],[2311, 2309])).
% 1.80/1.48 tff(2313,plain,
% 1.80/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a37) | c0_1(a37) | c2_1(a37) | c2_1(a1) | c1_1(a1) | c0_1(a1))),
% 1.80/1.48 inference(quant_inst,[status(thm)],[])).
% 1.80/1.48 tff(2314,plain,
% 1.80/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a37) | c3_1(a37) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | c2_1(a37)),
% 1.80/1.48 inference(modus_ponens,[status(thm)],[2313, 2312])).
% 1.80/1.48 tff(2315,plain,
% 1.80/1.48 (c2_1(a37)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2314, 169, 496, 2308, 2307, 477, 476, 55, 2304])).
% 1.80/1.48 tff(2316,plain,
% 1.80/1.48 (hskp25 | (~c2_1(a37))),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2162, 169, 84, 2308, 2307, 1107])).
% 1.80/1.48 tff(2317,plain,
% 1.80/1.48 (hskp25),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[2316, 2315])).
% 1.80/1.48 tff(2318,plain,
% 1.80/1.48 (c2_1(a9)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[859, 2317])).
% 1.80/1.48 tff(2319,plain,
% 1.80/1.48 (c1_1(a9)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[870, 2317])).
% 1.80/1.48 tff(2320,plain,
% 1.80/1.48 (c0_1(a9)),
% 1.80/1.48 inference(unit_resolution,[status(thm)],[881, 2317])).
% 1.80/1.48 tff(2321,plain,
% 1.80/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | c3_1(a30) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | c3_1(a30) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2322,plain,
% 1.80/1.48 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a30) | c2_1(a30) | (~c1_1(a30)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37))) <=> (c0_1(a37) | c3_1(a37) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | c3_1(a30) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.80/1.48 inference(rewrite,[status(thm)],[])).
% 1.80/1.48 tff(2323,plain,
% 1.80/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a30) | c2_1(a30) | (~c1_1(a30)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | c3_1(a30) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))))),
% 1.80/1.49 inference(monotonicity,[status(thm)],[2322])).
% 1.80/1.49 tff(2324,plain,
% 1.80/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a30) | c2_1(a30) | (~c1_1(a30)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | c3_1(a30) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.80/1.49 inference(transitivity,[status(thm)],[2323, 2321])).
% 1.80/1.49 tff(2325,plain,
% 1.80/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a30) | c2_1(a30) | (~c1_1(a30)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))),
% 1.80/1.49 inference(quant_inst,[status(thm)],[])).
% 1.80/1.49 tff(2326,plain,
% 1.80/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | c3_1(a30) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2325, 2324])).
% 1.80/1.49 tff(2327,plain,
% 1.80/1.49 ($false),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2326, 169, 2320, 2319, 2318, 1087, 2308, 2307, 1086, 34, 2315, 2297])).
% 1.80/1.49 tff(2328,plain,(hskp26 | (~c3_1(a1)) | c0_1(a1) | c2_1(a1) | hskp4 | (~c0_1(a31)) | c1_1(a31) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a16)) | c2_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.80/1.49 tff(2329,plain,
% 1.80/1.49 ($false),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2328, 2114, 2115, 2290, 2113, 205, 2110, 2111, 2273, 2109, 591, 580, 574])).
% 1.80/1.49 tff(2330,plain,(hskp4 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.80/1.49 tff(2331,plain,
% 1.80/1.49 (hskp4),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2330, 73])).
% 1.80/1.49 tff(2332,plain,
% 1.80/1.49 (~c2_1(a6)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[111, 2331])).
% 1.80/1.49 tff(2333,plain,
% 1.80/1.49 (hskp16),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[598, 2290])).
% 1.80/1.49 tff(2334,plain,
% 1.80/1.49 (~c2_1(a30)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[615, 2333])).
% 1.80/1.49 tff(2335,plain,
% 1.80/1.49 (~c0_1(a30)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[621, 2333])).
% 1.80/1.49 tff(2336,plain,
% 1.80/1.49 (c3_1(a6)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[122, 2331])).
% 1.80/1.49 tff(2337,plain,
% 1.80/1.49 (c1_1(a6)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[133, 2331])).
% 1.80/1.49 tff(2338,plain,
% 1.80/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2339,plain,
% 1.80/1.49 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30)) <=> (c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2340,plain,
% 1.80/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31))))),
% 1.80/1.49 inference(monotonicity,[status(thm)],[2339])).
% 1.80/1.49 tff(2341,plain,
% 1.80/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.49 inference(transitivity,[status(thm)],[2340, 2338])).
% 1.80/1.49 tff(2342,plain,
% 1.80/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30))),
% 1.80/1.49 inference(quant_inst,[status(thm)],[])).
% 1.80/1.49 tff(2343,plain,
% 1.80/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31))),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2342, 2341])).
% 1.80/1.49 tff(2344,plain,
% 1.80/1.49 (c3_1(a30)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2343, 169, 2110, 2337, 2336, 2111, 2335, 2334, 2332, 13, 2273])).
% 1.80/1.49 tff(2345,plain,
% 1.80/1.49 (hskp20),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2147, 2290, 2273])).
% 1.80/1.49 tff(2346,plain,
% 1.80/1.49 (~c3_1(a37)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[1239, 2345])).
% 1.80/1.49 tff(2347,plain,
% 1.80/1.49 (~c0_1(a37)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[1245, 2345])).
% 1.80/1.49 tff(2348,plain,
% 1.80/1.49 (hskp25 | (~c2_1(a37))),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2162, 169, 84, 2153, 2152, 1107])).
% 1.80/1.49 tff(2349,plain,
% 1.80/1.49 (hskp25),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2348, 2168])).
% 1.80/1.49 tff(2350,plain,
% 1.80/1.49 (c2_1(a9)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[859, 2349])).
% 1.80/1.49 tff(2351,plain,
% 1.80/1.49 (c1_1(a9)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[870, 2349])).
% 1.80/1.49 tff(2352,plain,
% 1.80/1.49 (c0_1(a9)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[881, 2349])).
% 1.80/1.49 tff(2353,plain,
% 1.80/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2354,plain,
% 1.80/1.49 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37))) <=> (c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2355,plain,
% 1.80/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))))),
% 1.80/1.49 inference(monotonicity,[status(thm)],[2354])).
% 1.80/1.49 tff(2356,plain,
% 1.80/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.80/1.49 inference(transitivity,[status(thm)],[2355, 2353])).
% 1.80/1.49 tff(2357,plain,
% 1.80/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a37) | c3_1(a37) | (~c2_1(a37)))),
% 1.80/1.49 inference(quant_inst,[status(thm)],[])).
% 1.80/1.49 tff(2358,plain,
% 1.80/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a37)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 1.80/1.49 tff(2359,plain,
% 1.80/1.49 ($false),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2358, 169, 2352, 2351, 2350, 2153, 2152, 24, 2, 34, 2168, 772])).
% 1.80/1.49 tff(2360,plain,((~c2_1(a37)) | c0_1(a37) | c3_1(a37) | c2_1(a16) | c3_1(a16) | (~c1_1(a16)) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.80/1.49 tff(2361,plain,
% 1.80/1.49 (~c2_1(a37)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2360, 2347, 2346, 580, 574, 2265, 2290])).
% 1.80/1.49 tff(2362,plain,
% 1.80/1.49 (c1_1(a30)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[609, 2333])).
% 1.80/1.49 tff(2363,plain,
% 1.80/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c1_1(a31) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c1_1(a31) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)) | c2_1(a37))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2364,plain,
% 1.80/1.49 (((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a37) | c0_1(a37) | c3_1(a37)) <=> (c0_1(a37) | c3_1(a37) | c1_1(a31) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)) | c2_1(a37))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2365,plain,
% 1.80/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c1_1(a31) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)) | c2_1(a37)))),
% 1.80/1.49 inference(monotonicity,[status(thm)],[2364])).
% 1.80/1.49 tff(2366,plain,
% 1.80/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c1_1(a31) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)) | c2_1(a37))),
% 1.80/1.49 inference(transitivity,[status(thm)],[2365, 2363])).
% 1.80/1.49 tff(2367,plain,
% 1.80/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a37) | c0_1(a37) | c3_1(a37))),
% 1.80/1.49 inference(quant_inst,[status(thm)],[])).
% 1.80/1.49 tff(2368,plain,
% 1.80/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c1_1(a31) | c2_1(a30) | (~ndr1_0) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a31) | (~c0_1(a31)) | c2_1(a37)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2367, 2366])).
% 1.80/1.49 tff(2369,plain,
% 1.80/1.49 ($false),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2368, 169, 2110, 2362, 2347, 2346, 2111, 2334, 13, 2273, 2361, 2344])).
% 1.80/1.49 tff(2370,plain,(hskp24), inference(lemma,lemma(discharge,[]))).
% 1.80/1.49 tff(2371,plain,
% 1.80/1.49 (((~hskp24) | c2_1(a3)) <=> ((~hskp24) | c2_1(a3))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2372,axiom,((~hskp24) | c2_1(a3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 1.80/1.49 tff(2373,plain,
% 1.80/1.49 ((~hskp24) | c2_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2372, 2371])).
% 1.80/1.49 tff(2374,plain,
% 1.80/1.49 ((~hskp24) | c2_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2373, 2371])).
% 1.80/1.49 tff(2375,plain,
% 1.80/1.49 ((~hskp24) | c2_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2374, 2371])).
% 1.80/1.49 tff(2376,plain,
% 1.80/1.49 ((~hskp24) | c2_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2375, 2371])).
% 1.80/1.49 tff(2377,plain,
% 1.80/1.49 ((~hskp24) | c2_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2376, 2371])).
% 1.80/1.49 tff(2378,plain,
% 1.80/1.49 ((~hskp24) | c2_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2377, 2371])).
% 1.80/1.49 tff(2379,plain,
% 1.80/1.49 ((~hskp24) | c2_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2378, 2371])).
% 1.80/1.49 tff(2380,plain,
% 1.80/1.49 ((~hskp24) | c2_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2379, 2371])).
% 1.80/1.49 tff(2381,plain,
% 1.80/1.49 (c2_1(a3)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2380, 2370])).
% 1.80/1.49 tff(2382,plain,
% 1.80/1.49 (((~hskp24) | c1_1(a3)) <=> ((~hskp24) | c1_1(a3))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2383,axiom,((~hskp24) | c1_1(a3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 1.80/1.49 tff(2384,plain,
% 1.80/1.49 ((~hskp24) | c1_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2383, 2382])).
% 1.80/1.49 tff(2385,plain,
% 1.80/1.49 ((~hskp24) | c1_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2384, 2382])).
% 1.80/1.49 tff(2386,plain,
% 1.80/1.49 ((~hskp24) | c1_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2385, 2382])).
% 1.80/1.49 tff(2387,plain,
% 1.80/1.49 ((~hskp24) | c1_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2386, 2382])).
% 1.80/1.49 tff(2388,plain,
% 1.80/1.49 ((~hskp24) | c1_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2387, 2382])).
% 1.80/1.49 tff(2389,plain,
% 1.80/1.49 ((~hskp24) | c1_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2388, 2382])).
% 1.80/1.49 tff(2390,plain,
% 1.80/1.49 ((~hskp24) | c1_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2389, 2382])).
% 1.80/1.49 tff(2391,plain,
% 1.80/1.49 ((~hskp24) | c1_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2390, 2382])).
% 1.80/1.49 tff(2392,plain,
% 1.80/1.49 (c1_1(a3)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2391, 2370])).
% 1.80/1.49 tff(2393,plain,
% 1.80/1.49 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c1_1(a16))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c1_1(a16))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2394,plain,
% 1.80/1.49 (((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a16) | c1_1(a16) | c0_1(a16)) <=> (c0_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c1_1(a16))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2395,plain,
% 1.80/1.49 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a16) | c1_1(a16) | c0_1(a16))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c1_1(a16)))),
% 1.80/1.49 inference(monotonicity,[status(thm)],[2394])).
% 1.80/1.49 tff(2396,plain,
% 1.80/1.49 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a16) | c1_1(a16) | c0_1(a16))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c1_1(a16))),
% 1.80/1.49 inference(transitivity,[status(thm)],[2395, 2393])).
% 1.80/1.49 tff(2397,plain,
% 1.80/1.49 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a16) | c1_1(a16) | c0_1(a16))),
% 1.80/1.49 inference(quant_inst,[status(thm)],[])).
% 1.80/1.49 tff(2398,plain,
% 1.80/1.49 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a16) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c1_1(a16)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2397, 2396])).
% 1.80/1.49 tff(2399,plain,
% 1.80/1.49 (c0_1(a16) | c0_1(a3) | c1_1(a16)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2398, 169, 2392, 2381, 2, 45])).
% 1.80/1.49 tff(2400,plain,
% 1.80/1.49 (c0_1(a3)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2399, 3, 35])).
% 1.80/1.49 tff(2401,plain,
% 1.80/1.49 (c2_1(a31)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[328, 66])).
% 1.80/1.49 tff(2402,plain,
% 1.80/1.49 (((~hskp24) | c3_1(a3)) <=> ((~hskp24) | c3_1(a3))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2403,axiom,((~hskp24) | c3_1(a3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 1.80/1.49 tff(2404,plain,
% 1.80/1.49 ((~hskp24) | c3_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 1.80/1.49 tff(2405,plain,
% 1.80/1.49 ((~hskp24) | c3_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2404, 2402])).
% 1.80/1.49 tff(2406,plain,
% 1.80/1.49 ((~hskp24) | c3_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2405, 2402])).
% 1.80/1.49 tff(2407,plain,
% 1.80/1.49 ((~hskp24) | c3_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2406, 2402])).
% 1.80/1.49 tff(2408,plain,
% 1.80/1.49 ((~hskp24) | c3_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2407, 2402])).
% 1.80/1.49 tff(2409,plain,
% 1.80/1.49 ((~hskp24) | c3_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2408, 2402])).
% 1.80/1.49 tff(2410,plain,
% 1.80/1.49 ((~hskp24) | c3_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2409, 2402])).
% 1.80/1.49 tff(2411,plain,
% 1.80/1.49 ((~hskp24) | c3_1(a3)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2410, 2402])).
% 1.80/1.49 tff(2412,plain,
% 1.80/1.49 (c3_1(a3)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2411, 2370])).
% 1.80/1.49 tff(2413,assumption,(c0_1(a3)), introduced(assumption)).
% 1.80/1.49 tff(2414,assumption,(c3_1(a3)), introduced(assumption)).
% 1.80/1.49 tff(2415,assumption,(c2_1(a3)), introduced(assumption)).
% 1.80/1.49 tff(2416,plain,
% 1.80/1.49 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a31) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a31) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2417,plain,
% 1.80/1.49 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31))) <=> (c1_1(a31) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2418,plain,
% 1.80/1.49 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a31) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31)))),
% 1.80/1.49 inference(monotonicity,[status(thm)],[2417])).
% 1.80/1.49 tff(2419,plain,
% 1.80/1.49 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a31) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31))),
% 1.80/1.49 inference(transitivity,[status(thm)],[2418, 2416])).
% 1.80/1.49 tff(2420,plain,
% 1.80/1.49 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))),
% 1.80/1.49 inference(quant_inst,[status(thm)],[])).
% 1.80/1.49 tff(2421,plain,
% 1.80/1.49 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a31) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31)),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2420, 2419])).
% 1.80/1.49 tff(2422,plain,
% 1.80/1.49 ($false),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2421, 169, 2415, 2414, 332, 343, 1580, 2279, 2413])).
% 1.80/1.49 tff(2423,plain,(c3_1(a31) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | c1_1(a31) | (~c0_1(a3))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.49 tff(2424,plain,
% 1.80/1.49 (c3_1(a31) | (~c2_1(a31)) | c1_1(a31) | (~c0_1(a3))),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2423, 2412, 2381])).
% 1.80/1.49 tff(2425,plain,
% 1.80/1.49 (c3_1(a31)),
% 1.80/1.49 inference(unit_resolution,[status(thm)],[2424, 2401, 2400, 72])).
% 1.80/1.49 tff(2426,plain,
% 1.80/1.49 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.80/1.49 inference(bind,[status(th)],[])).
% 1.80/1.49 tff(2427,plain,
% 1.80/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_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)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.80/1.49 inference(quant_intro,[status(thm)],[2426])).
% 1.80/1.49 tff(2428,plain,
% 1.80/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_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)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2429,plain,
% 1.80/1.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c1_1(V) | c2_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c1_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W))), (((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W))), ((((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)))), (((((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.80/1.49 inference(bind,[status(th)],[])).
% 1.80/1.49 tff(2430,plain,
% 1.80/1.49 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.80/1.49 inference(quant_intro,[status(thm)],[2429])).
% 1.80/1.49 tff(2431,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 1.80/1.49 tff(2432,plain,
% 1.80/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2431, 2430])).
% 1.80/1.49 tff(2433,plain,
% 1.80/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2432, 2428])).
% 1.80/1.49 tff(2434,plain,(
% 1.80/1.49 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.80/1.49 inference(skolemize,[status(sab)],[2433])).
% 1.80/1.49 tff(2435,plain,
% 1.80/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.80/1.49 inference(modus_ponens,[status(thm)],[2434, 2427])).
% 1.80/1.49 tff(2436,assumption,(hskp1), introduced(assumption)).
% 1.80/1.49 tff(2437,plain,
% 1.80/1.49 (((~hskp1) | (~c3_1(a2))) <=> ((~hskp1) | (~c3_1(a2)))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2438,plain,
% 1.80/1.49 (((~c3_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a2)))),
% 1.80/1.49 inference(rewrite,[status(thm)],[])).
% 1.80/1.49 tff(2439,axiom,((~c3_1(a2)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.80/1.49 tff(2440,plain,
% 1.80/1.49 ((~hskp1) | (~c3_1(a2))),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2439, 2438])).
% 1.80/1.50 tff(2441,plain,
% 1.80/1.50 ((~hskp1) | (~c3_1(a2))),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2440, 2437])).
% 1.80/1.50 tff(2442,plain,
% 1.80/1.50 (~c3_1(a2)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2441, 2436])).
% 1.80/1.50 tff(2443,plain,
% 1.80/1.50 (~c0_1(a2)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[1516, 2436])).
% 1.80/1.50 tff(2444,plain,
% 1.80/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a16))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a16))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2445,plain,
% 1.80/1.50 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c1_1(a16) | (~c2_1(a16))) <=> ((~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a16))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2446,plain,
% 1.80/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c1_1(a16) | (~c2_1(a16)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a16)))),
% 1.80/1.50 inference(monotonicity,[status(thm)],[2445])).
% 1.80/1.50 tff(2447,plain,
% 1.80/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c1_1(a16) | (~c2_1(a16)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a16))),
% 1.80/1.50 inference(transitivity,[status(thm)],[2446, 2444])).
% 1.80/1.50 tff(2448,plain,
% 1.80/1.50 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c1_1(a16) | (~c2_1(a16)))),
% 1.80/1.50 inference(quant_inst,[status(thm)],[])).
% 1.80/1.50 tff(2449,plain,
% 1.80/1.50 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a16)),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2448, 2447])).
% 1.80/1.50 tff(2450,plain,
% 1.80/1.50 ((~c2_1(a16)) | (~c0_1(a3)) | c1_1(a16)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2449, 169, 2381, 2412, 2, 1580])).
% 1.80/1.50 tff(2451,plain,
% 1.80/1.50 (~c2_1(a16)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2450, 2400, 3])).
% 1.80/1.50 tff(2452,plain,
% 1.80/1.50 (c2_1(a2)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[1527, 2436])).
% 1.80/1.50 tff(2453,plain,
% 1.80/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c2_1(a16) | c3_1(a16) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c2_1(a16) | c3_1(a16) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a16))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2454,plain,
% 1.80/1.50 (((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16)) <=> (c0_1(a16) | c2_1(a16) | c3_1(a16) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a16))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2455,plain,
% 1.80/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c2_1(a16) | c3_1(a16) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a16)))),
% 1.80/1.50 inference(monotonicity,[status(thm)],[2454])).
% 1.80/1.50 tff(2456,plain,
% 1.80/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c2_1(a16) | c3_1(a16) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a16))),
% 1.80/1.50 inference(transitivity,[status(thm)],[2455, 2453])).
% 1.80/1.50 tff(2457,plain,
% 1.80/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16))),
% 1.80/1.50 inference(quant_inst,[status(thm)],[])).
% 1.80/1.50 tff(2458,plain,
% 1.80/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c2_1(a16) | c3_1(a16) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a16)),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2457, 2456])).
% 1.80/1.50 tff(2459,plain,
% 1.80/1.50 ($false),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2458, 169, 35, 2452, 2451, 2, 2443, 2442, 2435, 3])).
% 1.80/1.50 tff(2460,plain,((~hskp1) | c0_1(a16) | c3_1(a16) | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.80/1.50 tff(2461,plain,
% 1.80/1.50 (~hskp1),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2460, 3, 2, 35])).
% 1.80/1.50 tff(2462,plain,
% 1.80/1.50 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a16) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a16) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2463,plain,
% 1.80/1.50 ((hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c1_1(a16) | c0_1(a16)) <=> (hskp1 | c0_1(a16) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2464,plain,
% 1.80/1.50 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c1_1(a16) | c0_1(a16))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a16) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.80/1.50 inference(monotonicity,[status(thm)],[2463])).
% 1.80/1.50 tff(2465,plain,
% 1.80/1.50 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c1_1(a16) | c0_1(a16))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a16) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.80/1.50 inference(transitivity,[status(thm)],[2464, 2462])).
% 1.80/1.50 tff(2466,plain,
% 1.80/1.50 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c1_1(a16) | c0_1(a16))),
% 1.80/1.50 inference(quant_inst,[status(thm)],[])).
% 1.80/1.50 tff(2467,plain,
% 1.80/1.50 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a16) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2466, 2465])).
% 1.80/1.50 tff(2468,plain,
% 1.80/1.50 ($false),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2467, 169, 2461, 2401, 35, 72, 2, 1493, 2425, 3])).
% 1.80/1.50 tff(2469,plain,((~hskp17) | c0_1(a16) | c3_1(a16) | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.80/1.50 tff(2470,plain,
% 1.80/1.50 (~hskp17),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2469, 3, 2, 35])).
% 1.80/1.50 tff(2471,plain,
% 1.80/1.50 (hskp8),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[306, 205, 2470])).
% 1.80/1.50 tff(2472,plain,
% 1.80/1.50 (~c2_1(a15)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[184, 2471])).
% 1.80/1.50 tff(2473,plain,
% 1.80/1.50 (~c1_1(a15)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[201, 2471])).
% 1.80/1.50 tff(2474,assumption,(~hskp15), introduced(assumption)).
% 1.80/1.50 tff(2475,plain,
% 1.80/1.50 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2476,plain,
% 1.80/1.50 ((hskp14 | hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15))) <=> (hskp14 | hskp2 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2477,plain,
% 1.80/1.50 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15))))),
% 1.80/1.50 inference(monotonicity,[status(thm)],[2476])).
% 1.80/1.50 tff(2478,plain,
% 1.80/1.50 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)))),
% 1.80/1.50 inference(transitivity,[status(thm)],[2477, 2475])).
% 1.80/1.50 tff(2479,plain,
% 1.80/1.50 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))),
% 1.80/1.50 inference(quant_inst,[status(thm)],[])).
% 1.80/1.50 tff(2480,plain,
% 1.80/1.50 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15))),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2479, 2478])).
% 1.80/1.50 tff(2481,plain,
% 1.80/1.50 ($false),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2480, 169, 655, 654, 196, 202, 185, 700])).
% 1.80/1.50 tff(2482,plain,((~hskp8) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.80/1.50 tff(2483,plain,
% 1.80/1.50 (~hskp8),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2482, 654, 655])).
% 1.80/1.50 tff(2484,plain,
% 1.80/1.50 (hskp17),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[306, 2483, 205])).
% 1.80/1.50 tff(2485,plain,
% 1.80/1.50 (c2_1(a31)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[328, 2484])).
% 1.80/1.50 tff(2486,plain,
% 1.80/1.50 (~c1_1(a31)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[71, 2484])).
% 1.80/1.50 tff(2487,plain,
% 1.80/1.50 (c0_1(a31)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[317, 2484])).
% 1.80/1.50 tff(2488,plain,
% 1.80/1.50 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.80/1.50 inference(bind,[status(th)],[])).
% 1.80/1.50 tff(2489,plain,
% 1.80/1.50 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.80/1.50 inference(quant_intro,[status(thm)],[2488])).
% 1.80/1.50 tff(2490,plain,
% 1.80/1.50 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2491,plain,
% 1.80/1.50 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.80/1.50 inference(bind,[status(th)],[])).
% 1.80/1.50 tff(2492,plain,
% 1.80/1.50 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.80/1.50 inference(quant_intro,[status(thm)],[2491])).
% 1.80/1.50 tff(2493,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 1.80/1.50 tff(2494,plain,
% 1.80/1.50 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2493, 2492])).
% 1.80/1.50 tff(2495,plain,
% 1.80/1.50 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2494, 2490])).
% 1.80/1.50 tff(2496,plain,(
% 1.80/1.50 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.80/1.50 inference(skolemize,[status(sab)],[2495])).
% 1.80/1.50 tff(2497,plain,
% 1.80/1.50 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2496, 2489])).
% 1.80/1.50 tff(2498,plain,
% 1.80/1.50 (^[U: $i] : refl((hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 1.80/1.50 inference(bind,[status(th)],[])).
% 1.80/1.50 tff(2499,plain,
% 1.80/1.50 (![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.80/1.50 inference(quant_intro,[status(thm)],[2498])).
% 1.80/1.50 tff(2500,plain,
% 1.80/1.50 (![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2501,plain,
% 1.80/1.50 (^[U: $i] : 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)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 1.80/1.50 inference(bind,[status(th)],[])).
% 1.80/1.50 tff(2502,plain,
% 1.80/1.50 (![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp7) <=> ![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.80/1.50 inference(quant_intro,[status(thm)],[2501])).
% 1.80/1.50 tff(2503,axiom,(![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.80/1.50 tff(2504,plain,
% 1.80/1.50 (![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2503, 2502])).
% 1.80/1.50 tff(2505,plain,
% 1.80/1.50 (![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2504, 2500])).
% 1.80/1.50 tff(2506,plain,(
% 1.80/1.50 ![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.80/1.50 inference(skolemize,[status(sab)],[2505])).
% 1.80/1.50 tff(2507,plain,
% 1.80/1.50 (![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2506, 2499])).
% 1.80/1.50 tff(2508,plain,
% 1.80/1.50 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2509,plain,
% 1.80/1.50 ((hskp7 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31))) <=> (hskp7 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2510,plain,
% 1.80/1.50 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31)))),
% 1.80/1.50 inference(monotonicity,[status(thm)],[2509])).
% 1.80/1.50 tff(2511,plain,
% 1.80/1.50 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 1.80/1.50 inference(transitivity,[status(thm)],[2510, 2508])).
% 1.80/1.50 tff(2512,plain,
% 1.80/1.50 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))),
% 1.80/1.50 inference(quant_inst,[status(thm)],[])).
% 1.80/1.50 tff(2513,plain,
% 1.80/1.50 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31)),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2512, 2511])).
% 1.80/1.50 tff(2514,plain,
% 1.80/1.50 (hskp7 | c3_1(a31)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2513, 169, 332, 343, 2507])).
% 1.80/1.50 tff(2515,plain,
% 1.80/1.50 (hskp7),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2514, 2279])).
% 1.80/1.50 tff(2516,plain,
% 1.80/1.50 (~c2_1(a14)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[525, 2515])).
% 1.80/1.50 tff(2517,plain,
% 1.80/1.50 (c3_1(a14)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[536, 2515])).
% 1.80/1.50 tff(2518,plain,
% 1.80/1.50 (c0_1(a14)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[558, 2515])).
% 1.80/1.50 tff(2519,plain,
% 1.80/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c2_1(a14) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a14)) | (~c0_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a14) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2520,plain,
% 1.80/1.50 ((hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1))) <=> (hskp15 | c2_1(a14) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2521,plain,
% 1.80/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c2_1(a14) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a14)) | (~c0_1(a14))))),
% 1.80/1.50 inference(monotonicity,[status(thm)],[2520])).
% 1.80/1.50 tff(2522,plain,
% 1.80/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a14) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.80/1.50 inference(transitivity,[status(thm)],[2521, 2519])).
% 1.80/1.50 tff(2523,plain,
% 1.80/1.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1)))),
% 1.80/1.50 inference(quant_inst,[status(thm)],[])).
% 1.80/1.50 tff(2524,plain,
% 1.80/1.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a14) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a14)) | (~c0_1(a14))),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2523, 2522])).
% 1.80/1.50 tff(2525,plain,
% 1.80/1.50 ($false),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2524, 169, 2474, 2518, 2517, 496, 2516, 476, 2497, 2304])).
% 1.80/1.50 tff(2526,plain,(c3_1(a31) | hskp15 | (~c3_1(a1)) | c2_1(a1) | hskp4 | (~c0_1(a31)) | c1_1(a31) | c0_1(a1) | (~c2_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.50 tff(2527,plain,
% 1.80/1.50 (c3_1(a31)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2526, 474, 2474, 471, 205, 2487, 2486, 472, 2485])).
% 1.80/1.50 tff(2528,assumption,(hskp22), introduced(assumption)).
% 1.80/1.50 tff(2529,plain,
% 1.80/1.50 (((~hskp22) | (~c1_1(a45))) <=> ((~hskp22) | (~c1_1(a45)))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2530,plain,
% 1.80/1.50 (((~c1_1(a45)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a45)))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2531,axiom,((~c1_1(a45)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.80/1.50 tff(2532,plain,
% 1.80/1.50 ((~hskp22) | (~c1_1(a45))),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2531, 2530])).
% 1.80/1.50 tff(2533,plain,
% 1.80/1.50 ((~hskp22) | (~c1_1(a45))),
% 1.80/1.50 inference(modus_ponens,[status(thm)],[2532, 2529])).
% 1.80/1.50 tff(2534,plain,
% 1.80/1.50 (~c1_1(a45)),
% 1.80/1.50 inference(unit_resolution,[status(thm)],[2533, 2528])).
% 1.80/1.50 tff(2535,plain,
% 1.80/1.50 (((~hskp22) | (~c3_1(a45))) <=> ((~hskp22) | (~c3_1(a45)))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2536,plain,
% 1.80/1.50 (((~c3_1(a45)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a45)))),
% 1.80/1.50 inference(rewrite,[status(thm)],[])).
% 1.80/1.50 tff(2537,axiom,((~c3_1(a45)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.80/1.50 tff(2538,plain,
% 1.80/1.51 ((~hskp22) | (~c3_1(a45))),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2537, 2536])).
% 1.80/1.51 tff(2539,plain,
% 1.80/1.51 ((~hskp22) | (~c3_1(a45))),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2538, 2535])).
% 1.80/1.51 tff(2540,plain,
% 1.80/1.51 (~c3_1(a45)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2539, 2528])).
% 1.80/1.51 tff(2541,assumption,(~c1_1(a45)), introduced(assumption)).
% 1.80/1.51 tff(2542,assumption,(~c3_1(a45)), introduced(assumption)).
% 1.80/1.51 tff(2543,assumption,(~c2_1(a45)), introduced(assumption)).
% 1.80/1.51 tff(2544,plain,
% 1.80/1.51 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c1_1(a45) | (~ndr1_0) | (~c0_1(a45)) | c2_1(a45))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a45) | (~ndr1_0) | (~c0_1(a45)) | c2_1(a45))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2545,plain,
% 1.80/1.51 ((hskp14 | hskp2 | (~ndr1_0) | c1_1(a45) | c2_1(a45) | (~c0_1(a45))) <=> (hskp14 | hskp2 | c1_1(a45) | (~ndr1_0) | (~c0_1(a45)) | c2_1(a45))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2546,plain,
% 1.80/1.51 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a45) | c2_1(a45) | (~c0_1(a45)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c1_1(a45) | (~ndr1_0) | (~c0_1(a45)) | c2_1(a45)))),
% 1.80/1.51 inference(monotonicity,[status(thm)],[2545])).
% 1.80/1.51 tff(2547,plain,
% 1.80/1.51 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a45) | c2_1(a45) | (~c0_1(a45)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a45) | (~ndr1_0) | (~c0_1(a45)) | c2_1(a45))),
% 1.80/1.51 inference(transitivity,[status(thm)],[2546, 2544])).
% 1.80/1.51 tff(2548,plain,
% 1.80/1.51 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a45) | c2_1(a45) | (~c0_1(a45)))),
% 1.80/1.51 inference(quant_inst,[status(thm)],[])).
% 1.80/1.51 tff(2549,plain,
% 1.80/1.51 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c1_1(a45) | (~ndr1_0) | (~c0_1(a45)) | c2_1(a45)),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2548, 2547])).
% 1.80/1.51 tff(2550,plain,
% 1.80/1.51 ((~c0_1(a45)) | c2_1(a45)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2549, 169, 655, 654, 2541, 700])).
% 1.80/1.51 tff(2551,plain,
% 1.80/1.51 (~c0_1(a45)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2550, 2543])).
% 1.80/1.51 tff(2552,plain,
% 1.80/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c2_1(a45))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2553,plain,
% 1.80/1.51 (((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a45) | c1_1(a45) | c0_1(a45)) <=> (c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c2_1(a45))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2554,plain,
% 1.80/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a45) | c1_1(a45) | c0_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c2_1(a45)))),
% 1.80/1.51 inference(monotonicity,[status(thm)],[2553])).
% 1.80/1.51 tff(2555,plain,
% 1.80/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a45) | c1_1(a45) | c0_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c2_1(a45))),
% 1.80/1.51 inference(transitivity,[status(thm)],[2554, 2552])).
% 1.80/1.51 tff(2556,plain,
% 1.80/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a45) | c1_1(a45) | c0_1(a45))),
% 1.80/1.51 inference(quant_inst,[status(thm)],[])).
% 1.80/1.51 tff(2557,plain,
% 1.80/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c2_1(a45)),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2556, 2555])).
% 1.80/1.51 tff(2558,plain,
% 1.80/1.51 ($false),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2557, 169, 2551, 496, 2541, 2542, 477, 476, 55, 2543])).
% 1.80/1.51 tff(2559,plain,(c2_1(a45) | (~c3_1(a1)) | c1_1(a45) | c3_1(a45) | c0_1(a1) | c2_1(a1) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.80/1.51 tff(2560,plain,
% 1.80/1.51 (c2_1(a45)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2559, 2541, 496, 2542, 477, 476, 655, 654])).
% 1.80/1.51 tff(2561,plain,
% 1.80/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c2_1(a45)))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2562,plain,
% 1.80/1.51 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45))) <=> (c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c2_1(a45)))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2563,plain,
% 1.80/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c2_1(a45))))),
% 1.80/1.51 inference(monotonicity,[status(thm)],[2562])).
% 1.80/1.51 tff(2564,plain,
% 1.80/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c2_1(a45)))),
% 1.80/1.51 inference(transitivity,[status(thm)],[2563, 2561])).
% 1.80/1.51 tff(2565,plain,
% 1.80/1.51 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))),
% 1.80/1.51 inference(quant_inst,[status(thm)],[])).
% 1.80/1.51 tff(2566,plain,
% 1.80/1.51 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c2_1(a45))),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2565, 2564])).
% 1.80/1.51 tff(2567,plain,
% 1.80/1.51 (c1_1(a45) | (~c3_1(a31)) | (~c2_1(a45))),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2566, 169, 2487, 2485, 2542, 1580])).
% 1.80/1.51 tff(2568,plain,
% 1.80/1.51 (~c3_1(a31)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2567, 2560, 2541])).
% 1.80/1.51 tff(2569,plain,
% 1.80/1.51 (~c1_1(a1)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2303, 169, 205, 2487, 496, 2486, 477, 632, 2568])).
% 1.80/1.51 tff(2570,plain,
% 1.80/1.51 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a45)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a45)))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2571,plain,
% 1.80/1.51 ((hskp7 | (~ndr1_0) | c3_1(a45) | c1_1(a45) | (~c2_1(a45))) <=> (hskp7 | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a45)))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2572,plain,
% 1.80/1.51 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a45))))),
% 1.80/1.51 inference(monotonicity,[status(thm)],[2571])).
% 1.80/1.51 tff(2573,plain,
% 1.80/1.51 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a45)))),
% 1.80/1.51 inference(transitivity,[status(thm)],[2572, 2570])).
% 1.80/1.51 tff(2574,plain,
% 1.80/1.51 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))),
% 1.80/1.51 inference(quant_inst,[status(thm)],[])).
% 1.80/1.51 tff(2575,plain,
% 1.80/1.51 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c2_1(a45))),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2574, 2573])).
% 1.80/1.51 tff(2576,plain,
% 1.80/1.51 (hskp7 | c1_1(a45) | (~c2_1(a45))),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2575, 169, 2542, 2507])).
% 1.80/1.51 tff(2577,plain,
% 1.80/1.51 (hskp7),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2576, 2560, 2541])).
% 1.80/1.51 tff(2578,plain,
% 1.80/1.51 (~c2_1(a14)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[525, 2577])).
% 1.80/1.51 tff(2579,plain,
% 1.80/1.51 (c3_1(a14)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[536, 2577])).
% 1.80/1.51 tff(2580,plain,
% 1.80/1.51 (c0_1(a14)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[558, 2577])).
% 1.80/1.51 tff(2581,plain,
% 1.80/1.51 ($false),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2524, 169, 2474, 2580, 2579, 496, 2578, 476, 2497, 2569])).
% 1.80/1.51 tff(2582,plain,(c1_1(a45) | hskp15 | (~c3_1(a1)) | c2_1(a1) | hskp4 | c0_1(a1) | c3_1(a45) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.80/1.51 tff(2583,plain,
% 1.80/1.51 ($false),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2582, 2540, 2534, 496, 476, 205, 477, 2474, 655, 654])).
% 1.80/1.51 tff(2584,plain,((~hskp22) | (~c3_1(a1)) | c2_1(a1) | hskp4 | c0_1(a1) | hskp15 | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.80/1.51 tff(2585,plain,
% 1.80/1.51 (~hskp22),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2584, 474, 471, 205, 472, 2474, 655, 654])).
% 1.80/1.51 tff(2586,plain,
% 1.80/1.51 (~hskp13),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[504, 475, 477, 476, 496])).
% 1.80/1.51 tff(2587,assumption,(~hskp22), introduced(assumption)).
% 1.80/1.51 tff(2588,assumption,(c3_1(a31)), introduced(assumption)).
% 1.80/1.51 tff(2589,plain,
% 1.80/1.51 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c2_1(a8) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a8)) | (~c0_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a8) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a8)) | (~c0_1(a8)))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2590,plain,
% 1.80/1.51 ((hskp15 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1))) <=> (hskp15 | c2_1(a8) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a8)) | (~c0_1(a8)))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2591,plain,
% 1.80/1.51 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c2_1(a8) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a8)) | (~c0_1(a8))))),
% 1.80/1.51 inference(monotonicity,[status(thm)],[2590])).
% 1.80/1.51 tff(2592,plain,
% 1.80/1.51 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a8) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a8)) | (~c0_1(a8)))),
% 1.80/1.51 inference(transitivity,[status(thm)],[2591, 2589])).
% 1.80/1.51 tff(2593,plain,
% 1.80/1.51 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a8) | (~c0_1(a8)) | (~c3_1(a8)) | c1_1(a1) | c2_1(a1) | (~c3_1(a1)))),
% 1.80/1.51 inference(quant_inst,[status(thm)],[])).
% 1.80/1.51 tff(2594,plain,
% 1.80/1.51 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a8) | c2_1(a1) | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c3_1(a8)) | (~c0_1(a8))),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2593, 2592])).
% 1.80/1.51 tff(2595,plain,
% 1.80/1.51 (~c3_1(a8)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2594, 169, 2474, 1370, 496, 1336, 476, 2497, 475])).
% 1.80/1.51 tff(2596,plain,
% 1.80/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2597,plain,
% 1.80/1.51 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2598,plain,
% 1.80/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.80/1.51 inference(monotonicity,[status(thm)],[2597])).
% 1.80/1.51 tff(2599,plain,
% 1.80/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.51 inference(transitivity,[status(thm)],[2598, 2596])).
% 1.80/1.51 tff(2600,plain,
% 1.80/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.80/1.51 inference(quant_inst,[status(thm)],[])).
% 1.80/1.51 tff(2601,plain,
% 1.80/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2600, 2599])).
% 1.80/1.51 tff(2602,plain,
% 1.80/1.51 ($false),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2601, 169, 331, 332, 1370, 1347, 1336, 439, 2588, 2595])).
% 1.80/1.51 tff(2603,plain,((~hskp6) | (~c0_1(a31)) | (~c2_1(a31)) | (~c3_1(a31)) | hskp15 | (~c3_1(a1)) | c2_1(a1) | c1_1(a1)), inference(lemma,lemma(discharge,[]))).
% 1.80/1.51 tff(2604,plain,
% 1.80/1.51 (~hskp6),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2603, 475, 332, 2588, 2474, 496, 476, 331])).
% 1.80/1.51 tff(2605,plain,
% 1.80/1.51 ((hskp26 | hskp22 | hskp6) <=> (hskp26 | hskp22 | hskp6)),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2606,plain,
% 1.80/1.51 (((hskp26 | hskp6) | hskp22) <=> (hskp26 | hskp22 | hskp6)),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2607,plain,
% 1.80/1.51 ((hskp6 | hskp26) <=> (hskp26 | hskp6)),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2608,plain,
% 1.80/1.51 (((hskp6 | hskp26) | hskp22) <=> ((hskp26 | hskp6) | hskp22)),
% 1.80/1.51 inference(monotonicity,[status(thm)],[2607])).
% 1.80/1.51 tff(2609,plain,
% 1.80/1.51 (((hskp6 | hskp26) | hskp22) <=> (hskp26 | hskp22 | hskp6)),
% 1.80/1.51 inference(transitivity,[status(thm)],[2608, 2606])).
% 1.80/1.51 tff(2610,axiom,((hskp6 | hskp26) | hskp22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause30')).
% 1.80/1.51 tff(2611,plain,
% 1.80/1.51 (hskp26 | hskp22 | hskp6),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2610, 2609])).
% 1.80/1.51 tff(2612,plain,
% 1.80/1.51 (hskp26 | hskp22 | hskp6),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2611, 2605])).
% 1.80/1.51 tff(2613,plain,
% 1.80/1.51 (hskp26 | hskp22 | hskp6),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2612, 2605])).
% 1.80/1.51 tff(2614,plain,
% 1.80/1.51 (hskp26 | hskp22 | hskp6),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2613, 2605])).
% 1.80/1.51 tff(2615,plain,
% 1.80/1.51 (hskp26 | hskp22 | hskp6),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2614, 2605])).
% 1.80/1.51 tff(2616,plain,
% 1.80/1.51 (hskp26 | hskp22 | hskp6),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2615, 2605])).
% 1.80/1.51 tff(2617,plain,
% 1.80/1.51 (hskp26 | hskp22 | hskp6),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2616, 2605])).
% 1.80/1.51 tff(2618,plain,
% 1.80/1.51 (hskp26 | hskp22 | hskp6),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2617, 2605])).
% 1.80/1.51 tff(2619,plain,
% 1.80/1.51 (hskp26),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2618, 2604, 2587])).
% 1.80/1.51 tff(2620,plain,
% 1.80/1.51 (c3_1(a10)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[689, 2619])).
% 1.80/1.51 tff(2621,plain,
% 1.80/1.51 (c2_1(a10)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[678, 2619])).
% 1.80/1.51 tff(2622,plain,
% 1.80/1.51 (c0_1(a10)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[666, 2619])).
% 1.80/1.51 tff(2623,plain,
% 1.80/1.51 (~hskp9),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[721, 2622, 2621, 2620, 655, 654])).
% 1.80/1.51 tff(2624,plain,
% 1.80/1.51 (hskp7),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[519, 2623, 2586])).
% 1.80/1.51 tff(2625,plain,
% 1.80/1.51 (~c2_1(a14)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[525, 2624])).
% 1.80/1.51 tff(2626,plain,
% 1.80/1.51 (c3_1(a14)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[536, 2624])).
% 1.80/1.51 tff(2627,plain,
% 1.80/1.51 (c0_1(a14)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[558, 2624])).
% 1.80/1.51 tff(2628,plain,
% 1.80/1.51 ($false),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2524, 169, 2474, 2627, 2626, 496, 2625, 476, 2497, 475])).
