TSTP Solution File: SYN504-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN504-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 23:56:01 EDT 2022
% Result : Unsatisfiable 1.26s 1.08s
% Output : Proof 1.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN504-1 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 04:47:33 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 1.26/1.08 % SZS status Unsatisfiable
% 1.26/1.08 % SZS output start Proof
% 1.26/1.08 tff(c3_1_type, type, (
% 1.26/1.08 c3_1: $i > $o)).
% 1.26/1.08 tff(a360_type, type, (
% 1.26/1.08 a360: $i)).
% 1.26/1.08 tff(hskp6_type, type, (
% 1.26/1.08 hskp6: $o)).
% 1.26/1.08 tff(c1_1_type, type, (
% 1.26/1.08 c1_1: $i > $o)).
% 1.26/1.08 tff(a369_type, type, (
% 1.26/1.08 a369: $i)).
% 1.26/1.08 tff(a353_type, type, (
% 1.26/1.08 a353: $i)).
% 1.26/1.08 tff(c2_1_type, type, (
% 1.26/1.08 c2_1: $i > $o)).
% 1.26/1.08 tff(a359_type, type, (
% 1.26/1.08 a359: $i)).
% 1.26/1.08 tff(c0_1_type, type, (
% 1.26/1.08 c0_1: $i > $o)).
% 1.26/1.08 tff(ndr1_0_type, type, (
% 1.26/1.08 ndr1_0: $o)).
% 1.26/1.08 tff(hskp5_type, type, (
% 1.26/1.08 hskp5: $o)).
% 1.26/1.08 tff(a387_type, type, (
% 1.26/1.08 a387: $i)).
% 1.26/1.08 tff(hskp19_type, type, (
% 1.26/1.08 hskp19: $o)).
% 1.26/1.08 tff(hskp28_type, type, (
% 1.26/1.08 hskp28: $o)).
% 1.26/1.08 tff(a379_type, type, (
% 1.26/1.08 a379: $i)).
% 1.26/1.08 tff(a365_type, type, (
% 1.26/1.08 a365: $i)).
% 1.26/1.08 tff(a382_type, type, (
% 1.26/1.08 a382: $i)).
% 1.26/1.08 tff(hskp18_type, type, (
% 1.26/1.08 hskp18: $o)).
% 1.26/1.08 tff(hskp21_type, type, (
% 1.26/1.08 hskp21: $o)).
% 1.26/1.08 tff(a395_type, type, (
% 1.26/1.08 a395: $i)).
% 1.26/1.08 tff(hskp13_type, type, (
% 1.26/1.08 hskp13: $o)).
% 1.26/1.08 tff(hskp29_type, type, (
% 1.26/1.08 hskp29: $o)).
% 1.26/1.08 tff(hskp15_type, type, (
% 1.26/1.08 hskp15: $o)).
% 1.26/1.08 tff(a358_type, type, (
% 1.26/1.08 a358: $i)).
% 1.26/1.08 tff(hskp4_type, type, (
% 1.26/1.08 hskp4: $o)).
% 1.26/1.08 tff(a388_type, type, (
% 1.26/1.08 a388: $i)).
% 1.26/1.08 tff(hskp20_type, type, (
% 1.26/1.08 hskp20: $o)).
% 1.26/1.08 tff(a357_type, type, (
% 1.26/1.08 a357: $i)).
% 1.26/1.08 tff(hskp3_type, type, (
% 1.26/1.08 hskp3: $o)).
% 1.26/1.08 tff(a370_type, type, (
% 1.26/1.08 a370: $i)).
% 1.26/1.08 tff(hskp16_type, type, (
% 1.26/1.08 hskp16: $o)).
% 1.26/1.08 tff(hskp0_type, type, (
% 1.26/1.08 hskp0: $o)).
% 1.26/1.08 tff(hskp12_type, type, (
% 1.26/1.08 hskp12: $o)).
% 1.26/1.08 tff(a418_type, type, (
% 1.26/1.08 a418: $i)).
% 1.26/1.08 tff(hskp26_type, type, (
% 1.26/1.08 hskp26: $o)).