% 1.80/1.51 tff(2629,plain,(c1_1(a1) | hskp15 | (~c3_1(a1)) | c2_1(a1) | hskp14 | hskp2 | c0_1(a1) | hskp22 | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.51 tff(2630,plain,
% 1.80/1.51 (c1_1(a1)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2629, 2585, 474, 471, 655, 654, 472, 2474, 2485, 2527, 2487])).
% 1.80/1.51 tff(2631,plain,
% 1.80/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2632,plain,
% 1.80/1.51 ((hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1))) <=> (hskp10 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2633,plain,
% 1.80/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.80/1.51 inference(monotonicity,[status(thm)],[2632])).
% 1.80/1.51 tff(2634,plain,
% 1.80/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.80/1.51 inference(transitivity,[status(thm)],[2633, 2631])).
% 1.80/1.51 tff(2635,plain,
% 1.80/1.51 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))),
% 1.80/1.51 inference(quant_inst,[status(thm)],[])).
% 1.80/1.51 tff(2636,plain,
% 1.80/1.51 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | c0_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.80/1.51 inference(modus_ponens,[status(thm)],[2635, 2634])).
% 1.80/1.51 tff(2637,plain,
% 1.80/1.51 (hskp10 | (~c1_1(a1)) | (~c3_1(a31))),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2636, 169, 2485, 474, 2486, 472, 1137])).
% 1.80/1.51 tff(2638,plain,
% 1.80/1.51 (hskp10),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[2637, 2630, 2527])).
% 1.80/1.51 tff(2639,plain,
% 1.80/1.51 (~c3_1(a18)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[1150, 2638])).
% 1.80/1.51 tff(2640,plain,
% 1.80/1.51 (c2_1(a18)),
% 1.80/1.51 inference(unit_resolution,[status(thm)],[1161, 2638])).
% 1.80/1.51 tff(2641,plain,
% 1.80/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2642,plain,
% 1.80/1.51 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.51 inference(rewrite,[status(thm)],[])).
% 1.80/1.51 tff(2643,plain,
% 1.80/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.80/1.51 inference(monotonicity,[status(thm)],[2642])).
% 1.80/1.51 tff(2644,plain,
% 1.80/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.51 inference(transitivity,[status(thm)],[2643, 2641])).
% 1.80/1.51 tff(2645,plain,
% 1.80/1.51 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 1.80/1.51 inference(quant_inst,[status(thm)],[])).
% 1.80/1.51 tff(2646,plain,
% 1.80/1.51 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.80/1.52 inference(modus_ponens,[status(thm)],[2645, 2644])).
% 1.80/1.52 tff(2647,plain,
% 1.80/1.52 (c1_1(a18)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2646, 169, 2487, 2485, 2640, 2639, 1580, 2527])).
% 1.80/1.52 tff(2648,plain,
% 1.80/1.52 (c0_1(a18)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[1172, 2638])).
% 1.80/1.52 tff(2649,plain,
% 1.80/1.52 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2650,plain,
% 1.80/1.52 ((hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a1) | (~c3_1(a1)) | (~c1_1(a1))) <=> (hskp19 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2651,plain,
% 1.80/1.52 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18))))),
% 1.80/1.52 inference(monotonicity,[status(thm)],[2650])).
% 1.80/1.52 tff(2652,plain,
% 1.80/1.52 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.80/1.52 inference(transitivity,[status(thm)],[2651, 2649])).
% 1.80/1.52 tff(2653,plain,
% 1.80/1.52 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))),
% 1.80/1.52 inference(quant_inst,[status(thm)],[])).
% 1.80/1.52 tff(2654,plain,
% 1.80/1.52 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18))),
% 1.80/1.52 inference(modus_ponens,[status(thm)],[2653, 2652])).
% 1.80/1.52 tff(2655,plain,
% 1.80/1.52 (hskp19 | (~c1_1(a18))),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2654, 169, 2648, 2640, 474, 471, 848, 2630])).
% 1.80/1.52 tff(2656,plain,
% 1.80/1.52 (hskp19),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2655, 2647])).
% 1.80/1.52 tff(2657,plain,
% 1.80/1.52 (~c0_1(a33)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[897, 2656])).
% 1.80/1.52 tff(2658,plain,
% 1.80/1.52 (c3_1(a33)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[1503, 2656])).
% 1.80/1.52 tff(2659,plain,
% 1.80/1.52 (c2_1(a33)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[908, 2656])).
% 1.80/1.52 tff(2660,plain,
% 1.80/1.52 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2661,plain,
% 1.80/1.52 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19))) <=> (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2662,plain,
% 1.80/1.52 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.80/1.52 inference(monotonicity,[status(thm)],[2661])).
% 1.80/1.52 tff(2663,plain,
% 1.80/1.52 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.80/1.52 inference(transitivity,[status(thm)],[2662, 2660])).
% 1.80/1.52 tff(2664,plain,
% 1.80/1.52 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))),
% 1.80/1.52 inference(quant_inst,[status(thm)],[])).
% 1.80/1.52 tff(2665,plain,
% 1.80/1.52 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.80/1.52 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 1.80/1.52 tff(2666,plain,
% 1.80/1.52 ($false),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2665, 169, 331, 332, 2247, 2246, 2245, 1580, 2588])).
% 1.80/1.52 tff(2667,plain,((~hskp11) | (~c0_1(a31)) | (~c2_1(a31)) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.52 tff(2668,plain,
% 1.80/1.52 (~hskp11),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2667, 2527, 2485, 2487])).
% 1.80/1.52 tff(2669,plain,
% 1.80/1.52 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2670,plain,
% 1.80/1.52 ((hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp11 | c0_1(a33) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2671,plain,
% 1.80/1.52 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c3_1(a33)) | (~c2_1(a33))))),
% 1.80/1.52 inference(monotonicity,[status(thm)],[2670])).
% 1.80/1.52 tff(2672,plain,
% 1.80/1.52 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.80/1.52 inference(transitivity,[status(thm)],[2671, 2669])).
% 1.80/1.52 tff(2673,plain,
% 1.80/1.52 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.80/1.52 inference(quant_inst,[status(thm)],[])).
% 1.80/1.52 tff(2674,plain,
% 1.80/1.52 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a18)) | (~c3_1(a33)) | (~c2_1(a33))),
% 1.80/1.52 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 1.80/1.52 tff(2675,plain,
% 1.80/1.52 ($false),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2674, 169, 2668, 2659, 2658, 2648, 2640, 2657, 2639, 1126])).
% 1.80/1.52 tff(2676,plain,((~hskp0) | hskp14 | hskp2 | hskp15 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.80/1.52 tff(2677,plain,
% 1.80/1.52 (~hskp0),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2676, 654, 655, 2474, 205])).
% 1.80/1.52 tff(2678,plain,
% 1.80/1.52 (hskp7 | c3_1(a31)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2513, 169, 2485, 2486, 2507])).
% 1.80/1.52 tff(2679,plain,
% 1.80/1.52 (hskp7),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2678, 2279])).
% 1.80/1.52 tff(2680,plain,
% 1.80/1.52 (~c2_1(a14)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[525, 2679])).
% 1.80/1.52 tff(2681,plain,
% 1.80/1.52 (c0_1(a14)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[558, 2679])).
% 1.80/1.52 tff(2682,plain,
% 1.80/1.52 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c0_1(a14)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c0_1(a14)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2683,plain,
% 1.80/1.52 ((hskp14 | hskp2 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14))) <=> (hskp14 | hskp2 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c0_1(a14)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2684,plain,
% 1.80/1.52 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c0_1(a14))))),
% 1.80/1.52 inference(monotonicity,[status(thm)],[2683])).
% 1.80/1.52 tff(2685,plain,
% 1.80/1.52 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c0_1(a14)))),
% 1.80/1.52 inference(transitivity,[status(thm)],[2684, 2682])).
% 1.80/1.52 tff(2686,plain,
% 1.80/1.52 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c1_1(a14) | c2_1(a14) | (~c0_1(a14)))),
% 1.80/1.52 inference(quant_inst,[status(thm)],[])).
% 1.80/1.52 tff(2687,plain,
% 1.80/1.52 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp14 | hskp2 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c0_1(a14))),
% 1.80/1.52 inference(modus_ponens,[status(thm)],[2686, 2685])).
% 1.80/1.52 tff(2688,plain,
% 1.80/1.52 (c1_1(a14)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2687, 169, 655, 654, 2681, 2680, 700])).
% 1.80/1.52 tff(2689,plain,
% 1.80/1.52 (c3_1(a14)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[536, 2679])).
% 1.80/1.52 tff(2690,plain,
% 1.80/1.52 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))),
% 1.80/1.52 inference(bind,[status(th)],[])).
% 1.80/1.52 tff(2691,plain,
% 1.80/1.52 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.80/1.52 inference(quant_intro,[status(thm)],[2690])).
% 1.80/1.52 tff(2692,plain,
% 1.80/1.52 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2693,plain,
% 1.80/1.52 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))))),
% 1.80/1.52 inference(bind,[status(th)],[])).
% 1.80/1.52 tff(2694,plain,
% 1.80/1.52 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.80/1.52 inference(quant_intro,[status(thm)],[2693])).
% 1.80/1.52 tff(2695,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.80/1.52 tff(2696,plain,
% 1.80/1.52 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.80/1.52 inference(modus_ponens,[status(thm)],[2695, 2694])).
% 1.80/1.52 tff(2697,plain,
% 1.80/1.52 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.80/1.52 inference(modus_ponens,[status(thm)],[2696, 2692])).
% 1.80/1.52 tff(2698,plain,(
% 1.80/1.52 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.80/1.52 inference(skolemize,[status(sab)],[2697])).
% 1.80/1.52 tff(2699,plain,
% 1.80/1.52 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 1.80/1.52 inference(modus_ponens,[status(thm)],[2698, 2691])).
% 1.80/1.52 tff(2700,assumption,(c1_1(a14)), introduced(assumption)).
% 1.80/1.52 tff(2701,plain,
% 1.80/1.52 (hskp24 | hskp9),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[543, 169, 2517, 2516, 104, 2700])).
% 1.80/1.52 tff(2702,plain,
% 1.80/1.52 (hskp24),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2701, 105])).
% 1.80/1.52 tff(2703,plain,
% 1.80/1.52 (c2_1(a3)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2380, 2702])).
% 1.80/1.52 tff(2704,plain,
% 1.80/1.52 (c1_1(a3)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2391, 2702])).
% 1.80/1.52 tff(2705,assumption,(~hskp8), introduced(assumption)).
% 1.80/1.52 tff(2706,plain,
% 1.80/1.52 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2707,plain,
% 1.80/1.52 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.80/1.52 inference(quant_inst,[status(thm)],[])).
% 1.80/1.52 tff(2708,plain,
% 1.80/1.52 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))),
% 1.80/1.52 inference(modus_ponens,[status(thm)],[2707, 2706])).
% 1.80/1.52 tff(2709,plain,
% 1.80/1.52 (c0_1(a3)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2708, 169, 105, 2705, 2704, 2703, 2699])).
% 1.80/1.52 tff(2710,plain,
% 1.80/1.52 (c3_1(a3)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2411, 2702])).
% 1.80/1.52 tff(2711,plain,
% 1.80/1.52 ($false),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2421, 169, 2703, 2710, 332, 343, 1580, 2279, 2709])).
% 1.80/1.52 tff(2712,plain,(hskp9 | (~c2_1(a31)) | c1_1(a31) | c3_1(a31) | hskp8 | (~c1_1(a14))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.52 tff(2713,plain,
% 1.80/1.52 (hskp9),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2712, 2279, 2486, 2485, 2483, 2688])).
% 1.80/1.52 tff(2714,plain,
% 1.80/1.52 (~c2_1(a16)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[579, 2713])).
% 1.80/1.52 tff(2715,assumption,(hskp16), introduced(assumption)).
% 1.80/1.52 tff(2716,plain,
% 1.80/1.52 (~c0_1(a30)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[621, 2715])).
% 1.80/1.52 tff(2717,plain,
% 1.80/1.52 (c1_1(a30)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[609, 2715])).
% 1.80/1.52 tff(2718,plain,
% 1.80/1.52 (~c3_1(a30)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2296, 169, 205, 331, 2717, 343, 2716, 632, 2279])).
% 1.80/1.52 tff(2719,assumption,(~c2_1(a14)), introduced(assumption)).
% 1.80/1.52 tff(2720,plain,
% 1.80/1.52 (~c2_1(a30)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[615, 2715])).
% 1.80/1.52 tff(2721,assumption,(c3_1(a14)), introduced(assumption)).
% 1.80/1.52 tff(2722,plain,
% 1.80/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2723,plain,
% 1.80/1.52 (((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30)) <=> (c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2724,plain,
% 1.80/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31))))),
% 1.80/1.52 inference(monotonicity,[status(thm)],[2723])).
% 1.80/1.52 tff(2725,plain,
% 1.80/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.52 inference(transitivity,[status(thm)],[2724, 2722])).
% 1.80/1.52 tff(2726,plain,
% 1.80/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a30) | c0_1(a30) | c3_1(a30))),
% 1.80/1.52 inference(quant_inst,[status(thm)],[])).
% 1.80/1.52 tff(2727,plain,
% 1.80/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a31) | c0_1(a30) | c2_1(a30) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a30) | c3_1(a31) | (~c0_1(a31))),
% 1.80/1.52 inference(modus_ponens,[status(thm)],[2726, 2725])).
% 1.80/1.52 tff(2728,plain,
% 1.80/1.52 ($false),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2727, 169, 331, 2721, 343, 2716, 2720, 2719, 13, 2279, 2700, 2718])).
% 1.80/1.52 tff(2729,plain,((~hskp16) | (~c0_1(a31)) | (~c3_1(a14)) | c1_1(a31) | c2_1(a14) | c3_1(a31) | (~c1_1(a14)) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.80/1.52 tff(2730,plain,
% 1.80/1.52 (~hskp16),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2729, 2689, 2487, 2486, 2680, 2279, 2688, 205])).
% 1.80/1.52 tff(2731,plain,
% 1.80/1.52 (~c3_1(a16)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[573, 2713])).
% 1.80/1.52 tff(2732,plain,
% 1.80/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2733,plain,
% 1.80/1.52 (((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16)) <=> (c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.52 inference(rewrite,[status(thm)],[])).
% 1.80/1.52 tff(2734,plain,
% 1.80/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | (~c0_1(a31))))),
% 1.80/1.52 inference(monotonicity,[status(thm)],[2733])).
% 1.80/1.52 tff(2735,plain,
% 1.80/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | (~c0_1(a31)))),
% 1.80/1.52 inference(transitivity,[status(thm)],[2734, 2732])).
% 1.80/1.52 tff(2736,plain,
% 1.80/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a14) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16))),
% 1.80/1.52 inference(quant_inst,[status(thm)],[])).
% 1.80/1.52 tff(2737,plain,
% 1.80/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | c3_1(a31) | (~c0_1(a31))),
% 1.80/1.52 inference(modus_ponens,[status(thm)],[2736, 2735])).
% 1.80/1.52 tff(2738,plain,
% 1.80/1.52 (c0_1(a16) | c3_1(a16)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2737, 169, 331, 2721, 343, 24, 2719, 13, 2279, 2700])).
% 1.80/1.52 tff(2739,plain,
% 1.80/1.52 (c0_1(a16)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2738, 2])).
% 1.80/1.52 tff(2740,assumption,(~hskp16), introduced(assumption)).
% 1.80/1.52 tff(2741,plain,
% 1.80/1.52 (c3_1(a16) | (~c0_1(a16))),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[597, 169, 84, 2740, 24, 94])).
% 1.80/1.52 tff(2742,plain,
% 1.80/1.52 ($false),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2741, 2739, 2])).
% 1.80/1.52 tff(2743,plain,(c3_1(a16) | hskp26 | hskp16 | c2_1(a16) | (~c0_1(a31)) | (~c3_1(a14)) | c1_1(a31) | c2_1(a14) | c3_1(a31) | (~c1_1(a14))), inference(lemma,lemma(discharge,[]))).
% 1.80/1.52 tff(2744,plain,
% 1.80/1.52 (hskp26),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2743, 2731, 2730, 2714, 2487, 2689, 2486, 2680, 2279, 2688])).
% 1.80/1.52 tff(2745,plain,
% 1.80/1.52 (c3_1(a10)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[689, 2744])).
% 1.80/1.52 tff(2746,plain,
% 1.80/1.52 (c0_1(a10)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[666, 2744])).
% 1.80/1.52 tff(2747,plain,
% 1.80/1.52 (c2_1(a10)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[678, 2744])).
% 1.80/1.52 tff(2748,plain,
% 1.80/1.52 ($false),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[721, 2747, 2746, 2713, 2745, 655, 654])).
% 1.80/1.52 tff(2749,plain,(c3_1(a31) | hskp14 | hskp2 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.80/1.52 tff(2750,plain,
% 1.80/1.52 (c3_1(a31)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2749, 654, 655, 205])).
% 1.80/1.52 tff(2751,assumption,(~c0_1(a45)), introduced(assumption)).
% 1.80/1.52 tff(2752,plain,
% 1.80/1.52 (c1_1(a45) | (~c2_1(a45))),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2566, 169, 331, 332, 2542, 1580, 2588])).
% 1.80/1.52 tff(2753,plain,
% 1.80/1.52 (~c2_1(a45)),
% 1.80/1.52 inference(unit_resolution,[status(thm)],[2752, 2541])).
% 1.87/1.53 tff(2754,plain,
% 1.87/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a45) | c1_1(a45) | c3_1(a45) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a45) | c1_1(a45) | c3_1(a45) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2755,plain,
% 1.87/1.53 ((hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | c0_1(a45)) <=> (hskp1 | c0_1(a45) | c1_1(a45) | c3_1(a45) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2756,plain,
% 1.87/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | c0_1(a45))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a45) | c1_1(a45) | c3_1(a45) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.87/1.53 inference(monotonicity,[status(thm)],[2755])).
% 1.87/1.53 tff(2757,plain,
% 1.87/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | c0_1(a45))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a45) | c1_1(a45) | c3_1(a45) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.87/1.53 inference(transitivity,[status(thm)],[2756, 2754])).
% 1.87/1.53 tff(2758,plain,
% 1.87/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c1_1(a45) | c0_1(a45))),
% 1.87/1.53 inference(quant_inst,[status(thm)],[])).
% 1.87/1.53 tff(2759,plain,
% 1.87/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a45) | c1_1(a45) | c3_1(a45) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2758, 2757])).
% 1.87/1.53 tff(2760,plain,
% 1.87/1.53 (hskp1 | c0_1(a45) | c1_1(a45)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2759, 169, 332, 2542, 343, 1493, 2588])).
% 1.87/1.53 tff(2761,plain,
% 1.87/1.53 (hskp1),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2760, 2541, 2751])).
% 1.87/1.53 tff(2762,plain,
% 1.87/1.53 (~c3_1(a2)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2441, 2761])).
% 1.87/1.53 tff(2763,plain,
% 1.87/1.53 (~c0_1(a2)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[1516, 2761])).
% 1.87/1.53 tff(2764,plain,
% 1.87/1.53 (c2_1(a2)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[1527, 2761])).
% 1.87/1.53 tff(2765,plain,
% 1.87/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a45))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2766,plain,
% 1.87/1.53 (((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a45) | c1_1(a45) | c2_1(a45) | c2_1(a45) | c0_1(a45) | c3_1(a45)) <=> (c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a45))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2767,plain,
% 1.87/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a45) | c1_1(a45) | c2_1(a45) | c2_1(a45) | c0_1(a45) | c3_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a45)))),
% 1.87/1.53 inference(monotonicity,[status(thm)],[2766])).
% 1.87/1.53 tff(2768,plain,
% 1.87/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a45) | c1_1(a45) | c2_1(a45) | c2_1(a45) | c0_1(a45) | c3_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a45))),
% 1.87/1.53 inference(transitivity,[status(thm)],[2767, 2765])).
% 1.87/1.53 tff(2769,plain,
% 1.87/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a45) | c1_1(a45) | c2_1(a45) | c2_1(a45) | c0_1(a45) | c3_1(a45))),
% 1.87/1.53 inference(quant_inst,[status(thm)],[])).
% 1.87/1.53 tff(2770,plain,
% 1.87/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a45) | c1_1(a45) | c3_1(a45) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a45)),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2769, 2768])).
% 1.87/1.53 tff(2771,plain,
% 1.87/1.53 ($false),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2770, 169, 2751, 2764, 2541, 2542, 2763, 2762, 2435, 2753])).
% 1.87/1.53 tff(2772,plain,(c1_1(a45) | c0_1(a45) | c3_1(a45) | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31)) | (~c0_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.87/1.53 tff(2773,plain,
% 1.87/1.53 (c1_1(a45)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2772, 2751, 2542, 332, 343, 2588, 331])).
% 1.87/1.53 tff(2774,plain,
% 1.87/1.53 ($false),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2271, 169, 331, 332, 702, 701, 710, 439, 2588, 709])).
% 1.87/1.53 tff(2775,plain,((~hskp9) | (~c0_1(a31)) | (~c2_1(a31)) | (~c3_1(a31)) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.87/1.53 tff(2776,plain,
% 1.87/1.53 (~hskp9),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2775, 331, 332, 2588, 655, 654])).
% 1.87/1.53 tff(2777,assumption,(c1_1(a45)), introduced(assumption)).
% 1.87/1.53 tff(2778,plain,
% 1.87/1.53 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | (~ndr1_0) | (~c2_1(a45)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | (~ndr1_0) | (~c2_1(a45)))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2779,plain,
% 1.87/1.53 ((hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a45)) | c0_1(a45) | (~c1_1(a45))) <=> (hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | (~ndr1_0) | (~c2_1(a45)))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2780,plain,
% 1.87/1.53 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a45)) | c0_1(a45) | (~c1_1(a45)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | (~ndr1_0) | (~c2_1(a45))))),
% 1.87/1.53 inference(monotonicity,[status(thm)],[2779])).
% 1.87/1.53 tff(2781,plain,
% 1.87/1.53 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a45)) | c0_1(a45) | (~c1_1(a45)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | (~ndr1_0) | (~c2_1(a45)))),
% 1.87/1.53 inference(transitivity,[status(thm)],[2780, 2778])).
% 1.87/1.53 tff(2782,plain,
% 1.87/1.53 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a45)) | c0_1(a45) | (~c1_1(a45)))),
% 1.87/1.53 inference(quant_inst,[status(thm)],[])).
% 1.87/1.53 tff(2783,plain,
% 1.87/1.53 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | (~ndr1_0) | (~c2_1(a45))),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2782, 2781])).
% 1.87/1.53 tff(2784,plain,
% 1.87/1.53 (hskp9 | (~c1_1(a45)) | (~c2_1(a45))),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2783, 169, 2705, 2751, 2699])).
% 1.87/1.53 tff(2785,plain,
% 1.87/1.53 (~c2_1(a45)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2784, 105, 2777])).
% 1.87/1.53 tff(2786,assumption,(c0_1(a8)), introduced(assumption)).
% 1.87/1.53 tff(2787,plain,
% 1.87/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~c1_1(a45)) | c3_1(a45) | c2_1(a8) | (~ndr1_0) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (~c1_1(a45)) | c3_1(a45) | c2_1(a8) | (~ndr1_0) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | c2_1(a45))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2788,plain,
% 1.87/1.53 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> ((~c1_1(a45)) | c3_1(a45) | c2_1(a8) | (~ndr1_0) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | c2_1(a45))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2789,plain,
% 1.87/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~c1_1(a45)) | c3_1(a45) | c2_1(a8) | (~ndr1_0) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | c2_1(a45)))),
% 1.87/1.53 inference(monotonicity,[status(thm)],[2788])).
% 1.87/1.53 tff(2790,plain,
% 1.87/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (~c1_1(a45)) | c3_1(a45) | c2_1(a8) | (~ndr1_0) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | c2_1(a45))),
% 1.87/1.53 inference(transitivity,[status(thm)],[2789, 2787])).
% 1.87/1.53 tff(2791,plain,
% 1.87/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.87/1.53 inference(quant_inst,[status(thm)],[])).
% 1.87/1.53 tff(2792,plain,
% 1.87/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (~c1_1(a45)) | c3_1(a45) | c2_1(a8) | (~ndr1_0) | c3_1(a8) | (~c0_1(a8)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | c2_1(a45)),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2791, 2790])).
% 1.87/1.53 tff(2793,plain,
% 1.87/1.53 ((~c1_1(a45)) | c3_1(a8) | c2_1(a45)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2792, 169, 331, 332, 2786, 2542, 1349, 439, 2588])).
% 1.87/1.53 tff(2794,plain,
% 1.87/1.53 (c3_1(a8)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2793, 2785, 2777])).
% 1.87/1.53 tff(2795,plain,
% 1.87/1.53 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2796,plain,
% 1.87/1.53 ((hskp24 | hskp9 | (~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8))) <=> (hskp24 | hskp9 | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2797,plain,
% 1.87/1.53 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8))))),
% 1.87/1.53 inference(monotonicity,[status(thm)],[2796])).
% 1.87/1.53 tff(2798,plain,
% 1.87/1.53 (((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)))) <=> ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.87/1.53 inference(transitivity,[status(thm)],[2797, 2795])).
% 1.87/1.53 tff(2799,plain,
% 1.87/1.53 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp24 | hskp9 | (~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.87/1.53 inference(quant_inst,[status(thm)],[])).
% 1.87/1.53 tff(2800,plain,
% 1.87/1.53 ((~![U: $i] : (hskp24 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp24 | hskp9 | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8))),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2799, 2798])).
% 1.87/1.53 tff(2801,plain,
% 1.87/1.53 (hskp24 | hskp9 | (~c3_1(a8))),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2800, 169, 1350, 1349, 104])).
% 1.87/1.53 tff(2802,plain,
% 1.87/1.53 (hskp24),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2801, 2794, 105])).
% 1.87/1.53 tff(2803,plain,
% 1.87/1.53 (c2_1(a3)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2380, 2802])).
% 1.87/1.53 tff(2804,plain,
% 1.87/1.53 (c1_1(a3)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2391, 2802])).
% 1.87/1.53 tff(2805,plain,
% 1.87/1.53 (c0_1(a3)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2708, 169, 105, 2705, 2804, 2803, 2699])).
% 1.87/1.53 tff(2806,plain,
% 1.87/1.53 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a8)) | (~c3_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2807,plain,
% 1.87/1.53 ((hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8))) <=> (hskp19 | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2808,plain,
% 1.87/1.53 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a8)) | (~c3_1(a8))))),
% 1.87/1.53 inference(monotonicity,[status(thm)],[2807])).
% 1.87/1.53 tff(2809,plain,
% 1.87/1.53 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.87/1.53 inference(transitivity,[status(thm)],[2808, 2806])).
% 1.87/1.53 tff(2810,plain,
% 1.87/1.53 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8)))),
% 1.87/1.53 inference(quant_inst,[status(thm)],[])).
% 1.87/1.53 tff(2811,plain,
% 1.87/1.53 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a8)) | (~c3_1(a8))),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2810, 2809])).
% 1.87/1.53 tff(2812,plain,
% 1.87/1.53 (hskp19),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2811, 169, 2804, 2803, 1350, 1349, 848, 2794, 2805])).
% 1.87/1.53 tff(2813,plain,
% 1.87/1.53 (~c0_1(a33)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[897, 2812])).
% 1.87/1.53 tff(2814,plain,
% 1.87/1.53 (c2_1(a33)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[908, 2812])).
% 1.87/1.53 tff(2815,plain,
% 1.87/1.53 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2816,plain,
% 1.87/1.53 ((hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33))) <=> (hskp9 | hskp8 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2817,plain,
% 1.87/1.53 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33))))),
% 1.87/1.53 inference(monotonicity,[status(thm)],[2816])).
% 1.87/1.53 tff(2818,plain,
% 1.87/1.53 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33)))),
% 1.87/1.53 inference(transitivity,[status(thm)],[2817, 2815])).
% 1.87/1.53 tff(2819,plain,
% 1.87/1.53 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a33)) | c0_1(a33) | (~c1_1(a33)))),
% 1.87/1.53 inference(quant_inst,[status(thm)],[])).
% 1.87/1.53 tff(2820,plain,
% 1.87/1.53 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a33))),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2819, 2818])).
% 1.87/1.53 tff(2821,plain,
% 1.87/1.53 (~c1_1(a33)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2820, 169, 105, 2705, 2814, 2813, 2699])).
% 1.87/1.53 tff(2822,plain,
% 1.87/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a45) | (~c1_1(a45)) | c3_1(a45) | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a45) | (~c1_1(a45)) | c3_1(a45) | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2823,plain,
% 1.87/1.53 (((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33))) <=> (c0_1(a45) | (~c1_1(a45)) | c3_1(a45) | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2824,plain,
% 1.87/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a45) | (~c1_1(a45)) | c3_1(a45) | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)))),
% 1.87/1.53 inference(monotonicity,[status(thm)],[2823])).
% 1.87/1.53 tff(2825,plain,
% 1.87/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a45) | (~c1_1(a45)) | c3_1(a45) | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.87/1.53 inference(transitivity,[status(thm)],[2824, 2822])).
% 1.87/1.53 tff(2826,plain,
% 1.87/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))),
% 1.87/1.53 inference(quant_inst,[status(thm)],[])).
% 1.87/1.53 tff(2827,plain,
% 1.87/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a45) | (~c1_1(a45)) | c3_1(a45) | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2826, 2825])).
% 1.87/1.53 tff(2828,plain,
% 1.87/1.53 ($false),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2827, 169, 2751, 2814, 332, 2777, 2542, 2813, 343, 83, 2588, 2821])).
% 1.87/1.53 tff(2829,plain,(hskp9 | c0_1(a45) | (~c2_1(a31)) | (~c1_1(a45)) | c3_1(a45) | c1_1(a31) | (~c3_1(a31)) | hskp8 | (~c1_1(a8)) | c2_1(a8) | (~c0_1(a31)) | (~c0_1(a8))), inference(lemma,lemma(discharge,[]))).
% 1.87/1.53 tff(2830,plain,
% 1.87/1.53 ($false),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2829, 1336, 1347, 332, 105, 2542, 343, 2588, 2705, 2751, 2773, 331, 1370])).
% 1.87/1.53 tff(2831,plain,((~hskp6) | (~c2_1(a31)) | hskp9 | c3_1(a45) | c1_1(a31) | (~c3_1(a31)) | hskp8 | c0_1(a45) | (~c0_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.87/1.53 tff(2832,plain,
% 1.87/1.53 (~hskp6),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2831, 2751, 2776, 2542, 343, 2588, 2483, 332, 331])).
% 1.87/1.53 tff(2833,assumption,(~c3_1(a14)), introduced(assumption)).
% 1.87/1.53 tff(2834,plain,
% 1.87/1.53 ((~c1_1(a45)) | (~c2_1(a45))),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2783, 169, 105, 2705, 2751, 2699])).
% 1.87/1.53 tff(2835,plain,
% 1.87/1.53 (~c2_1(a45)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2834, 2773])).
% 1.87/1.53 tff(2836,plain,
% 1.87/1.53 (((~hskp22) | c0_1(a45)) <=> ((~hskp22) | c0_1(a45))),
% 1.87/1.53 inference(rewrite,[status(thm)],[])).
% 1.87/1.53 tff(2837,axiom,((~hskp22) | c0_1(a45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.87/1.53 tff(2838,plain,
% 1.87/1.53 ((~hskp22) | c0_1(a45)),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2837, 2836])).
% 1.87/1.53 tff(2839,plain,
% 1.87/1.53 ((~hskp22) | c0_1(a45)),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2838, 2836])).
% 1.87/1.53 tff(2840,plain,
% 1.87/1.53 ((~hskp22) | c0_1(a45)),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2839, 2836])).
% 1.87/1.53 tff(2841,plain,
% 1.87/1.53 ((~hskp22) | c0_1(a45)),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2840, 2836])).
% 1.87/1.53 tff(2842,plain,
% 1.87/1.53 ((~hskp22) | c0_1(a45)),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2841, 2836])).
% 1.87/1.53 tff(2843,plain,
% 1.87/1.53 ((~hskp22) | c0_1(a45)),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2842, 2836])).
% 1.87/1.53 tff(2844,plain,
% 1.87/1.53 ((~hskp22) | c0_1(a45)),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2843, 2836])).
% 1.87/1.53 tff(2845,plain,
% 1.87/1.53 ((~hskp22) | c0_1(a45)),
% 1.87/1.53 inference(modus_ponens,[status(thm)],[2844, 2836])).
% 1.87/1.53 tff(2846,plain,
% 1.87/1.53 (~hskp22),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2845, 2751])).
% 1.87/1.53 tff(2847,plain,
% 1.87/1.53 (~hskp6),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2831, 2751, 105, 2542, 343, 2588, 2705, 332, 331])).
% 1.87/1.53 tff(2848,plain,
% 1.87/1.53 (hskp26),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[2618, 2847, 2846])).
% 1.87/1.53 tff(2849,plain,
% 1.87/1.53 (c3_1(a10)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[689, 2848])).
% 1.87/1.53 tff(2850,plain,
% 1.87/1.53 (c2_1(a10)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[678, 2848])).
% 1.87/1.53 tff(2851,plain,
% 1.87/1.53 (c0_1(a10)),
% 1.87/1.53 inference(unit_resolution,[status(thm)],[666, 2848])).
% 1.87/1.53 tff(2852,plain,
% 1.87/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a14) | (~c1_1(a45)) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a14)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a14) | (~c1_1(a45)) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a14)) | c2_1(a45))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2853,plain,
% 1.87/1.54 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a14) | c3_1(a14) | (~c0_1(a14))) <=> (c3_1(a14) | (~c1_1(a45)) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a14)) | c2_1(a45))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2854,plain,
% 1.87/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a14) | c3_1(a14) | (~c0_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a14) | (~c1_1(a45)) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a14)) | c2_1(a45)))),
% 1.87/1.54 inference(monotonicity,[status(thm)],[2853])).
% 1.87/1.54 tff(2855,plain,
% 1.87/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a14) | c3_1(a14) | (~c0_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a14) | (~c1_1(a45)) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a14)) | c2_1(a45))),
% 1.87/1.54 inference(transitivity,[status(thm)],[2854, 2852])).
% 1.87/1.54 tff(2856,plain,
% 1.87/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a14) | c3_1(a14) | (~c0_1(a14)))),
% 1.87/1.54 inference(quant_inst,[status(thm)],[])).
% 1.87/1.54 tff(2857,plain,
% 1.87/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a14) | (~c1_1(a45)) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c0_1(a14)) | c2_1(a45)),
% 1.87/1.54 inference(modus_ponens,[status(thm)],[2856, 2855])).
% 1.87/1.54 tff(2858,plain,
% 1.87/1.54 (c3_1(a14) | (~c0_1(a14))),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2857, 169, 2851, 2850, 2849, 2773, 2542, 2719, 439, 2835])).
% 1.87/1.54 tff(2859,plain,
% 1.87/1.54 (~c0_1(a14)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2858, 2833])).
% 1.87/1.54 tff(2860,plain,
% 1.87/1.54 (~hskp7),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[536, 2833])).
% 1.87/1.54 tff(2861,assumption,(hskp24), introduced(assumption)).
% 1.87/1.54 tff(2862,plain,
% 1.87/1.54 (c2_1(a3)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2380, 2861])).
% 1.87/1.54 tff(2863,plain,
% 1.87/1.54 (c1_1(a3)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2391, 2861])).
% 1.87/1.54 tff(2864,plain,
% 1.87/1.54 (c0_1(a3)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2708, 169, 105, 2705, 2863, 2862, 2699])).
% 1.87/1.54 tff(2865,plain,
% 1.87/1.54 (^[U: $i] : refl((hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 1.87/1.54 inference(bind,[status(th)],[])).
% 1.87/1.54 tff(2866,plain,
% 1.87/1.54 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.87/1.54 inference(quant_intro,[status(thm)],[2865])).
% 1.87/1.54 tff(2867,plain,
% 1.87/1.54 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2868,plain,
% 1.87/1.54 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp6) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp6))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp6) | hskp10) <=> ((hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp10))), rewrite(((hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp10) <=> (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp6) | hskp10) <=> (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.87/1.54 inference(bind,[status(th)],[])).
% 1.87/1.54 tff(2869,plain,
% 1.87/1.54 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp6) | hskp10) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.87/1.54 inference(quant_intro,[status(thm)],[2868])).
% 1.87/1.54 tff(2870,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp6) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.87/1.54 tff(2871,plain,
% 1.87/1.54 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.87/1.54 inference(modus_ponens,[status(thm)],[2870, 2869])).
% 1.87/1.54 tff(2872,plain,
% 1.87/1.54 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.87/1.54 inference(modus_ponens,[status(thm)],[2871, 2867])).
% 1.87/1.54 tff(2873,plain,(
% 1.87/1.54 ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.87/1.54 inference(skolemize,[status(sab)],[2872])).
% 1.87/1.54 tff(2874,plain,
% 1.87/1.54 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.87/1.54 inference(modus_ponens,[status(thm)],[2873, 2866])).
% 1.87/1.54 tff(2875,plain,
% 1.87/1.54 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp10 | hskp6 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp10 | hskp6 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2876,plain,
% 1.87/1.54 ((hskp10 | hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))) <=> (hskp10 | hskp6 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2877,plain,
% 1.87/1.54 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp10 | hskp6 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3))))),
% 1.87/1.54 inference(monotonicity,[status(thm)],[2876])).
% 1.87/1.54 tff(2878,plain,
% 1.87/1.54 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp10 | hskp6 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.87/1.54 inference(transitivity,[status(thm)],[2877, 2875])).
% 1.87/1.54 tff(2879,plain,
% 1.87/1.54 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 1.87/1.54 inference(quant_inst,[status(thm)],[])).
% 1.87/1.54 tff(2880,plain,
% 1.87/1.54 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp10 | hskp6 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3))),
% 1.87/1.54 inference(modus_ponens,[status(thm)],[2879, 2878])).
% 1.87/1.54 tff(2881,plain,
% 1.87/1.54 (hskp10 | (~c0_1(a3))),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2880, 169, 1270, 2863, 2862, 2874])).
% 1.87/1.54 tff(2882,plain,
% 1.87/1.54 (hskp10),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2881, 2864])).
% 1.87/1.54 tff(2883,plain,
% 1.87/1.54 (~c3_1(a18)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[1150, 2882])).
% 1.87/1.54 tff(2884,plain,
% 1.87/1.54 (c2_1(a18)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[1161, 2882])).
% 1.87/1.54 tff(2885,assumption,(~hskp7), introduced(assumption)).
% 1.87/1.54 tff(2886,plain,
% 1.87/1.54 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2887,plain,
% 1.87/1.54 ((hskp7 | (~ndr1_0) | c3_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (hskp7 | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2888,plain,
% 1.87/1.54 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18))))),
% 1.87/1.54 inference(monotonicity,[status(thm)],[2887])).
% 1.87/1.54 tff(2889,plain,
% 1.87/1.54 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18)))),
% 1.87/1.54 inference(transitivity,[status(thm)],[2888, 2886])).
% 1.87/1.54 tff(2890,plain,
% 1.87/1.54 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 1.87/1.54 inference(quant_inst,[status(thm)],[])).
% 1.87/1.54 tff(2891,plain,
% 1.87/1.54 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c3_1(a18) | (~ndr1_0) | c1_1(a18) | (~c2_1(a18))),
% 1.87/1.54 inference(modus_ponens,[status(thm)],[2890, 2889])).
% 1.87/1.54 tff(2892,plain,
% 1.87/1.54 (c1_1(a18)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2891, 169, 2885, 2884, 2883, 2507])).
% 1.87/1.54 tff(2893,plain,
% 1.87/1.54 (~c2_1(a45)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2834, 2777])).
% 1.87/1.54 tff(2894,plain,
% 1.87/1.54 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a45) | (~c1_1(a45)) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | c2_1(a45))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a45) | (~c1_1(a45)) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | c2_1(a45))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2895,plain,
% 1.87/1.54 ((hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a45) | c2_1(a45) | (~c1_1(a45))) <=> (hskp5 | c0_1(a45) | (~c1_1(a45)) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | c2_1(a45))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2896,plain,
% 1.87/1.54 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a45) | c2_1(a45) | (~c1_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a45) | (~c1_1(a45)) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | c2_1(a45)))),
% 1.87/1.54 inference(monotonicity,[status(thm)],[2895])).
% 1.87/1.54 tff(2897,plain,
% 1.87/1.54 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a45) | c2_1(a45) | (~c1_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a45) | (~c1_1(a45)) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | c2_1(a45))),
% 1.87/1.54 inference(transitivity,[status(thm)],[2896, 2894])).
% 1.87/1.54 tff(2898,plain,
% 1.87/1.54 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a45) | c2_1(a45) | (~c1_1(a45)))),
% 1.87/1.54 inference(quant_inst,[status(thm)],[])).
% 1.87/1.54 tff(2899,plain,
% 1.87/1.54 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a45) | (~c1_1(a45)) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | c2_1(a45)),
% 1.87/1.54 inference(modus_ponens,[status(thm)],[2898, 2897])).
% 1.87/1.54 tff(2900,plain,
% 1.87/1.54 (hskp5),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2899, 169, 2751, 2884, 2777, 2883, 1413, 2893, 2892])).
% 1.87/1.54 tff(2901,plain,
% 1.87/1.54 (~c0_1(a7)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[1419, 2900])).
% 1.87/1.54 tff(2902,plain,
% 1.87/1.54 (c1_1(a7)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[1430, 2900])).
% 1.87/1.54 tff(2903,plain,
% 1.87/1.54 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2904,plain,
% 1.87/1.54 ((hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7))) <=> (hskp9 | hskp8 | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2905,plain,
% 1.87/1.54 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7))))),
% 1.87/1.54 inference(monotonicity,[status(thm)],[2904])).
% 1.87/1.54 tff(2906,plain,
% 1.87/1.54 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7)))),
% 1.87/1.54 inference(transitivity,[status(thm)],[2905, 2903])).
% 1.87/1.54 tff(2907,plain,
% 1.87/1.54 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a7)) | c0_1(a7) | (~c1_1(a7)))),
% 1.87/1.54 inference(quant_inst,[status(thm)],[])).
% 1.87/1.54 tff(2908,plain,
% 1.87/1.54 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a7) | (~ndr1_0) | (~c1_1(a7)) | (~c2_1(a7))),
% 1.87/1.54 inference(modus_ponens,[status(thm)],[2907, 2906])).
% 1.87/1.54 tff(2909,plain,
% 1.87/1.54 (~c2_1(a7)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2908, 169, 105, 2705, 2902, 2901, 2699])).
% 1.87/1.54 tff(2910,plain,
% 1.87/1.54 (c3_1(a7)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[1454, 2900])).
% 1.87/1.54 tff(2911,plain,
% 1.87/1.54 (c3_1(a3)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2411, 2861])).
% 1.87/1.54 tff(2912,plain,
% 1.87/1.54 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a7) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a7)) | c2_1(a7))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a7) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a7)) | c2_1(a7))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2913,plain,
% 1.87/1.54 ((hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a7) | c2_1(a7) | (~c3_1(a7))) <=> (hskp6 | c0_1(a7) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a7)) | c2_1(a7))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2914,plain,
% 1.87/1.54 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a7) | c2_1(a7) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a7) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a7)) | c2_1(a7)))),
% 1.87/1.54 inference(monotonicity,[status(thm)],[2913])).
% 1.87/1.54 tff(2915,plain,
% 1.87/1.54 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a7) | c2_1(a7) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a7) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a7)) | c2_1(a7))),
% 1.87/1.54 inference(transitivity,[status(thm)],[2914, 2912])).
% 1.87/1.54 tff(2916,plain,
% 1.87/1.54 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a7) | c2_1(a7) | (~c3_1(a7)))),
% 1.87/1.54 inference(quant_inst,[status(thm)],[])).
% 1.87/1.54 tff(2917,plain,
% 1.87/1.54 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a7) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a7)) | c2_1(a7)),
% 1.87/1.54 inference(modus_ponens,[status(thm)],[2916, 2915])).
% 1.87/1.54 tff(2918,plain,
% 1.87/1.54 ($false),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2917, 169, 1270, 2863, 2862, 2911, 2910, 2901, 1298, 2909])).
% 1.87/1.54 tff(2919,plain,((~hskp24) | hskp6 | hskp9 | hskp8 | c0_1(a45) | (~c1_1(a45)) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.87/1.54 tff(2920,plain,
% 1.87/1.54 (~hskp24),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2919, 2860, 105, 2705, 2751, 2773, 2847])).
% 1.87/1.54 tff(2921,plain,
% 1.87/1.54 (hskp23),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[253, 2920, 344])).
% 1.87/1.54 tff(2922,assumption,(~c0_1(a14)), introduced(assumption)).
% 1.87/1.54 tff(2923,plain,
% 1.87/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a14) | c3_1(a14) | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c1_1(a14)) | (~c2_1(a53)) | (~c3_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a14) | c3_1(a14) | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c1_1(a14)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2924,plain,
% 1.87/1.54 (((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a14) | c0_1(a14) | (~c1_1(a14)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a14) | c3_1(a14) | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c1_1(a14)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2925,plain,
% 1.87/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a14) | c0_1(a14) | (~c1_1(a14)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a14) | c3_1(a14) | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c1_1(a14)) | (~c2_1(a53)) | (~c3_1(a53))))),
% 1.87/1.54 inference(monotonicity,[status(thm)],[2924])).
% 1.87/1.54 tff(2926,plain,
% 1.87/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a14) | c0_1(a14) | (~c1_1(a14)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a14) | c3_1(a14) | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c1_1(a14)) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.87/1.54 inference(transitivity,[status(thm)],[2925, 2923])).
% 1.87/1.54 tff(2927,plain,
% 1.87/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a14) | c0_1(a14) | (~c1_1(a14)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 1.87/1.54 inference(quant_inst,[status(thm)],[])).
% 1.87/1.54 tff(2928,plain,
% 1.87/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a14) | c3_1(a14) | c0_1(a53) | c1_1(a53) | (~ndr1_0) | (~c1_1(a14)) | (~c2_1(a53)) | (~c3_1(a53))),
% 1.87/1.54 inference(modus_ponens,[status(thm)],[2927, 2926])).
% 1.87/1.54 tff(2929,plain,
% 1.87/1.54 (~c2_1(a53)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2928, 169, 230, 2922, 2833, 219, 213, 83, 2700])).
% 1.87/1.54 tff(2930,plain,
% 1.87/1.54 ($false),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[353, 169, 344, 331, 332, 219, 213, 343, 342, 2929])).
% 1.87/1.54 tff(2931,plain,((~hskp23) | hskp0 | (~c0_1(a31)) | (~c2_1(a31)) | c1_1(a31) | c0_1(a14) | c3_1(a14) | (~c1_1(a14))), inference(lemma,lemma(discharge,[]))).
% 1.87/1.54 tff(2932,plain,
% 1.87/1.54 (~c1_1(a14)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2931, 2921, 331, 332, 343, 2859, 2833, 344])).
% 1.87/1.54 tff(2933,plain,
% 1.87/1.54 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a14) | c3_1(a14) | c1_1(a31) | (~ndr1_0) | c1_1(a14) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a14) | c3_1(a14) | c1_1(a31) | (~ndr1_0) | c1_1(a14) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2934,plain,
% 1.87/1.54 ((hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a14) | c1_1(a14) | c0_1(a14)) <=> (hskp1 | c0_1(a14) | c3_1(a14) | c1_1(a31) | (~ndr1_0) | c1_1(a14) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.87/1.54 inference(rewrite,[status(thm)],[])).
% 1.87/1.54 tff(2935,plain,
% 1.87/1.54 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a14) | c1_1(a14) | c0_1(a14))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a14) | c3_1(a14) | c1_1(a31) | (~ndr1_0) | c1_1(a14) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.87/1.54 inference(monotonicity,[status(thm)],[2934])).
% 1.87/1.54 tff(2936,plain,
% 1.87/1.54 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a14) | c1_1(a14) | c0_1(a14))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a14) | c3_1(a14) | c1_1(a31) | (~ndr1_0) | c1_1(a14) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.87/1.54 inference(transitivity,[status(thm)],[2935, 2933])).
% 1.87/1.54 tff(2937,plain,
% 1.87/1.54 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a14) | c1_1(a14) | c0_1(a14))),
% 1.87/1.54 inference(quant_inst,[status(thm)],[])).
% 1.87/1.54 tff(2938,plain,
% 1.87/1.54 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a14) | c3_1(a14) | c1_1(a31) | (~ndr1_0) | c1_1(a14) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.87/1.54 inference(modus_ponens,[status(thm)],[2937, 2936])).
% 1.87/1.54 tff(2939,plain,
% 1.87/1.54 (hskp1 | c1_1(a14)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2938, 169, 332, 2859, 2833, 343, 1493, 2588])).
% 1.87/1.54 tff(2940,plain,
% 1.87/1.54 (hskp1),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2939, 2932])).
% 1.87/1.54 tff(2941,plain,
% 1.87/1.54 (~c3_1(a2)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[2441, 2940])).
% 1.87/1.54 tff(2942,plain,
% 1.87/1.54 (~c0_1(a2)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[1516, 2940])).
% 1.87/1.54 tff(2943,plain,
% 1.87/1.54 (hskp13),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[519, 2860, 105])).
% 1.87/1.54 tff(2944,plain,
% 1.87/1.54 (~c3_1(a22)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[482, 2943])).
% 1.87/1.54 tff(2945,plain,
% 1.87/1.54 (~c2_1(a22)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[488, 2943])).
% 1.87/1.54 tff(2946,plain,
% 1.87/1.54 (~c0_1(a22)),
% 1.87/1.54 inference(unit_resolution,[status(thm)],[494, 2943])).
% 1.87/1.55 tff(2947,plain,
% 1.87/1.55 (c2_1(a2)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[1527, 2940])).
% 1.87/1.55 tff(2948,plain,
% 1.87/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a14) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a14) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a14) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a14) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a14))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(2949,plain,
% 1.87/1.55 (((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a14) | c1_1(a14) | c2_1(a14) | c2_1(a22) | c0_1(a22) | c3_1(a22)) <=> (c3_1(a14) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a14) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a14))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(2950,plain,
% 1.87/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a14) | c1_1(a14) | c2_1(a14) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a14) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a14) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a14)))),
% 1.87/1.55 inference(monotonicity,[status(thm)],[2949])).
% 1.87/1.55 tff(2951,plain,
% 1.87/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a14) | c1_1(a14) | c2_1(a14) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a14) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a14) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a14))),
% 1.87/1.55 inference(transitivity,[status(thm)],[2950, 2948])).
% 1.87/1.55 tff(2952,plain,
% 1.87/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a14) | c1_1(a14) | c2_1(a14) | c2_1(a22) | c0_1(a22) | c3_1(a22))),
% 1.87/1.55 inference(quant_inst,[status(thm)],[])).
% 1.87/1.55 tff(2953,plain,
% 1.87/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a14) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a14) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c1_1(a14)),
% 1.87/1.55 inference(modus_ponens,[status(thm)],[2952, 2951])).
% 1.87/1.55 tff(2954,plain,
% 1.87/1.55 ($false),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2953, 169, 2833, 2947, 2946, 2945, 2944, 2719, 2942, 2941, 2435, 2932])).
% 1.87/1.55 tff(2955,plain,(c3_1(a14) | c2_1(a14) | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31)) | (~c0_1(a31)) | hskp0 | hskp9 | hskp8 | c0_1(a45) | c3_1(a45)), inference(lemma,lemma(discharge,[]))).
% 1.87/1.55 tff(2956,plain,
% 1.87/1.55 (c3_1(a14)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2955, 2719, 332, 343, 2588, 331, 344, 2776, 2483, 2751, 2542])).
% 1.87/1.55 tff(2957,plain,
% 1.87/1.55 ((~c1_1(a45)) | (~c2_1(a45))),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2783, 169, 2776, 2483, 2751, 2699])).
% 1.87/1.55 tff(2958,plain,
% 1.87/1.55 (~c2_1(a45)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2957, 2773])).
% 1.87/1.55 tff(2959,assumption,(~c1_1(a14)), introduced(assumption)).
% 1.87/1.55 tff(2960,plain,
% 1.87/1.55 (c1_1(a14) | (~c0_1(a14))),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2687, 169, 655, 654, 2719, 700])).
% 1.87/1.55 tff(2961,plain,
% 1.87/1.55 (~c0_1(a14)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2960, 2959])).
% 1.87/1.55 tff(2962,plain,
% 1.87/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a45) | c0_1(a14) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a45) | c0_1(a14) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | c2_1(a45))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(2963,plain,
% 1.87/1.55 (((~ndr1_0) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a14) | c1_1(a14) | c0_1(a14)) <=> (c0_1(a45) | c0_1(a14) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | c2_1(a45))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(2964,plain,
% 1.87/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a14) | c1_1(a14) | c0_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a45) | c0_1(a14) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | c2_1(a45)))),
% 1.87/1.55 inference(monotonicity,[status(thm)],[2963])).
% 1.87/1.55 tff(2965,plain,
% 1.87/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a14) | c1_1(a14) | c0_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a45) | c0_1(a14) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | c2_1(a45))),
% 1.87/1.55 inference(transitivity,[status(thm)],[2964, 2962])).
% 1.87/1.55 tff(2966,plain,
% 1.87/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c3_1(a45) | c0_1(a45) | c2_1(a45) | c2_1(a14) | c1_1(a14) | c0_1(a14))),
% 1.87/1.55 inference(quant_inst,[status(thm)],[])).
% 1.87/1.55 tff(2967,plain,
% 1.87/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a45) | c0_1(a14) | c3_1(a45) | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | c2_1(a45)),
% 1.87/1.55 inference(modus_ponens,[status(thm)],[2966, 2965])).
% 1.87/1.55 tff(2968,plain,
% 1.87/1.55 (c0_1(a14) | c1_1(a14) | (~c3_1(a14))),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2967, 169, 2751, 2542, 2719, 55, 2543])).
% 1.87/1.55 tff(2969,plain,
% 1.87/1.55 ($false),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2968, 2961, 2959, 2721])).
% 1.87/1.55 tff(2970,plain,(c1_1(a14) | (~c3_1(a14)) | c0_1(a45) | c3_1(a45) | c2_1(a14) | c2_1(a45) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.87/1.55 tff(2971,plain,
% 1.87/1.55 (c1_1(a14)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2970, 2956, 2751, 2542, 2719, 2958, 655, 654])).
% 1.87/1.55 tff(2972,plain,
% 1.87/1.55 (hskp24 | (~c1_1(a14)) | (~c3_1(a14))),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[543, 169, 2776, 2719, 104])).
% 1.87/1.55 tff(2973,plain,
% 1.87/1.55 (hskp24),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2972, 2971, 2956])).
% 1.87/1.55 tff(2974,plain,
% 1.87/1.55 (c2_1(a3)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2380, 2973])).
% 1.87/1.55 tff(2975,plain,
% 1.87/1.55 (c1_1(a3)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2391, 2973])).
% 1.87/1.55 tff(2976,plain,
% 1.87/1.55 (c0_1(a3)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2708, 169, 2776, 2483, 2975, 2974, 2699])).
% 1.87/1.55 tff(2977,plain,
% 1.87/1.55 (hskp10 | (~c0_1(a3))),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2880, 169, 2832, 2975, 2974, 2874])).
% 1.87/1.55 tff(2978,plain,
% 1.87/1.55 (hskp10),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2977, 2976])).
% 1.87/1.55 tff(2979,plain,
% 1.87/1.55 (~c3_1(a18)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[1150, 2978])).
% 1.87/1.55 tff(2980,plain,
% 1.87/1.55 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a14) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a14)) | (~c3_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a14) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a14)) | (~c3_1(a14)))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(2981,plain,
% 1.87/1.55 ((hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14))) <=> (hskp19 | c2_1(a14) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a14)) | (~c3_1(a14)))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(2982,plain,
% 1.87/1.55 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a14) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a14)) | (~c3_1(a14))))),
% 1.87/1.55 inference(monotonicity,[status(thm)],[2981])).
% 1.87/1.55 tff(2983,plain,
% 1.87/1.55 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a14) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a14)) | (~c3_1(a14)))),
% 1.87/1.55 inference(transitivity,[status(thm)],[2982, 2980])).
% 1.87/1.55 tff(2984,plain,
% 1.87/1.55 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))),
% 1.87/1.55 inference(quant_inst,[status(thm)],[])).
% 1.87/1.55 tff(2985,plain,
% 1.87/1.55 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a14) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a14)) | (~c3_1(a14))),
% 1.87/1.55 inference(modus_ponens,[status(thm)],[2984, 2983])).
% 1.87/1.55 tff(2986,plain,
% 1.87/1.55 (hskp19),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2985, 169, 2975, 2974, 2956, 2719, 848, 2971, 2976])).
% 1.87/1.55 tff(2987,plain,
% 1.87/1.55 (~c0_1(a33)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[897, 2986])).
% 1.87/1.55 tff(2988,plain,
% 1.87/1.55 (c2_1(a18)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[1161, 2978])).
% 1.87/1.55 tff(2989,plain,
% 1.87/1.55 (c0_1(a18)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[1172, 2978])).
% 1.87/1.55 tff(2990,plain,
% 1.87/1.55 (c3_1(a33)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[1503, 2986])).
% 1.87/1.55 tff(2991,plain,
% 1.87/1.55 (c2_1(a33)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[908, 2986])).
% 1.87/1.55 tff(2992,plain,
% 1.87/1.55 (~hskp11),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2667, 2588, 332, 331])).
% 1.87/1.55 tff(2993,plain,
% 1.87/1.55 ($false),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2674, 169, 2992, 2991, 2990, 2989, 2988, 2987, 2979, 1126])).
% 1.87/1.55 tff(2994,plain,(c2_1(a14) | c0_1(a45) | c3_1(a45) | hskp14 | hskp2 | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31)) | (~c0_1(a31)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.87/1.55 tff(2995,plain,
% 1.87/1.55 (c2_1(a14)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2994, 2751, 2542, 655, 654, 332, 343, 2588, 331, 344])).
% 1.87/1.55 tff(2996,plain,
% 1.87/1.55 (~hskp7),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[525, 2995])).
% 1.87/1.55 tff(2997,plain,
% 1.87/1.55 (~hskp24),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2919, 2996, 2776, 2483, 2751, 2773, 2832])).
% 1.87/1.55 tff(2998,plain,
% 1.87/1.55 (hskp23),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[253, 2997, 344])).
% 1.87/1.55 tff(2999,plain,
% 1.87/1.55 (~c1_1(a53)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[212, 2998])).
% 1.87/1.55 tff(3000,plain,
% 1.87/1.55 (~c0_1(a53)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[218, 2998])).
% 1.87/1.55 tff(3001,plain,
% 1.87/1.55 (c3_1(a53)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[229, 2998])).
% 1.87/1.55 tff(3002,plain,
% 1.87/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a45) | c0_1(a53) | c1_1(a53) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a53)) | (~c3_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a45) | c0_1(a53) | c1_1(a53) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(3003,plain,
% 1.87/1.55 (((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53))) <=> (c0_1(a45) | c0_1(a53) | c1_1(a53) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(3004,plain,
% 1.87/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a45) | c0_1(a53) | c1_1(a53) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a53)) | (~c3_1(a53))))),
% 1.87/1.55 inference(monotonicity,[status(thm)],[3003])).
% 1.87/1.55 tff(3005,plain,
% 1.87/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a45) | c0_1(a53) | c1_1(a53) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a53)) | (~c3_1(a53)))),
% 1.87/1.55 inference(transitivity,[status(thm)],[3004, 3002])).
% 1.87/1.55 tff(3006,plain,
% 1.87/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a53) | (~c2_1(a53)) | (~c3_1(a53)) | c3_1(a45) | c0_1(a45) | (~c1_1(a45)) | c1_1(a53) | c0_1(a53) | (~c2_1(a53)))),
% 1.87/1.55 inference(quant_inst,[status(thm)],[])).
% 1.87/1.55 tff(3007,plain,
% 1.87/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a45) | c0_1(a53) | c1_1(a53) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a53)) | (~c3_1(a53))),
% 1.87/1.55 inference(modus_ponens,[status(thm)],[3006, 3005])).
% 1.87/1.55 tff(3008,plain,
% 1.87/1.55 (~c2_1(a53)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[3007, 169, 3001, 2751, 3000, 2999, 2773, 2542, 83])).
% 1.87/1.55 tff(3009,plain,
% 1.87/1.55 ($false),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[353, 169, 344, 331, 332, 3000, 2999, 343, 342, 3008])).
% 1.87/1.55 tff(3010,plain,(c0_1(a45) | hskp0 | (~c0_1(a31)) | (~c2_1(a31)) | c1_1(a31) | c3_1(a45) | hskp14 | hskp2 | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.87/1.55 tff(3011,plain,
% 1.87/1.55 (c0_1(a45)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[3010, 2542, 331, 332, 343, 344, 655, 654, 2588])).
% 1.87/1.55 tff(3012,assumption,(c0_1(a45)), introduced(assumption)).
% 1.87/1.55 tff(3013,plain,
% 1.87/1.55 (c1_1(a45) | c2_1(a45)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[2549, 169, 655, 654, 3012, 700])).
% 1.87/1.55 tff(3014,plain,
% 1.87/1.55 ($false),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[3013, 2753, 2541])).
% 1.87/1.55 tff(3015,plain,(c1_1(a45) | hskp14 | hskp2 | (~c0_1(a45)) | (~c0_1(a31)) | (~c2_1(a31)) | c3_1(a45) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.87/1.55 tff(3016,plain,
% 1.87/1.55 (c1_1(a45)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[3015, 3011, 654, 655, 331, 332, 2542, 2588])).
% 1.87/1.55 tff(3017,plain,
% 1.87/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c0_1(a45)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c0_1(a45)) | c2_1(a45))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(3018,plain,
% 1.87/1.55 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45))) <=> ((~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c0_1(a45)) | c2_1(a45))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(3019,plain,
% 1.87/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c0_1(a45)) | c2_1(a45)))),
% 1.87/1.55 inference(monotonicity,[status(thm)],[3018])).
% 1.87/1.55 tff(3020,plain,
% 1.87/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c0_1(a45)) | c2_1(a45))),
% 1.87/1.55 inference(transitivity,[status(thm)],[3019, 3017])).
% 1.87/1.55 tff(3021,plain,
% 1.87/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a45) | c2_1(a45) | (~c1_1(a45)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45)))),
% 1.87/1.55 inference(quant_inst,[status(thm)],[])).
% 1.87/1.55 tff(3022,plain,
% 1.87/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (~c1_1(a45)) | c3_1(a45) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)) | (~c0_1(a45)) | c2_1(a45)),
% 1.87/1.55 inference(modus_ponens,[status(thm)],[3021, 3020])).
% 1.87/1.55 tff(3023,plain,
% 1.87/1.55 ($false),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[3022, 169, 3012, 331, 332, 2777, 2542, 439, 2588, 2543])).
% 1.87/1.55 tff(3024,plain,(c2_1(a45) | (~c0_1(a45)) | (~c0_1(a31)) | (~c2_1(a31)) | (~c1_1(a45)) | c3_1(a45) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.87/1.55 tff(3025,plain,
% 1.87/1.55 (c2_1(a45)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[3024, 3011, 331, 332, 3016, 2542, 2588])).
% 1.87/1.55 tff(3026,assumption,(c2_1(a45)), introduced(assumption)).
% 1.87/1.55 tff(3027,assumption,(hskp19), introduced(assumption)).
% 1.87/1.55 tff(3028,plain,
% 1.87/1.55 (~c0_1(a33)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[897, 3027])).
% 1.87/1.55 tff(3029,plain,
% 1.87/1.55 (c3_1(a33)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[1503, 3027])).
% 1.87/1.55 tff(3030,plain,
% 1.87/1.55 (c2_1(a33)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[908, 3027])).
% 1.87/1.55 tff(3031,assumption,(~hskp11), introduced(assumption)).
% 1.87/1.55 tff(3032,plain,
% 1.87/1.55 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a45) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a45)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a45) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(3033,plain,
% 1.87/1.55 ((hskp11 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c0_1(a45)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp11 | c3_1(a45) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(3034,plain,
% 1.87/1.55 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c0_1(a45)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a45) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a45)) | (~c2_1(a45))))),
% 1.87/1.55 inference(monotonicity,[status(thm)],[3033])).
% 1.87/1.55 tff(3035,plain,
% 1.87/1.55 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c0_1(a45)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a45) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.87/1.55 inference(transitivity,[status(thm)],[3034, 3032])).
% 1.87/1.55 tff(3036,plain,
% 1.87/1.55 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c0_1(a45)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.87/1.55 inference(quant_inst,[status(thm)],[])).
% 1.87/1.55 tff(3037,plain,
% 1.87/1.55 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a45) | c0_1(a33) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a45)) | (~c2_1(a45))),
% 1.87/1.55 inference(modus_ponens,[status(thm)],[3036, 3035])).
% 1.87/1.55 tff(3038,plain,
% 1.87/1.55 ($false),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[3037, 169, 3031, 3012, 3030, 3029, 2542, 3028, 1126, 3026])).
% 1.87/1.55 tff(3039,plain,((~hskp19) | hskp11 | (~c0_1(a45)) | c3_1(a45) | (~c2_1(a45))), inference(lemma,lemma(discharge,[]))).
% 1.87/1.55 tff(3040,plain,
% 1.87/1.55 (~hskp19),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[3039, 3011, 2992, 2542, 3025])).
% 1.87/1.55 tff(3041,plain,
% 1.87/1.55 (hskp13),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[519, 2885, 105])).
% 1.87/1.55 tff(3042,plain,
% 1.87/1.55 (~c3_1(a22)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[482, 3041])).
% 1.87/1.55 tff(3043,plain,
% 1.87/1.55 (~c0_1(a22)),
% 1.87/1.55 inference(unit_resolution,[status(thm)],[494, 3041])).
% 1.87/1.55 tff(3044,assumption,(~c1_1(a22)), introduced(assumption)).
% 1.87/1.55 tff(3045,assumption,(~c3_1(a22)), introduced(assumption)).
% 1.87/1.55 tff(3046,assumption,(~c0_1(a22)), introduced(assumption)).
% 1.87/1.55 tff(3047,plain,
% 1.87/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | c1_1(a22) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | c1_1(a22) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(3048,plain,
% 1.87/1.55 ((hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c1_1(a22) | c0_1(a22)) <=> (hskp1 | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | c1_1(a22) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.87/1.55 inference(rewrite,[status(thm)],[])).
% 1.87/1.55 tff(3049,plain,
% 1.87/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | c1_1(a22) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.87/1.55 inference(monotonicity,[status(thm)],[3048])).
% 1.87/1.55 tff(3050,plain,
% 1.87/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | c1_1(a22) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.87/1.55 inference(transitivity,[status(thm)],[3049, 3047])).
% 1.87/1.55 tff(3051,plain,
% 1.87/1.55 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c1_1(a22) | c0_1(a22))),
% 1.87/1.56 inference(quant_inst,[status(thm)],[])).
% 1.87/1.56 tff(3052,plain,
% 1.87/1.56 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | c1_1(a22) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.87/1.56 inference(modus_ponens,[status(thm)],[3051, 3050])).
% 1.87/1.56 tff(3053,plain,
% 1.87/1.56 (hskp1 | c1_1(a22)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[3052, 169, 332, 343, 3046, 3045, 1493, 2588])).
% 1.87/1.56 tff(3054,plain,
% 1.87/1.56 (hskp1),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[3053, 3044])).
% 1.87/1.56 tff(3055,plain,
% 1.87/1.56 (~c0_1(a2)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[1516, 3054])).
% 1.87/1.56 tff(3056,plain,
% 1.87/1.56 (c2_1(a2)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[1527, 3054])).
% 1.87/1.56 tff(3057,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a22) | c3_1(a22) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)) | c1_1(a22))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a22) | c3_1(a22) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)) | c1_1(a22))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3058,plain,
% 1.87/1.56 (((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a22) | c1_1(a22) | c0_1(a22)) <=> (c0_1(a22) | c3_1(a22) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)) | c1_1(a22))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3059,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a22) | c3_1(a22) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)) | c1_1(a22)))),
% 1.87/1.56 inference(monotonicity,[status(thm)],[3058])).
% 1.87/1.56 tff(3060,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a22) | c3_1(a22) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)) | c1_1(a22))),
% 1.87/1.56 inference(transitivity,[status(thm)],[3059, 3057])).
% 1.87/1.56 tff(3061,plain,
% 1.87/1.56 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a2)) | c0_1(a2) | (~c1_1(a2)) | c3_1(a22) | c1_1(a22) | c0_1(a22))),
% 1.87/1.56 inference(quant_inst,[status(thm)],[])).
% 1.87/1.56 tff(3062,plain,
% 1.87/1.56 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a22) | c3_1(a22) | c0_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a2)) | c1_1(a22)),
% 1.87/1.56 inference(modus_ponens,[status(thm)],[3061, 3060])).
% 1.87/1.56 tff(3063,plain,
% 1.87/1.56 (~c1_1(a2)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[3062, 169, 3056, 3046, 3045, 3055, 45, 3044])).
% 1.87/1.56 tff(3064,plain,
% 1.87/1.56 (~c3_1(a2)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[2441, 3054])).
% 1.87/1.56 tff(3065,plain,
% 1.87/1.56 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3066,plain,
% 1.87/1.56 ((hskp7 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c2_1(a2))) <=> (hskp7 | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3067,plain,
% 1.87/1.56 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c2_1(a2)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2))))),
% 1.87/1.56 inference(monotonicity,[status(thm)],[3066])).
% 1.87/1.56 tff(3068,plain,
% 1.87/1.56 (((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c2_1(a2)))) <=> ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2)))),
% 1.87/1.56 inference(transitivity,[status(thm)],[3067, 3065])).
% 1.87/1.56 tff(3069,plain,
% 1.87/1.56 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp7 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c2_1(a2)))),
% 1.87/1.56 inference(quant_inst,[status(thm)],[])).
% 1.87/1.56 tff(3070,plain,
% 1.87/1.56 ((~![U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp7 | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a2))),
% 1.87/1.56 inference(modus_ponens,[status(thm)],[3069, 3068])).
% 1.87/1.56 tff(3071,plain,
% 1.87/1.56 ($false),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[3070, 169, 2885, 3056, 3064, 2507, 3063])).
% 1.87/1.56 tff(3072,plain,(c1_1(a22) | hskp7 | c0_1(a22) | c3_1(a22) | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.87/1.56 tff(3073,plain,
% 1.87/1.56 (c1_1(a22)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[3072, 2885, 3043, 3042, 332, 343, 2588])).
% 1.87/1.56 tff(3074,plain,
% 1.87/1.56 (~c2_1(a22)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[488, 3041])).
% 1.87/1.56 tff(3075,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~c1_1(a45)) | c3_1(a45) | c0_1(a22) | c2_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c1_1(a45)) | c3_1(a45) | c0_1(a22) | c2_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a45)))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3076,plain,
% 1.87/1.56 ((hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22))) <=> (hskp5 | (~c1_1(a45)) | c3_1(a45) | c0_1(a22) | c2_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a45)))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3077,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~c1_1(a45)) | c3_1(a45) | c0_1(a22) | c2_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a45))))),
% 1.87/1.56 inference(monotonicity,[status(thm)],[3076])).
% 1.87/1.56 tff(3078,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c1_1(a45)) | c3_1(a45) | c0_1(a22) | c2_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a45)))),
% 1.87/1.56 inference(transitivity,[status(thm)],[3077, 3075])).
% 1.87/1.56 tff(3079,plain,
% 1.87/1.56 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22)))),
% 1.87/1.56 inference(quant_inst,[status(thm)],[])).
% 1.87/1.56 tff(3080,plain,
% 1.87/1.56 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c1_1(a45)) | c3_1(a45) | c0_1(a22) | c2_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a45))),
% 1.87/1.56 inference(modus_ponens,[status(thm)],[3079, 3078])).
% 1.87/1.56 tff(3081,plain,
% 1.87/1.56 (hskp5 | (~c1_1(a22))),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[3080, 169, 2777, 2542, 3043, 3074, 1413, 3026])).
% 1.87/1.56 tff(3082,plain,
% 1.87/1.56 (hskp5),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[3081, 3073])).
% 1.87/1.56 tff(3083,plain,
% 1.87/1.56 (~c0_1(a7)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[1419, 3082])).
% 1.87/1.56 tff(3084,plain,
% 1.87/1.56 (c1_1(a7)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[1430, 3082])).
% 1.87/1.56 tff(3085,plain,
% 1.87/1.56 (~c2_1(a7)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[2908, 169, 105, 2705, 3084, 3083, 2699])).
% 1.87/1.56 tff(3086,plain,
% 1.87/1.56 (c3_1(a7)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[1454, 3082])).
% 1.87/1.56 tff(3087,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a31) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3088,plain,
% 1.87/1.56 ((hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a7) | (~c3_1(a7)) | (~c1_1(a7))) <=> (hskp10 | c1_1(a31) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3089,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a31) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.87/1.56 inference(monotonicity,[status(thm)],[3088])).
% 1.87/1.56 tff(3090,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.87/1.56 inference(transitivity,[status(thm)],[3089, 3087])).
% 1.87/1.56 tff(3091,plain,
% 1.87/1.56 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))),
% 1.87/1.56 inference(quant_inst,[status(thm)],[])).
% 1.87/1.56 tff(3092,plain,
% 1.87/1.56 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.87/1.56 inference(modus_ponens,[status(thm)],[3091, 3090])).
% 1.87/1.56 tff(3093,plain,
% 1.87/1.56 (hskp10),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[3092, 169, 332, 3084, 3086, 343, 3083, 1137, 2588])).
% 1.87/1.56 tff(3094,plain,
% 1.87/1.56 (~c3_1(a18)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[1150, 3093])).
% 1.87/1.56 tff(3095,plain,
% 1.87/1.56 (c0_1(a18)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[1172, 3093])).
% 1.87/1.56 tff(3096,plain,
% 1.87/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a18) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | c1_1(a18) | (~c0_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a18) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | c1_1(a18) | (~c0_1(a18)))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3097,plain,
% 1.87/1.56 (((~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a22) | c0_1(a22) | c3_1(a22)) <=> (c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a18) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | c1_1(a18) | (~c0_1(a18)))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3098,plain,
% 1.87/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a18) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | c1_1(a18) | (~c0_1(a18))))),
% 1.87/1.56 inference(monotonicity,[status(thm)],[3097])).
% 1.87/1.56 tff(3099,plain,
% 1.87/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a18) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | c1_1(a18) | (~c0_1(a18)))),
% 1.87/1.56 inference(transitivity,[status(thm)],[3098, 3096])).
% 1.87/1.56 tff(3100,plain,
% 1.87/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)) | c2_1(a22) | c0_1(a22) | c3_1(a22))),
% 1.87/1.56 inference(quant_inst,[status(thm)],[])).
% 1.87/1.56 tff(3101,plain,
% 1.87/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c3_1(a18) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | c1_1(a18) | (~c0_1(a18))),
% 1.87/1.56 inference(modus_ponens,[status(thm)],[3100, 3099])).
% 1.87/1.56 tff(3102,plain,
% 1.87/1.56 (c1_1(a18)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[3101, 169, 3095, 3084, 3086, 3043, 3074, 3042, 3094, 13, 3085])).
% 1.87/1.56 tff(3103,plain,
% 1.87/1.56 (c2_1(a18)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[1161, 3093])).
% 1.87/1.56 tff(3104,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3105,plain,
% 1.87/1.56 ((hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7))) <=> (hskp19 | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3106,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18))))),
% 1.87/1.56 inference(monotonicity,[status(thm)],[3105])).
% 1.87/1.56 tff(3107,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.87/1.56 inference(transitivity,[status(thm)],[3106, 3104])).
% 1.87/1.56 tff(3108,plain,
% 1.87/1.56 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a18)) | (~c0_1(a18)) | (~c1_1(a18)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))),
% 1.87/1.56 inference(quant_inst,[status(thm)],[])).
% 1.87/1.56 tff(3109,plain,
% 1.87/1.56 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a18)) | (~c2_1(a18)) | (~c1_1(a18))),
% 1.87/1.56 inference(modus_ponens,[status(thm)],[3108, 3107])).
% 1.87/1.56 tff(3110,plain,
% 1.87/1.56 ($false),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[3109, 169, 883, 3095, 3103, 3084, 3086, 848, 3085, 3102])).
% 1.87/1.56 tff(3111,plain,(hskp7 | hskp19 | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31)) | hskp9 | hskp8 | (~c1_1(a45)) | c3_1(a45) | (~c2_1(a45))), inference(lemma,lemma(discharge,[]))).
% 1.87/1.56 tff(3112,plain,
% 1.87/1.56 (hskp7),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[3111, 3040, 332, 343, 2588, 2776, 2483, 3016, 2542, 3025])).
% 1.87/1.56 tff(3113,plain,
% 1.87/1.56 (~c2_1(a14)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[525, 3112])).
% 1.87/1.56 tff(3114,plain,
% 1.87/1.56 (c0_1(a14)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[558, 3112])).
% 1.87/1.56 tff(3115,plain,
% 1.87/1.56 (c1_1(a14)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[2687, 169, 655, 654, 3114, 3113, 700])).
% 1.87/1.56 tff(3116,plain,
% 1.87/1.56 (c3_1(a14)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[536, 3112])).
% 1.87/1.56 tff(3117,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~c1_1(a45)) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | (~c0_1(a45)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~c1_1(a45)) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3118,plain,
% 1.87/1.56 ((hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14))) <=> (hskp19 | (~c1_1(a45)) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.87/1.56 inference(rewrite,[status(thm)],[])).
% 1.87/1.56 tff(3119,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~c1_1(a45)) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | (~c0_1(a45)) | (~c2_1(a45))))),
% 1.87/1.56 inference(monotonicity,[status(thm)],[3118])).
% 1.87/1.56 tff(3120,plain,
% 1.87/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~c1_1(a45)) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.87/1.56 inference(transitivity,[status(thm)],[3119, 3117])).
% 1.87/1.56 tff(3121,plain,
% 1.87/1.56 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))),
% 1.87/1.56 inference(quant_inst,[status(thm)],[])).
% 1.87/1.56 tff(3122,plain,
% 1.87/1.56 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~c1_1(a45)) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c3_1(a14)) | (~c0_1(a45)) | (~c2_1(a45))),
% 1.87/1.56 inference(modus_ponens,[status(thm)],[3121, 3120])).
% 1.87/1.56 tff(3123,plain,
% 1.87/1.56 ($false),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[3122, 169, 3040, 3011, 3116, 3016, 3113, 848, 3025, 3115])).
% 1.87/1.56 tff(3124,plain,(c3_1(a45) | hskp14 | hskp2 | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31)) | (~c0_1(a31)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.87/1.56 tff(3125,plain,
% 1.87/1.56 (c3_1(a45)),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[3124, 654, 655, 2485, 2486, 2750, 2487, 2677])).
% 1.87/1.56 tff(3126,plain,
% 1.87/1.56 (~hskp22),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[2539, 3125])).
% 1.87/1.56 tff(3127,plain,
% 1.87/1.56 (~hskp9),
% 1.87/1.56 inference(unit_resolution,[status(thm)],[2775, 2487, 2485, 2750, 655, 654])).
% 1.91/1.56 tff(3128,plain,
% 1.91/1.56 (~c0_1(a5)),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[934, 169, 655, 654, 368, 362, 700])).
% 1.91/1.56 tff(3129,plain,
% 1.91/1.56 ($false),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[384, 169, 344, 331, 332, 343, 368, 362, 342, 3128])).
% 1.91/1.56 tff(3130,plain,((~hskp3) | hskp0 | (~c0_1(a31)) | (~c2_1(a31)) | c1_1(a31) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.91/1.56 tff(3131,plain,
% 1.91/1.56 (~hskp3),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[3130, 2677, 2487, 2485, 2486, 655, 654])).
% 1.91/1.56 tff(3132,plain,
% 1.91/1.56 (~c1_1(a33)),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[2820, 169, 105, 2705, 3030, 3028, 2699])).
% 1.91/1.56 tff(3133,plain,
% 1.91/1.56 ($false),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[923, 169, 792, 654, 3030, 3028, 23, 3132])).
% 1.91/1.56 tff(3134,plain,((~hskp19) | hskp3 | hskp2 | hskp9 | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.91/1.56 tff(3135,plain,
% 1.91/1.56 (~hskp19),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[3134, 3131, 654, 3127, 2483])).
% 1.91/1.56 tff(3136,plain,
% 1.91/1.56 (c0_1(a3)),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[2708, 169, 105, 2483, 2863, 2862, 2699])).
% 1.91/1.56 tff(3137,plain,
% 1.91/1.56 (c1_1(a22)),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[3072, 3042, 3043, 2885, 332, 343, 2588])).
% 1.91/1.56 tff(3138,assumption,(c1_1(a22)), introduced(assumption)).
% 1.91/1.56 tff(3139,assumption,(~c2_1(a22)), introduced(assumption)).
% 1.91/1.56 tff(3140,assumption,(c1_1(a3)), introduced(assumption)).
% 1.91/1.56 tff(3141,plain,
% 1.91/1.56 (c0_1(a3)),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[2708, 169, 105, 2705, 3140, 2415, 2699])).
% 1.91/1.56 tff(3142,plain,
% 1.91/1.56 (hskp10 | hskp6 | (~c0_1(a3))),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[2880, 169, 3140, 2415, 2874])).
% 1.91/1.56 tff(3143,plain,
% 1.91/1.56 (hskp10),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[3142, 1270, 3141])).
% 1.91/1.56 tff(3144,plain,
% 1.91/1.56 (~c3_1(a18)),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[1150, 3143])).
% 1.91/1.56 tff(3145,plain,
% 1.91/1.56 (c2_1(a18)),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[1161, 3143])).
% 1.91/1.56 tff(3146,plain,
% 1.91/1.56 (hskp26),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[2618, 1270, 2587])).
% 1.91/1.56 tff(3147,plain,
% 1.91/1.56 (c3_1(a10)),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[689, 3146])).
% 1.91/1.56 tff(3148,plain,
% 1.91/1.56 (c2_1(a10)),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[678, 3146])).
% 1.91/1.56 tff(3149,plain,
% 1.91/1.56 (c0_1(a10)),
% 1.91/1.56 inference(unit_resolution,[status(thm)],[666, 3146])).
% 1.91/1.56 tff(3150,plain,
% 1.91/1.56 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c3_1(a18) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a18) | (~c2_1(a18)))),
% 1.91/1.56 inference(rewrite,[status(thm)],[])).
% 1.91/1.56 tff(3151,plain,
% 1.91/1.56 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (c3_1(a18) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a18) | (~c2_1(a18)))),
% 1.91/1.56 inference(rewrite,[status(thm)],[])).
% 1.91/1.56 tff(3152,plain,
% 1.91/1.56 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c3_1(a18) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a18) | (~c2_1(a18))))),
% 1.91/1.56 inference(monotonicity,[status(thm)],[3151])).
% 1.91/1.56 tff(3153,plain,
% 1.91/1.56 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a18) | (~c2_1(a18)))),
% 1.91/1.56 inference(transitivity,[status(thm)],[3152, 3150])).
% 1.91/1.56 tff(3154,plain,
% 1.91/1.56 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 1.91/1.57 inference(quant_inst,[status(thm)],[])).
% 1.91/1.57 tff(3155,plain,
% 1.91/1.57 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a18) | (~c2_1(a18))),
% 1.91/1.57 inference(modus_ponens,[status(thm)],[3154, 3153])).
% 1.91/1.57 tff(3156,plain,
% 1.91/1.57 (c1_1(a18)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3155, 169, 3149, 3148, 3147, 3145, 3144, 1580])).
% 1.91/1.57 tff(3157,plain,
% 1.91/1.57 (~c2_1(a7)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[2908, 169, 105, 2705, 1431, 1420, 2699])).
% 1.91/1.57 tff(3158,plain,
% 1.91/1.57 ($false),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[2917, 169, 1270, 3140, 2415, 2414, 1455, 1420, 1298, 3157])).
% 1.91/1.57 tff(3159,plain,((~hskp5) | hskp6 | (~c1_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | hskp9 | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.91/1.57 tff(3160,plain,
% 1.91/1.57 (~hskp5),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3159, 1270, 3140, 2415, 2414, 105, 2705])).
% 1.91/1.57 tff(3161,plain,
% 1.91/1.57 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a22) | c2_1(a22) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a22) | c2_1(a22) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a22)))),
% 1.91/1.57 inference(rewrite,[status(thm)],[])).
% 1.91/1.57 tff(3162,plain,
% 1.91/1.57 ((hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22))) <=> (hskp5 | c0_1(a22) | c2_1(a22) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a22)))),
% 1.91/1.57 inference(rewrite,[status(thm)],[])).
% 1.91/1.57 tff(3163,plain,
% 1.91/1.57 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a22) | c2_1(a22) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a22))))),
% 1.91/1.57 inference(monotonicity,[status(thm)],[3162])).
% 1.91/1.57 tff(3164,plain,
% 1.91/1.57 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a22) | c2_1(a22) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a22)))),
% 1.91/1.57 inference(transitivity,[status(thm)],[3163, 3161])).
% 1.91/1.57 tff(3165,plain,
% 1.91/1.57 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a22) | c2_1(a22) | (~c1_1(a22)))),
% 1.91/1.57 inference(quant_inst,[status(thm)],[])).
% 1.91/1.57 tff(3166,plain,
% 1.91/1.57 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a22) | c2_1(a22) | c3_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c1_1(a18)) | (~c1_1(a22))),
% 1.91/1.57 inference(modus_ponens,[status(thm)],[3165, 3164])).
% 1.91/1.57 tff(3167,plain,
% 1.91/1.57 ($false),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3166, 169, 3160, 3145, 3046, 3139, 3144, 1413, 3138, 3156])).
% 1.91/1.57 tff(3168,plain,(hskp6 | c0_1(a22) | c2_1(a22) | (~c1_1(a22)) | (~c1_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | hskp9 | hskp8 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.91/1.57 tff(3169,plain,
% 1.91/1.57 (hskp6),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3168, 2863, 3139, 3138, 3046, 2862, 2911, 105, 2705, 2587])).
% 1.91/1.57 tff(3170,plain,
% 1.91/1.57 (~c2_1(a8)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[1335, 3169])).
% 1.91/1.57 tff(3171,plain,
% 1.91/1.57 (c0_1(a8)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[1369, 3169])).
% 1.91/1.57 tff(3172,plain,
% 1.91/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a22) | c3_1(a22) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a22) | c3_1(a22) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a22)))),
% 1.91/1.57 inference(rewrite,[status(thm)],[])).
% 1.91/1.57 tff(3173,plain,
% 1.91/1.57 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a22) | c2_1(a22) | (~c1_1(a22)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (c2_1(a22) | c3_1(a22) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a22)))),
% 1.91/1.57 inference(rewrite,[status(thm)],[])).
% 1.91/1.57 tff(3174,plain,
% 1.91/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a22) | c2_1(a22) | (~c1_1(a22)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a22) | c3_1(a22) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a22))))),
% 1.91/1.57 inference(monotonicity,[status(thm)],[3173])).
% 1.91/1.57 tff(3175,plain,
% 1.91/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a22) | c2_1(a22) | (~c1_1(a22)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a22) | c3_1(a22) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a22)))),
% 1.91/1.57 inference(transitivity,[status(thm)],[3174, 3172])).
% 1.91/1.57 tff(3176,plain,
% 1.91/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a22) | c2_1(a22) | (~c1_1(a22)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.91/1.57 inference(quant_inst,[status(thm)],[])).
% 1.91/1.57 tff(3177,plain,
% 1.91/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a22) | c3_1(a22) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a22))),
% 1.91/1.57 inference(modus_ponens,[status(thm)],[3176, 3175])).
% 1.91/1.57 tff(3178,plain,
% 1.91/1.57 (c3_1(a8)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3177, 169, 2862, 2911, 3171, 3139, 3045, 3170, 439, 3138, 2864])).
% 1.91/1.57 tff(3179,plain,
% 1.91/1.57 (c1_1(a8)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[1346, 3169])).
% 1.91/1.57 tff(3180,plain,
% 1.91/1.57 ($false),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[2811, 169, 883, 2863, 2862, 3179, 3170, 848, 2864, 3178])).
% 1.91/1.57 tff(3181,plain,((~hskp24) | hskp19 | c2_1(a22) | c3_1(a22) | (~c1_1(a22)) | c0_1(a22) | hskp9 | hskp8 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.91/1.57 tff(3182,plain,
% 1.91/1.57 ($false),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3181, 3137, 3042, 883, 2861, 3074, 3043, 105, 2705, 2587])).
% 1.91/1.57 tff(3183,plain,(hskp7 | hskp19 | (~hskp24) | hskp9 | hskp8 | hskp22 | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.57 tff(3184,plain,
% 1.91/1.57 (hskp7),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3183, 2861, 883, 105, 2483, 2587, 332, 343, 2588])).
% 1.91/1.57 tff(3185,plain,
% 1.91/1.57 (~c2_1(a14)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[525, 3184])).
% 1.91/1.57 tff(3186,plain,
% 1.91/1.57 (c0_1(a14)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[558, 3184])).