% 1.26/1.08 tff(a398_type, type, (
% 1.26/1.08 a398: $i)).
% 1.26/1.08 tff(a410_type, type, (
% 1.26/1.08 a410: $i)).
% 1.26/1.08 tff(hskp31_type, type, (
% 1.26/1.08 hskp31: $o)).
% 1.26/1.08 tff(a355_type, type, (
% 1.26/1.08 a355: $i)).
% 1.26/1.08 tff(hskp1_type, type, (
% 1.26/1.08 hskp1: $o)).
% 1.26/1.08 tff(hskp23_type, type, (
% 1.26/1.08 hskp23: $o)).
% 1.26/1.08 tff(a366_type, type, (
% 1.26/1.08 a366: $i)).
% 1.26/1.08 tff(hskp10_type, type, (
% 1.26/1.08 hskp10: $o)).
% 1.26/1.08 tff(1,plain,
% 1.26/1.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.26/1.08 inference(bind,[status(th)],[])).
% 1.26/1.08 tff(2,plain,
% 1.26/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.26/1.08 inference(quant_intro,[status(thm)],[1])).
% 1.26/1.08 tff(3,plain,
% 1.26/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(4,plain,
% 1.26/1.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.26/1.08 inference(bind,[status(th)],[])).
% 1.26/1.08 tff(5,plain,
% 1.26/1.08 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.26/1.08 inference(quant_intro,[status(thm)],[4])).
% 1.26/1.08 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.26/1.08 tff(7,plain,
% 1.26/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.26/1.08 tff(8,plain,
% 1.26/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.26/1.08 tff(9,plain,(
% 1.26/1.08 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.26/1.08 inference(skolemize,[status(sab)],[8])).
% 1.26/1.08 tff(10,plain,
% 1.26/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.26/1.08 tff(11,plain,
% 1.26/1.08 (^[U: $i] : refl((hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.26/1.08 inference(bind,[status(th)],[])).
% 1.26/1.08 tff(12,plain,
% 1.26/1.08 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.26/1.08 inference(quant_intro,[status(thm)],[11])).
% 1.26/1.08 tff(13,plain,
% 1.26/1.08 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(14,plain,
% 1.26/1.08 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp6) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp6))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp6) <=> (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp6) <=> (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.26/1.08 inference(bind,[status(th)],[])).
% 1.26/1.08 tff(15,plain,
% 1.26/1.08 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp6) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.26/1.08 inference(quant_intro,[status(thm)],[14])).
% 1.26/1.08 tff(16,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.26/1.08 tff(17,plain,
% 1.26/1.08 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.26/1.08 tff(18,plain,
% 1.26/1.08 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.26/1.08 tff(19,plain,(
% 1.26/1.08 ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.26/1.08 inference(skolemize,[status(sab)],[18])).
% 1.26/1.08 tff(20,plain,
% 1.26/1.08 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.26/1.08 tff(21,assumption,(~hskp6), introduced(assumption)).
% 1.26/1.08 tff(22,assumption,(hskp28), introduced(assumption)).
% 1.26/1.08 tff(23,plain,
% 1.26/1.08 (((~hskp28) | c1_1(a365)) <=> ((~hskp28) | c1_1(a365))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(24,axiom,((~hskp28) | c1_1(a365)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 1.26/1.08 tff(25,plain,
% 1.26/1.08 ((~hskp28) | c1_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.26/1.08 tff(26,plain,
% 1.26/1.08 ((~hskp28) | c1_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[25, 23])).
% 1.26/1.08 tff(27,plain,
% 1.26/1.08 ((~hskp28) | c1_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[26, 23])).
% 1.26/1.08 tff(28,plain,
% 1.26/1.08 ((~hskp28) | c1_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.26/1.08 tff(29,plain,
% 1.26/1.08 ((~hskp28) | c1_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[28, 23])).
% 1.26/1.08 tff(30,plain,
% 1.26/1.08 ((~hskp28) | c1_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[29, 23])).