% 1.91/1.57 tff(3187,plain,
% 1.91/1.57 (c1_1(a14)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[2687, 169, 655, 654, 3186, 3185, 700])).
% 1.91/1.57 tff(3188,plain,
% 1.91/1.57 (c3_1(a14)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[536, 3184])).
% 1.91/1.57 tff(3189,plain,
% 1.91/1.57 ($false),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[2985, 169, 883, 2863, 2862, 3188, 3185, 848, 3187, 3136])).
% 1.91/1.57 tff(3190,plain,((~hskp24) | hskp19 | hskp14 | hskp2 | hskp9 | hskp22 | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.57 tff(3191,plain,
% 1.91/1.57 (~hskp24),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3190, 3135, 655, 654, 3127, 3126, 2485, 2486, 2750])).
% 1.91/1.57 tff(3192,plain,
% 1.91/1.57 (hskp23),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[253, 3191, 2677])).
% 1.91/1.57 tff(3193,plain,
% 1.91/1.57 (~c1_1(a53)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[212, 3192])).
% 1.91/1.57 tff(3194,plain,
% 1.91/1.57 (~c0_1(a53)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[218, 3192])).
% 1.91/1.57 tff(3195,plain,
% 1.91/1.57 (~c2_1(a53)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[393, 169, 3131, 654, 3194, 3193, 23])).
% 1.91/1.57 tff(3196,plain,
% 1.91/1.57 ($false),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[353, 169, 2677, 2487, 2485, 3194, 3193, 2486, 342, 3195])).
% 1.91/1.57 tff(3197,plain,(hskp2 | hskp14 | hskp4 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.91/1.57 tff(3198,plain,
% 1.91/1.57 (hskp2),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3197, 2474, 205, 655])).
% 1.91/1.57 tff(3199,plain,
% 1.91/1.57 (c1_1(a4)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[411, 3198])).
% 1.91/1.57 tff(3200,plain,
% 1.91/1.57 (~c3_1(a4)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[400, 3198])).
% 1.91/1.57 tff(3201,plain,
% 1.91/1.57 (~c2_1(a4)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[417, 3198])).
% 1.91/1.57 tff(3202,plain,
% 1.91/1.57 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.91/1.57 inference(rewrite,[status(thm)],[])).
% 1.91/1.57 tff(3203,plain,
% 1.91/1.57 ((hskp15 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c3_1(a15))) <=> (hskp15 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.91/1.57 inference(rewrite,[status(thm)],[])).
% 1.91/1.57 tff(3204,plain,
% 1.91/1.57 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15))))),
% 1.91/1.57 inference(monotonicity,[status(thm)],[3203])).
% 1.91/1.57 tff(3205,plain,
% 1.91/1.57 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.91/1.57 inference(transitivity,[status(thm)],[3204, 3202])).
% 1.91/1.57 tff(3206,plain,
% 1.91/1.57 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)))),
% 1.91/1.57 inference(quant_inst,[status(thm)],[])).
% 1.91/1.57 tff(3207,plain,
% 1.91/1.57 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15))),
% 1.91/1.57 inference(modus_ponens,[status(thm)],[3206, 3205])).
% 1.91/1.57 tff(3208,plain,
% 1.91/1.57 (~c3_1(a15)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3207, 169, 2474, 196, 202, 185, 2497])).
% 1.91/1.57 tff(3209,plain,
% 1.91/1.57 (~hskp23),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[238, 196, 205, 202, 185])).
% 1.91/1.57 tff(3210,plain,
% 1.91/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))),
% 1.91/1.57 inference(rewrite,[status(thm)],[])).
% 1.91/1.57 tff(3211,plain,
% 1.91/1.57 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15))) <=> (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))),
% 1.91/1.57 inference(rewrite,[status(thm)],[])).
% 1.91/1.57 tff(3212,plain,
% 1.91/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15))))),
% 1.91/1.57 inference(monotonicity,[status(thm)],[3211])).
% 1.91/1.57 tff(3213,plain,
% 1.91/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))),
% 1.91/1.57 inference(transitivity,[status(thm)],[3212, 3210])).
% 1.91/1.57 tff(3214,plain,
% 1.91/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))),
% 1.91/1.57 inference(quant_inst,[status(thm)],[])).
% 1.91/1.57 tff(3215,plain,
% 1.91/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15))),
% 1.91/1.57 inference(modus_ponens,[status(thm)],[3214, 3213])).
% 1.91/1.57 tff(3216,plain,
% 1.91/1.57 (~c0_1(a3)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3215, 169, 2862, 2911, 204, 421, 203, 440, 420, 439, 2016])).
% 1.91/1.57 tff(3217,plain,
% 1.91/1.57 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a15) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a15) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))),
% 1.91/1.57 inference(rewrite,[status(thm)],[])).
% 1.91/1.57 tff(3218,plain,
% 1.91/1.57 ((hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp4 | c1_1(a15) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))),
% 1.91/1.57 inference(rewrite,[status(thm)],[])).
% 1.91/1.57 tff(3219,plain,
% 1.91/1.57 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a15) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15))))),
% 1.91/1.57 inference(monotonicity,[status(thm)],[3218])).
% 1.91/1.57 tff(3220,plain,
% 1.91/1.57 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a15) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15)))),
% 1.91/1.57 inference(transitivity,[status(thm)],[3219, 3217])).
% 1.91/1.57 tff(3221,plain,
% 1.91/1.57 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.91/1.57 inference(quant_inst,[status(thm)],[])).
% 1.91/1.57 tff(3222,plain,
% 1.91/1.57 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a15) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a15) | (~c0_1(a15))),
% 1.91/1.57 inference(modus_ponens,[status(thm)],[3221, 3220])).
% 1.91/1.57 tff(3223,plain,
% 1.91/1.57 ($false),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3222, 169, 205, 2863, 2911, 204, 206, 632, 2016, 3216])).
% 1.91/1.57 tff(3224,plain,((~hskp24) | hskp4 | (~c0_1(a15)) | c1_1(a15) | c3_1(a15) | (~c1_1(a4)) | c2_1(a15) | c2_1(a4) | c3_1(a4)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.57 tff(3225,plain,
% 1.91/1.57 (~hskp24),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3224, 196, 205, 202, 3208, 421, 185, 440, 420])).
% 1.91/1.57 tff(3226,plain,
% 1.91/1.57 (hskp0),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[253, 3225, 3209])).
% 1.91/1.57 tff(3227,plain,
% 1.91/1.57 (~c0_1(a1)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[283, 3226])).
% 1.91/1.57 tff(3228,plain,
% 1.91/1.57 (c3_1(a1)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[270, 3226])).
% 1.91/1.57 tff(3229,plain,
% 1.91/1.57 (~c1_1(a1)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[2029, 169, 205, 196, 3228, 202, 3227, 632, 3208])).
% 1.91/1.57 tff(3230,plain,
% 1.91/1.57 ($false),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[290, 169, 205, 196, 3228, 202, 185, 3227, 65, 3229])).
% 1.91/1.57 tff(3231,plain,((~hskp8) | hskp4 | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.91/1.57 tff(3232,plain,
% 1.91/1.57 (~hskp8),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3231, 421, 205, 440, 420, 2474])).
% 1.91/1.57 tff(3233,plain,
% 1.91/1.57 (hskp17),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[306, 3232, 205])).
% 1.91/1.57 tff(3234,plain,
% 1.91/1.57 (c2_1(a31)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[328, 3233])).
% 1.91/1.57 tff(3235,plain,
% 1.91/1.57 (~c1_1(a31)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[71, 3233])).
% 1.91/1.57 tff(3236,plain,
% 1.91/1.57 (c0_1(a31)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[317, 3233])).
% 1.91/1.57 tff(3237,plain,
% 1.91/1.57 (~c2_1(a53)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[466, 219, 421, 3236, 213, 3235, 440, 420, 3234, 230])).
% 1.91/1.57 tff(3238,plain,
% 1.91/1.57 (hskp0 | c2_1(a53)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[353, 169, 3236, 3234, 219, 213, 3235, 342])).
% 1.91/1.57 tff(3239,plain,
% 1.91/1.57 (hskp0),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3238, 3237])).
% 1.91/1.57 tff(3240,plain,
% 1.91/1.57 (~c0_1(a1)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[283, 3239])).
% 1.91/1.57 tff(3241,plain,
% 1.91/1.57 (c3_1(a1)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[270, 3239])).
% 1.91/1.57 tff(3242,plain,
% 1.91/1.57 (~c2_1(a1)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[259, 3239])).
% 1.91/1.57 tff(3243,plain,
% 1.91/1.57 (c3_1(a31)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[2526, 3242, 3234, 3241, 205, 3236, 3235, 3240, 2474])).
% 1.91/1.57 tff(3244,plain,
% 1.91/1.57 ((~c0_1(a4)) | (~c3_1(a31))),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[446, 169, 3236, 3234, 421, 440, 420, 439])).
% 1.91/1.57 tff(3245,plain,
% 1.91/1.57 (~c0_1(a4)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3244, 3243])).
% 1.91/1.57 tff(3246,plain,
% 1.91/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a53) | c1_1(a53) | c2_1(a4) | c3_1(a4) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a4) | c2_1(a53))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a53) | c1_1(a53) | c2_1(a4) | c3_1(a4) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a4) | c2_1(a53))),
% 1.91/1.57 inference(rewrite,[status(thm)],[])).
% 1.91/1.57 tff(3247,plain,
% 1.91/1.57 (((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a4) | c0_1(a4) | c2_1(a4) | c2_1(a53) | c1_1(a53) | c0_1(a53)) <=> (c0_1(a53) | c1_1(a53) | c2_1(a4) | c3_1(a4) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a4) | c2_1(a53))),
% 1.91/1.57 inference(rewrite,[status(thm)],[])).
% 1.91/1.57 tff(3248,plain,
% 1.91/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a4) | c0_1(a4) | c2_1(a4) | c2_1(a53) | c1_1(a53) | c0_1(a53))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a53) | c1_1(a53) | c2_1(a4) | c3_1(a4) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a4) | c2_1(a53)))),
% 1.91/1.57 inference(monotonicity,[status(thm)],[3247])).
% 1.91/1.57 tff(3249,plain,
% 1.91/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a4) | c0_1(a4) | c2_1(a4) | c2_1(a53) | c1_1(a53) | c0_1(a53))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a53) | c1_1(a53) | c2_1(a4) | c3_1(a4) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a4) | c2_1(a53))),
% 1.91/1.57 inference(transitivity,[status(thm)],[3248, 3246])).
% 1.91/1.57 tff(3250,plain,
% 1.91/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a4) | c0_1(a4) | c2_1(a4) | c2_1(a53) | c1_1(a53) | c0_1(a53))),
% 1.91/1.57 inference(quant_inst,[status(thm)],[])).
% 1.91/1.57 tff(3251,plain,
% 1.91/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a53) | c1_1(a53) | c2_1(a4) | c3_1(a4) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a4) | c2_1(a53)),
% 1.91/1.57 inference(modus_ponens,[status(thm)],[3250, 3249])).
% 1.91/1.57 tff(3252,plain,
% 1.91/1.57 ($false),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3251, 169, 3241, 219, 213, 440, 420, 3240, 3242, 55, 3245, 3237])).
% 1.91/1.57 tff(3253,plain,((~hskp23) | c2_1(a4) | c3_1(a4) | (~c1_1(a4)) | hskp4 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.91/1.57 tff(3254,plain,
% 1.91/1.57 (~hskp23),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3253, 3201, 3200, 3199, 205, 2474])).
% 1.91/1.57 tff(3255,plain,
% 1.91/1.57 (~hskp8),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[3231, 3199, 205, 3201, 3200, 2474])).
% 1.91/1.57 tff(3256,plain,
% 1.91/1.57 (hskp17),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[306, 3255, 205])).
% 1.91/1.57 tff(3257,plain,
% 1.91/1.57 (~c1_1(a31)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[71, 3256])).
% 1.91/1.57 tff(3258,plain,
% 1.91/1.57 (c0_1(a31)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[317, 3256])).
% 1.91/1.57 tff(3259,plain,
% 1.91/1.57 (c2_1(a31)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[328, 3256])).
% 1.91/1.57 tff(3260,assumption,(~hskp23), introduced(assumption)).
% 1.91/1.57 tff(3261,plain,
% 1.91/1.57 (hskp0),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[253, 73, 3260])).
% 1.91/1.57 tff(3262,plain,
% 1.91/1.57 (~c2_1(a1)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[259, 3261])).
% 1.91/1.57 tff(3263,plain,
% 1.91/1.57 (c3_1(a1)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[270, 3261])).
% 1.91/1.57 tff(3264,plain,
% 1.91/1.57 (~c1_1(a1)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[277, 169, 73, 105, 3263, 3262, 104])).
% 1.91/1.57 tff(3265,plain,
% 1.91/1.57 (~c0_1(a1)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[283, 3261])).
% 1.91/1.57 tff(3266,plain,
% 1.91/1.57 (~hskp13),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[504, 3264, 3265, 3262, 3263])).
% 1.91/1.57 tff(3267,plain,
% 1.91/1.57 (hskp7),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[519, 3266, 105])).
% 1.91/1.57 tff(3268,plain,
% 1.91/1.57 (~c2_1(a14)),
% 1.91/1.57 inference(unit_resolution,[status(thm)],[525, 3267])).
% 1.91/1.57 tff(3269,plain,
% 1.91/1.57 (c3_1(a14)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[536, 3267])).
% 1.91/1.58 tff(3270,plain,
% 1.91/1.58 (c0_1(a14)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[558, 3267])).
% 1.91/1.58 tff(3271,plain,
% 1.91/1.58 ($false),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[2524, 169, 2474, 3270, 3269, 3263, 3268, 3262, 2497, 3264])).
% 1.91/1.58 tff(3272,plain,(hskp24 | hskp15 | hskp9 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.91/1.58 tff(3273,plain,
% 1.91/1.58 (hskp24),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3272, 105, 2474, 3260])).
% 1.91/1.58 tff(3274,plain,
% 1.91/1.58 (c1_1(a3)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[2391, 3273])).
% 1.91/1.58 tff(3275,plain,
% 1.91/1.58 (c3_1(a3)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[2411, 3273])).
% 1.91/1.58 tff(3276,plain,
% 1.91/1.58 (c2_1(a3)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[2380, 3273])).
% 1.91/1.58 tff(3277,plain,
% 1.91/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)))),
% 1.91/1.58 inference(rewrite,[status(thm)],[])).
% 1.91/1.58 tff(3278,plain,
% 1.91/1.58 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4))) <=> (c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)))),
% 1.91/1.58 inference(rewrite,[status(thm)],[])).
% 1.91/1.58 tff(3279,plain,
% 1.91/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3))))),
% 1.91/1.58 inference(monotonicity,[status(thm)],[3278])).
% 1.91/1.58 tff(3280,plain,
% 1.91/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)))),
% 1.91/1.58 inference(transitivity,[status(thm)],[3279, 3277])).
% 1.91/1.58 tff(3281,plain,
% 1.91/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c0_1(a4)))),
% 1.91/1.58 inference(quant_inst,[status(thm)],[])).
% 1.91/1.58 tff(3282,plain,
% 1.91/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3))),
% 1.91/1.58 inference(modus_ponens,[status(thm)],[3281, 3280])).
% 1.91/1.58 tff(3283,plain,
% 1.91/1.58 (~c0_1(a4)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3282, 169, 2415, 2414, 421, 440, 420, 439, 3141])).
% 1.91/1.58 tff(3284,plain,
% 1.91/1.58 (c3_1(a31)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[2423, 2415, 2414, 332, 343, 3141])).
% 1.91/1.58 tff(3285,plain,
% 1.91/1.58 (~hskp6),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[2831, 2751, 331, 105, 343, 3284, 2705, 2542, 332])).
% 1.91/1.58 tff(3286,plain,
% 1.91/1.58 (hskp10),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3142, 3285, 3141])).
% 1.91/1.58 tff(3287,plain,
% 1.91/1.58 (~c3_1(a18)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[1150, 3286])).
% 1.91/1.58 tff(3288,plain,
% 1.91/1.58 (c2_1(a18)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[1161, 3286])).
% 1.91/1.58 tff(3289,plain,
% 1.91/1.58 (hskp26),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[2618, 3285, 2846])).
% 1.91/1.58 tff(3290,plain,
% 1.91/1.58 (c3_1(a10)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[689, 3289])).
% 1.91/1.58 tff(3291,plain,
% 1.91/1.58 (c2_1(a10)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[678, 3289])).
% 1.91/1.58 tff(3292,plain,
% 1.91/1.58 (c0_1(a10)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[666, 3289])).
% 1.91/1.58 tff(3293,plain,
% 1.91/1.58 (c1_1(a18)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3155, 169, 3292, 3291, 3290, 3288, 3287, 1580])).
% 1.91/1.58 tff(3294,assumption,(~c0_1(a4)), introduced(assumption)).
% 1.91/1.58 tff(3295,plain,
% 1.91/1.58 (~hskp5),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3159, 3285, 3140, 2415, 2414, 105, 2705])).
% 1.91/1.58 tff(3296,plain,
% 1.91/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a18) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a18)) | (~c1_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a18) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.91/1.58 inference(rewrite,[status(thm)],[])).
% 1.91/1.58 tff(3297,plain,
% 1.91/1.58 ((hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4))) <=> (hskp5 | c3_1(a18) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.91/1.58 inference(rewrite,[status(thm)],[])).
% 1.91/1.58 tff(3298,plain,
% 1.91/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a18) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a18)) | (~c1_1(a18))))),
% 1.91/1.58 inference(monotonicity,[status(thm)],[3297])).
% 1.91/1.58 tff(3299,plain,
% 1.91/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a18) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a18)) | (~c1_1(a18)))),
% 1.91/1.58 inference(transitivity,[status(thm)],[3298, 3296])).
% 1.91/1.58 tff(3300,plain,
% 1.91/1.58 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c1_1(a18)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))),
% 1.91/1.58 inference(quant_inst,[status(thm)],[])).
% 1.91/1.58 tff(3301,plain,
% 1.91/1.58 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a18) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a18)) | (~c1_1(a18))),
% 1.91/1.58 inference(modus_ponens,[status(thm)],[3300, 3299])).
% 1.91/1.58 tff(3302,plain,
% 1.91/1.58 ($false),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3301, 169, 3295, 3288, 421, 3287, 440, 1413, 3294, 3293])).
% 1.91/1.58 tff(3303,plain,(c0_1(a45) | (~c1_1(a4)) | c2_1(a4) | c0_1(a4) | (~c1_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | hskp9 | hskp8 | (~c0_1(a31)) | c1_1(a31) | c3_1(a45) | (~c2_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.58 tff(3304,plain,
% 1.91/1.58 (c0_1(a45)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3303, 2542, 440, 3283, 3140, 2415, 2414, 105, 2705, 331, 343, 421, 332])).
% 1.91/1.58 tff(3305,plain,
% 1.91/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a45) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | c2_1(a45))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a45) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | c2_1(a45))),
% 1.91/1.58 inference(rewrite,[status(thm)],[])).
% 1.91/1.58 tff(3306,plain,
% 1.91/1.58 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45))) <=> (c3_1(a45) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | c2_1(a45))),
% 1.91/1.58 inference(rewrite,[status(thm)],[])).
% 1.91/1.58 tff(3307,plain,
% 1.91/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a45) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | c2_1(a45)))),
% 1.91/1.58 inference(monotonicity,[status(thm)],[3306])).
% 1.91/1.58 tff(3308,plain,
% 1.91/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a45) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | c2_1(a45))),
% 1.91/1.58 inference(transitivity,[status(thm)],[3307, 3305])).
% 1.91/1.58 tff(3309,plain,
% 1.91/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a45) | c3_1(a45) | (~c0_1(a45)))),
% 1.91/1.58 inference(quant_inst,[status(thm)],[])).
% 1.91/1.58 tff(3310,plain,
% 1.91/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a45) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | c2_1(a45)),
% 1.91/1.58 inference(modus_ponens,[status(thm)],[3309, 3308])).
% 1.91/1.58 tff(3311,plain,
% 1.91/1.58 ($false),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3310, 169, 2415, 2414, 3012, 421, 2542, 440, 420, 439, 2543, 2413])).
% 1.91/1.58 tff(3312,plain,(c2_1(a45) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a45)) | (~c1_1(a4)) | c3_1(a45) | c2_1(a4) | c3_1(a4) | (~c0_1(a3))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.58 tff(3313,plain,
% 1.91/1.58 (c2_1(a45)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3312, 3304, 2414, 2415, 421, 2542, 440, 420, 3141])).
% 1.91/1.58 tff(3314,plain,
% 1.91/1.58 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a45)))),
% 1.91/1.58 inference(rewrite,[status(thm)],[])).
% 1.91/1.58 tff(3315,plain,
% 1.91/1.58 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45))) <=> (c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a45)))),
% 1.91/1.58 inference(rewrite,[status(thm)],[])).
% 1.91/1.58 tff(3316,plain,
% 1.91/1.58 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a45))))),
% 1.91/1.58 inference(monotonicity,[status(thm)],[3315])).
% 1.91/1.58 tff(3317,plain,
% 1.91/1.58 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a45)))),
% 1.91/1.58 inference(transitivity,[status(thm)],[3316, 3314])).
% 1.91/1.58 tff(3318,plain,
% 1.91/1.58 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a45) | c1_1(a45) | (~c2_1(a45)))),
% 1.91/1.58 inference(quant_inst,[status(thm)],[])).
% 1.91/1.58 tff(3319,plain,
% 1.91/1.58 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a45) | c3_1(a45) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a45))),
% 1.91/1.58 inference(modus_ponens,[status(thm)],[3318, 3317])).
% 1.91/1.58 tff(3320,plain,
% 1.91/1.58 (c1_1(a45) | (~c2_1(a45))),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3319, 169, 2415, 2414, 2542, 1580, 3141])).
% 1.91/1.58 tff(3321,plain,
% 1.91/1.58 (c1_1(a45)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3320, 3313])).
% 1.91/1.58 tff(3322,plain,
% 1.91/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~c1_1(a45)) | c3_1(a45) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c1_1(a45)) | c3_1(a45) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a45)))),
% 1.91/1.58 inference(rewrite,[status(thm)],[])).
% 1.91/1.58 tff(3323,plain,
% 1.91/1.58 ((hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4))) <=> (hskp5 | (~c1_1(a45)) | c3_1(a45) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a45)))),
% 1.91/1.58 inference(rewrite,[status(thm)],[])).
% 1.91/1.58 tff(3324,plain,
% 1.91/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~c1_1(a45)) | c3_1(a45) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a45))))),
% 1.91/1.58 inference(monotonicity,[status(thm)],[3323])).
% 1.91/1.58 tff(3325,plain,
% 1.91/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c1_1(a45)) | c3_1(a45) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a45)))),
% 1.91/1.58 inference(transitivity,[status(thm)],[3324, 3322])).
% 1.91/1.58 tff(3326,plain,
% 1.91/1.58 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a45) | (~c2_1(a45)) | (~c1_1(a45)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))),
% 1.91/1.58 inference(quant_inst,[status(thm)],[])).
% 1.91/1.58 tff(3327,plain,
% 1.91/1.58 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c1_1(a45)) | c3_1(a45) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a45))),
% 1.91/1.58 inference(modus_ponens,[status(thm)],[3326, 3325])).
% 1.91/1.58 tff(3328,plain,
% 1.91/1.58 (hskp5 | (~c1_1(a45)) | (~c2_1(a45))),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3327, 169, 421, 2542, 440, 1413, 3283])).
% 1.91/1.58 tff(3329,plain,
% 1.91/1.58 (hskp5),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3328, 3313, 3321])).
% 1.91/1.58 tff(3330,plain,
% 1.91/1.58 (hskp6),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[3159, 3329, 3140, 2415, 2414, 105, 2705])).
% 1.91/1.58 tff(3331,plain,
% 1.91/1.58 (~c2_1(a8)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[1335, 3330])).
% 1.91/1.58 tff(3332,plain,
% 1.91/1.58 (c1_1(a8)),
% 1.91/1.58 inference(unit_resolution,[status(thm)],[1346, 3330])).
% 1.91/1.59 tff(3333,plain,
% 1.91/1.59 (~hskp11),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[2667, 3284, 332, 331])).
% 1.91/1.59 tff(3334,plain,
% 1.91/1.59 (~hskp19),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[3039, 3313, 3304, 2542, 3333])).
% 1.91/1.59 tff(3335,plain,
% 1.91/1.59 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~c1_1(a45)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c0_1(a45)) | (~c2_1(a45)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~c1_1(a45)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.91/1.59 inference(rewrite,[status(thm)],[])).
% 1.91/1.59 tff(3336,plain,
% 1.91/1.59 ((hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8))) <=> (hskp19 | (~c1_1(a45)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.91/1.59 inference(rewrite,[status(thm)],[])).
% 1.91/1.59 tff(3337,plain,
% 1.91/1.59 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~c1_1(a45)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c0_1(a45)) | (~c2_1(a45))))),
% 1.91/1.59 inference(monotonicity,[status(thm)],[3336])).
% 1.91/1.59 tff(3338,plain,
% 1.91/1.59 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~c1_1(a45)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c0_1(a45)) | (~c2_1(a45)))),
% 1.91/1.59 inference(transitivity,[status(thm)],[3337, 3335])).
% 1.91/1.59 tff(3339,plain,
% 1.91/1.59 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a45)) | (~c0_1(a45)) | (~c1_1(a45)) | c2_1(a8) | (~c3_1(a8)) | (~c1_1(a8)))),
% 1.91/1.59 inference(quant_inst,[status(thm)],[])).
% 1.91/1.59 tff(3340,plain,
% 1.91/1.59 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~c1_1(a45)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c0_1(a45)) | (~c2_1(a45))),
% 1.91/1.59 inference(modus_ponens,[status(thm)],[3339, 3338])).
% 1.91/1.59 tff(3341,plain,
% 1.91/1.59 (~c3_1(a8)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[3340, 169, 3334, 3304, 3332, 3321, 3331, 848, 3313])).
% 1.91/1.59 tff(3342,plain,
% 1.91/1.59 (c0_1(a8)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[1369, 3330])).
% 1.91/1.59 tff(3343,plain,
% 1.91/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a8) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)))),
% 1.91/1.59 inference(rewrite,[status(thm)],[])).
% 1.91/1.59 tff(3344,plain,
% 1.91/1.59 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (c2_1(a8) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)))),
% 1.91/1.59 inference(rewrite,[status(thm)],[])).
% 1.91/1.59 tff(3345,plain,
% 1.91/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a8) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8))))),
% 1.91/1.59 inference(monotonicity,[status(thm)],[3344])).
% 1.91/1.59 tff(3346,plain,
% 1.91/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)))),
% 1.91/1.59 inference(transitivity,[status(thm)],[3345, 3343])).
% 1.91/1.59 tff(3347,plain,
% 1.91/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.91/1.59 inference(quant_inst,[status(thm)],[])).
% 1.91/1.59 tff(3348,plain,
% 1.91/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8))),
% 1.91/1.59 inference(modus_ponens,[status(thm)],[3347, 3346])).
% 1.91/1.59 tff(3349,plain,
% 1.91/1.59 ($false),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[3348, 169, 2415, 2414, 3342, 421, 3331, 440, 420, 439, 3141, 3341])).
% 1.91/1.59 tff(3350,plain,(c3_1(a45) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | (~c1_1(a3)) | hskp9 | hskp8 | (~c0_1(a31)) | c1_1(a31) | (~c2_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.59 tff(3351,plain,
% 1.91/1.59 (c3_1(a45)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[3350, 3276, 3275, 421, 440, 420, 3274, 105, 2705, 331, 343, 332])).
% 1.91/1.59 tff(3352,plain,
% 1.91/1.59 (~hskp22),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[2539, 3351])).
% 1.91/1.59 tff(3353,plain,
% 1.91/1.59 (c3_1(a31)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[2423, 2862, 2911, 332, 343, 2864])).
% 1.91/1.59 tff(3354,plain,
% 1.91/1.59 (hskp7),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[3183, 883, 2861, 105, 2705, 3353, 332, 343, 2587])).
% 1.91/1.59 tff(3355,plain,
% 1.91/1.59 (~c2_1(a14)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[525, 3354])).
% 1.91/1.59 tff(3356,plain,
% 1.91/1.59 (c3_1(a14)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[536, 3354])).
% 1.91/1.59 tff(3357,plain,
% 1.91/1.59 (~c1_1(a14)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[2985, 169, 883, 2863, 2862, 3356, 3355, 848, 2864])).
% 1.91/1.59 tff(3358,plain,
% 1.91/1.59 (c0_1(a14)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[558, 3354])).
% 1.91/1.59 tff(3359,plain,
% 1.91/1.59 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | (~c0_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.91/1.59 inference(rewrite,[status(thm)],[])).
% 1.91/1.59 tff(3360,plain,
% 1.91/1.59 ((hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a14) | c2_1(a14) | (~c3_1(a14))) <=> (hskp15 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.91/1.59 inference(rewrite,[status(thm)],[])).
% 1.91/1.59 tff(3361,plain,
% 1.91/1.59 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a14) | c2_1(a14) | (~c3_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | (~c0_1(a14))))),
% 1.91/1.59 inference(monotonicity,[status(thm)],[3360])).
% 1.91/1.59 tff(3362,plain,
% 1.91/1.59 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a14) | c2_1(a14) | (~c3_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | (~c0_1(a14)))),
% 1.91/1.59 inference(transitivity,[status(thm)],[3361, 3359])).
% 1.91/1.59 tff(3363,plain,
% 1.91/1.59 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)) | c1_1(a14) | c2_1(a14) | (~c3_1(a14)))),
% 1.91/1.59 inference(quant_inst,[status(thm)],[])).
% 1.91/1.59 tff(3364,plain,
% 1.91/1.59 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp15 | c2_1(a14) | (~ndr1_0) | c1_1(a14) | (~c3_1(a14)) | (~c0_1(a14))),
% 1.91/1.59 inference(modus_ponens,[status(thm)],[3363, 3362])).
% 1.91/1.59 tff(3365,plain,
% 1.91/1.59 ($false),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[3364, 169, 2474, 3358, 3356, 3355, 2497, 3357])).
% 1.91/1.59 tff(3366,plain,(hskp19 | hskp15 | (~hskp24) | hskp9 | hskp8 | (~c2_1(a31)) | c1_1(a31) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.91/1.59 tff(3367,plain,
% 1.91/1.59 (hskp19),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[3366, 3273, 2474, 105, 2705, 332, 343, 3352])).
% 1.91/1.59 tff(3368,plain,
% 1.91/1.59 (~c0_1(a33)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[897, 3367])).
% 1.91/1.59 tff(3369,plain,
% 1.91/1.59 (c2_1(a33)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[908, 3367])).
% 1.91/1.59 tff(3370,plain,
% 1.91/1.59 (~c1_1(a33)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[2820, 169, 105, 2705, 3369, 3368, 2699])).
% 1.91/1.59 tff(3371,plain,
% 1.91/1.59 (c0_1(a3)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[2708, 169, 105, 2705, 3274, 3276, 2699])).
% 1.91/1.59 tff(3372,plain,
% 1.91/1.59 (~c0_1(a4)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[3282, 169, 3276, 3275, 421, 440, 420, 439, 3371])).
% 1.91/1.59 tff(3373,plain,
% 1.91/1.59 (c3_1(a31)),
% 1.91/1.59 inference(unit_resolution,[status(thm)],[2423, 3276, 3275, 332, 343, 3371])).
% 1.91/1.59 tff(3374,plain,
% 1.91/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a33) | c1_1(a31) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a33) | c1_1(a31) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.91/1.59 inference(rewrite,[status(thm)],[])).
% 1.91/1.59 tff(3375,plain,
% 1.91/1.59 (((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33))) <=> (c0_1(a33) | c1_1(a31) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.91/1.59 inference(rewrite,[status(thm)],[])).
% 1.91/1.59 tff(3376,plain,
% 1.91/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a33) | c1_1(a31) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)))),
% 1.91/1.59 inference(monotonicity,[status(thm)],[3375])).
% 1.91/1.59 tff(3377,plain,
% 1.91/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a33) | c1_1(a31) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.91/1.60 inference(transitivity,[status(thm)],[3376, 3374])).
% 1.91/1.60 tff(3378,plain,
% 1.91/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c0_1(a4) | (~c1_1(a4)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))),
% 1.91/1.60 inference(quant_inst,[status(thm)],[])).
% 1.91/1.60 tff(3379,plain,
% 1.91/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a33) | c1_1(a31) | c3_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3378, 3377])).
% 1.91/1.60 tff(3380,plain,
% 1.91/1.60 ($false),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3379, 169, 3369, 332, 421, 3368, 343, 420, 83, 3373, 3372, 3370])).
% 1.91/1.60 tff(3381,plain,(hskp9 | (~c2_1(a31)) | (~c1_1(a4)) | c1_1(a31) | c3_1(a4) | hskp8 | hskp15 | c2_1(a4) | (~c0_1(a31)) | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.91/1.60 tff(3382,plain,
% 1.91/1.60 (hskp9),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3381, 3259, 3199, 3257, 3200, 3255, 2474, 3201, 3258, 3254])).
% 1.91/1.60 tff(3383,plain,
% 1.91/1.60 (~c3_1(a16)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[573, 3382])).
% 1.91/1.60 tff(3384,plain,
% 1.91/1.60 (~c2_1(a16)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[579, 3382])).
% 1.91/1.60 tff(3385,plain,
% 1.91/1.60 (c0_1(a16)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[590, 3382])).
% 1.91/1.60 tff(3386,plain,
% 1.91/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3387,plain,
% 1.91/1.60 (((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3388,plain,
% 1.91/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.91/1.60 inference(monotonicity,[status(thm)],[3387])).
% 1.91/1.60 tff(3389,plain,
% 1.91/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.91/1.60 inference(transitivity,[status(thm)],[3388, 3386])).
% 1.91/1.60 tff(3390,plain,
% 1.91/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a31)) | (~c0_1(a31)) | (~c3_1(a31)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.91/1.60 inference(quant_inst,[status(thm)],[])).
% 1.91/1.60 tff(3391,plain,
% 1.91/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3390, 3389])).
% 1.91/1.60 tff(3392,plain,
% 1.91/1.60 (~c3_1(a31)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3391, 169, 3258, 3259, 3385, 3199, 3384, 3383, 3201, 3200, 439])).
% 1.91/1.60 tff(3393,plain,
% 1.91/1.60 ($false),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[2526, 471, 474, 332, 2279, 205, 331, 343, 472, 2474])).
% 1.91/1.60 tff(3394,plain,((~hskp0) | (~c2_1(a31)) | c3_1(a31) | hskp4 | (~c0_1(a31)) | c1_1(a31) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.91/1.60 tff(3395,plain,
% 1.91/1.60 (~hskp0),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3394, 3259, 3392, 205, 3258, 3257, 2474])).
% 1.91/1.60 tff(3396,plain,
% 1.91/1.60 (hskp24),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[253, 3395, 3254])).
% 1.91/1.60 tff(3397,plain,
% 1.91/1.60 (c2_1(a3)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[2380, 3396])).
% 1.91/1.60 tff(3398,plain,
% 1.91/1.60 (c3_1(a3)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[2411, 3396])).
% 1.91/1.60 tff(3399,plain,
% 1.91/1.60 (~c0_1(a3)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[2423, 3398, 3392, 3259, 3257, 3397])).
% 1.91/1.60 tff(3400,plain,
% 1.91/1.60 (c1_1(a3)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[2391, 3396])).
% 1.91/1.60 tff(3401,plain,
% 1.91/1.60 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a31) | (~c0_1(a31)))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3402,plain,
% 1.91/1.60 ((hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp4 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a31) | (~c0_1(a31)))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3403,plain,
% 1.91/1.60 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a31) | (~c0_1(a31))))),
% 1.91/1.60 inference(monotonicity,[status(thm)],[3402])).
% 1.91/1.60 tff(3404,plain,
% 1.91/1.60 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a31) | (~c0_1(a31)))),
% 1.91/1.60 inference(transitivity,[status(thm)],[3403, 3401])).
% 1.91/1.60 tff(3405,plain,
% 1.91/1.60 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.91/1.60 inference(quant_inst,[status(thm)],[])).
% 1.91/1.60 tff(3406,plain,
% 1.91/1.60 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c3_1(a31) | (~c0_1(a31))),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3405, 3404])).
% 1.91/1.60 tff(3407,plain,
% 1.91/1.60 ($false),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3406, 169, 205, 3400, 3398, 3258, 3257, 632, 3392, 3399])).
% 1.91/1.60 tff(3408,plain,(hskp15 | hskp4 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.91/1.60 tff(3409,plain,
% 1.91/1.60 (hskp15),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3408, 205, 655])).
% 1.91/1.60 tff(3410,plain,
% 1.91/1.60 (((~hskp15) | (~c3_1(a25))) <=> ((~hskp15) | (~c3_1(a25)))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3411,plain,
% 1.91/1.60 (((~c3_1(a25)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a25)))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3412,axiom,((~c3_1(a25)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 1.91/1.60 tff(3413,plain,
% 1.91/1.60 ((~hskp15) | (~c3_1(a25))),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3412, 3411])).
% 1.91/1.60 tff(3414,plain,
% 1.91/1.60 ((~hskp15) | (~c3_1(a25))),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3413, 3410])).
% 1.91/1.60 tff(3415,plain,
% 1.91/1.60 (~c3_1(a25)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3414, 3409])).
% 1.91/1.60 tff(3416,plain,
% 1.91/1.60 (hskp8),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[306, 643, 205])).
% 1.91/1.60 tff(3417,plain,
% 1.91/1.60 (hskp2),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[2482, 3416, 655])).
% 1.91/1.60 tff(3418,plain,
% 1.91/1.60 (~c3_1(a4)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[400, 3417])).
% 1.91/1.60 tff(3419,plain,
% 1.91/1.60 (~c2_1(a4)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[417, 3417])).
% 1.91/1.60 tff(3420,plain,
% 1.91/1.60 (~c2_1(a15)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[184, 3416])).
% 1.91/1.60 tff(3421,plain,
% 1.91/1.60 (~c1_1(a15)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[201, 3416])).
% 1.91/1.60 tff(3422,plain,
% 1.91/1.60 (c0_1(a15)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[195, 3416])).
% 1.91/1.60 tff(3423,plain,
% 1.91/1.60 (((~hskp15) | c0_1(a25)) <=> ((~hskp15) | c0_1(a25))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3424,axiom,((~hskp15) | c0_1(a25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.91/1.60 tff(3425,plain,
% 1.91/1.60 ((~hskp15) | c0_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3424, 3423])).
% 1.91/1.60 tff(3426,plain,
% 1.91/1.60 ((~hskp15) | c0_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3425, 3423])).
% 1.91/1.60 tff(3427,plain,
% 1.91/1.60 ((~hskp15) | c0_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3426, 3423])).
% 1.91/1.60 tff(3428,plain,
% 1.91/1.60 ((~hskp15) | c0_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3427, 3423])).
% 1.91/1.60 tff(3429,plain,
% 1.91/1.60 ((~hskp15) | c0_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3428, 3423])).
% 1.91/1.60 tff(3430,plain,
% 1.91/1.60 ((~hskp15) | c0_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3429, 3423])).
% 1.91/1.60 tff(3431,plain,
% 1.91/1.60 ((~hskp15) | c0_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3430, 3423])).
% 1.91/1.60 tff(3432,plain,
% 1.91/1.60 ((~hskp15) | c0_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3431, 3423])).
% 1.91/1.60 tff(3433,plain,
% 1.91/1.60 (c0_1(a25)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3432, 3409])).
% 1.91/1.60 tff(3434,plain,
% 1.91/1.60 (((~hskp15) | c1_1(a25)) <=> ((~hskp15) | c1_1(a25))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3435,axiom,((~hskp15) | c1_1(a25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.91/1.60 tff(3436,plain,
% 1.91/1.60 ((~hskp15) | c1_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3435, 3434])).
% 1.91/1.60 tff(3437,plain,
% 1.91/1.60 ((~hskp15) | c1_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3436, 3434])).
% 1.91/1.60 tff(3438,plain,
% 1.91/1.60 ((~hskp15) | c1_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3437, 3434])).
% 1.91/1.60 tff(3439,plain,
% 1.91/1.60 ((~hskp15) | c1_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3438, 3434])).
% 1.91/1.60 tff(3440,plain,
% 1.91/1.60 ((~hskp15) | c1_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3439, 3434])).
% 1.91/1.60 tff(3441,plain,
% 1.91/1.60 ((~hskp15) | c1_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3440, 3434])).
% 1.91/1.60 tff(3442,plain,
% 1.91/1.60 ((~hskp15) | c1_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3441, 3434])).
% 1.91/1.60 tff(3443,plain,
% 1.91/1.60 ((~hskp15) | c1_1(a25)),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3442, 3434])).
% 1.91/1.60 tff(3444,plain,
% 1.91/1.60 (c1_1(a25)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3443, 3409])).
% 1.91/1.60 tff(3445,plain,
% 1.91/1.60 (c1_1(a4)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[411, 3417])).
% 1.91/1.60 tff(3446,plain,
% 1.91/1.60 (c3_1(a15)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3224, 2861, 3422, 3421, 420, 421, 3420, 440, 205])).
% 1.91/1.60 tff(3447,plain,
% 1.91/1.60 (hskp18 | (~c3_1(a15))),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[2045, 169, 643, 3422, 3420, 741])).
% 1.91/1.60 tff(3448,plain,
% 1.91/1.60 (hskp18),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3447, 3446])).
% 1.91/1.60 tff(3449,plain,
% 1.91/1.60 (~c3_1(a32)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[969, 3448])).
% 1.91/1.60 tff(3450,plain,
% 1.91/1.60 (~c1_1(a32)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[963, 3448])).
% 1.91/1.60 tff(3451,plain,
% 1.91/1.60 (~c0_1(a32)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[1385, 3448])).
% 1.91/1.60 tff(3452,plain,
% 1.91/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3453,plain,
% 1.91/1.60 (((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3454,plain,
% 1.91/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))))),
% 1.91/1.60 inference(monotonicity,[status(thm)],[3453])).
% 1.91/1.60 tff(3455,plain,
% 1.91/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.91/1.60 inference(transitivity,[status(thm)],[3454, 3452])).
% 1.91/1.60 tff(3456,plain,
% 1.91/1.60 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 1.91/1.60 inference(quant_inst,[status(thm)],[])).
% 1.91/1.60 tff(3457,plain,
% 1.91/1.60 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3456, 3455])).
% 1.91/1.60 tff(3458,plain,
% 1.91/1.60 (c0_1(a3)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3457, 169, 2863, 2862, 3451, 3450, 3449, 45])).
% 1.91/1.60 tff(3459,plain,
% 1.91/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a32) | c3_1(a32) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c2_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a32) | c3_1(a32) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c2_1(a32)))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3460,plain,
% 1.91/1.60 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a32) | c3_1(a32) | (~c2_1(a32))) <=> (c0_1(a32) | c3_1(a32) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c2_1(a32)))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3461,plain,
% 1.91/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a32) | c3_1(a32) | (~c2_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a32) | c3_1(a32) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c2_1(a32))))),
% 1.91/1.60 inference(monotonicity,[status(thm)],[3460])).
% 1.91/1.60 tff(3462,plain,
% 1.91/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a32) | c3_1(a32) | (~c2_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a32) | c3_1(a32) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c2_1(a32)))),
% 1.91/1.60 inference(transitivity,[status(thm)],[3461, 3459])).
% 1.91/1.60 tff(3463,plain,
% 1.91/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a32) | c3_1(a32) | (~c2_1(a32)))),
% 1.91/1.60 inference(quant_inst,[status(thm)],[])).
% 1.91/1.60 tff(3464,plain,
% 1.91/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a32) | c3_1(a32) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c2_1(a32))),
% 1.91/1.60 inference(modus_ponens,[status(thm)],[3463, 3462])).
% 1.91/1.60 tff(3465,plain,
% 1.91/1.60 ((~c0_1(a3)) | (~c2_1(a32))),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3464, 169, 2863, 2862, 421, 3451, 3449, 440, 420, 34])).
% 1.91/1.60 tff(3466,plain,
% 1.91/1.60 (~c2_1(a32)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3465, 3458])).
% 1.91/1.60 tff(3467,plain,
% 1.91/1.60 (~hskp5),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[1463, 3451, 3450, 3449, 3466])).
% 1.91/1.60 tff(3468,plain,
% 1.91/1.60 ((~c0_1(a4)) | (~c0_1(a3))),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3282, 169, 2862, 2911, 421, 440, 420, 439])).
% 1.91/1.60 tff(3469,plain,
% 1.91/1.60 (~c0_1(a4)),
% 1.91/1.60 inference(unit_resolution,[status(thm)],[3468, 3458])).
% 1.91/1.60 tff(3470,assumption,(~c3_1(a25)), introduced(assumption)).
% 1.91/1.60 tff(3471,assumption,(c1_1(a25)), introduced(assumption)).
% 1.91/1.60 tff(3472,plain,
% 1.91/1.60 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a25) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a25)) | (~c2_1(a25)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a25) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3473,plain,
% 1.91/1.60 ((hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4))) <=> (hskp5 | c3_1(a25) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.91/1.60 inference(rewrite,[status(thm)],[])).
% 1.91/1.60 tff(3474,plain,
% 1.91/1.60 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a25) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a25)) | (~c2_1(a25))))),
% 1.91/1.60 inference(monotonicity,[status(thm)],[3473])).
% 1.91/1.60 tff(3475,plain,
% 1.91/1.60 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a25) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.91/1.60 inference(transitivity,[status(thm)],[3474, 3472])).
% 1.91/1.60 tff(3476,plain,
% 1.91/1.60 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))),
% 1.91/1.60 inference(quant_inst,[status(thm)],[])).
% 1.91/1.60 tff(3477,plain,
% 1.91/1.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a25) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a25)) | (~c2_1(a25))),
% 1.91/1.61 inference(modus_ponens,[status(thm)],[3476, 3475])).
% 1.91/1.61 tff(3478,plain,
% 1.91/1.61 (hskp5 | (~c2_1(a25))),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3477, 169, 3471, 421, 3470, 440, 1413, 3469])).
% 1.91/1.61 tff(3479,plain,
% 1.91/1.61 (~c2_1(a25)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3478, 3467])).
% 1.91/1.61 tff(3480,assumption,(c0_1(a25)), introduced(assumption)).
% 1.91/1.61 tff(3481,plain,
% 1.91/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a25) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a25) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3482,plain,
% 1.91/1.61 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25))) <=> (c3_1(a25) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3483,plain,
% 1.91/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a25) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25)))),
% 1.91/1.61 inference(monotonicity,[status(thm)],[3482])).
% 1.91/1.61 tff(3484,plain,
% 1.91/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a25) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))),
% 1.91/1.61 inference(transitivity,[status(thm)],[3483, 3481])).
% 1.91/1.61 tff(3485,plain,
% 1.91/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)))),
% 1.91/1.61 inference(quant_inst,[status(thm)],[])).
% 1.91/1.61 tff(3486,plain,
% 1.91/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a25) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25)),
% 1.91/1.61 inference(modus_ponens,[status(thm)],[3485, 3484])).
% 1.91/1.61 tff(3487,plain,
% 1.91/1.61 ($false),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3486, 169, 2862, 2911, 3480, 3471, 3470, 439, 3458, 3479])).
% 1.91/1.61 tff(3488,plain,((~hskp24) | (~c0_1(a25)) | (~c1_1(a25)) | c3_1(a25) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4) | hskp17 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.91/1.61 tff(3489,plain,
% 1.91/1.61 (~hskp24),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3488, 3445, 3444, 3415, 3433, 3419, 3418, 643, 205])).
% 1.91/1.61 tff(3490,plain,
% 1.91/1.61 (hskp9),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[292, 3489, 3422, 3421, 3420, 205])).
% 1.91/1.61 tff(3491,plain,
% 1.91/1.61 (~c3_1(a16)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[573, 3490])).
% 1.91/1.61 tff(3492,plain,
% 1.91/1.61 (~c2_1(a16)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[579, 3490])).
% 1.91/1.61 tff(3493,plain,
% 1.91/1.61 (c0_1(a16)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[590, 3490])).
% 1.91/1.61 tff(3494,plain,
% 1.91/1.61 (~hskp26),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[1668, 3493, 3445, 3492, 3491, 3419, 3418])).
% 1.91/1.61 tff(3495,plain,
% 1.91/1.61 (hskp26 | hskp16),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[597, 169, 3493, 3492, 3491, 94])).
% 1.91/1.61 tff(3496,plain,
% 1.91/1.61 (hskp16),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3495, 3494])).
% 1.91/1.61 tff(3497,plain,
% 1.91/1.61 (c1_1(a30)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[609, 3496])).
% 1.91/1.61 tff(3498,plain,
% 1.91/1.61 (~hskp23),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[238, 3421, 205, 3422, 3420])).
% 1.91/1.61 tff(3499,plain,
% 1.91/1.61 (hskp0),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[253, 3489, 3498])).
% 1.91/1.61 tff(3500,plain,
% 1.91/1.61 (~c2_1(a1)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[259, 3499])).
% 1.91/1.61 tff(3501,plain,
% 1.91/1.61 (~c0_1(a1)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[283, 3499])).
% 1.91/1.61 tff(3502,plain,
% 1.91/1.61 (~c2_1(a30)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[615, 3496])).
% 1.91/1.61 tff(3503,plain,
% 1.91/1.61 (~c0_1(a30)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[621, 3496])).
% 1.91/1.61 tff(3504,plain,
% 1.91/1.61 (c3_1(a1)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[270, 3499])).
% 1.91/1.61 tff(3505,plain,
% 1.91/1.61 (c3_1(a15)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[2038, 3504, 3503, 3502, 3501, 3500, 205, 3422, 3421, 3497])).
% 1.91/1.61 tff(3506,plain,
% 1.91/1.61 (hskp18),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3447, 3505])).
% 1.91/1.61 tff(3507,plain,
% 1.91/1.61 (~c3_1(a32)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[969, 3506])).
% 1.91/1.61 tff(3508,plain,
% 1.91/1.61 (~c1_1(a32)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[963, 3506])).
% 1.91/1.61 tff(3509,plain,
% 1.91/1.61 (~c0_1(a32)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[1385, 3506])).
% 1.91/1.61 tff(3510,plain,
% 1.91/1.61 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a25) | (~ndr1_0) | (~c1_1(a25)) | (~c0_1(a25)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a25) | (~ndr1_0) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3511,plain,
% 1.91/1.61 ((hskp24 | (~ndr1_0) | c3_1(a25) | (~c0_1(a25)) | (~c1_1(a25)) | c3_1(a32) | c1_1(a32) | c0_1(a32)) <=> (hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a25) | (~ndr1_0) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3512,plain,
% 1.91/1.61 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a25) | (~c0_1(a25)) | (~c1_1(a25)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a25) | (~ndr1_0) | (~c1_1(a25)) | (~c0_1(a25))))),
% 1.91/1.61 inference(monotonicity,[status(thm)],[3511])).
% 1.91/1.61 tff(3513,plain,
% 1.91/1.61 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a25) | (~c0_1(a25)) | (~c1_1(a25)) | c3_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a25) | (~ndr1_0) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.91/1.61 inference(transitivity,[status(thm)],[3512, 3510])).
% 1.91/1.61 tff(3514,plain,
% 1.91/1.61 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp24 | (~ndr1_0) | c3_1(a25) | (~c0_1(a25)) | (~c1_1(a25)) | c3_1(a32) | c1_1(a32) | c0_1(a32))),
% 1.91/1.61 inference(quant_inst,[status(thm)],[])).
% 1.91/1.61 tff(3515,plain,
% 1.91/1.61 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp24 | c0_1(a32) | c1_1(a32) | c3_1(a32) | c3_1(a25) | (~ndr1_0) | (~c1_1(a25)) | (~c0_1(a25))),
% 1.91/1.61 inference(modus_ponens,[status(thm)],[3514, 3513])).
% 1.91/1.61 tff(3516,plain,
% 1.91/1.61 ($false),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3515, 169, 3489, 3433, 3444, 3509, 3508, 3507, 3415, 982])).
% 1.91/1.61 tff(3517,plain,(hskp17 | hskp4 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.91/1.61 tff(3518,plain,
% 1.91/1.61 (hskp14),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3517, 205, 2470])).
% 1.91/1.61 tff(3519,plain,
% 1.91/1.61 (~c1_1(a24)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[1024, 3518])).
% 1.91/1.61 tff(3520,plain,
% 1.91/1.61 (~c0_1(a24)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[1030, 3518])).
% 1.91/1.61 tff(3521,plain,
% 1.91/1.61 (c0_1(a15)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[195, 2471])).
% 1.91/1.61 tff(3522,plain,
% 1.91/1.61 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a24)))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3523,plain,
% 1.91/1.61 ((hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24))) <=> (hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a24)))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3524,plain,
% 1.91/1.61 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a24))))),
% 1.91/1.61 inference(monotonicity,[status(thm)],[3523])).
% 1.91/1.61 tff(3525,plain,
% 1.91/1.61 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a24)))),
% 1.91/1.61 inference(transitivity,[status(thm)],[3524, 3522])).
% 1.91/1.61 tff(3526,plain,
% 1.91/1.61 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))),
% 1.91/1.61 inference(quant_inst,[status(thm)],[])).
% 1.91/1.61 tff(3527,plain,
% 1.91/1.61 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a24))),
% 1.91/1.61 inference(modus_ponens,[status(thm)],[3526, 3525])).
% 1.91/1.61 tff(3528,plain,
% 1.91/1.61 (~c3_1(a24)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3527, 169, 205, 3521, 3520, 3519, 2473, 2472, 65])).
% 1.91/1.61 tff(3529,plain,
% 1.91/1.61 (c2_1(a24)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[1041, 3518])).
% 1.91/1.61 tff(3530,plain,
% 1.91/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a24)) | c3_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a24)) | c3_1(a24))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3531,plain,
% 1.91/1.61 (((~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16)) <=> (c0_1(a16) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a24)) | c3_1(a24))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3532,plain,
% 1.91/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a24)) | c3_1(a24)))),
% 1.91/1.61 inference(monotonicity,[status(thm)],[3531])).
% 1.91/1.61 tff(3533,plain,
% 1.91/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a24)) | c3_1(a24))),
% 1.91/1.61 inference(transitivity,[status(thm)],[3532, 3530])).
% 1.91/1.61 tff(3534,plain,
% 1.91/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a24) | (~c2_1(a24)) | c0_1(a24) | c3_1(a16) | c1_1(a16) | c2_1(a16) | c2_1(a16) | c0_1(a16) | c3_1(a16))),
% 1.91/1.61 inference(quant_inst,[status(thm)],[])).
% 1.91/1.61 tff(3535,plain,
% 1.91/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | c1_1(a16) | (~c2_1(a24)) | c3_1(a24)),
% 1.91/1.61 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 1.91/1.61 tff(3536,plain,
% 1.91/1.61 ($false),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3535, 169, 3529, 35, 3520, 2451, 2, 2435, 3, 3528])).
% 1.91/1.61 tff(3537,plain,(hskp4 | c0_1(a16) | c3_1(a16) | c1_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.61 tff(3538,plain,
% 1.91/1.61 (hskp4),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3537, 3, 2, 35])).
% 1.91/1.61 tff(3539,plain,
% 1.91/1.61 (~c2_1(a6)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[111, 3538])).
% 1.91/1.61 tff(3540,plain,
% 1.91/1.61 (c3_1(a6)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[122, 3538])).
% 1.91/1.61 tff(3541,plain,
% 1.91/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a16) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | c0_1(a6) | c1_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a16) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | c0_1(a6) | c1_1(a16))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3542,plain,
% 1.91/1.61 (((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a16) | c0_1(a16) | c2_1(a16) | c2_1(a16) | c1_1(a16) | c0_1(a16)) <=> (c0_1(a16) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | c0_1(a6) | c1_1(a16))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3543,plain,
% 1.91/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a16) | c0_1(a16) | c2_1(a16) | c2_1(a16) | c1_1(a16) | c0_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a16) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | c0_1(a6) | c1_1(a16)))),
% 1.91/1.61 inference(monotonicity,[status(thm)],[3542])).
% 1.91/1.61 tff(3544,plain,
% 1.91/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a16) | c0_1(a16) | c2_1(a16) | c2_1(a16) | c1_1(a16) | c0_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a16) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | c0_1(a6) | c1_1(a16))),
% 1.91/1.61 inference(transitivity,[status(thm)],[3543, 3541])).
% 1.91/1.61 tff(3545,plain,
% 1.91/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a6) | c0_1(a6) | (~c3_1(a6)) | c3_1(a16) | c0_1(a16) | c2_1(a16) | c2_1(a16) | c1_1(a16) | c0_1(a16))),
% 1.91/1.61 inference(quant_inst,[status(thm)],[])).
% 1.91/1.61 tff(3546,plain,
% 1.91/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a16) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c3_1(a6)) | c0_1(a6) | c1_1(a16)),
% 1.91/1.61 inference(modus_ponens,[status(thm)],[3545, 3544])).
% 1.91/1.61 tff(3547,plain,
% 1.91/1.61 (c0_1(a6)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3546, 169, 35, 3540, 2451, 2, 3539, 55, 3])).
% 1.91/1.61 tff(3548,plain,
% 1.91/1.61 (hskp18 | (~c0_1(a6))),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[941, 169, 2470, 3540, 3539, 741])).
% 1.91/1.61 tff(3549,plain,
% 1.91/1.61 (hskp18),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3548, 3547])).
% 1.91/1.61 tff(3550,plain,
% 1.91/1.61 (~c3_1(a32)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[969, 3549])).
% 1.91/1.61 tff(3551,plain,
% 1.91/1.61 (~c1_1(a32)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[963, 3549])).
% 1.91/1.61 tff(3552,plain,
% 1.91/1.61 (~c0_1(a32)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[1385, 3549])).
% 1.91/1.61 tff(3553,plain,
% 1.91/1.61 (c1_1(a6)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[133, 3538])).
% 1.91/1.61 tff(3554,plain,
% 1.91/1.61 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a6) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3555,plain,
% 1.91/1.61 ((hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6))) <=> (hskp19 | c2_1(a6) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3556,plain,
% 1.91/1.61 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | c2_1(a6) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a6)) | (~c3_1(a6))))),
% 1.91/1.61 inference(monotonicity,[status(thm)],[3555])).
% 1.91/1.61 tff(3557,plain,
% 1.91/1.61 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a6)) | (~c3_1(a6)))),
% 1.91/1.61 inference(transitivity,[status(thm)],[3556, 3554])).
% 1.91/1.61 tff(3558,plain,
% 1.91/1.61 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a6) | (~c3_1(a6)) | (~c1_1(a6)))),
% 1.91/1.61 inference(quant_inst,[status(thm)],[])).
% 1.91/1.61 tff(3559,plain,
% 1.91/1.61 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | c2_1(a6) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a6)) | (~c3_1(a6))),
% 1.91/1.61 inference(modus_ponens,[status(thm)],[3558, 3557])).
% 1.91/1.61 tff(3560,plain,
% 1.91/1.61 (hskp19),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3559, 169, 2392, 2381, 3553, 3540, 3539, 848, 2400])).
% 1.91/1.61 tff(3561,plain,
% 1.91/1.61 (~c0_1(a33)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[897, 3560])).
% 1.91/1.61 tff(3562,plain,
% 1.91/1.61 (c2_1(a33)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[908, 3560])).
% 1.91/1.61 tff(3563,plain,
% 1.91/1.61 (~c1_1(a33)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[1482, 169, 3562, 3561, 3552, 3551, 3550, 45])).
% 1.91/1.61 tff(3564,plain,
% 1.91/1.61 (c3_1(a33)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[1503, 3560])).
% 1.91/1.61 tff(3565,plain,
% 1.91/1.61 ($false),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[1510, 169, 2461, 3562, 3564, 3552, 3551, 3550, 1493, 3563])).
% 1.91/1.61 tff(3566,plain,(c1_1(a16) | c0_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.61 tff(3567,plain,
% 1.91/1.61 (c1_1(a16)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3566, 35, 2])).
% 1.91/1.61 tff(3568,assumption,(hskp14), introduced(assumption)).
% 1.91/1.61 tff(3569,plain,
% 1.91/1.61 (~c1_1(a24)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[1024, 3568])).
% 1.91/1.61 tff(3570,plain,
% 1.91/1.61 (~c0_1(a24)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[1030, 3568])).
% 1.91/1.61 tff(3571,plain,
% 1.91/1.61 (c2_1(a24)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[1041, 3568])).
% 1.91/1.61 tff(3572,plain,
% 1.91/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3573,plain,
% 1.91/1.61 (((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24))) <=> (c0_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.91/1.61 inference(rewrite,[status(thm)],[])).
% 1.91/1.61 tff(3574,plain,
% 1.91/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a24)) | (~c3_1(a24))))),
% 1.91/1.61 inference(monotonicity,[status(thm)],[3573])).
% 1.91/1.61 tff(3575,plain,
% 1.91/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 1.91/1.61 inference(transitivity,[status(thm)],[3574, 3572])).
% 1.91/1.61 tff(3576,plain,
% 1.91/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))),
% 1.91/1.61 inference(quant_inst,[status(thm)],[])).
% 1.91/1.61 tff(3577,plain,
% 1.91/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a24) | c1_1(a24) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a24)) | (~c3_1(a24))),
% 1.91/1.61 inference(modus_ponens,[status(thm)],[3576, 3575])).
% 1.91/1.61 tff(3578,plain,
% 1.91/1.61 (~c3_1(a24)),
% 1.91/1.61 inference(unit_resolution,[status(thm)],[3577, 169, 3571, 35, 3570, 3569, 2, 83, 3567])).
% 1.91/1.61 tff(3579,plain,
% 1.91/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c2_1(a24)) | c3_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c2_1(a24)) | c3_1(a24))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3580,plain,
% 1.91/1.62 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a24) | c3_1(a24) | (~c2_1(a24))) <=> (c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c2_1(a24)) | c3_1(a24))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3581,plain,
% 1.91/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a24) | c3_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c2_1(a24)) | c3_1(a24)))),
% 1.91/1.62 inference(monotonicity,[status(thm)],[3580])).
% 1.91/1.62 tff(3582,plain,
% 1.91/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a24) | c3_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c2_1(a24)) | c3_1(a24))),
% 1.91/1.62 inference(transitivity,[status(thm)],[3581, 3579])).
% 1.91/1.62 tff(3583,plain,
% 1.91/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c0_1(a24) | c3_1(a24) | (~c2_1(a24)))),
% 1.91/1.62 inference(quant_inst,[status(thm)],[])).
% 1.91/1.62 tff(3584,plain,
% 1.91/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a24) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c2_1(a24)) | c3_1(a24)),
% 1.91/1.62 inference(modus_ponens,[status(thm)],[3583, 3582])).
% 1.91/1.62 tff(3585,plain,
% 1.91/1.62 ((~c0_1(a3)) | c3_1(a24)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[3584, 169, 2392, 2381, 3571, 3570, 24, 2, 34, 3567])).
% 1.91/1.62 tff(3586,plain,
% 1.91/1.62 (~c0_1(a3)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[3585, 3578])).
% 1.91/1.62 tff(3587,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3588,plain,
% 1.91/1.62 (((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24) | c1_1(a24) | c0_1(a24)) <=> (c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3589,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24) | c1_1(a24) | c0_1(a24))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24)))),
% 1.91/1.62 inference(monotonicity,[status(thm)],[3588])).
% 1.91/1.62 tff(3590,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24) | c1_1(a24) | c0_1(a24))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24))),
% 1.91/1.62 inference(transitivity,[status(thm)],[3589, 3587])).
% 1.91/1.62 tff(3591,plain,
% 1.91/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24) | c1_1(a24) | c0_1(a24))),
% 1.91/1.62 inference(quant_inst,[status(thm)],[])).
% 1.91/1.62 tff(3592,plain,
% 1.91/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c0_1(a24) | c1_1(a24) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a24)),
% 1.91/1.62 inference(modus_ponens,[status(thm)],[3591, 3590])).
% 1.91/1.62 tff(3593,plain,
% 1.91/1.62 ($false),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[3592, 169, 2392, 2381, 3570, 3569, 45, 3586, 3578])).
% 1.91/1.62 tff(3594,plain,((~hskp14) | c2_1(a16) | c3_1(a16) | c0_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.62 tff(3595,plain,
% 1.91/1.62 (~hskp14),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[3594, 24, 2, 35])).
% 1.91/1.62 tff(3596,plain,
% 1.91/1.62 (c0_1(a31)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[317, 66])).
% 1.91/1.62 tff(3597,plain,
% 1.91/1.62 (~c0_1(a3)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[2424, 2279, 332, 343])).
% 1.91/1.62 tff(3598,plain,
% 1.91/1.62 ($false),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[3406, 169, 205, 2392, 2412, 331, 343, 632, 2279, 3597])).
% 1.91/1.62 tff(3599,plain,(c3_1(a31) | hskp4 | (~c0_1(a31)) | c1_1(a31) | (~c2_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.62 tff(3600,plain,
% 1.91/1.62 (c3_1(a31)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[3599, 205, 331, 343, 332])).
% 1.91/1.62 tff(3601,plain,
% 1.91/1.62 (~hskp11),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[2667, 3600, 332, 331])).
% 1.91/1.62 tff(3602,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3603,plain,
% 1.91/1.62 ((hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp10 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3604,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | (~c3_1(a31))))),
% 1.91/1.62 inference(monotonicity,[status(thm)],[3603])).
% 1.91/1.62 tff(3605,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 1.91/1.62 inference(transitivity,[status(thm)],[3604, 3602])).
% 1.91/1.62 tff(3606,plain,
% 1.91/1.62 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.91/1.62 inference(quant_inst,[status(thm)],[])).
% 1.91/1.62 tff(3607,plain,
% 1.91/1.62 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a31) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a31)) | (~c3_1(a31))),
% 1.91/1.62 inference(modus_ponens,[status(thm)],[3606, 3605])).
% 1.91/1.62 tff(3608,plain,
% 1.91/1.62 (hskp10),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[3607, 169, 2392, 2412, 332, 343, 1137, 2588, 1])).
% 1.91/1.62 tff(3609,plain,
% 1.91/1.62 (~c3_1(a18)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[1150, 3608])).
% 1.91/1.62 tff(3610,plain,
% 1.91/1.62 (c2_1(a18)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[1161, 3608])).
% 1.91/1.62 tff(3611,plain,
% 1.91/1.62 (c0_1(a18)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[1172, 3608])).
% 1.91/1.62 tff(3612,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a18) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a18)) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a18)) | (~c2_1(a18)))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3613,plain,
% 1.91/1.62 ((hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3))) <=> (hskp11 | c3_1(a18) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a18)) | (~c2_1(a18)))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3614,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a18) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a18)) | (~c2_1(a18))))),
% 1.91/1.62 inference(monotonicity,[status(thm)],[3613])).
% 1.91/1.62 tff(3615,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a18)) | (~c2_1(a18)))),
% 1.91/1.62 inference(transitivity,[status(thm)],[3614, 3612])).
% 1.91/1.62 tff(3616,plain,
% 1.91/1.62 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))),
% 1.91/1.62 inference(quant_inst,[status(thm)],[])).
% 1.91/1.62 tff(3617,plain,
% 1.91/1.62 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a18)) | (~c2_1(a18))),
% 1.91/1.62 inference(modus_ponens,[status(thm)],[3616, 3615])).
% 1.91/1.62 tff(3618,plain,
% 1.91/1.62 ($false),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[3617, 169, 3031, 2381, 2412, 3611, 3610, 3609, 1126, 1])).
% 1.91/1.62 tff(3619,plain,(c0_1(a3) | hskp11 | (~c2_1(a31)) | c1_1(a31) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.62 tff(3620,plain,
% 1.91/1.62 (c0_1(a3)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[3619, 3601, 332, 343, 3600])).
% 1.91/1.62 tff(3621,assumption,(c2_1(a25)), introduced(assumption)).
% 1.91/1.62 tff(3622,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a16) | c3_1(a25) | c2_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c1_1(a25)) | (~c2_1(a25)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a16) | c3_1(a25) | c2_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3623,plain,
% 1.91/1.62 ((hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a16) | c2_1(a16) | (~c1_1(a16))) <=> (hskp5 | c0_1(a16) | c3_1(a25) | c2_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3624,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a16) | c2_1(a16) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a16) | c3_1(a25) | c2_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c1_1(a25)) | (~c2_1(a25))))),
% 1.91/1.62 inference(monotonicity,[status(thm)],[3623])).
% 1.91/1.62 tff(3625,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a16) | c2_1(a16) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a16) | c3_1(a25) | c2_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.91/1.62 inference(transitivity,[status(thm)],[3624, 3622])).
% 1.91/1.62 tff(3626,plain,
% 1.91/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)) | c0_1(a16) | c2_1(a16) | (~c1_1(a16)))),
% 1.91/1.62 inference(quant_inst,[status(thm)],[])).
% 1.91/1.62 tff(3627,plain,
% 1.91/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a16) | c3_1(a25) | c2_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c1_1(a25)) | (~c2_1(a25))),
% 1.91/1.62 inference(modus_ponens,[status(thm)],[3626, 3625])).
% 1.91/1.62 tff(3628,plain,
% 1.91/1.62 (hskp5 | (~c2_1(a25))),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[3627, 169, 3471, 35, 3470, 24, 1413, 772])).
% 1.91/1.62 tff(3629,plain,
% 1.91/1.62 (hskp5),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[3628, 3621])).
% 1.91/1.62 tff(3630,plain,
% 1.91/1.62 (~c0_1(a7)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[1419, 3629])).
% 1.91/1.62 tff(3631,plain,
% 1.91/1.62 (c3_1(a7)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[1454, 3629])).
% 1.91/1.62 tff(3632,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a25) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a25)) | (~c2_1(a25)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a25) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3633,plain,
% 1.91/1.62 ((hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7))) <=> (hskp11 | c3_1(a25) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3634,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a25) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a25)) | (~c2_1(a25))))),
% 1.91/1.62 inference(monotonicity,[status(thm)],[3633])).
% 1.91/1.62 tff(3635,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a25) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.91/1.62 inference(transitivity,[status(thm)],[3634, 3632])).
% 1.91/1.62 tff(3636,plain,
% 1.91/1.62 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))),
% 1.91/1.62 inference(quant_inst,[status(thm)],[])).
% 1.91/1.62 tff(3637,plain,
% 1.91/1.62 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a25) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a25)) | (~c2_1(a25))),
% 1.91/1.62 inference(modus_ponens,[status(thm)],[3636, 3635])).
% 1.91/1.62 tff(3638,plain,
% 1.91/1.62 (~c2_1(a7)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[3637, 169, 3031, 3480, 3631, 3470, 3630, 1126, 3621])).
% 1.91/1.62 tff(3639,plain,
% 1.91/1.62 (c1_1(a7)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[1430, 3629])).
% 1.91/1.62 tff(3640,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3641,plain,
% 1.91/1.62 ((hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7))) <=> (hskp19 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3642,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7)))),
% 1.91/1.62 inference(monotonicity,[status(thm)],[3641])).
% 1.91/1.62 tff(3643,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7))),
% 1.91/1.62 inference(transitivity,[status(thm)],[3642, 3640])).
% 1.91/1.62 tff(3644,plain,
% 1.91/1.62 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)))),
% 1.91/1.62 inference(quant_inst,[status(thm)],[])).
% 1.91/1.62 tff(3645,plain,
% 1.91/1.62 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp19 | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7)),
% 1.91/1.62 inference(modus_ponens,[status(thm)],[3644, 3643])).
% 1.91/1.62 tff(3646,plain,
% 1.91/1.62 (hskp19),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[3645, 169, 2392, 2381, 3639, 3631, 848, 2413, 3638])).
% 1.91/1.62 tff(3647,plain,
% 1.91/1.62 (~c0_1(a33)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[897, 3646])).
% 1.91/1.62 tff(3648,plain,
% 1.91/1.62 (c3_1(a33)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[1503, 3646])).
% 1.91/1.62 tff(3649,plain,
% 1.91/1.62 (c2_1(a33)),
% 1.91/1.62 inference(unit_resolution,[status(thm)],[908, 3646])).
% 1.91/1.62 tff(3650,plain,
% 1.91/1.62 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | c3_1(a25) | (~ndr1_0) | (~c0_1(a25)) | (~c2_1(a25)) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | c3_1(a25) | (~ndr1_0) | (~c0_1(a25)) | (~c2_1(a25)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.91/1.62 inference(rewrite,[status(thm)],[])).
% 1.91/1.62 tff(3651,plain,
% 1.91/1.62 ((hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp11 | c0_1(a33) | c3_1(a25) | (~ndr1_0) | (~c0_1(a25)) | (~c2_1(a25)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.91/1.63 inference(rewrite,[status(thm)],[])).
% 1.91/1.63 tff(3652,plain,
% 1.91/1.63 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | c3_1(a25) | (~ndr1_0) | (~c0_1(a25)) | (~c2_1(a25)) | (~c3_1(a33)) | (~c2_1(a33))))),
% 1.91/1.63 inference(monotonicity,[status(thm)],[3651])).
% 1.91/1.63 tff(3653,plain,
% 1.91/1.63 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | c3_1(a25) | (~ndr1_0) | (~c0_1(a25)) | (~c2_1(a25)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.91/1.63 inference(transitivity,[status(thm)],[3652, 3650])).
% 1.91/1.63 tff(3654,plain,
% 1.91/1.63 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 1.91/1.63 inference(quant_inst,[status(thm)],[])).
% 1.91/1.63 tff(3655,plain,
% 1.91/1.63 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | c3_1(a25) | (~ndr1_0) | (~c0_1(a25)) | (~c2_1(a25)) | (~c3_1(a33)) | (~c2_1(a33))),
% 1.91/1.63 inference(modus_ponens,[status(thm)],[3654, 3653])).
% 1.91/1.63 tff(3656,plain,
% 1.91/1.63 ($false),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3655, 169, 3031, 3649, 3648, 3480, 3647, 3470, 1126, 3621])).
% 1.91/1.63 tff(3657,plain,((~c2_1(a25)) | hskp11 | (~c0_1(a25)) | c3_1(a25) | (~c0_1(a3)) | (~c1_1(a25)) | c0_1(a16) | c2_1(a16) | (~c1_1(a16))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.63 tff(3658,plain,
% 1.91/1.63 (~c2_1(a25)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3657, 3601, 3433, 3415, 3620, 3444, 35, 24, 772])).
% 1.91/1.63 tff(3659,plain,
% 1.91/1.63 ($false),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3486, 169, 2381, 2412, 3433, 3444, 3415, 439, 3620, 3658])).
% 1.91/1.63 tff(3660,plain,(hskp4 | c0_1(a16) | c2_1(a16) | (~c1_1(a16)) | (~c2_1(a31)) | c1_1(a31) | (~c0_1(a31)) | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.91/1.63 tff(3661,plain,
% 1.91/1.63 (hskp4),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3660, 2401, 24, 3567, 35, 72, 3596, 3595])).
% 1.91/1.63 tff(3662,plain,
% 1.91/1.63 (~c2_1(a6)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[111, 3661])).
% 1.91/1.63 tff(3663,plain,
% 1.91/1.63 (c3_1(a6)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[122, 3661])).
% 1.91/1.63 tff(3664,plain,
% 1.91/1.63 (c1_1(a6)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[133, 3661])).
% 1.91/1.63 tff(3665,plain,
% 1.91/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | (~c0_1(a31)))),
% 1.91/1.63 inference(rewrite,[status(thm)],[])).
% 1.91/1.63 tff(3666,plain,
% 1.91/1.63 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16)) <=> (c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | (~c0_1(a31)))),
% 1.91/1.63 inference(rewrite,[status(thm)],[])).
% 1.91/1.63 tff(3667,plain,
% 1.91/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | (~c0_1(a31))))),
% 1.91/1.63 inference(monotonicity,[status(thm)],[3666])).
% 1.91/1.63 tff(3668,plain,
% 1.91/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | (~c0_1(a31)))),
% 1.91/1.63 inference(transitivity,[status(thm)],[3667, 3665])).
% 1.91/1.63 tff(3669,plain,
% 1.91/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | c1_1(a31) | (~c0_1(a31)) | c2_1(a16) | c0_1(a16) | c3_1(a16))),
% 1.91/1.63 inference(quant_inst,[status(thm)],[])).
% 1.91/1.63 tff(3670,plain,
% 1.91/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a16) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a31) | (~c0_1(a31))),
% 1.91/1.63 inference(modus_ponens,[status(thm)],[3669, 3668])).
% 1.91/1.63 tff(3671,plain,
% 1.91/1.63 ($false),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3670, 169, 331, 35, 730, 729, 343, 24, 2, 728, 13, 2279])).
% 1.91/1.63 tff(3672,plain,(c3_1(a31) | (~c0_1(a31)) | c0_1(a16) | (~c1_1(a6)) | (~c3_1(a6)) | c1_1(a31) | c2_1(a16) | c3_1(a16) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.63 tff(3673,plain,
% 1.91/1.63 (c3_1(a31)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3672, 3596, 35, 3664, 3663, 72, 24, 2, 3662])).
% 1.91/1.63 tff(3674,plain,
% 1.91/1.63 (~hskp11),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[2667, 3673, 2401, 3596])).
% 1.91/1.63 tff(3675,plain,
% 1.91/1.63 (c0_1(a3)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3619, 3674, 2401, 72, 3673])).
% 1.91/1.63 tff(3676,plain,
% 1.91/1.63 (hskp19 | (~c0_1(a3))),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3559, 169, 2392, 2381, 3664, 3663, 3662, 848])).
% 1.91/1.63 tff(3677,plain,
% 1.91/1.63 (hskp19),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3676, 3675])).
% 1.91/1.63 tff(3678,plain,
% 1.91/1.63 (~c0_1(a33)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[897, 3677])).
% 1.91/1.63 tff(3679,plain,
% 1.91/1.63 (c2_1(a33)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[908, 3677])).
% 1.91/1.63 tff(3680,assumption,(~c1_1(a33)), introduced(assumption)).
% 1.91/1.63 tff(3681,assumption,(~c0_1(a33)), introduced(assumption)).
% 1.91/1.63 tff(3682,assumption,(c2_1(a33)), introduced(assumption)).
% 1.91/1.63 tff(3683,plain,
% 1.91/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.91/1.63 inference(rewrite,[status(thm)],[])).
% 1.91/1.63 tff(3684,plain,
% 1.91/1.63 (((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33))) <=> (c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.91/1.63 inference(rewrite,[status(thm)],[])).
% 1.91/1.63 tff(3685,plain,
% 1.91/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)))),
% 1.91/1.63 inference(monotonicity,[status(thm)],[3684])).
% 1.91/1.63 tff(3686,plain,
% 1.91/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 1.91/1.63 inference(transitivity,[status(thm)],[3685, 3683])).
% 1.91/1.63 tff(3687,plain,
% 1.91/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))),
% 1.91/1.63 inference(quant_inst,[status(thm)],[])).
% 1.91/1.63 tff(3688,plain,
% 1.91/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)),
% 1.91/1.63 inference(modus_ponens,[status(thm)],[3687, 3686])).
% 1.91/1.63 tff(3689,plain,
% 1.91/1.63 ($false),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3688, 169, 3682, 332, 35, 3681, 343, 2, 83, 2588, 3567, 3680])).
% 1.91/1.63 tff(3690,plain,(c1_1(a33) | (~c2_1(a33)) | (~c2_1(a31)) | c0_1(a16) | c0_1(a33) | c1_1(a31) | c3_1(a16) | (~c3_1(a31))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.63 tff(3691,plain,
% 1.91/1.63 (c1_1(a33)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3690, 3679, 2401, 35, 3678, 72, 2, 3673])).
% 1.91/1.63 tff(3692,plain,
% 1.91/1.63 (c3_1(a33)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[1503, 3677])).
% 1.91/1.63 tff(3693,plain,
% 1.91/1.63 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c3_1(a33)) | (~c1_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c3_1(a33)) | (~c1_1(a33)))),
% 1.91/1.63 inference(rewrite,[status(thm)],[])).
% 1.91/1.63 tff(3694,plain,
% 1.91/1.63 ((hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c1_1(a33))) <=> (hskp10 | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c3_1(a33)) | (~c1_1(a33)))),
% 1.91/1.63 inference(rewrite,[status(thm)],[])).
% 1.91/1.63 tff(3695,plain,
% 1.91/1.63 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c1_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c3_1(a33)) | (~c1_1(a33))))),
% 1.91/1.63 inference(monotonicity,[status(thm)],[3694])).
% 1.91/1.63 tff(3696,plain,
% 1.91/1.63 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c1_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c3_1(a33)) | (~c1_1(a33)))),
% 1.91/1.63 inference(transitivity,[status(thm)],[3695, 3693])).
% 1.91/1.63 tff(3697,plain,
% 1.91/1.63 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c0_1(a33) | (~c3_1(a33)) | (~c1_1(a33)))),
% 1.91/1.63 inference(quant_inst,[status(thm)],[])).
% 1.91/1.63 tff(3698,plain,
% 1.91/1.63 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c0_1(a33) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | (~c3_1(a31)) | (~c3_1(a33)) | (~c1_1(a33))),
% 1.91/1.63 inference(modus_ponens,[status(thm)],[3697, 3696])).
% 1.91/1.63 tff(3699,plain,
% 1.91/1.63 (hskp10 | (~c1_1(a33))),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3698, 169, 3692, 2401, 3678, 72, 1137, 3673])).
% 1.91/1.63 tff(3700,plain,
% 1.91/1.63 (hskp10),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3699, 3691])).
% 1.91/1.63 tff(3701,plain,
% 1.91/1.63 (~c3_1(a18)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[1150, 3700])).
% 1.91/1.63 tff(3702,plain,
% 1.91/1.63 (c2_1(a18)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[1161, 3700])).
% 1.91/1.63 tff(3703,plain,
% 1.91/1.63 (c0_1(a18)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[1172, 3700])).
% 1.91/1.63 tff(3704,plain,
% 1.91/1.63 ($false),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[2674, 169, 3674, 3679, 3692, 3703, 3702, 3678, 3701, 1126])).
% 1.91/1.63 tff(3705,plain,((~hskp17) | c0_1(a16) | c3_1(a16) | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.63 tff(3706,plain,
% 1.91/1.63 (~hskp17),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3705, 24, 2, 35])).
% 1.91/1.63 tff(3707,plain,
% 1.91/1.63 (hskp4),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3517, 3706, 3595])).
% 1.91/1.63 tff(3708,plain,
% 1.91/1.63 (~c2_1(a6)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[111, 3707])).
% 1.91/1.63 tff(3709,plain,
% 1.91/1.63 (c3_1(a6)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[122, 3707])).
% 1.91/1.63 tff(3710,plain,
% 1.91/1.63 (c1_1(a6)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[133, 3707])).
% 1.91/1.63 tff(3711,plain,
% 1.91/1.63 (c0_1(a3)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3457, 169, 2392, 2381, 2012, 1569, 1570, 45])).
% 1.91/1.63 tff(3712,plain,
% 1.91/1.63 (hskp19 | (~c0_1(a3))),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3559, 169, 2392, 2381, 730, 729, 728, 848])).
% 1.91/1.63 tff(3713,plain,
% 1.91/1.63 (hskp19),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3712, 3711])).
% 1.91/1.63 tff(3714,plain,
% 1.91/1.63 (~c0_1(a33)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[897, 3713])).
% 1.91/1.63 tff(3715,plain,
% 1.91/1.63 (c2_1(a33)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[908, 3713])).
% 1.91/1.63 tff(3716,plain,
% 1.91/1.63 (~c1_1(a33)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[1482, 169, 3715, 3714, 2012, 1569, 1570, 45])).
% 1.91/1.63 tff(3717,plain,
% 1.91/1.63 (c3_1(a33)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[1503, 3713])).
% 1.91/1.63 tff(3718,plain,
% 1.91/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a16) | c0_1(a33) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a33) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 1.91/1.63 inference(rewrite,[status(thm)],[])).
% 1.91/1.63 tff(3719,plain,
% 1.91/1.63 (((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33))) <=> (c0_1(a16) | c0_1(a33) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 1.91/1.63 inference(rewrite,[status(thm)],[])).
% 1.91/1.63 tff(3720,plain,
% 1.91/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a16) | c0_1(a33) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33)))),
% 1.91/1.63 inference(monotonicity,[status(thm)],[3719])).
% 1.91/1.63 tff(3721,plain,
% 1.91/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a33) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33))),
% 1.91/1.63 inference(transitivity,[status(thm)],[3720, 3718])).
% 1.91/1.63 tff(3722,plain,
% 1.91/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c3_1(a16) | c0_1(a16) | (~c1_1(a16)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))),
% 1.91/1.63 inference(quant_inst,[status(thm)],[])).
% 1.91/1.63 tff(3723,plain,
% 1.91/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a16) | c0_1(a33) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a33)),
% 1.91/1.63 inference(modus_ponens,[status(thm)],[3722, 3721])).
% 1.91/1.63 tff(3724,plain,
% 1.91/1.63 ($false),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3723, 169, 3715, 3717, 35, 3714, 2, 83, 3567, 3716])).
% 1.91/1.63 tff(3725,plain,((~hskp18) | c0_1(a16) | c3_1(a16) | (~c1_1(a6)) | (~c3_1(a6)) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.63 tff(3726,plain,
% 1.91/1.63 (~hskp18),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3725, 3710, 2, 35, 3709, 3708])).
% 1.91/1.63 tff(3727,plain,
% 1.91/1.63 (~c0_1(a6)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[941, 169, 3726, 3706, 3709, 3708, 741])).
% 1.91/1.63 tff(3728,plain,
% 1.91/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a6)) | c0_1(a6))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a6)) | c0_1(a6))),
% 1.91/1.63 inference(rewrite,[status(thm)],[])).
% 1.91/1.63 tff(3729,plain,
% 1.91/1.63 ((hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6))) <=> (hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a6)) | c0_1(a6))),
% 1.91/1.63 inference(rewrite,[status(thm)],[])).
% 1.91/1.63 tff(3730,plain,
% 1.91/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a6)) | c0_1(a6)))),
% 1.91/1.63 inference(monotonicity,[status(thm)],[3729])).
% 1.91/1.63 tff(3731,plain,
% 1.91/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a6)) | c0_1(a6))),
% 1.91/1.63 inference(transitivity,[status(thm)],[3730, 3728])).
% 1.91/1.63 tff(3732,plain,
% 1.91/1.63 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a6) | c2_1(a6) | (~c3_1(a6)))),
% 1.91/1.63 inference(quant_inst,[status(thm)],[])).
% 1.91/1.63 tff(3733,plain,
% 1.91/1.63 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a6) | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | (~c3_1(a6)) | c0_1(a6)),
% 1.91/1.63 inference(modus_ponens,[status(thm)],[3732, 3731])).
% 1.91/1.63 tff(3734,plain,
% 1.91/1.63 (hskp6),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3733, 169, 2392, 2381, 2412, 3709, 3708, 1298, 3727])).
% 1.91/1.63 tff(3735,plain,
% 1.91/1.63 (~c2_1(a8)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[1335, 3734])).
% 1.91/1.63 tff(3736,plain,
% 1.91/1.63 (c0_1(a8)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[1369, 3734])).
% 1.91/1.63 tff(3737,plain,
% 1.91/1.63 (~c3_1(a8)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[1376, 169, 3726, 3706, 3736, 3735, 741])).
% 1.91/1.63 tff(3738,plain,
% 1.91/1.63 (hskp4),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3517, 643, 3595])).
% 1.91/1.63 tff(3739,plain,
% 1.91/1.63 (~c2_1(a6)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[111, 3738])).
% 1.91/1.63 tff(3740,plain,
% 1.91/1.63 (c3_1(a6)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[122, 3738])).
% 1.91/1.63 tff(3741,plain,
% 1.91/1.63 (c1_1(a6)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[133, 3738])).
% 1.91/1.63 tff(3742,plain,
% 1.91/1.63 (~hskp18),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3725, 3741, 2, 35, 3740, 3739])).
% 1.91/1.63 tff(3743,plain,
% 1.91/1.63 (hskp18 | (~c0_1(a6))),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[941, 169, 643, 3740, 3739, 741])).
% 1.91/1.63 tff(3744,plain,
% 1.91/1.63 (~c0_1(a6)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3743, 3742])).
% 1.91/1.63 tff(3745,plain,
% 1.91/1.63 (hskp6),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[3733, 169, 2392, 2381, 2412, 3740, 3739, 1298, 3744])).
% 1.91/1.63 tff(3746,plain,
% 1.91/1.63 (~c2_1(a8)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[1335, 3745])).
% 1.91/1.63 tff(3747,plain,
% 1.91/1.63 (c0_1(a8)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[1369, 3745])).