% 1.26/1.08 tff(31,plain,
% 1.26/1.08 ((~hskp28) | c1_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.26/1.08 tff(32,plain,
% 1.26/1.08 ((~hskp28) | c1_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[31, 23])).
% 1.26/1.08 tff(33,plain,
% 1.26/1.08 (c1_1(a365)),
% 1.26/1.08 inference(unit_resolution,[status(thm)],[32, 22])).
% 1.26/1.08 tff(34,plain,
% 1.26/1.08 (((~hskp28) | c3_1(a365)) <=> ((~hskp28) | c3_1(a365))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(35,axiom,((~hskp28) | c3_1(a365)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 1.26/1.08 tff(36,plain,
% 1.26/1.08 ((~hskp28) | c3_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.26/1.08 tff(37,plain,
% 1.26/1.08 ((~hskp28) | c3_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[36, 34])).
% 1.26/1.08 tff(38,plain,
% 1.26/1.08 ((~hskp28) | c3_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[37, 34])).
% 1.26/1.08 tff(39,plain,
% 1.26/1.08 ((~hskp28) | c3_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.26/1.08 tff(40,plain,
% 1.26/1.08 ((~hskp28) | c3_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[39, 34])).
% 1.26/1.08 tff(41,plain,
% 1.26/1.08 ((~hskp28) | c3_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[40, 34])).
% 1.26/1.08 tff(42,plain,
% 1.26/1.08 ((~hskp28) | c3_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[41, 34])).
% 1.26/1.08 tff(43,plain,
% 1.26/1.08 ((~hskp28) | c3_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[42, 34])).
% 1.26/1.08 tff(44,plain,
% 1.26/1.08 (c3_1(a365)),
% 1.26/1.08 inference(unit_resolution,[status(thm)],[43, 22])).
% 1.26/1.08 tff(45,plain,
% 1.26/1.08 (((~hskp28) | c2_1(a365)) <=> ((~hskp28) | c2_1(a365))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(46,axiom,((~hskp28) | c2_1(a365)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.26/1.08 tff(47,plain,
% 1.26/1.08 ((~hskp28) | c2_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[46, 45])).
% 1.26/1.08 tff(48,plain,
% 1.26/1.08 ((~hskp28) | c2_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[47, 45])).
% 1.26/1.08 tff(49,plain,
% 1.26/1.08 ((~hskp28) | c2_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[48, 45])).
% 1.26/1.08 tff(50,plain,
% 1.26/1.08 ((~hskp28) | c2_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[49, 45])).
% 1.26/1.08 tff(51,plain,
% 1.26/1.08 ((~hskp28) | c2_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[50, 45])).
% 1.26/1.08 tff(52,plain,
% 1.26/1.08 ((~hskp28) | c2_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[51, 45])).
% 1.26/1.08 tff(53,plain,
% 1.26/1.08 ((~hskp28) | c2_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.26/1.08 tff(54,plain,
% 1.26/1.08 ((~hskp28) | c2_1(a365)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[53, 45])).
% 1.26/1.08 tff(55,plain,
% 1.26/1.08 (c2_1(a365)),
% 1.26/1.08 inference(unit_resolution,[status(thm)],[54, 22])).
% 1.26/1.08 tff(56,assumption,(c0_1(a365)), introduced(assumption)).
% 1.26/1.08 tff(57,plain,
% 1.26/1.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.26/1.08 inference(bind,[status(th)],[])).
% 1.26/1.08 tff(58,plain,
% 1.26/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.26/1.08 inference(quant_intro,[status(thm)],[57])).
% 1.26/1.08 tff(59,plain,
% 1.26/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(60,plain,
% 1.26/1.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.26/1.08 inference(bind,[status(th)],[])).
% 1.26/1.08 tff(61,plain,
% 1.26/1.08 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.26/1.08 inference(quant_intro,[status(thm)],[60])).
% 1.26/1.08 tff(62,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause207')).
% 1.26/1.08 tff(63,plain,
% 1.26/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.26/1.08 tff(64,plain,
% 1.26/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[63, 59])).
% 1.26/1.08 tff(65,plain,(
% 1.26/1.08 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.26/1.08 inference(skolemize,[status(sab)],[64])).