% 1.91/1.63 tff(3748,plain,
% 1.91/1.63 (~c3_1(a8)),
% 1.91/1.63 inference(unit_resolution,[status(thm)],[1376, 169, 3742, 643, 3747, 3746, 741])).
% 1.91/1.63 tff(3749,plain,
% 1.91/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))),
% 1.91/1.63 inference(rewrite,[status(thm)],[])).
% 1.91/1.63 tff(3750,plain,
% 1.91/1.63 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))),
% 1.91/1.63 inference(rewrite,[status(thm)],[])).
% 1.91/1.63 tff(3751,plain,
% 1.91/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16))))),
% 1.91/1.63 inference(monotonicity,[status(thm)],[3750])).
% 1.91/1.63 tff(3752,plain,
% 1.91/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))),
% 1.91/1.63 inference(transitivity,[status(thm)],[3751, 3749])).
% 1.91/1.63 tff(3753,plain,
% 1.91/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.91/1.63 inference(quant_inst,[status(thm)],[])).
% 1.91/1.63 tff(3754,plain,
% 1.91/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16))),
% 1.91/1.64 inference(modus_ponens,[status(thm)],[3753, 3752])).
% 1.91/1.64 tff(3755,plain,
% 1.91/1.64 (~c0_1(a3)),
% 1.91/1.64 inference(unit_resolution,[status(thm)],[3754, 169, 2381, 2412, 3747, 24, 2, 3746, 439, 3567, 3748])).
% 1.91/1.64 tff(3756,plain,
% 1.91/1.64 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.91/1.64 inference(rewrite,[status(thm)],[])).
% 1.91/1.64 tff(3757,plain,
% 1.91/1.64 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.91/1.64 inference(quant_inst,[status(thm)],[])).
% 1.91/1.64 tff(3758,plain,
% 1.91/1.64 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp26 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))),
% 1.91/1.64 inference(modus_ponens,[status(thm)],[3757, 3756])).
% 1.91/1.64 tff(3759,plain,
% 1.91/1.64 (hskp27 | hskp26 | c0_1(a3)),
% 1.91/1.64 inference(unit_resolution,[status(thm)],[3758, 169, 2392, 2381, 791])).
% 1.91/1.64 tff(3760,plain,
% 1.91/1.64 (hskp27),
% 1.91/1.64 inference(unit_resolution,[status(thm)],[3759, 3755, 84])).
% 1.91/1.64 tff(3761,plain,
% 1.91/1.64 (c3_1(a11)),
% 1.91/1.64 inference(unit_resolution,[status(thm)],[752, 3760])).
% 1.91/1.64 tff(3762,plain,
% 1.91/1.64 (c0_1(a11)),
% 1.91/1.64 inference(unit_resolution,[status(thm)],[763, 3760])).
% 1.91/1.64 tff(3763,plain,
% 1.91/1.64 (c2_1(a11)),
% 1.91/1.64 inference(unit_resolution,[status(thm)],[770, 169, 3742, 643, 3762, 3761, 741])).
% 1.91/1.64 tff(3764,plain,
% 1.91/1.64 (~hskp9),
% 1.91/1.64 inference(unit_resolution,[status(thm)],[590, 35])).
% 1.91/1.64 tff(3765,plain,
% 1.91/1.64 (hskp9 | hskp8 | c0_1(a3)),
% 1.91/1.64 inference(unit_resolution,[status(thm)],[2708, 169, 2392, 2381, 2699])).
% 1.91/1.64 tff(3766,plain,
% 1.91/1.64 (hskp8),
% 1.91/1.64 inference(unit_resolution,[status(thm)],[3765, 3755, 3764])).
% 1.91/1.64 tff(3767,plain,
% 1.91/1.64 (~c2_1(a15)),
% 1.91/1.64 inference(unit_resolution,[status(thm)],[184, 3766])).
% 1.91/1.64 tff(3768,plain,
% 1.91/1.64 (c0_1(a15)),
% 1.91/1.64 inference(unit_resolution,[status(thm)],[195, 3766])).
% 1.91/1.64 tff(3769,plain,
% 1.91/1.64 (~c3_1(a15)),
% 1.91/1.64 inference(unit_resolution,[status(thm)],[2045, 169, 3742, 643, 3768, 3767, 741])).
% 1.91/1.64 tff(3770,plain,
% 1.91/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))),
% 1.91/1.64 inference(rewrite,[status(thm)],[])).
% 1.91/1.64 tff(3771,plain,
% 1.91/1.64 (((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))),
% 1.91/1.64 inference(rewrite,[status(thm)],[])).
% 1.91/1.64 tff(3772,plain,
% 1.91/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16))))),
% 1.91/1.64 inference(monotonicity,[status(thm)],[3771])).
% 1.91/1.64 tff(3773,plain,
% 1.91/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16)))),
% 1.98/1.65 inference(transitivity,[status(thm)],[3772, 3770])).
% 1.98/1.65 tff(3774,plain,
% 1.98/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))),
% 1.98/1.65 inference(quant_inst,[status(thm)],[])).
% 1.98/1.65 tff(3775,plain,
% 1.98/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | (~c1_1(a16))),
% 1.98/1.65 inference(modus_ponens,[status(thm)],[3774, 3773])).
% 1.98/1.65 tff(3776,plain,
% 1.98/1.65 ($false),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3775, 169, 3762, 3761, 3768, 24, 2, 3767, 439, 3567, 3769, 3763])).
% 1.98/1.65 tff(3777,plain,(hskp17 | c2_1(a16) | c3_1(a16) | hskp26 | c0_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.65 tff(3778,plain,
% 1.98/1.65 (hskp26),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3777, 3706, 2, 24, 35])).
% 1.98/1.65 tff(3779,plain,
% 1.98/1.65 (c3_1(a10)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[689, 3778])).
% 1.98/1.65 tff(3780,plain,
% 1.98/1.65 (c2_1(a10)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[678, 3778])).
% 1.98/1.65 tff(3781,plain,
% 1.98/1.65 (c0_1(a10)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[666, 3778])).
% 1.98/1.65 tff(3782,plain,
% 1.98/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3783,plain,
% 1.98/1.65 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3784,plain,
% 1.98/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16))))),
% 1.98/1.65 inference(monotonicity,[status(thm)],[3783])).
% 1.98/1.65 tff(3785,plain,
% 1.98/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16)))),
% 1.98/1.65 inference(transitivity,[status(thm)],[3784, 3782])).
% 1.98/1.65 tff(3786,plain,
% 1.98/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.98/1.65 inference(quant_inst,[status(thm)],[])).
% 1.98/1.65 tff(3787,plain,
% 1.98/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a8) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a8) | (~c0_1(a8)) | (~c1_1(a16))),
% 1.98/1.65 inference(modus_ponens,[status(thm)],[3786, 3785])).
% 1.98/1.65 tff(3788,plain,
% 1.98/1.65 ($false),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3787, 169, 3781, 3780, 3779, 3736, 24, 2, 3735, 439, 3567, 3737])).
% 1.98/1.65 tff(3789,plain,(c2_1(a16) | c3_1(a16) | c0_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.65 tff(3790,plain,
% 1.98/1.65 (c2_1(a16)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3789, 35, 2])).
% 1.98/1.65 tff(3791,plain,
% 1.98/1.65 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a16) | (~c2_1(a16)) | (~ndr1_0) | (~c1_1(a16)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a16) | (~c2_1(a16)) | (~ndr1_0) | (~c1_1(a16)))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3792,plain,
% 1.98/1.65 ((hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a16)) | c0_1(a16) | (~c1_1(a16))) <=> (hskp9 | hskp8 | c0_1(a16) | (~c2_1(a16)) | (~ndr1_0) | (~c1_1(a16)))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3793,plain,
% 1.98/1.65 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a16)) | c0_1(a16) | (~c1_1(a16)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a16) | (~c2_1(a16)) | (~ndr1_0) | (~c1_1(a16))))),
% 1.98/1.65 inference(monotonicity,[status(thm)],[3792])).
% 1.98/1.65 tff(3794,plain,
% 1.98/1.65 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a16)) | c0_1(a16) | (~c1_1(a16)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a16) | (~c2_1(a16)) | (~ndr1_0) | (~c1_1(a16)))),
% 1.98/1.65 inference(transitivity,[status(thm)],[3793, 3791])).
% 1.98/1.65 tff(3795,plain,
% 1.98/1.65 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(a16)) | c0_1(a16) | (~c1_1(a16)))),
% 1.98/1.65 inference(quant_inst,[status(thm)],[])).
% 1.98/1.65 tff(3796,plain,
% 1.98/1.65 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a16) | (~c2_1(a16)) | (~ndr1_0) | (~c1_1(a16))),
% 1.98/1.65 inference(modus_ponens,[status(thm)],[3795, 3794])).
% 1.98/1.65 tff(3797,plain,
% 1.98/1.65 (hskp8 | (~c2_1(a16)) | (~c1_1(a16))),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3796, 169, 3764, 35, 2699])).
% 1.98/1.65 tff(3798,plain,
% 1.98/1.65 (hskp8),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3797, 3790, 3567])).
% 1.98/1.65 tff(3799,plain,
% 1.98/1.65 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a24) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | c3_1(a24))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a24) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | c3_1(a24))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3800,plain,
% 1.98/1.65 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24))) <=> (c1_1(a24) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | c3_1(a24))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3801,plain,
% 1.98/1.65 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a24) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | c3_1(a24)))),
% 1.98/1.65 inference(monotonicity,[status(thm)],[3800])).
% 1.98/1.65 tff(3802,plain,
% 1.98/1.65 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a24) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | c3_1(a24))),
% 1.98/1.65 inference(transitivity,[status(thm)],[3801, 3799])).
% 1.98/1.65 tff(3803,plain,
% 1.98/1.65 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a24) | c1_1(a24) | (~c2_1(a24)))),
% 1.98/1.65 inference(quant_inst,[status(thm)],[])).
% 1.98/1.65 tff(3804,plain,
% 1.98/1.65 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a24) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | c3_1(a24)),
% 1.98/1.65 inference(modus_ponens,[status(thm)],[3803, 3802])).
% 1.98/1.65 tff(3805,plain,
% 1.98/1.65 (~c0_1(a3)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3804, 169, 2381, 2412, 3571, 3569, 1580, 3578])).
% 1.98/1.65 tff(3806,plain,
% 1.98/1.65 ($false),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3592, 169, 2392, 2381, 3570, 3569, 45, 3805, 3578])).
% 1.98/1.65 tff(3807,plain,((~hskp14) | c0_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.65 tff(3808,plain,
% 1.98/1.65 (~hskp14),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3807, 35, 2])).
% 1.98/1.65 tff(3809,plain,
% 1.98/1.65 (hskp2),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[2482, 3808, 3798])).
% 1.98/1.65 tff(3810,plain,
% 1.98/1.65 (~c3_1(a4)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[400, 3809])).
% 1.98/1.65 tff(3811,plain,
% 1.98/1.65 (~c2_1(a4)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[417, 3809])).
% 1.98/1.65 tff(3812,plain,
% 1.98/1.65 (c1_1(a4)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[411, 3809])).
% 1.98/1.65 tff(3813,plain,
% 1.98/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3814,plain,
% 1.98/1.65 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16))) <=> (c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3815,plain,
% 1.98/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3))))),
% 1.98/1.65 inference(monotonicity,[status(thm)],[3814])).
% 1.98/1.65 tff(3816,plain,
% 1.98/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 1.98/1.65 inference(transitivity,[status(thm)],[3815, 3813])).
% 1.98/1.65 tff(3817,plain,
% 1.98/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16)))),
% 1.98/1.65 inference(quant_inst,[status(thm)],[])).
% 1.98/1.65 tff(3818,plain,
% 1.98/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3))),
% 1.98/1.65 inference(modus_ponens,[status(thm)],[3817, 3816])).
% 1.98/1.65 tff(3819,plain,
% 1.98/1.65 (~c0_1(a3)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3818, 169, 2392, 2381, 35, 3812, 3790, 2, 3811, 3810, 34])).
% 1.98/1.65 tff(3820,plain,
% 1.98/1.65 (~c2_1(a15)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[184, 3798])).
% 1.98/1.65 tff(3821,plain,
% 1.98/1.65 (c0_1(a15)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[195, 3798])).
% 1.98/1.65 tff(3822,plain,
% 1.98/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3823,plain,
% 1.98/1.65 (((~ndr1_0) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16))) <=> (c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3824,plain,
% 1.98/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))))),
% 1.98/1.65 inference(monotonicity,[status(thm)],[3823])).
% 1.98/1.65 tff(3825,plain,
% 1.98/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)))),
% 1.98/1.65 inference(transitivity,[status(thm)],[3824, 3822])).
% 1.98/1.65 tff(3826,plain,
% 1.98/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a16) | c3_1(a16) | (~c2_1(a16)))),
% 1.98/1.65 inference(quant_inst,[status(thm)],[])).
% 1.98/1.65 tff(3827,plain,
% 1.98/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a9)) | (~c0_1(a9)) | (~c1_1(a9))),
% 1.98/1.65 inference(modus_ponens,[status(thm)],[3826, 3825])).
% 1.98/1.65 tff(3828,plain,
% 1.98/1.65 ($false),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3827, 169, 882, 871, 860, 35, 3812, 3790, 2, 3811, 3810, 34])).
% 1.98/1.65 tff(3829,plain,((~hskp25) | c0_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.65 tff(3830,plain,
% 1.98/1.65 (~hskp25),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3829, 35, 2])).
% 1.98/1.65 tff(3831,plain,
% 1.98/1.65 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3832,plain,
% 1.98/1.65 ((hskp26 | hskp25 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | c0_1(a16)) <=> (hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3833,plain,
% 1.98/1.65 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | c0_1(a16))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0)))),
% 1.98/1.65 inference(monotonicity,[status(thm)],[3832])).
% 1.98/1.65 tff(3834,plain,
% 1.98/1.65 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | c0_1(a16))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0))),
% 1.98/1.65 inference(transitivity,[status(thm)],[3833, 3831])).
% 1.98/1.65 tff(3835,plain,
% 1.98/1.65 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | (hskp26 | hskp25 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | c0_1(a16))),
% 1.98/1.65 inference(quant_inst,[status(thm)],[])).
% 1.98/1.65 tff(3836,plain,
% 1.98/1.65 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U))) | hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0)),
% 1.98/1.65 inference(modus_ponens,[status(thm)],[3835, 3834])).
% 1.98/1.65 tff(3837,plain,
% 1.98/1.65 (hskp26 | hskp25 | c0_1(a16) | (~c2_1(a16))),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3836, 169, 2, 1107])).
% 1.98/1.65 tff(3838,plain,
% 1.98/1.65 (hskp26),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[3837, 3830, 35, 3790])).
% 1.98/1.65 tff(3839,plain,
% 1.98/1.65 (c3_1(a10)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[689, 3838])).
% 1.98/1.65 tff(3840,plain,
% 1.98/1.65 (c2_1(a10)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[678, 3838])).
% 1.98/1.65 tff(3841,plain,
% 1.98/1.65 (c0_1(a10)),
% 1.98/1.65 inference(unit_resolution,[status(thm)],[666, 3838])).
% 1.98/1.65 tff(3842,plain,
% 1.98/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3843,plain,
% 1.98/1.65 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15))) <=> (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)))),
% 1.98/1.65 inference(rewrite,[status(thm)],[])).
% 1.98/1.65 tff(3844,plain,
% 1.98/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15))))),
% 1.98/1.66 inference(monotonicity,[status(thm)],[3843])).
% 1.98/1.66 tff(3845,plain,
% 1.98/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)))),
% 1.98/1.66 inference(transitivity,[status(thm)],[3844, 3842])).
% 1.98/1.66 tff(3846,plain,
% 1.98/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))),
% 1.98/1.66 inference(quant_inst,[status(thm)],[])).
% 1.98/1.66 tff(3847,plain,
% 1.98/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15))),
% 1.98/1.66 inference(modus_ponens,[status(thm)],[3846, 3845])).
% 1.98/1.66 tff(3848,plain,
% 1.98/1.66 (c3_1(a15)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3847, 169, 3841, 3840, 3839, 3821, 3812, 3820, 3811, 3810, 439])).
% 1.98/1.66 tff(3849,plain,
% 1.98/1.66 (~c1_1(a15)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[201, 3798])).
% 1.98/1.66 tff(3850,plain,
% 1.98/1.66 (hskp15 | (~c3_1(a15))),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3207, 169, 3821, 3849, 3820, 2497])).
% 1.98/1.66 tff(3851,plain,
% 1.98/1.66 (hskp15),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3850, 3848])).
% 1.98/1.66 tff(3852,plain,
% 1.98/1.66 (~c3_1(a25)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3414, 3851])).
% 1.98/1.66 tff(3853,plain,
% 1.98/1.66 (c0_1(a25)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3432, 3851])).
% 1.98/1.66 tff(3854,plain,
% 1.98/1.66 (~hskp11),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[2255, 3841, 3840, 3839])).
% 1.98/1.66 tff(3855,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a25) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a25) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3856,plain,
% 1.98/1.66 ((hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3))) <=> (hskp11 | c3_1(a25) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3857,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a25) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a25)) | (~c2_1(a25))))),
% 1.98/1.66 inference(monotonicity,[status(thm)],[3856])).
% 1.98/1.66 tff(3858,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a25) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 1.98/1.66 inference(transitivity,[status(thm)],[3857, 3855])).
% 1.98/1.66 tff(3859,plain,
% 1.98/1.66 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))),
% 1.98/1.66 inference(quant_inst,[status(thm)],[])).
% 1.98/1.66 tff(3860,plain,
% 1.98/1.66 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a25) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a25)) | (~c2_1(a25))),
% 1.98/1.66 inference(modus_ponens,[status(thm)],[3859, 3858])).
% 1.98/1.66 tff(3861,plain,
% 1.98/1.66 (~c2_1(a25)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3860, 169, 3854, 2381, 2412, 3853, 3852, 1126, 3819])).
% 1.98/1.66 tff(3862,plain,
% 1.98/1.66 (c1_1(a25)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3443, 3851])).
% 1.98/1.66 tff(3863,plain,
% 1.98/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a25) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a25) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3864,plain,
% 1.98/1.66 (((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25))) <=> (c3_1(a25) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3865,plain,
% 1.98/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a25) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25)))),
% 1.98/1.66 inference(monotonicity,[status(thm)],[3864])).
% 1.98/1.66 tff(3866,plain,
% 1.98/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a25) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25))),
% 1.98/1.66 inference(transitivity,[status(thm)],[3865, 3863])).
% 1.98/1.66 tff(3867,plain,
% 1.98/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | c3_1(a25) | c2_1(a25) | (~c1_1(a25)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)))),
% 1.98/1.66 inference(quant_inst,[status(thm)],[])).
% 1.98/1.66 tff(3868,plain,
% 1.98/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a25) | (~ndr1_0) | (~c2_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a25)),
% 1.98/1.66 inference(modus_ponens,[status(thm)],[3867, 3866])).
% 1.98/1.66 tff(3869,plain,
% 1.98/1.66 ($false),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3868, 169, 3841, 3840, 3839, 3853, 3862, 3852, 439, 3861])).
% 1.98/1.66 tff(3870,plain,(c0_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.66 tff(3871,plain,
% 1.98/1.66 (c0_1(a16)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3870, 2])).
% 1.98/1.66 tff(3872,plain,
% 1.98/1.66 (~hskp26),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1981, 1860, 3871, 2, 24])).
% 1.98/1.66 tff(3873,plain,
% 1.98/1.66 (hskp26 | hskp16 | c2_1(a16) | (~c0_1(a16))),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[597, 169, 2, 94])).
% 1.98/1.66 tff(3874,plain,
% 1.98/1.66 (hskp16),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3873, 3872, 3871, 24])).
% 1.98/1.66 tff(3875,plain,
% 1.98/1.66 (c1_1(a30)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[609, 3874])).
% 1.98/1.66 tff(3876,plain,
% 1.98/1.66 (~c2_1(a30)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[615, 3874])).
% 1.98/1.66 tff(3877,plain,
% 1.98/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3878,plain,
% 1.98/1.66 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3879,plain,
% 1.98/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16))))),
% 1.98/1.66 inference(monotonicity,[status(thm)],[3878])).
% 1.98/1.66 tff(3880,plain,
% 1.98/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)))),
% 1.98/1.66 inference(transitivity,[status(thm)],[3879, 3877])).
% 1.98/1.66 tff(3881,plain,
% 1.98/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.98/1.66 inference(quant_inst,[status(thm)],[])).
% 1.98/1.66 tff(3882,plain,
% 1.98/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16))),
% 1.98/1.66 inference(modus_ponens,[status(thm)],[3881, 3880])).
% 1.98/1.66 tff(3883,plain,
% 1.98/1.66 (~c0_1(a3)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3882, 169, 2381, 2412, 3871, 1863, 24, 2, 1862, 1861, 439])).
% 1.98/1.66 tff(3884,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c3_1(a16) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c1_1(a16) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c3_1(a16) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c1_1(a16) | (~c0_1(a16)))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3885,plain,
% 1.98/1.66 ((hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp4 | c3_1(a16) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c1_1(a16) | (~c0_1(a16)))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3886,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c3_1(a16) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c1_1(a16) | (~c0_1(a16))))),
% 1.98/1.66 inference(monotonicity,[status(thm)],[3885])).
% 1.98/1.66 tff(3887,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c3_1(a16) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c1_1(a16) | (~c0_1(a16)))),
% 1.98/1.66 inference(transitivity,[status(thm)],[3886, 3884])).
% 1.98/1.66 tff(3888,plain,
% 1.98/1.66 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a16) | c1_1(a16) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.98/1.66 inference(quant_inst,[status(thm)],[])).
% 1.98/1.66 tff(3889,plain,
% 1.98/1.66 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c3_1(a16) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | c1_1(a16) | (~c0_1(a16))),
% 1.98/1.66 inference(modus_ponens,[status(thm)],[3888, 3887])).
% 1.98/1.66 tff(3890,plain,
% 1.98/1.66 (hskp4),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3889, 169, 2392, 2412, 3871, 2, 632, 3, 3883])).
% 1.98/1.66 tff(3891,plain,
% 1.98/1.66 (c1_1(a6)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[133, 3890])).
% 1.98/1.66 tff(3892,plain,
% 1.98/1.66 (c3_1(a6)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[122, 3890])).
% 1.98/1.66 tff(3893,plain,
% 1.98/1.66 (~c2_1(a6)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[111, 3890])).
% 1.98/1.66 tff(3894,plain,
% 1.98/1.66 (hskp17),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1978, 3893, 3871, 3, 24, 2, 3872, 3892, 3891])).
% 1.98/1.66 tff(3895,plain,
% 1.98/1.66 (~c1_1(a31)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[71, 3894])).
% 1.98/1.66 tff(3896,plain,
% 1.98/1.66 (c0_1(a31)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[317, 3894])).
% 1.98/1.66 tff(3897,plain,
% 1.98/1.66 (~hskp13),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[2224, 3892, 3871, 3, 2, 3893, 3891])).
% 1.98/1.66 tff(3898,plain,
% 1.98/1.66 (~c3_1(a31)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[2138, 169, 3897, 3896, 3871, 3895, 24, 1616, 3])).
% 1.98/1.66 tff(3899,plain,
% 1.98/1.66 (c2_1(a31)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[328, 3894])).
% 1.98/1.66 tff(3900,plain,
% 1.98/1.66 (hskp20),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[2146, 169, 3872, 3896, 3899, 1227, 3898])).
% 1.98/1.66 tff(3901,plain,
% 1.98/1.66 (~c3_1(a37)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1239, 3900])).
% 1.98/1.66 tff(3902,plain,
% 1.98/1.66 (~c0_1(a37)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1245, 3900])).
% 1.98/1.66 tff(3903,plain,
% 1.98/1.66 (~c0_1(a30)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[621, 3874])).
% 1.98/1.66 tff(3904,plain,
% 1.98/1.66 (c3_1(a30)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1095, 169, 3871, 3891, 3892, 3903, 3876, 2, 3893, 13, 3])).
% 1.98/1.66 tff(3905,plain,
% 1.98/1.66 (c2_1(a37)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[2155, 3904, 3871, 3902, 3901, 3876, 2, 3, 3875])).
% 1.98/1.66 tff(3906,plain,
% 1.98/1.66 (hskp25),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[2162, 169, 3872, 3902, 3901, 1107, 3905])).
% 1.98/1.66 tff(3907,plain,
% 1.98/1.66 (c2_1(a9)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[859, 3906])).
% 1.98/1.66 tff(3908,plain,
% 1.98/1.66 (c0_1(a9)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[881, 3906])).
% 1.98/1.66 tff(3909,plain,
% 1.98/1.66 (c1_1(a9)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[870, 3906])).
% 1.98/1.66 tff(3910,plain,
% 1.98/1.66 ($false),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[2170, 3909, 3908, 1860, 3902, 3901, 3907, 3905])).
% 1.98/1.66 tff(3911,plain,((~hskp2) | c3_1(a16) | c1_1(a16) | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.66 tff(3912,plain,
% 1.98/1.66 (~hskp2),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3911, 24, 3, 2])).
% 1.98/1.66 tff(3913,plain,
% 1.98/1.66 (hskp14 | hskp2 | c2_1(a16) | c1_1(a16)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[708, 169, 3871, 700])).
% 1.98/1.66 tff(3914,plain,
% 1.98/1.66 (hskp14),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3913, 3912, 24, 3])).
% 1.98/1.66 tff(3915,plain,
% 1.98/1.66 (~c1_1(a24)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1024, 3914])).
% 1.98/1.66 tff(3916,plain,
% 1.98/1.66 (~c0_1(a24)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1030, 3914])).
% 1.98/1.66 tff(3917,plain,
% 1.98/1.66 (c2_1(a24)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1041, 3914])).
% 1.98/1.66 tff(3918,plain,
% 1.98/1.66 (hskp3),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1048, 169, 3912, 3917, 3916, 3915, 23])).
% 1.98/1.66 tff(3919,plain,
% 1.98/1.66 (~c3_1(a5)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[948, 3918])).
% 1.98/1.66 tff(3920,plain,
% 1.98/1.66 (~c2_1(a5)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[361, 3918])).
% 1.98/1.66 tff(3921,plain,
% 1.98/1.66 (~c1_1(a5)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[367, 3918])).
% 1.98/1.66 tff(3922,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3923,plain,
% 1.98/1.66 (((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a5) | c1_1(a5) | c0_1(a5)) <=> (c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3924,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))))),
% 1.98/1.66 inference(monotonicity,[status(thm)],[3923])).
% 1.98/1.66 tff(3925,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 1.98/1.66 inference(transitivity,[status(thm)],[3924, 3922])).
% 1.98/1.66 tff(3926,plain,
% 1.98/1.66 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a5) | c1_1(a5) | c0_1(a5))),
% 1.98/1.66 inference(quant_inst,[status(thm)],[])).
% 1.98/1.66 tff(3927,plain,
% 1.98/1.66 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | c0_1(a5) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))),
% 1.98/1.66 inference(modus_ponens,[status(thm)],[3926, 3925])).
% 1.98/1.66 tff(3928,plain,
% 1.98/1.66 (c0_1(a5) | c0_1(a3)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3927, 169, 2392, 2381, 3921, 3919, 45])).
% 1.98/1.66 tff(3929,plain,
% 1.98/1.66 (c0_1(a5)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3928, 1])).
% 1.98/1.66 tff(3930,plain,
% 1.98/1.66 (hskp4),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3889, 169, 2392, 2412, 3871, 2, 632, 3, 1])).
% 1.98/1.66 tff(3931,plain,
% 1.98/1.66 (c1_1(a6)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[133, 3930])).
% 1.98/1.66 tff(3932,plain,
% 1.98/1.66 (~c2_1(a6)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[111, 3930])).
% 1.98/1.66 tff(3933,plain,
% 1.98/1.66 (c3_1(a6)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[122, 3930])).
% 1.98/1.66 tff(3934,plain,
% 1.98/1.66 (~hskp13),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[2224, 729, 3871, 3, 2, 728, 730])).
% 1.98/1.66 tff(3935,plain,
% 1.98/1.66 (hskp26),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1978, 643, 3871, 3, 24, 2, 728, 729, 730])).
% 1.98/1.66 tff(3936,plain,
% 1.98/1.66 (c0_1(a10)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[666, 3935])).
% 1.98/1.66 tff(3937,plain,
% 1.98/1.66 (c3_1(a10)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[689, 3935])).
% 1.98/1.66 tff(3938,plain,
% 1.98/1.66 (c1_1(a10)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1625, 3937, 3921, 1566, 3936, 3920, 3934])).
% 1.98/1.66 tff(3939,plain,
% 1.98/1.66 (c2_1(a10)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[678, 3935])).
% 1.98/1.66 tff(3940,plain,
% 1.98/1.66 (~hskp18),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1639, 3936, 3917, 728, 730, 3937, 3921, 3920, 1566, 3939, 643, 3871, 3, 3916, 3915, 2, 729])).
% 1.98/1.66 tff(3941,plain,
% 1.98/1.66 (hskp18 | hskp17 | (~c0_1(a6))),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[941, 169, 729, 728, 741])).
% 1.98/1.66 tff(3942,plain,
% 1.98/1.66 (~c0_1(a6)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3941, 3940, 643])).
% 1.98/1.66 tff(3943,plain,
% 1.98/1.66 (~hskp6),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1378, 3940, 3871, 3, 643, 3915, 3917, 2, 3916])).
% 1.98/1.66 tff(3944,plain,
% 1.98/1.66 ($false),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1604, 169, 3943, 3939, 3937, 729, 728, 1298, 3942, 3938])).
% 1.98/1.66 tff(3945,plain,(hskp17 | (~c3_1(a6)) | c2_1(a6) | c1_1(a16) | c3_1(a16) | (~c0_1(a5)) | (~c1_1(a6)) | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.66 tff(3946,plain,
% 1.98/1.66 (hskp17),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3945, 3933, 3932, 3, 2, 3929, 3931, 24])).
% 1.98/1.66 tff(3947,plain,
% 1.98/1.66 (~c1_1(a31)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[71, 3946])).
% 1.98/1.66 tff(3948,plain,
% 1.98/1.66 (c0_1(a31)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[317, 3946])).
% 1.98/1.66 tff(3949,plain,
% 1.98/1.66 (~hskp13),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[2224, 3933, 3871, 3, 2, 3932, 3931])).
% 1.98/1.66 tff(3950,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3951,plain,
% 1.98/1.66 ((hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5))) <=> (hskp13 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3952,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 1.98/1.66 inference(monotonicity,[status(thm)],[3951])).
% 1.98/1.66 tff(3953,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 1.98/1.66 inference(transitivity,[status(thm)],[3952, 3950])).
% 1.98/1.66 tff(3954,plain,
% 1.98/1.66 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)))),
% 1.98/1.66 inference(quant_inst,[status(thm)],[])).
% 1.98/1.66 tff(3955,plain,
% 1.98/1.66 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a31)) | (~c0_1(a31))),
% 1.98/1.66 inference(modus_ponens,[status(thm)],[3954, 3953])).
% 1.98/1.66 tff(3956,plain,
% 1.98/1.66 (~c3_1(a31)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3955, 169, 3949, 3948, 3947, 3921, 3920, 1616, 3929])).
% 1.98/1.66 tff(3957,plain,
% 1.98/1.66 ($false),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3592, 169, 2392, 2381, 1055, 1054, 45, 1, 2201])).
% 1.98/1.66 tff(3958,plain,(c3_1(a24) | c0_1(a24) | c1_1(a24) | c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.66 tff(3959,plain,
% 1.98/1.66 (c3_1(a24)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3958, 1, 3915, 3916])).
% 1.98/1.66 tff(3960,assumption,(c3_1(a24)), introduced(assumption)).
% 1.98/1.66 tff(3961,assumption,(hskp20), introduced(assumption)).
% 1.98/1.66 tff(3962,plain,
% 1.98/1.66 (~c3_1(a37)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1239, 3961])).
% 1.98/1.66 tff(3963,plain,
% 1.98/1.66 (~c0_1(a37)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1245, 3961])).
% 1.98/1.66 tff(3964,plain,
% 1.98/1.66 (c1_1(a37)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1256, 3961])).
% 1.98/1.66 tff(3965,plain,
% 1.98/1.66 ($false),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[1326, 169, 3964, 1056, 3963, 3962, 1055, 1054, 83, 3960])).
% 1.98/1.66 tff(3966,plain,((~hskp20) | (~c2_1(a24)) | c0_1(a24) | c1_1(a24) | (~c3_1(a24))), inference(lemma,lemma(discharge,[]))).
% 1.98/1.66 tff(3967,plain,
% 1.98/1.66 (~hskp20),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3966, 3959, 3916, 3915, 3917])).
% 1.98/1.66 tff(3968,plain,
% 1.98/1.66 (c2_1(a31)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[328, 3946])).
% 1.98/1.66 tff(3969,plain,
% 1.98/1.66 (hskp26 | hskp20 | c3_1(a31)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[2146, 169, 3948, 3968, 1227])).
% 1.98/1.66 tff(3970,plain,
% 1.98/1.66 (hskp26),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3969, 3967, 3956])).
% 1.98/1.66 tff(3971,plain,
% 1.98/1.66 (c3_1(a10)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[689, 3970])).
% 1.98/1.66 tff(3972,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3973,plain,
% 1.98/1.66 ((hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3))) <=> (hskp11 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.98/1.66 inference(rewrite,[status(thm)],[])).
% 1.98/1.66 tff(3974,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31))))),
% 1.98/1.66 inference(monotonicity,[status(thm)],[3973])).
% 1.98/1.66 tff(3975,plain,
% 1.98/1.66 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31)))),
% 1.98/1.66 inference(transitivity,[status(thm)],[3974, 3972])).
% 1.98/1.66 tff(3976,plain,
% 1.98/1.66 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c0_1(a31)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))),
% 1.98/1.66 inference(quant_inst,[status(thm)],[])).
% 1.98/1.66 tff(3977,plain,
% 1.98/1.66 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a31)) | c3_1(a31) | (~c0_1(a31))),
% 1.98/1.66 inference(modus_ponens,[status(thm)],[3976, 3975])).
% 1.98/1.66 tff(3978,plain,
% 1.98/1.66 (hskp11),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[3977, 169, 2381, 2412, 3948, 3968, 1126, 3956, 1])).
% 1.98/1.66 tff(3979,plain,
% 1.98/1.66 (c0_1(a10)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[666, 3970])).
% 1.98/1.66 tff(3980,plain,
% 1.98/1.66 (c2_1(a10)),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[678, 3970])).
% 1.98/1.66 tff(3981,plain,
% 1.98/1.66 ($false),
% 1.98/1.66 inference(unit_resolution,[status(thm)],[2255, 3980, 3979, 3978, 3971])).
% 1.98/1.66 tff(3982,plain,(c0_1(a3) | c1_1(a16) | c3_1(a16) | c2_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.67 tff(3983,plain,
% 1.98/1.67 (c0_1(a3)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3982, 24, 2, 3])).
% 1.98/1.67 tff(3984,plain,
% 1.98/1.67 ($false),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3804, 169, 2381, 2412, 1056, 1054, 1580, 2413, 2201])).
% 1.98/1.67 tff(3985,plain,(c3_1(a24) | (~c2_1(a24)) | c1_1(a24) | (~c0_1(a3))), inference(lemma,lemma(discharge,[]))).
% 1.98/1.67 tff(3986,plain,
% 1.98/1.67 (c3_1(a24)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3985, 3917, 3915, 3983])).
% 1.98/1.67 tff(3987,plain,
% 1.98/1.67 (hskp4 | (~c3_1(a24))),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[2217, 169, 3871, 3916, 3915, 24, 65, 3])).
% 1.98/1.67 tff(3988,plain,
% 1.98/1.67 (hskp4),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3987, 3986])).
% 1.98/1.67 tff(3989,plain,
% 1.98/1.67 (~c2_1(a6)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[111, 3988])).
% 1.98/1.67 tff(3990,plain,
% 1.98/1.67 (c3_1(a6)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[122, 3988])).
% 1.98/1.67 tff(3991,plain,
% 1.98/1.67 (c1_1(a6)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[133, 3988])).
% 1.98/1.67 tff(3992,plain,
% 1.98/1.67 (c0_1(a5)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[1081, 169, 3871, 3991, 3990, 2, 3989, 3920, 3919, 13, 3])).
% 1.98/1.67 tff(3993,plain,
% 1.98/1.67 (hskp17),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3945, 3992, 3989, 3, 2, 3990, 3991, 24])).
% 1.98/1.67 tff(3994,plain,
% 1.98/1.67 (~c1_1(a31)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[71, 3993])).
% 1.98/1.67 tff(3995,plain,
% 1.98/1.67 (c2_1(a31)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[328, 3993])).
% 1.98/1.67 tff(3996,plain,
% 1.98/1.67 (c3_1(a31)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[2424, 3995, 3983, 3994])).
% 1.98/1.67 tff(3997,plain,
% 1.98/1.67 (c0_1(a31)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[317, 3993])).
% 1.98/1.67 tff(3998,plain,
% 1.98/1.67 (~hskp13),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[2224, 3990, 3871, 3, 2, 3989, 3991])).
% 1.98/1.67 tff(3999,plain,
% 1.98/1.67 ($false),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3955, 169, 3998, 3997, 3994, 3921, 3920, 1616, 3996, 3992])).
% 1.98/1.67 tff(4000,plain,(c2_1(a16) | c1_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.67 tff(4001,plain,
% 1.98/1.67 (c2_1(a16)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4000, 3, 2])).
% 1.98/1.67 tff(4002,plain,
% 1.98/1.67 (~c0_1(a3)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[2450, 4001, 3])).
% 1.98/1.67 tff(4003,plain,
% 1.98/1.67 (~hskp9),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[579, 4001])).
% 1.98/1.67 tff(4004,plain,
% 1.98/1.67 (hskp8),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3765, 4003, 4002])).
% 1.98/1.67 tff(4005,plain,
% 1.98/1.67 (hskp4),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3889, 169, 2392, 2412, 3871, 2, 632, 3, 4002])).
% 1.98/1.67 tff(4006,plain,
% 1.98/1.67 (c1_1(a6)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[133, 4005])).
% 1.98/1.67 tff(4007,plain,
% 1.98/1.67 (~c2_1(a6)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[111, 4005])).
% 1.98/1.67 tff(4008,plain,
% 1.98/1.67 (c3_1(a6)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[122, 4005])).
% 1.98/1.67 tff(4009,plain,
% 1.98/1.67 (~hskp13),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[2224, 4008, 3871, 3, 2, 4007, 4006])).
% 1.98/1.67 tff(4010,plain,
% 1.98/1.67 (~c2_1(a15)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[184, 4004])).
% 1.98/1.67 tff(4011,plain,
% 1.98/1.67 (~c1_1(a15)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[201, 4004])).
% 1.98/1.67 tff(4012,plain,
% 1.98/1.67 (c0_1(a15)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[195, 4004])).
% 1.98/1.67 tff(4013,plain,
% 1.98/1.67 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4014,plain,
% 1.98/1.67 ((hskp13 | (~ndr1_0) | c1_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15))) <=> (hskp13 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4015,plain,
% 1.98/1.67 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15))))),
% 1.98/1.67 inference(monotonicity,[status(thm)],[4014])).
% 1.98/1.67 tff(4016,plain,
% 1.98/1.67 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.98/1.67 inference(transitivity,[status(thm)],[4015, 4013])).
% 1.98/1.67 tff(4017,plain,
% 1.98/1.67 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a15) | (~c0_1(a15)) | (~c3_1(a15)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))),
% 1.98/1.67 inference(quant_inst,[status(thm)],[])).
% 1.98/1.67 tff(4018,plain,
% 1.98/1.67 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c0_1(a15))),
% 1.98/1.67 inference(modus_ponens,[status(thm)],[4017, 4016])).
% 1.98/1.67 tff(4019,plain,
% 1.98/1.67 (hskp13 | (~c3_1(a15))),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4018, 169, 4012, 4011, 4010, 1616])).
% 1.98/1.67 tff(4020,plain,
% 1.98/1.67 (~c3_1(a15)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4019, 4009])).
% 1.98/1.67 tff(4021,plain,
% 1.98/1.67 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a16)))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4022,plain,
% 1.98/1.67 ((hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3))) <=> (hskp11 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a16)))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4023,plain,
% 1.98/1.67 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a16))))),
% 1.98/1.67 inference(monotonicity,[status(thm)],[4022])).
% 1.98/1.67 tff(4024,plain,
% 1.98/1.67 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a16)))),
% 1.98/1.67 inference(transitivity,[status(thm)],[4023, 4021])).
% 1.98/1.67 tff(4025,plain,
% 1.98/1.67 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a3) | (~c3_1(a3)) | (~c2_1(a3)))),
% 1.98/1.67 inference(quant_inst,[status(thm)],[])).
% 1.98/1.67 tff(4026,plain,
% 1.98/1.67 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c3_1(a3)) | (~c0_1(a16))),
% 1.98/1.67 inference(modus_ponens,[status(thm)],[4025, 4024])).
% 1.98/1.67 tff(4027,plain,
% 1.98/1.67 (hskp11),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4026, 169, 2381, 2412, 3871, 4001, 2, 1126, 4002])).
% 1.98/1.67 tff(4028,plain,
% 1.98/1.67 ($false),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[2255, 679, 667, 2244, 690])).
% 1.98/1.67 tff(4029,plain,((~hskp26) | (~hskp11)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.67 tff(4030,plain,
% 1.98/1.67 (~hskp26),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4029, 4027])).
% 1.98/1.67 tff(4031,plain,
% 1.98/1.67 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp26 | hskp16 | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4032,plain,
% 1.98/1.67 ((hskp26 | hskp16 | (~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c0_1(a15))) <=> (hskp26 | hskp16 | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4033,plain,
% 1.98/1.67 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15))))),
% 1.98/1.67 inference(monotonicity,[status(thm)],[4032])).
% 1.98/1.67 tff(4034,plain,
% 1.98/1.67 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp26 | hskp16 | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15)))),
% 1.98/1.67 inference(transitivity,[status(thm)],[4033, 4031])).
% 1.98/1.67 tff(4035,plain,
% 1.98/1.67 ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c0_1(a15)))),
% 1.98/1.67 inference(quant_inst,[status(thm)],[])).
% 1.98/1.67 tff(4036,plain,
% 1.98/1.67 ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp26 | hskp16 | c2_1(a15) | (~ndr1_0) | c3_1(a15) | (~c0_1(a15))),
% 1.98/1.67 inference(modus_ponens,[status(thm)],[4035, 4034])).
% 1.98/1.67 tff(4037,plain,
% 1.98/1.67 (hskp26 | hskp16 | c3_1(a15)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4036, 169, 4012, 4010, 94])).
% 1.98/1.67 tff(4038,plain,
% 1.98/1.67 (hskp16),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4037, 4030, 4020])).
% 1.98/1.67 tff(4039,plain,
% 1.98/1.67 (c1_1(a30)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[609, 4038])).
% 1.98/1.67 tff(4040,plain,
% 1.98/1.67 (~c2_1(a30)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[615, 4038])).
% 1.98/1.67 tff(4041,plain,
% 1.98/1.67 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4042,plain,
% 1.98/1.67 ((hskp26 | hskp20 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16))) <=> (hskp26 | hskp20 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4043,plain,
% 1.98/1.67 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16))))),
% 1.98/1.67 inference(monotonicity,[status(thm)],[4042])).
% 1.98/1.67 tff(4044,plain,
% 1.98/1.67 (((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)))),
% 1.98/1.67 inference(transitivity,[status(thm)],[4043, 4041])).
% 1.98/1.67 tff(4045,plain,
% 1.98/1.67 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp20 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)))),
% 1.98/1.67 inference(quant_inst,[status(thm)],[])).
% 1.98/1.67 tff(4046,plain,
% 1.98/1.67 ((~![U: $i] : (hskp26 | hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp20 | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16))),
% 1.98/1.67 inference(modus_ponens,[status(thm)],[4045, 4044])).
% 1.98/1.67 tff(4047,plain,
% 1.98/1.67 (hskp26 | hskp20 | (~c2_1(a16)) | (~c0_1(a16))),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4046, 169, 2, 1227])).
% 1.98/1.67 tff(4048,plain,
% 1.98/1.67 (hskp20),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4047, 4030, 3871, 4001])).
% 1.98/1.67 tff(4049,plain,
% 1.98/1.67 (~c3_1(a37)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[1239, 4048])).
% 1.98/1.67 tff(4050,plain,
% 1.98/1.67 (~c0_1(a37)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[1245, 4048])).
% 1.98/1.67 tff(4051,plain,
% 1.98/1.67 (~c3_1(a19)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[1185, 4027])).
% 1.98/1.67 tff(4052,plain,
% 1.98/1.67 (~c1_1(a19)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[1209, 4027])).
% 1.98/1.67 tff(4053,plain,
% 1.98/1.67 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c0_1(a19))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c0_1(a19))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4054,plain,
% 1.98/1.67 (((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a19) | c1_1(a19) | c0_1(a19)) <=> (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c0_1(a19))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4055,plain,
% 1.98/1.67 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a19) | c1_1(a19) | c0_1(a19))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c0_1(a19)))),
% 1.98/1.67 inference(monotonicity,[status(thm)],[4054])).
% 1.98/1.67 tff(4056,plain,
% 1.98/1.67 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a19) | c1_1(a19) | c0_1(a19))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c0_1(a19))),
% 1.98/1.67 inference(transitivity,[status(thm)],[4055, 4053])).
% 1.98/1.67 tff(4057,plain,
% 1.98/1.67 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | ((~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c3_1(a19) | c1_1(a19) | c0_1(a19))),
% 1.98/1.67 inference(quant_inst,[status(thm)],[])).
% 1.98/1.67 tff(4058,plain,
% 1.98/1.67 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)) | c0_1(a19)),
% 1.98/1.67 inference(modus_ponens,[status(thm)],[4057, 4056])).
% 1.98/1.67 tff(4059,plain,
% 1.98/1.67 (c0_1(a19)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4058, 169, 2392, 2381, 4052, 4051, 45, 4002])).
% 1.98/1.67 tff(4060,plain,
% 1.98/1.67 (~c0_1(a30)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[621, 4038])).
% 1.98/1.67 tff(4061,plain,
% 1.98/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a30) | c2_1(a30) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a30) | c2_1(a30) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c3_1(a30))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4062,plain,
% 1.98/1.67 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a30) | c0_1(a30) | c3_1(a30)) <=> (c0_1(a30) | c2_1(a30) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c3_1(a30))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4063,plain,
% 1.98/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a30) | c2_1(a30) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c3_1(a30)))),
% 1.98/1.67 inference(monotonicity,[status(thm)],[4062])).
% 1.98/1.67 tff(4064,plain,
% 1.98/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a30) | c0_1(a30) | c3_1(a30))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a30) | c2_1(a30) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c3_1(a30))),
% 1.98/1.67 inference(transitivity,[status(thm)],[4063, 4061])).
% 1.98/1.67 tff(4065,plain,
% 1.98/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a30) | c0_1(a30) | c3_1(a30))),
% 1.98/1.67 inference(quant_inst,[status(thm)],[])).
% 1.98/1.67 tff(4066,plain,
% 1.98/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a30) | c2_1(a30) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c3_1(a30)),
% 1.98/1.67 inference(modus_ponens,[status(thm)],[4065, 4064])).
% 1.98/1.67 tff(4067,plain,
% 1.98/1.67 (c3_1(a30)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4066, 169, 4006, 4008, 4060, 4040, 4052, 4051, 4007, 13, 4059])).
% 1.98/1.67 tff(4068,plain,
% 1.98/1.67 (c2_1(a37)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[2155, 4067, 3871, 4050, 4049, 4040, 2, 3, 4039])).
% 1.98/1.67 tff(4069,plain,
% 1.98/1.67 (hskp25 | (~c2_1(a37))),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[2162, 169, 4030, 4050, 4049, 1107])).
% 1.98/1.67 tff(4070,plain,
% 1.98/1.67 (hskp25),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4069, 4068])).
% 1.98/1.67 tff(4071,plain,
% 1.98/1.67 (c2_1(a9)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[859, 4070])).
% 1.98/1.67 tff(4072,plain,
% 1.98/1.67 (c0_1(a9)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[881, 4070])).
% 1.98/1.67 tff(4073,plain,
% 1.98/1.67 (c1_1(a9)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[870, 4070])).
% 1.98/1.67 tff(4074,plain,
% 1.98/1.67 (~hskp2),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[2170, 4073, 4072, 4050, 4049, 4071, 4068])).
% 1.98/1.67 tff(4075,plain,
% 1.98/1.67 (hskp14),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[2482, 4074, 4004])).
% 1.98/1.67 tff(4076,plain,
% 1.98/1.67 (c2_1(a24)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[1041, 4075])).
% 1.98/1.67 tff(4077,plain,
% 1.98/1.67 (~c1_1(a24)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[1024, 4075])).
% 1.98/1.67 tff(4078,plain,
% 1.98/1.67 (~c0_1(a24)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[1030, 4075])).
% 1.98/1.67 tff(4079,plain,
% 1.98/1.67 (c3_1(a24)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3958, 4078, 4002, 4077])).
% 1.98/1.67 tff(4080,plain,
% 1.98/1.67 ($false),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3966, 4079, 4078, 4048, 4077, 4076])).
% 1.98/1.67 tff(4081,plain,(c1_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.67 tff(4082,plain,
% 1.98/1.67 (c1_1(a16)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4081, 2])).
% 1.98/1.67 tff(4083,plain,
% 1.98/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)) | (~c1_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4084,plain,
% 1.98/1.67 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16))) <=> (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.98/1.67 inference(rewrite,[status(thm)],[])).
% 1.98/1.67 tff(4085,plain,
% 1.98/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)) | (~c1_1(a16))))),
% 1.98/1.67 inference(monotonicity,[status(thm)],[4084])).
% 1.98/1.67 tff(4086,plain,
% 1.98/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.98/1.67 inference(transitivity,[status(thm)],[4085, 4083])).
% 1.98/1.67 tff(4087,plain,
% 1.98/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a16) | c3_1(a16) | (~c0_1(a16)))),
% 1.98/1.67 inference(quant_inst,[status(thm)],[])).
% 1.98/1.67 tff(4088,plain,
% 1.98/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a16) | c3_1(a16) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c0_1(a16)) | (~c1_1(a16))),
% 1.98/1.67 inference(modus_ponens,[status(thm)],[4087, 4086])).
% 1.98/1.67 tff(4089,plain,
% 1.98/1.67 (~c0_1(a3)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4088, 169, 2381, 2412, 3871, 24, 2, 439, 4082])).
% 1.98/1.67 tff(4090,plain,
% 1.98/1.67 ($false),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3457, 169, 2392, 2381, 2012, 1569, 1570, 45, 1])).
% 1.98/1.67 tff(4091,plain,((~hskp18) | c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.67 tff(4092,plain,
% 1.98/1.67 (~hskp18),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[4091, 4089])).
% 1.98/1.67 tff(4093,plain,
% 1.98/1.67 (hskp27),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3759, 84, 4089])).
% 1.98/1.67 tff(4094,plain,
% 1.98/1.67 (hskp17),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[780, 4093, 3871, 2, 4082, 24, 4092])).
% 1.98/1.67 tff(4095,plain,
% 1.98/1.67 (c2_1(a31)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[328, 4094])).
% 1.98/1.67 tff(4096,plain,
% 1.98/1.67 (c0_1(a31)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[317, 4094])).
% 1.98/1.67 tff(4097,plain,
% 1.98/1.67 (~c3_1(a31)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[2271, 169, 4096, 4095, 3871, 24, 2, 439, 4082])).
% 1.98/1.67 tff(4098,plain,
% 1.98/1.67 (~c1_1(a31)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[71, 4094])).
% 1.98/1.67 tff(4099,plain,
% 1.98/1.67 (hskp4),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3599, 4097, 4096, 4098, 4095])).
% 1.98/1.67 tff(4100,plain,
% 1.98/1.67 (~c2_1(a6)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[111, 4099])).
% 1.98/1.67 tff(4101,plain,
% 1.98/1.67 (hskp16),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[3873, 84, 3871, 24])).
% 1.98/1.67 tff(4102,plain,
% 1.98/1.67 (~c2_1(a30)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[615, 4101])).
% 1.98/1.67 tff(4103,plain,
% 1.98/1.67 (~c0_1(a30)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[621, 4101])).
% 1.98/1.67 tff(4104,plain,
% 1.98/1.67 (c3_1(a6)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[122, 4099])).
% 1.98/1.67 tff(4105,plain,
% 1.98/1.67 (c1_1(a6)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[133, 4099])).
% 1.98/1.67 tff(4106,plain,
% 1.98/1.67 (c3_1(a30)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[2343, 169, 4096, 4105, 4104, 4098, 4103, 4102, 4100, 13, 4097])).
% 1.98/1.67 tff(4107,plain,
% 1.98/1.67 (hskp20 | c3_1(a31)),
% 1.98/1.67 inference(unit_resolution,[status(thm)],[2146, 169, 84, 4096, 4095, 1227])).
% 1.98/1.68 tff(4108,plain,
% 1.98/1.68 (hskp20),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[4107, 4097])).
% 1.98/1.68 tff(4109,plain,
% 1.98/1.68 (~c0_1(a37)),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[1245, 4108])).
% 1.98/1.68 tff(4110,plain,
% 1.98/1.68 (~c3_1(a37)),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[1239, 4108])).
% 1.98/1.68 tff(4111,plain,
% 1.98/1.68 (~c2_1(a37)),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[2360, 4110, 4082, 24, 2, 4109, 84])).
% 1.98/1.68 tff(4112,plain,
% 1.98/1.68 (hskp11),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[3977, 169, 2381, 2412, 4096, 4095, 1126, 4097, 4089])).
% 1.98/1.68 tff(4113,plain,
% 1.98/1.68 (~c3_1(a19)),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[1185, 4112])).
% 1.98/1.68 tff(4114,plain,
% 1.98/1.68 (~c1_1(a19)),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[1209, 4112])).
% 1.98/1.68 tff(4115,plain,
% 1.98/1.68 (c1_1(a30)),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[609, 4101])).
% 1.98/1.68 tff(4116,plain,
% 1.98/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c2_1(a30) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))),
% 1.98/1.68 inference(rewrite,[status(thm)],[])).
% 1.98/1.68 tff(4117,plain,
% 1.98/1.68 (((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37)) <=> (c0_1(a37) | c3_1(a37) | c2_1(a30) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))),
% 1.98/1.68 inference(rewrite,[status(thm)],[])).
% 1.98/1.68 tff(4118,plain,
% 1.98/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c2_1(a30) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37)))),
% 1.98/1.68 inference(monotonicity,[status(thm)],[4117])).
% 1.98/1.68 tff(4119,plain,
% 1.98/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37))),
% 1.98/1.68 inference(transitivity,[status(thm)],[4118, 4116])).
% 1.98/1.68 tff(4120,plain,
% 1.98/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a30) | (~c1_1(a30)) | (~c3_1(a30)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37))),
% 1.98/1.68 inference(quant_inst,[status(thm)],[])).
% 1.98/1.68 tff(4121,plain,
% 1.98/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c2_1(a30) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a30)) | (~c3_1(a30)) | c2_1(a37)),
% 1.98/1.68 inference(modus_ponens,[status(thm)],[4120, 4119])).
% 1.98/1.68 tff(4122,plain,
% 1.98/1.68 (~c0_1(a19)),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[4121, 169, 4115, 4109, 4110, 4102, 4114, 4113, 13, 4111, 4106])).
% 1.98/1.68 tff(4123,plain,
% 1.98/1.68 ($false),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[4058, 169, 2392, 2381, 4114, 4113, 45, 4089, 4122])).
% 1.98/1.68 tff(4124,plain,(hskp26 | c2_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.68 tff(4125,plain,
% 1.98/1.68 (hskp26),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[4124, 24, 2])).
% 1.98/1.68 tff(4126,plain,
% 1.98/1.68 (c3_1(a10)),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[689, 4125])).
% 1.98/1.68 tff(4127,plain,
% 1.98/1.68 (c2_1(a10)),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[678, 4125])).
% 1.98/1.68 tff(4128,plain,
% 1.98/1.68 (c0_1(a10)),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[666, 4125])).
% 1.98/1.68 tff(4129,plain,
% 1.98/1.68 ($false),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[719, 169, 4128, 4127, 4126, 3871, 24, 2, 439, 4082])).
% 1.98/1.68 tff(4130,plain,(c2_1(a16) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.68 tff(4131,plain,
% 1.98/1.68 (c2_1(a16)),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[4130, 2])).
% 1.98/1.68 tff(4132,plain,
% 1.98/1.68 (~hskp9),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[579, 4131])).
% 1.98/1.68 tff(4133,plain,
% 1.98/1.68 (hskp8),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[3765, 1, 4132])).
% 1.98/1.68 tff(4134,plain,
% 1.98/1.68 (hskp11),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[4026, 169, 2381, 2412, 3871, 4131, 2, 1126, 1])).
% 1.98/1.68 tff(4135,plain,
% 1.98/1.68 (~c3_1(a19)),
% 1.98/1.68 inference(unit_resolution,[status(thm)],[1185, 4134])).
% 1.98/1.68 tff(4136,plain,
% 2.01/1.68 (~c1_1(a19)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[1209, 4134])).
% 2.01/1.68 tff(4137,plain,
% 2.01/1.68 (c0_1(a19)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4058, 169, 2392, 2381, 4136, 4135, 45, 1])).
% 2.01/1.68 tff(4138,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c0_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c0_1(a19)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(4139,plain,
% 2.01/1.68 ((hskp4 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp4 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c0_1(a19)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(4140,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c0_1(a19))))),
% 2.01/1.68 inference(monotonicity,[status(thm)],[4139])).
% 2.01/1.68 tff(4141,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c0_1(a19)))),
% 2.01/1.68 inference(transitivity,[status(thm)],[4140, 4138])).
% 2.01/1.68 tff(4142,plain,
% 2.01/1.68 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.01/1.68 inference(quant_inst,[status(thm)],[])).
% 2.01/1.68 tff(4143,plain,
% 2.01/1.68 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a19) | c3_1(a19) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c0_1(a19))),
% 2.01/1.68 inference(modus_ponens,[status(thm)],[4142, 4141])).
% 2.01/1.68 tff(4144,plain,
% 2.01/1.68 (hskp4 | (~c0_1(a19))),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4143, 169, 2392, 2412, 4136, 4135, 632, 1])).
% 2.01/1.68 tff(4145,plain,
% 2.01/1.68 (hskp4),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4144, 4137])).
% 2.01/1.68 tff(4146,plain,
% 2.01/1.68 (~c2_1(a6)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[111, 4145])).
% 2.01/1.68 tff(4147,plain,
% 2.01/1.68 (~hskp26),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4029, 4134])).
% 2.01/1.68 tff(4148,plain,
% 2.01/1.68 (hskp20),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4047, 4147, 3871, 4131])).
% 2.01/1.68 tff(4149,plain,
% 2.01/1.68 (~c3_1(a37)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[1239, 4148])).
% 2.01/1.68 tff(4150,plain,
% 2.01/1.68 (~c0_1(a37)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[1245, 4148])).
% 2.01/1.68 tff(4151,plain,
% 2.01/1.68 (c3_1(a6)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[122, 4145])).
% 2.01/1.68 tff(4152,plain,
% 2.01/1.68 (c1_1(a6)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[133, 4145])).
% 2.01/1.68 tff(4153,assumption,(c0_1(a19)), introduced(assumption)).
% 2.01/1.68 tff(4154,assumption,(~c3_1(a19)), introduced(assumption)).
% 2.01/1.68 tff(4155,assumption,(~c1_1(a19)), introduced(assumption)).
% 2.01/1.68 tff(4156,plain,
% 2.01/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c2_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c2_1(a37))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(4157,plain,
% 2.01/1.68 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37)) <=> (c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c2_1(a37))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(4158,plain,
% 2.01/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c2_1(a37)))),
% 2.01/1.68 inference(monotonicity,[status(thm)],[4157])).
% 2.01/1.68 tff(4159,plain,
% 2.01/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c2_1(a37))),
% 2.01/1.68 inference(transitivity,[status(thm)],[4158, 4156])).
% 2.01/1.68 tff(4160,plain,
% 2.01/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c3_1(a19) | c1_1(a19) | (~c0_1(a19)) | c2_1(a37) | c0_1(a37) | c3_1(a37))),
% 2.01/1.68 inference(quant_inst,[status(thm)],[])).
% 2.01/1.68 tff(4161,plain,
% 2.01/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a19)) | c2_1(a37)),
% 2.01/1.68 inference(modus_ponens,[status(thm)],[4160, 4159])).
% 2.01/1.68 tff(4162,plain,
% 2.01/1.68 ($false),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4161, 169, 730, 729, 2153, 2152, 4155, 4154, 728, 13, 2151, 4153])).
% 2.01/1.68 tff(4163,plain,(c2_1(a37) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a37) | c3_1(a37) | c1_1(a19) | c3_1(a19) | c2_1(a6) | (~c0_1(a19))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.68 tff(4164,plain,
% 2.01/1.68 (c2_1(a37)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4163, 4152, 4151, 4150, 4149, 4136, 4135, 4146, 4137])).
% 2.01/1.68 tff(4165,plain,
% 2.01/1.68 (hskp25 | (~c2_1(a37))),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2162, 169, 4147, 4150, 4149, 1107])).
% 2.01/1.68 tff(4166,plain,
% 2.01/1.68 (hskp25),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4165, 4164])).
% 2.01/1.68 tff(4167,plain,
% 2.01/1.68 (c2_1(a9)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[859, 4166])).
% 2.01/1.68 tff(4168,plain,
% 2.01/1.68 (c0_1(a9)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[881, 4166])).
% 2.01/1.68 tff(4169,plain,
% 2.01/1.68 (c1_1(a9)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[870, 4166])).
% 2.01/1.68 tff(4170,plain,
% 2.01/1.68 (~hskp2),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2170, 4169, 4168, 4150, 4149, 4167, 4164])).
% 2.01/1.68 tff(4171,plain,
% 2.01/1.68 (hskp14),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2482, 4170, 4133])).
% 2.01/1.68 tff(4172,plain,
% 2.01/1.68 (c2_1(a24)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[1041, 4171])).
% 2.01/1.68 tff(4173,plain,
% 2.01/1.68 (~c1_1(a24)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[1024, 4171])).
% 2.01/1.68 tff(4174,plain,
% 2.01/1.68 (~c0_1(a24)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[1030, 4171])).
% 2.01/1.68 tff(4175,plain,
% 2.01/1.68 (c3_1(a24)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3958, 4174, 1, 4173])).
% 2.01/1.68 tff(4176,plain,
% 2.01/1.68 ($false),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3966, 4175, 4174, 4148, 4173, 4172])).
% 2.01/1.68 tff(4177,plain,(c0_1(a3) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.68 tff(4178,plain,
% 2.01/1.68 (c0_1(a3)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4177, 2])).
% 2.01/1.68 tff(4179,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a19)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(4180,plain,
% 2.01/1.68 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19))) <=> (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a19)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(4181,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a19))))),
% 2.01/1.68 inference(monotonicity,[status(thm)],[4180])).
% 2.01/1.68 tff(4182,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a19)))),
% 2.01/1.68 inference(transitivity,[status(thm)],[4181, 4179])).
% 2.01/1.68 tff(4183,plain,
% 2.01/1.68 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a19) | c1_1(a19) | (~c2_1(a19)))),
% 2.01/1.68 inference(quant_inst,[status(thm)],[])).
% 2.01/1.68 tff(4184,plain,
% 2.01/1.68 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a19) | c3_1(a19) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a19))),
% 2.01/1.68 inference(modus_ponens,[status(thm)],[4183, 4182])).
% 2.01/1.68 tff(4185,plain,
% 2.01/1.68 ($false),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4184, 169, 2381, 2412, 2247, 2246, 2245, 1580, 2413])).
% 2.01/1.68 tff(4186,plain,((~hskp11) | (~c0_1(a3))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.68 tff(4187,plain,
% 2.01/1.68 (~hskp11),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4186, 4178])).
% 2.01/1.68 tff(4188,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(4189,plain,
% 2.01/1.68 ((hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp11 | c0_1(a33) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(4190,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a33) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c3_1(a33)) | (~c2_1(a33))))),
% 2.01/1.68 inference(monotonicity,[status(thm)],[4189])).
% 2.01/1.68 tff(4191,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c3_1(a33)) | (~c2_1(a33)))),
% 2.01/1.68 inference(transitivity,[status(thm)],[4190, 4188])).
% 2.01/1.68 tff(4192,plain,
% 2.01/1.68 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 2.01/1.68 inference(quant_inst,[status(thm)],[])).
% 2.01/1.68 tff(4193,plain,
% 2.01/1.68 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a33) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c3_1(a33)) | (~c2_1(a33))),
% 2.01/1.68 inference(modus_ponens,[status(thm)],[4192, 4191])).
% 2.01/1.68 tff(4194,plain,
% 2.01/1.68 ($false),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4193, 169, 4187, 3030, 3029, 3871, 3028, 4131, 2, 1126])).
% 2.01/1.68 tff(4195,plain,((~hskp19) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.68 tff(4196,plain,
% 2.01/1.68 (~hskp19),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4195, 2])).
% 2.01/1.68 tff(4197,plain,
% 2.01/1.68 ($false),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3559, 169, 883, 2392, 2381, 134, 123, 112, 848, 2413])).
% 2.01/1.68 tff(4198,plain,((~hskp4) | hskp19 | (~c0_1(a3))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.68 tff(4199,plain,
% 2.01/1.68 (~hskp4),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4198, 4196, 4178])).
% 2.01/1.68 tff(4200,plain,
% 2.01/1.68 (hskp17),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3517, 655, 4199])).
% 2.01/1.68 tff(4201,plain,
% 2.01/1.68 (c2_1(a31)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[328, 4200])).
% 2.01/1.68 tff(4202,plain,
% 2.01/1.68 (~c1_1(a31)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[71, 4200])).
% 2.01/1.68 tff(4203,plain,
% 2.01/1.68 (c0_1(a31)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[317, 4200])).
% 2.01/1.68 tff(4204,plain,
% 2.01/1.68 (c3_1(a31)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3599, 4203, 4199, 4202, 4201])).
% 2.01/1.68 tff(4205,plain,
% 2.01/1.68 (hskp17),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3517, 205, 655])).
% 2.01/1.68 tff(4206,plain,
% 2.01/1.68 (c0_1(a31)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[317, 4205])).
% 2.01/1.68 tff(4207,plain,
% 2.01/1.68 (~c1_1(a31)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[71, 4205])).
% 2.01/1.68 tff(4208,plain,
% 2.01/1.68 (c2_1(a31)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[328, 4205])).
% 2.01/1.68 tff(4209,plain,
% 2.01/1.68 (~hskp9),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2775, 654, 332, 2588, 655, 331])).
% 2.01/1.68 tff(4210,assumption,(hskp7), introduced(assumption)).
% 2.01/1.68 tff(4211,plain,
% 2.01/1.68 (~c2_1(a14)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[525, 4210])).
% 2.01/1.68 tff(4212,plain,
% 2.01/1.68 (c0_1(a14)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[558, 4210])).
% 2.01/1.68 tff(4213,plain,
% 2.01/1.68 (c1_1(a14)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2687, 169, 655, 654, 4212, 4211, 700])).
% 2.01/1.68 tff(4214,plain,
% 2.01/1.68 (c3_1(a14)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[536, 4210])).
% 2.01/1.68 tff(4215,plain,
% 2.01/1.68 ($false),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[543, 169, 73, 105, 4214, 4211, 104, 4213])).
% 2.01/1.68 tff(4216,plain,((~hskp7) | hskp24 | hskp9 | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.01/1.68 tff(4217,plain,
% 2.01/1.68 (~hskp7),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4216, 73, 105, 655, 654])).
% 2.01/1.68 tff(4218,plain,
% 2.01/1.68 (hskp13),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[519, 4217, 105])).
% 2.01/1.68 tff(4219,plain,
% 2.01/1.68 (~hskp0),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[507, 73, 105, 4218])).
% 2.01/1.68 tff(4220,plain,
% 2.01/1.68 (hskp23),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[253, 4219, 73])).
% 2.01/1.68 tff(4221,plain,
% 2.01/1.68 (~c1_1(a53)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[212, 4220])).
% 2.01/1.68 tff(4222,plain,
% 2.01/1.68 (~c0_1(a53)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[218, 4220])).
% 2.01/1.68 tff(4223,plain,
% 2.01/1.68 (~hskp3),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3130, 4219, 331, 332, 343, 655, 654])).
% 2.01/1.68 tff(4224,plain,
% 2.01/1.68 (~c2_1(a53)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[393, 169, 4223, 654, 4222, 4221, 23])).
% 2.01/1.68 tff(4225,plain,
% 2.01/1.68 ($false),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[353, 169, 4219, 331, 332, 4222, 4221, 343, 342, 4224])).
% 2.01/1.68 tff(4226,plain,(hskp24 | (~c0_1(a31)) | (~c2_1(a31)) | c1_1(a31) | hskp2 | hskp14 | hskp9), inference(lemma,lemma(discharge,[]))).
% 2.01/1.68 tff(4227,plain,
% 2.01/1.68 (hskp24),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4226, 654, 332, 343, 331, 655, 4209])).
% 2.01/1.68 tff(4228,plain,
% 2.01/1.68 (c3_1(a45)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3124, 344, 654, 332, 343, 2588, 331, 655])).
% 2.01/1.68 tff(4229,plain,
% 2.01/1.68 (~hskp22),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2539, 4228])).
% 2.01/1.68 tff(4230,plain,
% 2.01/1.68 (~hskp3),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3130, 344, 331, 332, 343, 655, 654])).
% 2.01/1.68 tff(4231,plain,
% 2.01/1.68 (~hskp19),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3134, 4230, 654, 4209, 2483])).
% 2.01/1.68 tff(4232,plain,
% 2.01/1.68 ($false),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3190, 4231, 4229, 655, 654, 4209, 2588, 332, 343, 4227])).
% 2.01/1.68 tff(4233,plain,(hskp0 | hskp14 | hskp2 | (~c3_1(a31)) | (~c2_1(a31)) | c1_1(a31) | (~c0_1(a31))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.68 tff(4234,plain,
% 2.01/1.68 (hskp0),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4233, 654, 655, 2750, 4208, 4207, 4206])).
% 2.01/1.68 tff(4235,plain,
% 2.01/1.68 (~c2_1(a1)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[259, 4234])).
% 2.01/1.68 tff(4236,plain,
% 2.01/1.68 (~c0_1(a1)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[283, 4234])).
% 2.01/1.68 tff(4237,plain,
% 2.01/1.68 (~hskp9),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2775, 654, 4208, 2750, 655, 4206])).
% 2.01/1.68 tff(4238,plain,
% 2.01/1.68 (hskp24),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4226, 654, 4208, 4207, 4206, 655, 4237])).
% 2.01/1.68 tff(4239,plain,
% 2.01/1.68 (hskp0),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4233, 654, 655, 2588, 332, 343, 331])).
% 2.01/1.68 tff(4240,plain,
% 2.01/1.68 (~c2_1(a1)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[259, 4239])).
% 2.01/1.68 tff(4241,plain,
% 2.01/1.68 (~c0_1(a1)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[283, 4239])).
% 2.01/1.68 tff(4242,plain,
% 2.01/1.68 (c3_1(a1)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[270, 4239])).
% 2.01/1.68 tff(4243,plain,
% 2.01/1.68 (c3_1(a3)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2411, 4227])).
% 2.01/1.68 tff(4244,plain,
% 2.01/1.68 (c2_1(a3)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2380, 4227])).
% 2.01/1.68 tff(4245,plain,
% 2.01/1.68 (c1_1(a3)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2391, 4227])).
% 2.01/1.68 tff(4246,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(4247,plain,
% 2.01/1.68 ((hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1))) <=> (hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(4248,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3))))),
% 2.01/1.68 inference(monotonicity,[status(thm)],[4247])).
% 2.01/1.68 tff(4249,plain,
% 2.01/1.68 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)))),
% 2.01/1.68 inference(transitivity,[status(thm)],[4248, 4246])).
% 2.01/1.68 tff(4250,plain,
% 2.01/1.68 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3)) | c0_1(a1) | c2_1(a1) | (~c3_1(a1)))),
% 2.01/1.68 inference(quant_inst,[status(thm)],[])).
% 2.01/1.68 tff(4251,plain,
% 2.01/1.68 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c2_1(a3)) | (~c1_1(a3)) | (~c3_1(a3))),
% 2.01/1.68 inference(modus_ponens,[status(thm)],[4250, 4249])).
% 2.01/1.68 tff(4252,plain,
% 2.01/1.68 (hskp6),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4251, 169, 4245, 4244, 4243, 4242, 4241, 4240, 1298])).
% 2.01/1.68 tff(4253,plain,
% 2.01/1.68 (c0_1(a45)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2831, 2542, 331, 4209, 343, 2588, 2483, 4252, 332])).
% 2.01/1.68 tff(4254,plain,
% 2.01/1.68 (c1_1(a45)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3015, 2542, 654, 2588, 331, 332, 4253, 655])).
% 2.01/1.68 tff(4255,plain,
% 2.01/1.68 (c2_1(a45)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3024, 4254, 331, 332, 2588, 2542, 4253])).
% 2.01/1.68 tff(4256,plain,
% 2.01/1.68 (~hskp22),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2533, 4254])).
% 2.01/1.68 tff(4257,plain,
% 2.01/1.68 (hskp19),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3190, 4256, 655, 654, 4209, 2588, 332, 343, 4227])).
% 2.01/1.68 tff(4258,plain,
% 2.01/1.68 ($false),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3039, 4257, 4255, 2992, 2542, 4253])).
% 2.01/1.68 tff(4259,plain,(c3_1(a45) | hskp14 | hskp2 | (~c3_1(a31)) | (~c2_1(a31)) | c1_1(a31) | (~c0_1(a31))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.68 tff(4260,plain,
% 2.01/1.68 (c3_1(a45)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[4259, 654, 655, 2750, 4208, 4207, 4206])).
% 2.01/1.68 tff(4261,plain,
% 2.01/1.68 (~hskp22),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[2539, 4260])).
% 2.01/1.68 tff(4262,plain,
% 2.01/1.68 (hskp19),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3190, 4261, 655, 654, 4237, 2750, 4208, 4207, 4238])).
% 2.01/1.68 tff(4263,plain,
% 2.01/1.68 (hskp3),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[3134, 4262, 654, 4237, 2483])).
% 2.01/1.68 tff(4264,plain,
% 2.01/1.68 (~c3_1(a5)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[948, 4263])).
% 2.01/1.68 tff(4265,plain,
% 2.01/1.68 (~c2_1(a5)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[361, 4263])).
% 2.01/1.68 tff(4266,plain,
% 2.01/1.68 (~c1_1(a5)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[367, 4263])).
% 2.01/1.68 tff(4267,plain,
% 2.01/1.68 (c3_1(a1)),
% 2.01/1.68 inference(unit_resolution,[status(thm)],[270, 4234])).
% 2.01/1.68 tff(4268,plain,
% 2.01/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a5) | c2_1(a5) | c3_1(a5) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a5) | c2_1(a5) | c3_1(a5) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a5))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(4269,plain,
% 2.01/1.68 (((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5)) <=> (c1_1(a5) | c2_1(a5) | c3_1(a5) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a5))),
% 2.01/1.68 inference(rewrite,[status(thm)],[])).
% 2.01/1.68 tff(4270,plain,
% 2.01/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a5) | c2_1(a5) | c3_1(a5) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a5)))),
% 2.01/1.69 inference(monotonicity,[status(thm)],[4269])).
% 2.01/1.69 tff(4271,plain,
% 2.01/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a5) | c2_1(a5) | c3_1(a5) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a5))),
% 2.01/1.69 inference(transitivity,[status(thm)],[4270, 4268])).
% 2.01/1.69 tff(4272,plain,
% 2.01/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | c0_1(a1) | (~c3_1(a1)) | c3_1(a5) | c0_1(a5) | c2_1(a5) | c2_1(a5) | c1_1(a5) | c0_1(a5))),
% 2.01/1.69 inference(quant_inst,[status(thm)],[])).
% 2.01/1.69 tff(4273,plain,
% 2.01/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a5) | c2_1(a5) | c3_1(a5) | c0_1(a1) | c2_1(a1) | (~ndr1_0) | (~c3_1(a1)) | c0_1(a5)),
% 2.01/1.69 inference(modus_ponens,[status(thm)],[4272, 4271])).
% 2.01/1.69 tff(4274,plain,
% 2.01/1.69 (c0_1(a5)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4273, 169, 4267, 4266, 4265, 4264, 4236, 4235, 55])).
% 2.01/1.69 tff(4275,plain,
% 2.01/1.69 ($false),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[934, 169, 655, 654, 4266, 4265, 700, 4274])).
% 2.01/1.69 tff(4276,plain,(hskp2 | hskp14 | hskp4), inference(lemma,lemma(discharge,[]))).
% 2.01/1.69 tff(4277,plain,
% 2.01/1.69 (hskp2),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4276, 655, 4199])).
% 2.01/1.69 tff(4278,plain,
% 2.01/1.69 (~c3_1(a4)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[400, 4277])).
% 2.01/1.69 tff(4279,plain,
% 2.01/1.69 (~c2_1(a4)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[417, 4277])).
% 2.01/1.69 tff(4280,plain,
% 2.01/1.69 (c1_1(a4)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[411, 4277])).
% 2.01/1.69 tff(4281,plain,
% 2.01/1.69 (~c0_1(a4)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[446, 169, 4203, 4201, 4280, 4279, 4278, 439, 4204])).
% 2.01/1.69 tff(4282,plain,
% 2.01/1.69 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~c2_1(a16)) | c3_1(a16) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~c2_1(a16)) | c3_1(a16) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a16)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4283,plain,
% 2.01/1.69 ((hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7))) <=> (hskp11 | (~c2_1(a16)) | c3_1(a16) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a16)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4284,plain,
% 2.01/1.69 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~c2_1(a16)) | c3_1(a16) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a16))))),
% 2.01/1.69 inference(monotonicity,[status(thm)],[4283])).
% 2.01/1.69 tff(4285,plain,
% 2.01/1.69 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~c2_1(a16)) | c3_1(a16) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a16)))),
% 2.01/1.69 inference(transitivity,[status(thm)],[4284, 4282])).
% 2.01/1.69 tff(4286,plain,
% 2.01/1.69 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))),
% 2.01/1.69 inference(quant_inst,[status(thm)],[])).
% 2.01/1.69 tff(4287,plain,
% 2.01/1.69 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | (~c2_1(a16)) | c3_1(a16) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a16))),
% 2.01/1.69 inference(modus_ponens,[status(thm)],[4286, 4285])).
% 2.01/1.69 tff(4288,plain,
% 2.01/1.69 (~c2_1(a7)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4287, 169, 4187, 3871, 1455, 4131, 2, 1420, 1126])).
% 2.01/1.69 tff(4289,plain,
% 2.01/1.69 ($false),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[3645, 169, 4196, 2392, 2381, 1431, 1455, 848, 4178, 4288])).
% 2.01/1.69 tff(4290,plain,((~hskp5) | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.69 tff(4291,plain,
% 2.01/1.69 (~hskp5),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4290, 2])).
% 2.01/1.69 tff(4292,plain,
% 2.01/1.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a16)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4293,plain,
% 2.01/1.69 ((hskp5 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4))) <=> (hskp5 | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a16)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4294,plain,
% 2.01/1.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a16))))),
% 2.01/1.69 inference(monotonicity,[status(thm)],[4293])).
% 2.01/1.69 tff(4295,plain,
% 2.01/1.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a16)))),
% 2.01/1.69 inference(transitivity,[status(thm)],[4294, 4292])).
% 2.01/1.69 tff(4296,plain,
% 2.01/1.69 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c0_1(a4) | c2_1(a4) | (~c1_1(a4)))),
% 2.01/1.69 inference(quant_inst,[status(thm)],[])).
% 2.01/1.69 tff(4297,plain,
% 2.01/1.69 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | (~c2_1(a16)) | c3_1(a16) | c2_1(a4) | (~ndr1_0) | c0_1(a4) | (~c1_1(a4)) | (~c1_1(a16))),
% 2.01/1.69 inference(modus_ponens,[status(thm)],[4296, 4295])).
% 2.01/1.69 tff(4298,plain,
% 2.01/1.69 ($false),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4297, 169, 4291, 4280, 4131, 2, 4279, 1413, 4082, 4281])).
% 2.01/1.69 tff(4299,plain,(hskp14 | c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.69 tff(4300,plain,
% 2.01/1.69 (hskp14),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4299, 2])).
% 2.01/1.69 tff(4301,plain,
% 2.01/1.69 (~c1_1(a24)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[1024, 4300])).
% 2.01/1.69 tff(4302,plain,
% 2.01/1.69 (c2_1(a24)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[1041, 4300])).
% 2.01/1.69 tff(4303,plain,
% 2.01/1.69 (c3_1(a24)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[3985, 4302, 4178, 4301])).
% 2.01/1.69 tff(4304,plain,
% 2.01/1.69 (~c0_1(a24)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[1030, 4300])).
% 2.01/1.69 tff(4305,plain,
% 2.01/1.69 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a24) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4306,plain,
% 2.01/1.69 ((hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24))) <=> (hskp11 | c0_1(a24) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4307,plain,
% 2.01/1.69 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a24) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a24)) | (~c3_1(a24))))),
% 2.01/1.69 inference(monotonicity,[status(thm)],[4306])).
% 2.01/1.69 tff(4308,plain,
% 2.01/1.69 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 2.01/1.69 inference(transitivity,[status(thm)],[4307, 4305])).
% 2.01/1.69 tff(4309,plain,
% 2.01/1.69 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c0_1(a16)) | c0_1(a24) | (~c3_1(a24)) | (~c2_1(a24)))),
% 2.01/1.69 inference(quant_inst,[status(thm)],[])).
% 2.01/1.69 tff(4310,plain,
% 2.01/1.69 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a24) | (~c2_1(a16)) | c3_1(a16) | (~ndr1_0) | (~c0_1(a16)) | (~c2_1(a24)) | (~c3_1(a24))),
% 2.01/1.69 inference(modus_ponens,[status(thm)],[4309, 4308])).
% 2.01/1.69 tff(4311,plain,
% 2.01/1.69 ($false),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4310, 169, 4187, 4302, 3871, 4304, 4131, 2, 1126, 4303])).
% 2.01/1.69 tff(4312,plain,(c3_1(a16)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.69 tff(4313,plain,
% 2.01/1.69 (~hskp9),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[573, 4312])).
% 2.01/1.69 tff(4314,plain,
% 2.01/1.69 (hskp8 | c0_1(a3)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[3765, 4313])).
% 2.01/1.69 tff(4315,plain,
% 2.01/1.69 (hskp8),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4314, 1])).
% 2.01/1.69 tff(4316,plain,
% 2.01/1.69 (~c3_1(a31)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[3619, 2401, 1, 3031, 72])).
% 2.01/1.69 tff(4317,plain,
% 2.01/1.69 ($false),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[3977, 169, 3031, 2381, 2412, 3596, 2401, 1126, 4316, 1])).
% 2.01/1.69 tff(4318,plain,((~hskp17) | hskp11 | c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.69 tff(4319,plain,
% 2.01/1.69 (hskp11),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4318, 66, 1])).
% 2.01/1.69 tff(4320,plain,
% 2.01/1.69 (~c3_1(a31)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[2667, 4319, 2401, 3596])).
% 2.01/1.69 tff(4321,plain,
% 2.01/1.69 (hskp8),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[3765, 1, 4313])).
% 2.01/1.69 tff(4322,plain,
% 2.01/1.69 (~hskp18),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4091, 1])).
% 2.01/1.69 tff(4323,plain,
% 2.01/1.69 (hskp18 | hskp17 | (~c3_1(a8))),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[1376, 169, 2786, 1349, 741])).
% 2.01/1.69 tff(4324,plain,
% 2.01/1.69 (~c3_1(a8)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4323, 643, 4322])).
% 2.01/1.69 tff(4325,plain,
% 2.01/1.69 (~c2_1(a15)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[184, 4321])).
% 2.01/1.69 tff(4326,plain,
% 2.01/1.69 (c0_1(a15)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[195, 4321])).
% 2.01/1.69 tff(4327,plain,
% 2.01/1.69 (hskp17 | (~c3_1(a15))),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[2045, 169, 4322, 4326, 4325, 741])).
% 2.01/1.69 tff(4328,plain,
% 2.01/1.69 (~c3_1(a15)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4327, 643])).
% 2.01/1.69 tff(4329,plain,
% 2.01/1.69 (~c1_1(a15)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[201, 4321])).
% 2.01/1.69 tff(4330,plain,
% 2.01/1.69 (hskp17 | (~c3_1(a15))),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[2045, 169, 731, 204, 203, 741])).
% 2.01/1.69 tff(4331,plain,
% 2.01/1.69 (~c3_1(a15)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4330, 643])).
% 2.01/1.69 tff(4332,plain,
% 2.01/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4333,plain,
% 2.01/1.69 (((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15))) <=> (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4334,plain,
% 2.01/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11))))),
% 2.01/1.69 inference(monotonicity,[status(thm)],[4333])).
% 2.01/1.69 tff(4335,plain,
% 2.01/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)))),
% 2.01/1.69 inference(transitivity,[status(thm)],[4334, 4332])).
% 2.01/1.69 tff(4336,plain,
% 2.01/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c2_1(a15) | c3_1(a15) | (~c0_1(a15)))),
% 2.01/1.69 inference(quant_inst,[status(thm)],[])).
% 2.01/1.69 tff(4337,plain,
% 2.01/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a15) | c2_1(a4) | c3_1(a4) | (~ndr1_0) | (~c1_1(a4)) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a11)) | (~c0_1(a11)) | (~c3_1(a11))),
% 2.01/1.69 inference(modus_ponens,[status(thm)],[4336, 4335])).
% 2.01/1.69 tff(4338,plain,
% 2.01/1.69 ($false),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4337, 169, 764, 753, 204, 421, 203, 440, 420, 439, 4331, 771])).
% 2.01/1.69 tff(4339,plain,((~hskp27) | (~c0_1(a15)) | (~c1_1(a4)) | c2_1(a15) | c2_1(a4) | c3_1(a4) | hskp18 | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.01/1.69 tff(4340,plain,
% 2.01/1.69 (~hskp27),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4339, 643, 421, 4325, 440, 420, 4322, 4326])).
% 2.01/1.69 tff(4341,plain,
% 2.01/1.69 (^[U: $i] : refl((hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))),
% 2.01/1.69 inference(bind,[status(th)],[])).
% 2.01/1.69 tff(4342,plain,
% 2.01/1.69 (![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 2.01/1.69 inference(quant_intro,[status(thm)],[4341])).
% 2.01/1.69 tff(4343,plain,
% 2.01/1.69 (![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4344,plain,
% 2.01/1.69 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp7) <=> ((hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp7))), rewrite(((hskp27 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U))) | hskp7) <=> (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp7) <=> (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))))),
% 2.01/1.69 inference(bind,[status(th)],[])).
% 2.01/1.69 tff(4345,plain,
% 2.01/1.69 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp7) <=> ![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 2.01/1.69 inference(quant_intro,[status(thm)],[4344])).
% 2.01/1.69 tff(4346,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 2.01/1.69 tff(4347,plain,
% 2.01/1.69 (![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 2.01/1.69 inference(modus_ponens,[status(thm)],[4346, 4345])).
% 2.01/1.69 tff(4348,plain,
% 2.01/1.69 (![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 2.01/1.69 inference(modus_ponens,[status(thm)],[4347, 4343])).
% 2.01/1.69 tff(4349,plain,(
% 2.01/1.69 ![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 2.01/1.69 inference(skolemize,[status(sab)],[4348])).
% 2.01/1.69 tff(4350,plain,
% 2.01/1.69 (![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))),
% 2.01/1.69 inference(modus_ponens,[status(thm)],[4349, 4342])).
% 2.01/1.69 tff(4351,plain,
% 2.01/1.69 (((~![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp7 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4352,plain,
% 2.01/1.69 ((~![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3)))),
% 2.01/1.69 inference(quant_inst,[status(thm)],[])).
% 2.01/1.69 tff(4353,plain,
% 2.01/1.69 ((~![U: $i] : (hskp27 | hskp7 | (~ndr1_0) | (~c2_1(U)) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp7 | (~ndr1_0) | (~c2_1(a3)) | c0_1(a3) | (~c1_1(a3))),
% 2.01/1.69 inference(modus_ponens,[status(thm)],[4352, 4351])).
% 2.01/1.69 tff(4354,plain,
% 2.01/1.69 (hskp27 | hskp7 | c0_1(a3)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4353, 169, 2392, 2381, 4350])).
% 2.01/1.69 tff(4355,plain,
% 2.01/1.69 (hskp7),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4354, 4340, 1])).
% 2.01/1.69 tff(4356,plain,
% 2.01/1.69 (~c2_1(a14)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[525, 4355])).