% 1.26/1.08 tff(66,plain,
% 1.26/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[65, 58])).
% 1.26/1.08 tff(67,assumption,(c1_1(a365)), introduced(assumption)).
% 1.26/1.08 tff(68,assumption,(c3_1(a365)), introduced(assumption)).
% 1.26/1.08 tff(69,assumption,(c2_1(a365)), introduced(assumption)).
% 1.26/1.08 tff(70,assumption,(hskp21), introduced(assumption)).
% 1.26/1.08 tff(71,plain,
% 1.26/1.08 (((~hskp21) | (~c2_1(a395))) <=> ((~hskp21) | (~c2_1(a395)))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(72,plain,
% 1.26/1.08 (((~c2_1(a395)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a395)))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(73,axiom,((~c2_1(a395)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.26/1.08 tff(74,plain,
% 1.26/1.08 ((~hskp21) | (~c2_1(a395))),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.26/1.08 tff(75,plain,
% 1.26/1.08 ((~hskp21) | (~c2_1(a395))),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[74, 71])).
% 1.26/1.08 tff(76,plain,
% 1.26/1.08 (~c2_1(a395)),
% 1.26/1.08 inference(unit_resolution,[status(thm)],[75, 70])).
% 1.26/1.08 tff(77,plain,
% 1.26/1.08 (((~hskp21) | (~c0_1(a395))) <=> ((~hskp21) | (~c0_1(a395)))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(78,plain,
% 1.26/1.08 (((~c0_1(a395)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a395)))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(79,axiom,((~c0_1(a395)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.26/1.08 tff(80,plain,
% 1.26/1.08 ((~hskp21) | (~c0_1(a395))),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.26/1.08 tff(81,plain,
% 1.26/1.08 ((~hskp21) | (~c0_1(a395))),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[80, 77])).
% 1.26/1.08 tff(82,plain,
% 1.26/1.08 (~c0_1(a395)),
% 1.26/1.08 inference(unit_resolution,[status(thm)],[81, 70])).
% 1.26/1.08 tff(83,assumption,(~ndr1_0), introduced(assumption)).
% 1.26/1.08 tff(84,plain,
% 1.26/1.08 ((ndr1_0 | (~hskp13)) <=> (ndr1_0 | (~hskp13))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(85,plain,
% 1.26/1.08 (((~hskp13) | ndr1_0) <=> (ndr1_0 | (~hskp13))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(86,axiom,((~hskp13) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause20')).
% 1.26/1.08 tff(87,plain,
% 1.26/1.08 (ndr1_0 | (~hskp13)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.26/1.08 tff(88,plain,
% 1.26/1.08 (ndr1_0 | (~hskp13)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[87, 84])).
% 1.26/1.08 tff(89,plain,
% 1.26/1.08 (~hskp13),
% 1.26/1.08 inference(unit_resolution,[status(thm)],[88, 83])).
% 1.26/1.08 tff(90,plain,
% 1.26/1.08 ((ndr1_0 | (~hskp29)) <=> (ndr1_0 | (~hskp29))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(91,plain,
% 1.26/1.08 (((~hskp29) | ndr1_0) <=> (ndr1_0 | (~hskp29))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(92,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 1.26/1.08 tff(93,plain,
% 1.26/1.08 (ndr1_0 | (~hskp29)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.26/1.08 tff(94,plain,
% 1.26/1.08 (ndr1_0 | (~hskp29)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[93, 90])).
% 1.26/1.08 tff(95,plain,
% 1.26/1.08 (~hskp29),
% 1.26/1.08 inference(unit_resolution,[status(thm)],[94, 83])).
% 1.26/1.08 tff(96,plain,
% 1.26/1.08 ((ndr1_0 | (~hskp15)) <=> (ndr1_0 | (~hskp15))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(97,plain,
% 1.26/1.08 (((~hskp15) | ndr1_0) <=> (ndr1_0 | (~hskp15))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(98,axiom,((~hskp15) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause18')).
% 1.26/1.08 tff(99,plain,
% 1.26/1.08 (ndr1_0 | (~hskp15)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.26/1.08 tff(100,plain,
% 1.26/1.08 (ndr1_0 | (~hskp15)),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[99, 96])).
% 1.26/1.08 tff(101,plain,
% 1.26/1.08 (~hskp15),
% 1.26/1.08 inference(unit_resolution,[status(thm)],[100, 83])).
% 1.26/1.08 tff(102,plain,
% 1.26/1.08 ((hskp29 | hskp15 | hskp13) <=> (hskp29 | hskp15 | hskp13)),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(103,plain,
% 1.26/1.08 (((hskp29 | hskp13) | hskp15) <=> (hskp29 | hskp15 | hskp13)),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(104,plain,
% 1.26/1.08 ((hskp29 | hskp13) <=> (hskp29 | hskp13)),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(105,plain,
% 1.26/1.08 (((hskp29 | hskp13) | hskp15) <=> ((hskp29 | hskp13) | hskp15)),
% 1.26/1.08 inference(monotonicity,[status(thm)],[104])).
% 1.26/1.08 tff(106,plain,
% 1.26/1.08 (((hskp29 | hskp13) | hskp15) <=> (hskp29 | hskp15 | hskp13)),
% 1.26/1.08 inference(transitivity,[status(thm)],[105, 103])).
% 1.26/1.08 tff(107,axiom,((hskp29 | hskp13) | hskp15), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 1.26/1.08 tff(108,plain,
% 1.26/1.08 (hskp29 | hskp15 | hskp13),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.26/1.08 tff(109,plain,
% 1.26/1.08 (hskp29 | hskp15 | hskp13),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[108, 102])).
% 1.26/1.08 tff(110,plain,
% 1.26/1.08 (hskp29 | hskp15 | hskp13),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[109, 102])).
% 1.26/1.08 tff(111,plain,
% 1.26/1.08 (hskp29 | hskp15 | hskp13),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[110, 102])).
% 1.26/1.08 tff(112,plain,
% 1.26/1.08 (hskp29 | hskp15 | hskp13),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[111, 102])).
% 1.26/1.08 tff(113,plain,
% 1.26/1.08 (hskp29 | hskp15 | hskp13),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[112, 102])).
% 1.26/1.08 tff(114,plain,
% 1.26/1.08 (hskp29 | hskp15 | hskp13),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[113, 102])).
% 1.26/1.08 tff(115,plain,
% 1.26/1.08 (hskp29 | hskp15 | hskp13),
% 1.26/1.08 inference(modus_ponens,[status(thm)],[114, 102])).
% 1.26/1.08 tff(116,plain,
% 1.26/1.08 ($false),
% 1.26/1.08 inference(unit_resolution,[status(thm)],[115, 101, 95, 89])).
% 1.26/1.08 tff(117,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.26/1.08 tff(118,plain,
% 1.26/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a395)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a395)))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(119,plain,
% 1.26/1.08 (((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a395) | c0_1(a395) | (~c3_1(a395))) <=> (c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a395)))),
% 1.26/1.08 inference(rewrite,[status(thm)],[])).
% 1.26/1.08 tff(120,plain,
% 1.26/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a395) | c0_1(a395) | (~c3_1(a395)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a395))))),
% 1.26/1.08 inference(monotonicity,[status(thm)],[119])).
% 1.26/1.08 tff(121,plain,
% 1.26/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a395) | c0_1(a395) | (~c3_1(a395)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a395)))),
% 1.26/1.09 inference(transitivity,[status(thm)],[120, 118])).
% 1.26/1.09 tff(122,plain,
% 1.26/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a395) | c0_1(a395) | (~c3_1(a395)))),
% 1.26/1.09 inference(quant_inst,[status(thm)],[])).
% 1.26/1.09 tff(123,plain,
% 1.26/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a395))),
% 1.26/1.09 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.26/1.09 tff(124,plain,
% 1.26/1.09 (~c3_1(a395)),
% 1.26/1.09 inference(unit_resolution,[status(thm)],[123, 117, 67, 69, 68, 82, 76, 66, 56])).