% 2.01/1.69 tff(4357,plain,
% 2.01/1.69 (c3_1(a14)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[536, 4355])).
% 2.01/1.69 tff(4358,plain,
% 2.01/1.69 (c0_1(a14)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[558, 4355])).
% 2.01/1.69 tff(4359,plain,
% 2.01/1.69 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c0_1(a14)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c0_1(a14)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4360,plain,
% 2.01/1.69 ((hskp18 | hskp17 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14))) <=> (hskp18 | hskp17 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c0_1(a14)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4361,plain,
% 2.01/1.69 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c0_1(a14))))),
% 2.01/1.69 inference(monotonicity,[status(thm)],[4360])).
% 2.01/1.69 tff(4362,plain,
% 2.01/1.69 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c0_1(a14)))),
% 2.01/1.69 inference(transitivity,[status(thm)],[4361, 4359])).
% 2.01/1.69 tff(4363,plain,
% 2.01/1.69 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c2_1(a14) | (~c0_1(a14)) | (~c3_1(a14)))),
% 2.01/1.69 inference(quant_inst,[status(thm)],[])).
% 2.01/1.69 tff(4364,plain,
% 2.01/1.69 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp18 | hskp17 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c0_1(a14))),
% 2.01/1.69 inference(modus_ponens,[status(thm)],[4363, 4362])).
% 2.01/1.69 tff(4365,plain,
% 2.01/1.69 ($false),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4364, 169, 4322, 643, 4358, 4357, 4356, 741])).
% 2.01/1.69 tff(4366,plain,(hskp17 | c0_1(a3) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.69 tff(4367,plain,
% 2.01/1.69 ($false),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4366, 1862, 1863, 1, 643, 1861])).
% 2.01/1.69 tff(4368,plain,((~hskp2) | c0_1(a3) | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.01/1.69 tff(4369,plain,
% 2.01/1.69 (~hskp2),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[4368, 643, 1])).
% 2.01/1.69 tff(4370,plain,
% 2.01/1.69 (hskp14),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[2482, 4369, 4321])).
% 2.01/1.69 tff(4371,plain,
% 2.01/1.69 (~c1_1(a24)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[1024, 4370])).
% 2.01/1.69 tff(4372,plain,
% 2.01/1.69 (~c0_1(a24)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[1030, 4370])).
% 2.01/1.69 tff(4373,plain,
% 2.01/1.69 (c2_1(a24)),
% 2.01/1.69 inference(unit_resolution,[status(thm)],[1041, 4370])).
% 2.01/1.69 tff(4374,plain,
% 2.01/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a24)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4375,plain,
% 2.01/1.69 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24))) <=> (c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a24)))),
% 2.01/1.69 inference(rewrite,[status(thm)],[])).
% 2.01/1.69 tff(4376,plain,
% 2.01/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a24))))),
% 2.01/1.70 inference(monotonicity,[status(thm)],[4375])).
% 2.01/1.70 tff(4377,plain,
% 2.01/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a24)))),
% 2.01/1.70 inference(transitivity,[status(thm)],[4376, 4374])).
% 2.01/1.70 tff(4378,plain,
% 2.01/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c1_1(a24) | c0_1(a24) | (~c2_1(a24)))),
% 2.01/1.70 inference(quant_inst,[status(thm)],[])).
% 2.01/1.70 tff(4379,plain,
% 2.01/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a24) | c1_1(a24) | c1_1(a15) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c3_1(a8) | c3_1(a15) | (~c0_1(a15)) | (~c2_1(a24))),
% 2.01/1.70 inference(modus_ponens,[status(thm)],[4378, 4377])).
% 2.01/1.70 tff(4380,plain,
% 2.01/1.70 ($false),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4379, 169, 4373, 4326, 1350, 4372, 4371, 4329, 1349, 458, 4328, 4324])).
% 2.01/1.70 tff(4381,plain,(hskp17 | (~c1_1(a8)) | c2_1(a8) | c0_1(a3) | (~c0_1(a8))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.70 tff(4382,plain,
% 2.01/1.70 (hskp17),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4381, 1, 1349, 1350, 2786])).
% 2.01/1.70 tff(4383,plain,
% 2.01/1.70 (c2_1(a31)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[328, 4382])).
% 2.01/1.70 tff(4384,plain,
% 2.01/1.70 (~c1_1(a31)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[71, 4382])).
% 2.01/1.70 tff(4385,plain,
% 2.01/1.70 (c0_1(a31)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[317, 4382])).
% 2.01/1.70 tff(4386,plain,
% 2.01/1.70 (hskp11),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4318, 4382, 1])).
% 2.01/1.70 tff(4387,plain,
% 2.01/1.70 (~c3_1(a31)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[2667, 4386, 4383, 4385])).
% 2.01/1.70 tff(4388,plain,
% 2.01/1.70 (hskp4),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[3599, 4387, 4385, 4384, 4383])).
% 2.01/1.70 tff(4389,plain,
% 2.01/1.70 (c1_1(a6)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[133, 4388])).
% 2.01/1.70 tff(4390,plain,
% 2.01/1.70 (~c2_1(a6)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[111, 4388])).
% 2.01/1.70 tff(4391,plain,
% 2.01/1.70 (~c3_1(a19)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1185, 4386])).
% 2.01/1.70 tff(4392,plain,
% 2.01/1.70 (~c1_1(a19)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1209, 4386])).
% 2.01/1.70 tff(4393,plain,
% 2.01/1.70 (~hskp26),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4029, 4386])).
% 2.01/1.70 tff(4394,plain,
% 2.01/1.70 (hskp20),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[2146, 169, 4393, 4385, 4383, 1227, 4387])).
% 2.01/1.70 tff(4395,plain,
% 2.01/1.70 (~c3_1(a37)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1239, 4394])).
% 2.01/1.70 tff(4396,plain,
% 2.01/1.70 (~c0_1(a37)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1245, 4394])).
% 2.01/1.70 tff(4397,plain,
% 2.01/1.70 (c3_1(a6)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[122, 4388])).
% 2.01/1.70 tff(4398,plain,
% 2.01/1.70 (c0_1(a19)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4058, 169, 2392, 2381, 4392, 4391, 45, 1])).
% 2.01/1.70 tff(4399,plain,
% 2.01/1.70 (c2_1(a37)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4163, 4398, 4397, 4396, 4395, 4392, 4391, 4390, 4389])).
% 2.01/1.70 tff(4400,plain,
% 2.01/1.70 (hskp25),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[2162, 169, 4393, 4396, 4395, 1107, 4399])).
% 2.01/1.70 tff(4401,plain,
% 2.01/1.70 (c2_1(a9)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[859, 4400])).
% 2.01/1.70 tff(4402,plain,
% 2.01/1.70 (c0_1(a9)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[881, 4400])).
% 2.01/1.70 tff(4403,plain,
% 2.01/1.70 (c1_1(a9)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[870, 4400])).
% 2.01/1.70 tff(4404,plain,
% 2.01/1.70 (~hskp2),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[2170, 4403, 4402, 4396, 4395, 4401, 4399])).
% 2.01/1.70 tff(4405,plain,
% 2.01/1.70 (hskp14),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[2482, 4404, 4321])).
% 2.01/1.70 tff(4406,plain,
% 2.01/1.70 (c2_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1041, 4405])).
% 2.01/1.70 tff(4407,plain,
% 2.01/1.70 (~c1_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1024, 4405])).
% 2.01/1.70 tff(4408,plain,
% 2.01/1.70 (~c0_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1030, 4405])).
% 2.01/1.70 tff(4409,plain,
% 2.01/1.70 (c3_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[3958, 4408, 1, 4407])).
% 2.01/1.70 tff(4410,plain,
% 2.01/1.70 ($false),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[3966, 4409, 4408, 4394, 4407, 4406])).
% 2.01/1.70 tff(4411,plain,(c0_1(a3) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.70 tff(4412,plain,
% 2.01/1.70 ($false),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4411, 1336, 1347, 1, 1370])).
% 2.01/1.70 tff(4413,plain,((~hskp6) | c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.70 tff(4414,plain,
% 2.01/1.70 (~hskp6),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4413, 1])).
% 2.01/1.70 tff(4415,plain,
% 2.01/1.70 (~hskp26),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4029, 4319])).
% 2.01/1.70 tff(4416,plain,
% 2.01/1.70 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 2.01/1.70 inference(rewrite,[status(thm)],[])).
% 2.01/1.70 tff(4417,plain,
% 2.01/1.70 ((hskp26 | hskp6 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31))) <=> (hskp26 | hskp6 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 2.01/1.70 inference(rewrite,[status(thm)],[])).
% 2.01/1.70 tff(4418,plain,
% 2.01/1.70 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31)))),
% 2.01/1.70 inference(monotonicity,[status(thm)],[4417])).
% 2.01/1.70 tff(4419,plain,
% 2.01/1.70 (((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))) <=> ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 2.01/1.70 inference(transitivity,[status(thm)],[4418, 4416])).
% 2.01/1.70 tff(4420,plain,
% 2.01/1.70 ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp26 | hskp6 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | (~c2_1(a31)))),
% 2.01/1.70 inference(quant_inst,[status(thm)],[])).
% 2.01/1.70 tff(4421,plain,
% 2.01/1.70 ((~![U: $i] : (hskp26 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp26 | hskp6 | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31)),
% 2.01/1.70 inference(modus_ponens,[status(thm)],[4420, 4419])).
% 2.01/1.70 tff(4422,plain,
% 2.01/1.70 ($false),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4421, 169, 4415, 4414, 2401, 72, 1280, 4320])).
% 2.01/1.70 tff(4423,plain,((~hskp17) | c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.70 tff(4424,plain,
% 2.01/1.70 (~hskp17),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4423, 1])).
% 2.01/1.70 tff(4425,plain,
% 2.01/1.70 (~hskp2),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4368, 4424, 1])).
% 2.01/1.70 tff(4426,plain,
% 2.01/1.70 (hskp14),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[2482, 4425, 4315])).
% 2.01/1.70 tff(4427,plain,
% 2.01/1.70 (~c1_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1024, 4426])).
% 2.01/1.70 tff(4428,plain,
% 2.01/1.70 (~c0_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1030, 4426])).
% 2.01/1.70 tff(4429,plain,
% 2.01/1.70 (c3_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[3958, 4428, 1, 4427])).
% 2.01/1.70 tff(4430,plain,
% 2.01/1.70 (c2_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1041, 4426])).
% 2.01/1.70 tff(4431,plain,
% 2.01/1.70 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a24) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a24) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 2.01/1.70 inference(rewrite,[status(thm)],[])).
% 2.01/1.70 tff(4432,plain,
% 2.01/1.70 ((hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp10 | c1_1(a24) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 2.01/1.70 inference(rewrite,[status(thm)],[])).
% 2.01/1.70 tff(4433,plain,
% 2.01/1.70 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c1_1(a24) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | (~c3_1(a24))))),
% 2.01/1.70 inference(monotonicity,[status(thm)],[4432])).
% 2.01/1.70 tff(4434,plain,
% 2.01/1.70 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a24) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | (~c3_1(a24)))),
% 2.01/1.70 inference(transitivity,[status(thm)],[4433, 4431])).
% 2.01/1.70 tff(4435,plain,
% 2.01/1.70 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a24) | (~c2_1(a24)) | (~c3_1(a24)) | c0_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 2.01/1.70 inference(quant_inst,[status(thm)],[])).
% 2.01/1.70 tff(4436,plain,
% 2.01/1.70 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c1_1(a24) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c3_1(a3)) | (~c2_1(a24)) | (~c3_1(a24))),
% 2.01/1.70 inference(modus_ponens,[status(thm)],[4435, 4434])).
% 2.01/1.70 tff(4437,plain,
% 2.01/1.70 (hskp10),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4436, 169, 2392, 2412, 4430, 4427, 1137, 1, 4429])).
% 2.01/1.70 tff(4438,plain,
% 2.01/1.70 (~c3_1(a18)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1150, 4437])).
% 2.01/1.70 tff(4439,plain,
% 2.01/1.70 (c2_1(a18)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1161, 4437])).
% 2.01/1.70 tff(4440,plain,
% 2.01/1.70 (c0_1(a18)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1172, 4437])).
% 2.01/1.70 tff(4441,plain,
% 2.01/1.70 (hskp11),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1179, 169, 4430, 4440, 4439, 4428, 4438, 1126, 4429])).
% 2.01/1.70 tff(4442,plain,
% 2.01/1.70 (~hskp20),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[3966, 4429, 4428, 4427, 4430])).
% 2.01/1.70 tff(4443,plain,
% 2.01/1.70 (hskp26),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1233, 169, 4442, 4440, 4439, 4438, 1227])).
% 2.01/1.70 tff(4444,plain,
% 2.01/1.70 ($false),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4029, 4443, 4441])).
% 2.01/1.70 tff(4445,plain,(c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.70 tff(4446,plain,
% 2.01/1.70 (~hskp11),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4186, 2413])).
% 2.01/1.70 tff(4447,assumption,(hskp10), introduced(assumption)).
% 2.01/1.70 tff(4448,plain,
% 2.01/1.70 (~c3_1(a18)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1150, 4447])).
% 2.01/1.70 tff(4449,plain,
% 2.01/1.70 (c2_1(a18)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1161, 4447])).
% 2.01/1.70 tff(4450,plain,
% 2.01/1.70 (c0_1(a18)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1172, 4447])).
% 2.01/1.70 tff(4451,assumption,(c3_1(a33)), introduced(assumption)).
% 2.01/1.70 tff(4452,plain,
% 2.01/1.70 ($false),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[2674, 169, 3031, 3682, 4451, 4450, 4449, 3681, 4448, 1126])).
% 2.01/1.70 tff(4453,plain,((~hskp10) | hskp11 | (~c2_1(a33)) | (~c3_1(a33)) | c0_1(a33)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.70 tff(4454,plain,
% 2.01/1.70 (~hskp10),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4453, 3030, 4446, 3029, 3028])).
% 2.01/1.70 tff(4455,plain,
% 2.01/1.70 (hskp10 | hskp6 | (~c0_1(a3))),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[2880, 169, 2392, 2381, 2874])).
% 2.01/1.70 tff(4456,plain,
% 2.01/1.70 (hskp6),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4455, 4454, 2413])).
% 2.01/1.70 tff(4457,plain,
% 2.01/1.70 (~c2_1(a8)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1335, 4456])).
% 2.01/1.70 tff(4458,plain,
% 2.01/1.70 (c1_1(a8)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1346, 4456])).
% 2.01/1.70 tff(4459,plain,
% 2.01/1.70 (c0_1(a8)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1369, 4456])).
% 2.01/1.70 tff(4460,plain,
% 2.01/1.70 (c0_1(a3)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4411, 1349, 1350, 2786])).
% 2.01/1.70 tff(4461,plain,
% 2.01/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)))),
% 2.01/1.70 inference(rewrite,[status(thm)],[])).
% 2.01/1.70 tff(4462,plain,
% 2.01/1.70 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)))),
% 2.01/1.70 inference(rewrite,[status(thm)],[])).
% 2.01/1.70 tff(4463,plain,
% 2.01/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8))))),
% 2.01/1.70 inference(monotonicity,[status(thm)],[4462])).
% 2.01/1.70 tff(4464,plain,
% 2.01/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8)))),
% 2.01/1.70 inference(transitivity,[status(thm)],[4463, 4461])).
% 2.01/1.70 tff(4465,plain,
% 2.01/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 2.01/1.70 inference(quant_inst,[status(thm)],[])).
% 2.01/1.70 tff(4466,plain,
% 2.01/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a8) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c1_1(a8)) | c3_1(a8) | (~c0_1(a8))),
% 2.01/1.70 inference(modus_ponens,[status(thm)],[4465, 4464])).
% 2.01/1.70 tff(4467,plain,
% 2.01/1.70 ($false),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4466, 169, 2381, 2412, 2786, 1350, 1349, 439, 4460, 1348])).
% 2.01/1.70 tff(4468,plain,(c3_1(a8) | (~c0_1(a8)) | (~c1_1(a8)) | c2_1(a8)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.70 tff(4469,plain,
% 2.01/1.70 (c3_1(a8)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4468, 4459, 4458, 4457])).
% 2.01/1.70 tff(4470,plain,
% 2.01/1.70 (hskp18),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1376, 169, 643, 4459, 4457, 741, 4469])).
% 2.01/1.70 tff(4471,plain,
% 2.01/1.70 (~c3_1(a32)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[969, 4470])).
% 2.01/1.70 tff(4472,plain,
% 2.01/1.70 (~c1_1(a32)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[963, 4470])).
% 2.01/1.70 tff(4473,plain,
% 2.01/1.70 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a32)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a32)))),
% 2.01/1.70 inference(rewrite,[status(thm)],[])).
% 2.01/1.70 tff(4474,plain,
% 2.01/1.70 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32))) <=> (c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a32)))),
% 2.01/1.70 inference(rewrite,[status(thm)],[])).
% 2.01/1.70 tff(4475,plain,
% 2.01/1.70 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a32))))),
% 2.01/1.70 inference(monotonicity,[status(thm)],[4474])).
% 2.01/1.70 tff(4476,plain,
% 2.01/1.70 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a32)))),
% 2.01/1.70 inference(transitivity,[status(thm)],[4475, 4473])).
% 2.01/1.70 tff(4477,plain,
% 2.01/1.70 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a32) | c1_1(a32) | (~c2_1(a32)))),
% 2.01/1.70 inference(quant_inst,[status(thm)],[])).
% 2.01/1.70 tff(4478,plain,
% 2.01/1.70 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c1_1(a32) | c3_1(a32) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | (~c2_1(a32))),
% 2.01/1.70 inference(modus_ponens,[status(thm)],[4477, 4476])).
% 2.01/1.70 tff(4479,plain,
% 2.01/1.70 (~c2_1(a32)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4478, 169, 2381, 2412, 4472, 4471, 1580, 2413])).
% 2.01/1.70 tff(4480,plain,
% 2.01/1.70 (~c0_1(a32)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1385, 4470])).
% 2.01/1.70 tff(4481,plain,
% 2.01/1.70 (~c1_1(a33)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1482, 169, 3030, 3028, 4480, 4472, 4471, 45])).
% 2.01/1.70 tff(4482,plain,
% 2.01/1.70 (hskp1),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1510, 169, 3030, 3029, 4480, 4472, 4471, 1493, 4481])).
% 2.01/1.70 tff(4483,plain,
% 2.01/1.70 (~c3_1(a2)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[2441, 4482])).
% 2.01/1.70 tff(4484,plain,
% 2.01/1.70 (~c0_1(a2)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1516, 4482])).
% 2.01/1.70 tff(4485,plain,
% 2.01/1.70 (c2_1(a2)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1527, 4482])).
% 2.01/1.70 tff(4486,plain,
% 2.01/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a32))),
% 2.01/1.70 inference(rewrite,[status(thm)],[])).
% 2.01/1.70 tff(4487,plain,
% 2.01/1.70 (((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a32) | c1_1(a32) | c2_1(a32) | c2_1(a32) | c0_1(a32) | c3_1(a32)) <=> (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a32))),
% 2.01/1.70 inference(rewrite,[status(thm)],[])).
% 2.01/1.70 tff(4488,plain,
% 2.01/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a32) | c1_1(a32) | c2_1(a32) | c2_1(a32) | c0_1(a32) | c3_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a32)))),
% 2.01/1.70 inference(monotonicity,[status(thm)],[4487])).
% 2.01/1.70 tff(4489,plain,
% 2.01/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a32) | c1_1(a32) | c2_1(a32) | c2_1(a32) | c0_1(a32) | c3_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a32))),
% 2.01/1.70 inference(transitivity,[status(thm)],[4488, 4486])).
% 2.01/1.70 tff(4490,plain,
% 2.01/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | (~c2_1(a2)) | c0_1(a2) | c3_1(a32) | c1_1(a32) | c2_1(a32) | c2_1(a32) | c0_1(a32) | c3_1(a32))),
% 2.01/1.70 inference(quant_inst,[status(thm)],[])).
% 2.01/1.70 tff(4491,plain,
% 2.01/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | c0_1(U) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a32) | c1_1(a32) | c3_1(a32) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | c2_1(a32)),
% 2.01/1.70 inference(modus_ponens,[status(thm)],[4490, 4489])).
% 2.01/1.70 tff(4492,plain,
% 2.01/1.70 ($false),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4491, 169, 4485, 4480, 4472, 4471, 4484, 4483, 2435, 4479])).
% 2.01/1.70 tff(4493,plain,((~hskp19) | (~c0_1(a3)) | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.01/1.70 tff(4494,plain,
% 2.01/1.70 (~hskp19),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4493, 643, 2413])).
% 2.01/1.70 tff(4495,plain,
% 2.01/1.70 (~hskp4),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4198, 4494, 2413])).
% 2.01/1.70 tff(4496,plain,
% 2.01/1.70 (hskp14),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[3517, 4495, 643])).
% 2.01/1.70 tff(4497,plain,
% 2.01/1.70 (~c1_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1024, 4496])).
% 2.01/1.70 tff(4498,plain,
% 2.01/1.70 (c2_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1041, 4496])).
% 2.01/1.70 tff(4499,plain,
% 2.01/1.70 (c3_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[3985, 4498, 2413, 4497])).
% 2.01/1.70 tff(4500,plain,
% 2.01/1.70 (hskp8),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[306, 4495, 643])).
% 2.01/1.70 tff(4501,plain,
% 2.01/1.70 (~c2_1(a15)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[184, 4500])).
% 2.01/1.70 tff(4502,plain,
% 2.01/1.70 (~c1_1(a15)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[201, 4500])).
% 2.01/1.70 tff(4503,plain,
% 2.01/1.70 (~c0_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1030, 4496])).
% 2.01/1.70 tff(4504,plain,
% 2.01/1.70 (c0_1(a15)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[195, 4500])).
% 2.01/1.70 tff(4505,plain,
% 2.01/1.70 ($false),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[3527, 169, 4495, 4504, 4503, 4497, 4502, 4501, 65, 4499])).
% 2.01/1.70 tff(4506,plain,(hskp17 | (~c0_1(a3))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.70 tff(4507,plain,
% 2.01/1.70 (hskp17),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4506, 4445])).
% 2.01/1.70 tff(4508,plain,
% 2.01/1.70 (c2_1(a31)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[328, 4507])).
% 2.01/1.70 tff(4509,plain,
% 2.01/1.70 (~c1_1(a31)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[71, 4507])).
% 2.01/1.70 tff(4510,plain,
% 2.01/1.70 (c3_1(a31)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[2424, 4509, 4445, 4508])).
% 2.01/1.70 tff(4511,plain,
% 2.01/1.70 (hskp10),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4455, 1270, 4445])).
% 2.01/1.70 tff(4512,plain,
% 2.01/1.70 (~c3_1(a18)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1150, 4511])).
% 2.01/1.70 tff(4513,plain,
% 2.01/1.70 (c2_1(a18)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1161, 4511])).
% 2.01/1.70 tff(4514,plain,
% 2.01/1.70 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c3_1(a18) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a18) | (~c2_1(a18)))),
% 2.01/1.70 inference(rewrite,[status(thm)],[])).
% 2.01/1.70 tff(4515,plain,
% 2.01/1.70 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (c3_1(a18) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a18) | (~c2_1(a18)))),
% 2.01/1.70 inference(rewrite,[status(thm)],[])).
% 2.01/1.70 tff(4516,plain,
% 2.01/1.70 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (c3_1(a18) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a18) | (~c2_1(a18))))),
% 2.01/1.70 inference(monotonicity,[status(thm)],[4515])).
% 2.01/1.70 tff(4517,plain,
% 2.01/1.70 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a18) | (~c2_1(a18)))),
% 2.01/1.70 inference(transitivity,[status(thm)],[4516, 4514])).
% 2.01/1.70 tff(4518,plain,
% 2.01/1.70 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c3_1(a3)) | c3_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 2.01/1.70 inference(quant_inst,[status(thm)],[])).
% 2.01/1.70 tff(4519,plain,
% 2.01/1.70 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | c3_1(a18) | (~ndr1_0) | (~c0_1(a3)) | (~c2_1(a3)) | (~c3_1(a3)) | c1_1(a18) | (~c2_1(a18))),
% 2.01/1.70 inference(modus_ponens,[status(thm)],[4518, 4517])).
% 2.01/1.70 tff(4520,plain,
% 2.01/1.70 (c1_1(a18)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4519, 169, 2381, 2412, 4513, 4512, 1580, 4445])).
% 2.01/1.70 tff(4521,plain,
% 2.01/1.70 (~hskp8),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[2482, 655, 654])).
% 2.01/1.70 tff(4522,plain,
% 2.01/1.70 (hskp4),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4276, 655, 654])).
% 2.01/1.70 tff(4523,plain,
% 2.01/1.70 (hskp19),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4198, 4522, 4445])).
% 2.01/1.70 tff(4524,plain,
% 2.01/1.70 ((~hskp19) | hskp3 | hskp2 | hskp8),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[3134, 4313])).
% 2.01/1.70 tff(4525,plain,
% 2.01/1.70 (hskp3),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4524, 4523, 654, 4521])).
% 2.01/1.70 tff(4526,plain,
% 2.01/1.70 (~c1_1(a5)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[367, 4525])).
% 2.01/1.70 tff(4527,plain,
% 2.01/1.70 (~c3_1(a5)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[948, 4525])).
% 2.01/1.70 tff(4528,plain,
% 2.01/1.70 (c0_1(a31)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[317, 4507])).
% 2.01/1.70 tff(4529,plain,
% 2.01/1.70 (~c2_1(a5)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[361, 4525])).
% 2.01/1.70 tff(4530,assumption,(~c0_1(a5)), introduced(assumption)).
% 2.01/1.70 tff(4531,plain,
% 2.01/1.70 (hskp0 | c0_1(a5)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[384, 169, 331, 332, 343, 1053, 1567, 342])).
% 2.01/1.70 tff(4532,plain,
% 2.01/1.70 (hskp0),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4531, 4530])).
% 2.01/1.70 tff(4533,plain,
% 2.01/1.70 (~c2_1(a1)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[259, 4532])).
% 2.01/1.70 tff(4534,plain,
% 2.01/1.70 (~c0_1(a1)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[283, 4532])).
% 2.01/1.70 tff(4535,plain,
% 2.01/1.70 (c3_1(a1)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[270, 4532])).
% 2.01/1.70 tff(4536,plain,
% 2.01/1.70 ($false),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4273, 169, 4535, 1053, 1567, 1052, 4534, 4533, 55, 4530])).
% 2.01/1.70 tff(4537,plain,(c0_1(a5) | c1_1(a5) | c2_1(a5) | c3_1(a5) | (~c0_1(a31)) | (~c2_1(a31)) | c1_1(a31)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.70 tff(4538,plain,
% 2.01/1.70 (c0_1(a5)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4537, 4529, 4528, 4527, 4526, 4508, 4509])).
% 2.01/1.70 tff(4539,plain,
% 2.01/1.70 ($false),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[934, 169, 655, 654, 4526, 4529, 700, 4538])).
% 2.01/1.70 tff(4540,plain,(hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.01/1.70 tff(4541,plain,
% 2.01/1.70 (hskp14),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[4540, 654])).
% 2.01/1.70 tff(4542,plain,
% 2.01/1.70 (~c1_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1024, 4541])).
% 2.01/1.70 tff(4543,plain,
% 2.01/1.70 (~c0_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1030, 4541])).
% 2.01/1.70 tff(4544,plain,
% 2.01/1.70 (c2_1(a24)),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1041, 4541])).
% 2.01/1.70 tff(4545,plain,
% 2.01/1.70 (hskp3),
% 2.01/1.70 inference(unit_resolution,[status(thm)],[1048, 169, 654, 4544, 4543, 4542, 23])).
% 2.01/1.71 tff(4546,plain,
% 2.01/1.71 (~c1_1(a5)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[367, 4545])).
% 2.01/1.71 tff(4547,plain,
% 2.01/1.71 (~c3_1(a5)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[948, 4545])).
% 2.01/1.71 tff(4548,plain,
% 2.01/1.71 (~c2_1(a5)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[361, 4545])).
% 2.01/1.71 tff(4549,plain,
% 2.01/1.71 (c0_1(a5)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4537, 4548, 4528, 4547, 4546, 4508, 4509])).
% 2.01/1.71 tff(4550,plain,
% 2.01/1.71 (c3_1(a24)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[3985, 4544, 4445, 4542])).
% 2.01/1.71 tff(4551,plain,
% 2.01/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a24)))),
% 2.01/1.71 inference(rewrite,[status(thm)],[])).
% 2.01/1.71 tff(4552,plain,
% 2.01/1.71 ((hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24))) <=> (hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a24)))),
% 2.01/1.71 inference(rewrite,[status(thm)],[])).
% 2.01/1.71 tff(4553,plain,
% 2.01/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a24))))),
% 2.01/1.71 inference(monotonicity,[status(thm)],[4552])).
% 2.01/1.71 tff(4554,plain,
% 2.01/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a24)))),
% 2.01/1.71 inference(transitivity,[status(thm)],[4553, 4551])).
% 2.01/1.71 tff(4555,plain,
% 2.01/1.71 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a5) | c2_1(a5) | (~c0_1(a5)) | c1_1(a24) | c0_1(a24) | (~c3_1(a24)))),
% 2.01/1.71 inference(quant_inst,[status(thm)],[])).
% 2.01/1.71 tff(4556,plain,
% 2.01/1.71 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a24) | c1_1(a24) | c1_1(a5) | c2_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c3_1(a24))),
% 2.01/1.71 inference(modus_ponens,[status(thm)],[4555, 4554])).
% 2.01/1.71 tff(4557,plain,
% 2.01/1.71 (hskp4),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4556, 169, 4543, 4542, 4546, 4548, 65, 4549, 4550])).
% 2.01/1.71 tff(4558,plain,
% 2.01/1.71 (hskp19),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4198, 4557, 4445])).
% 2.01/1.71 tff(4559,plain,
% 2.01/1.71 (~c0_1(a33)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[897, 4558])).
% 2.01/1.71 tff(4560,plain,
% 2.01/1.71 (c2_1(a33)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[908, 4558])).
% 2.01/1.71 tff(4561,plain,
% 2.01/1.71 (~hskp11),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4186, 4445])).
% 2.01/1.71 tff(4562,plain,
% 2.01/1.71 (c3_1(a33)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[1503, 4558])).
% 2.01/1.71 tff(4563,plain,
% 2.01/1.71 (~hskp10),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4453, 4562, 4561, 4560, 4559])).
% 2.01/1.71 tff(4564,plain,
% 2.01/1.71 (hskp6),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4455, 4563, 4445])).
% 2.01/1.71 tff(4565,plain,
% 2.01/1.71 (~c2_1(a8)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[1335, 4564])).
% 2.01/1.71 tff(4566,plain,
% 2.01/1.71 (c1_1(a8)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[1346, 4564])).
% 2.01/1.71 tff(4567,plain,
% 2.01/1.71 (c0_1(a8)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[1369, 4564])).
% 2.01/1.71 tff(4568,plain,
% 2.01/1.71 (c3_1(a8)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4468, 4567, 4566, 4565])).
% 2.01/1.71 tff(4569,plain,
% 2.01/1.71 (hskp13),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[3955, 169, 4528, 4509, 4546, 4548, 1616, 4510, 4549])).
% 2.01/1.71 tff(4570,plain,
% 2.01/1.71 (~c3_1(a22)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[482, 4569])).
% 2.01/1.71 tff(4571,plain,
% 2.01/1.71 (~c2_1(a22)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[488, 4569])).
% 2.01/1.71 tff(4572,plain,
% 2.01/1.71 (~c0_1(a22)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[494, 4569])).
% 2.01/1.71 tff(4573,plain,
% 2.01/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a8) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a8)) | (~c3_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a8) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 2.01/1.71 inference(rewrite,[status(thm)],[])).
% 2.01/1.71 tff(4574,plain,
% 2.01/1.71 (((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a22) | c0_1(a22) | c3_1(a22)) <=> (c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a8) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 2.01/1.71 inference(rewrite,[status(thm)],[])).
% 2.01/1.71 tff(4575,plain,
% 2.01/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a8) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a8)) | (~c3_1(a8))))),
% 2.01/1.71 inference(monotonicity,[status(thm)],[4574])).
% 2.01/1.71 tff(4576,plain,
% 2.01/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a22) | c0_1(a22) | c3_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a8) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 2.01/1.71 inference(transitivity,[status(thm)],[4575, 4573])).
% 2.01/1.71 tff(4577,plain,
% 2.01/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c3_1(a8)) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a22) | c0_1(a22) | c3_1(a22))),
% 2.01/1.71 inference(quant_inst,[status(thm)],[])).
% 2.01/1.71 tff(4578,plain,
% 2.01/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a22) | c2_1(a22) | c3_1(a22) | c2_1(a8) | c1_1(a5) | c3_1(a5) | (~ndr1_0) | (~c0_1(a5)) | (~c1_1(a8)) | (~c3_1(a8))),
% 2.01/1.71 inference(modus_ponens,[status(thm)],[4577, 4576])).
% 2.01/1.71 tff(4579,plain,
% 2.01/1.71 ($false),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4578, 169, 4566, 4572, 4571, 4570, 4565, 4546, 4547, 13, 4568, 4549])).
% 2.01/1.71 tff(4580,plain,(hskp2), inference(lemma,lemma(discharge,[]))).
% 2.01/1.71 tff(4581,plain,
% 2.01/1.71 (~c3_1(a4)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[400, 4580])).
% 2.01/1.71 tff(4582,plain,
% 2.01/1.71 (~c2_1(a4)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[417, 4580])).
% 2.01/1.71 tff(4583,plain,
% 2.01/1.71 (c1_1(a4)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[411, 4580])).
% 2.01/1.71 tff(4584,plain,
% 2.01/1.71 (~c0_1(a4)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[3282, 169, 2381, 2412, 4583, 4582, 4581, 439, 4445])).
% 2.01/1.71 tff(4585,plain,
% 2.01/1.71 (hskp5),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[3301, 169, 4513, 4583, 4512, 4582, 1413, 4584, 4520])).
% 2.01/1.71 tff(4586,plain,
% 2.01/1.71 (~c0_1(a7)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[1419, 4585])).
% 2.01/1.71 tff(4587,plain,
% 2.01/1.71 (c3_1(a7)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[1454, 4585])).
% 2.01/1.71 tff(4588,plain,
% 2.01/1.71 (c0_1(a18)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[1172, 4511])).
% 2.01/1.71 tff(4589,plain,
% 2.01/1.71 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a18) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a18)) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a18)) | (~c2_1(a18)))),
% 2.01/1.71 inference(rewrite,[status(thm)],[])).
% 2.01/1.71 tff(4590,plain,
% 2.01/1.71 ((hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7))) <=> (hskp11 | c3_1(a18) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a18)) | (~c2_1(a18)))),
% 2.01/1.71 inference(rewrite,[status(thm)],[])).
% 2.01/1.71 tff(4591,plain,
% 2.01/1.71 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | c3_1(a18) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a18)) | (~c2_1(a18))))),
% 2.01/1.71 inference(monotonicity,[status(thm)],[4590])).
% 2.01/1.71 tff(4592,plain,
% 2.01/1.71 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a18)) | (~c2_1(a18)))),
% 2.01/1.71 inference(transitivity,[status(thm)],[4591, 4589])).
% 2.01/1.71 tff(4593,plain,
% 2.01/1.71 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a18) | (~c2_1(a18)) | (~c0_1(a18)) | c0_1(a7) | (~c3_1(a7)) | (~c2_1(a7)))),
% 2.01/1.71 inference(quant_inst,[status(thm)],[])).
% 2.01/1.71 tff(4594,plain,
% 2.01/1.71 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp11 | c3_1(a18) | c0_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c2_1(a7)) | (~c0_1(a18)) | (~c2_1(a18))),
% 2.01/1.71 inference(modus_ponens,[status(thm)],[4593, 4592])).
% 2.01/1.71 tff(4595,plain,
% 2.01/1.71 (~c2_1(a7)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4594, 169, 4561, 4588, 4513, 4587, 4512, 4586, 1126])).
% 2.01/1.71 tff(4596,plain,
% 2.01/1.71 ($false),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[2917, 169, 1270, 2392, 2381, 2412, 4587, 4586, 1298, 4595])).
% 2.01/1.71 tff(4597,plain,(hskp6), inference(lemma,lemma(discharge,[]))).
% 2.01/1.71 tff(4598,plain,
% 2.01/1.71 (c3_1(a8)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4468, 1370, 1347, 1336])).
% 2.01/1.71 tff(4599,plain,
% 2.01/1.71 ($false),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[2811, 169, 883, 2392, 2381, 1347, 1336, 848, 4445, 4598])).
% 2.01/1.71 tff(4600,plain,((~hskp6) | hskp19), inference(lemma,lemma(discharge,[]))).
% 2.01/1.71 tff(4601,plain,
% 2.01/1.71 (hskp19),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4600, 4597])).
% 2.01/1.71 tff(4602,plain,
% 2.01/1.71 (~c0_1(a33)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[897, 4601])).
% 2.01/1.71 tff(4603,plain,
% 2.01/1.71 (c3_1(a33)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[1503, 4601])).
% 2.01/1.71 tff(4604,plain,
% 2.01/1.71 (c2_1(a33)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[908, 4601])).
% 2.01/1.71 tff(4605,plain,
% 2.01/1.71 (~hskp10),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4453, 4603, 4561, 4604, 4602])).
% 2.01/1.71 tff(4606,plain,
% 2.01/1.71 (~c1_1(a33)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[3698, 169, 4605, 4603, 4508, 4602, 4509, 1137, 4510])).
% 2.01/1.71 tff(4607,plain,
% 2.01/1.71 (~c1_1(a33)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[2820, 169, 4313, 2705, 3030, 3028, 2699])).
% 2.01/1.71 tff(4608,plain,
% 2.01/1.71 ($false),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[3379, 169, 3030, 4508, 421, 3028, 4509, 420, 83, 4510, 3294, 4607])).
% 2.01/1.71 tff(4609,plain,((~hskp19) | (~c1_1(a4)) | c3_1(a4) | c0_1(a4) | hskp8), inference(lemma,lemma(discharge,[]))).
% 2.01/1.71 tff(4610,plain,
% 2.01/1.71 (hskp8),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4609, 4601, 4581, 4584, 4583])).
% 2.01/1.71 tff(4611,plain,
% 2.01/1.71 (~c2_1(a15)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[184, 4610])).
% 2.01/1.71 tff(4612,plain,
% 2.01/1.71 (~c1_1(a15)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[201, 4610])).
% 2.01/1.71 tff(4613,plain,
% 2.01/1.71 (c0_1(a15)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[195, 4610])).
% 2.01/1.71 tff(4614,plain,
% 2.01/1.71 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a31)) | (~c0_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 2.01/1.71 inference(rewrite,[status(thm)],[])).
% 2.01/1.71 tff(4615,plain,
% 2.01/1.71 ((hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15))) <=> (hskp13 | c1_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 2.01/1.71 inference(rewrite,[status(thm)],[])).
% 2.01/1.71 tff(4616,plain,
% 2.01/1.71 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a31)) | (~c0_1(a31))))),
% 2.01/1.71 inference(monotonicity,[status(thm)],[4615])).
% 2.01/1.71 tff(4617,plain,
% 2.01/1.71 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a31)) | (~c0_1(a31)))),
% 2.01/1.71 inference(transitivity,[status(thm)],[4616, 4614])).
% 2.01/1.71 tff(4618,plain,
% 2.01/1.71 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a31) | (~c0_1(a31)) | (~c3_1(a31)) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)))),
% 2.01/1.71 inference(quant_inst,[status(thm)],[])).
% 2.01/1.71 tff(4619,plain,
% 2.01/1.71 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a31)) | (~c0_1(a31))),
% 2.01/1.71 inference(modus_ponens,[status(thm)],[4618, 4617])).
% 2.01/1.71 tff(4620,plain,
% 2.01/1.71 (hskp13),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4619, 169, 4528, 4613, 4509, 4612, 4611, 1616, 4510])).
% 2.01/1.71 tff(4621,plain,
% 2.01/1.71 (~c3_1(a22)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[482, 4620])).
% 2.01/1.71 tff(4622,plain,
% 2.01/1.71 (~c0_1(a22)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[494, 4620])).
% 2.01/1.71 tff(4623,plain,
% 2.01/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a33) | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a33) | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 2.01/1.71 inference(rewrite,[status(thm)],[])).
% 2.01/1.71 tff(4624,plain,
% 2.01/1.71 (((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c0_1(a22) | (~c1_1(a22)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33))) <=> (c0_1(a33) | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 2.01/1.71 inference(rewrite,[status(thm)],[])).
% 2.01/1.71 tff(4625,plain,
% 2.01/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c0_1(a22) | (~c1_1(a22)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a33) | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)))),
% 2.01/1.71 inference(monotonicity,[status(thm)],[4624])).
% 2.01/1.71 tff(4626,plain,
% 2.01/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c0_1(a22) | (~c1_1(a22)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a33) | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33))),
% 2.01/1.71 inference(transitivity,[status(thm)],[4625, 4623])).
% 2.01/1.71 tff(4627,plain,
% 2.01/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a31) | (~c2_1(a31)) | (~c3_1(a31)) | c3_1(a22) | c0_1(a22) | (~c1_1(a22)) | c1_1(a33) | c0_1(a33) | (~c2_1(a33)))),
% 2.01/1.71 inference(quant_inst,[status(thm)],[])).
% 2.01/1.71 tff(4628,plain,
% 2.01/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a33) | c1_1(a31) | c0_1(a22) | c3_1(a22) | (~ndr1_0) | (~c1_1(a22)) | (~c2_1(a31)) | (~c3_1(a31)) | (~c2_1(a33)) | c1_1(a33)),
% 2.01/1.71 inference(modus_ponens,[status(thm)],[4627, 4626])).
% 2.01/1.71 tff(4629,plain,
% 2.01/1.71 (~c1_1(a22)),
% 2.01/1.71 inference(unit_resolution,[status(thm)],[4628, 169, 4604, 4508, 4602, 4509, 4622, 4621, 83, 4510, 4606])).
% 2.01/1.71 tff(4630,plain,
% 2.01/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a4) | c3_1(a4) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a4) | c3_1(a4) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 2.01/1.71 inference(rewrite,[status(thm)],[])).
% 2.01/1.71 tff(4631,plain,
% 2.01/1.71 (((~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a2) | c3_1(a2) | (~c2_1(a2))) <=> (c2_1(a4) | c3_1(a4) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 2.01/1.71 inference(rewrite,[status(thm)],[])).
% 2.01/1.71 tff(4632,plain,
% 2.01/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a2) | c3_1(a2) | (~c2_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a4) | c3_1(a4) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3))))),
% 2.01/1.71 inference(monotonicity,[status(thm)],[4631])).
% 2.01/1.71 tff(4633,plain,
% 2.01/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a2) | c3_1(a2) | (~c2_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a4) | c3_1(a4) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3)))),
% 2.01/1.72 inference(transitivity,[status(thm)],[4632, 4630])).
% 2.01/1.72 tff(4634,plain,
% 2.01/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_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) | (~c2_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | c3_1(a4) | c2_1(a4) | (~c1_1(a4)) | c0_1(a2) | c3_1(a2) | (~c2_1(a2)))),
% 2.01/1.72 inference(quant_inst,[status(thm)],[])).
% 2.01/1.72 tff(4635,plain,
% 2.01/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a4) | c3_1(a4) | c0_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a2)) | (~c1_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | (~c1_1(a3))),
% 2.01/1.72 inference(modus_ponens,[status(thm)],[4634, 4633])).
% 2.01/1.72 tff(4636,plain,
% 2.01/1.72 ($false),
% 2.01/1.72 inference(unit_resolution,[status(thm)],[4635, 169, 2392, 2381, 421, 2452, 440, 420, 2443, 2442, 34, 4445])).
% 2.01/1.72 tff(4637,plain,((~hskp1) | (~c1_1(a4)) | c2_1(a4) | c3_1(a4)), inference(lemma,lemma(discharge,[]))).
% 2.01/1.72 tff(4638,plain,
% 2.01/1.72 (~hskp1),
% 2.01/1.72 inference(unit_resolution,[status(thm)],[4637, 4583, 4582, 4581])).
% 2.01/1.72 tff(4639,plain,
% 2.01/1.72 ($false),
% 2.01/1.72 inference(unit_resolution,[status(thm)],[3052, 169, 4638, 4508, 4509, 4622, 4621, 1493, 4510, 4629])).
% 2.01/1.72 % SZS output end Proof
%------------------------------------------------------------------------------