% 1.26/1.09 tff(125,plain,
% 1.26/1.09 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.26/1.09 inference(bind,[status(th)],[])).
% 1.26/1.09 tff(126,plain,
% 1.26/1.09 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.26/1.09 inference(quant_intro,[status(thm)],[125])).
% 1.26/1.09 tff(127,plain,
% 1.26/1.09 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.26/1.09 inference(rewrite,[status(thm)],[])).
% 1.26/1.09 tff(128,plain,
% 1.26/1.09 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp13))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.26/1.09 inference(bind,[status(th)],[])).
% 1.26/1.09 tff(129,plain,
% 1.26/1.09 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.26/1.09 inference(quant_intro,[status(thm)],[128])).
% 1.26/1.09 tff(130,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.26/1.09 tff(131,plain,
% 1.26/1.09 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.26/1.09 inference(modus_ponens,[status(thm)],[130, 129])).
% 1.26/1.09 tff(132,plain,
% 1.26/1.09 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.26/1.09 inference(modus_ponens,[status(thm)],[131, 127])).
% 1.26/1.09 tff(133,plain,(
% 1.26/1.09 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.26/1.09 inference(skolemize,[status(sab)],[132])).
% 1.26/1.09 tff(134,plain,
% 1.26/1.09 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.26/1.09 inference(modus_ponens,[status(thm)],[133, 126])).
% 1.26/1.09 tff(135,plain,
% 1.26/1.09 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 1.26/1.09 inference(bind,[status(th)],[])).
% 1.26/1.09 tff(136,plain,
% 1.26/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.26/1.09 inference(quant_intro,[status(thm)],[135])).
% 1.26/1.09 tff(137,plain,
% 1.26/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.26/1.09 inference(rewrite,[status(thm)],[])).
% 1.26/1.09 tff(138,plain,
% 1.26/1.09 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 1.26/1.09 inference(bind,[status(th)],[])).
% 1.26/1.09 tff(139,plain,
% 1.26/1.09 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.26/1.09 inference(quant_intro,[status(thm)],[138])).
% 1.26/1.09 tff(140,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause206')).
% 1.26/1.09 tff(141,plain,
% 1.26/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.26/1.09 inference(modus_ponens,[status(thm)],[140, 139])).
% 1.26/1.09 tff(142,plain,
% 1.26/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[141, 137])).
% 1.36/1.09 tff(143,plain,(
% 1.36/1.09 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.36/1.09 inference(skolemize,[status(sab)],[142])).
% 1.36/1.09 tff(144,plain,
% 1.36/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[143, 136])).
% 1.36/1.09 tff(145,assumption,(~hskp4), introduced(assumption)).
% 1.36/1.09 tff(146,assumption,(~c0_1(a388)), introduced(assumption)).
% 1.36/1.09 tff(147,plain,
% 1.36/1.09 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.36/1.09 inference(bind,[status(th)],[])).
% 1.36/1.09 tff(148,plain,
% 1.36/1.09 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.09 inference(quant_intro,[status(thm)],[147])).
% 1.36/1.09 tff(149,plain,
% 1.36/1.09 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(150,plain,
% 1.36/1.09 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.36/1.09 inference(bind,[status(th)],[])).
% 1.36/1.09 tff(151,plain,
% 1.36/1.09 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.09 inference(quant_intro,[status(thm)],[150])).
% 1.36/1.09 tff(152,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.36/1.09 tff(153,plain,
% 1.36/1.09 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.36/1.09 tff(154,plain,
% 1.36/1.09 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[153, 149])).
% 1.36/1.09 tff(155,plain,(
% 1.36/1.09 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.09 inference(skolemize,[status(sab)],[154])).
% 1.36/1.09 tff(156,plain,
% 1.36/1.09 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[155, 148])).
% 1.36/1.09 tff(157,plain,
% 1.36/1.09 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.36/1.09 inference(bind,[status(th)],[])).
% 1.36/1.09 tff(158,plain,
% 1.36/1.09 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.09 inference(quant_intro,[status(thm)],[157])).
% 1.36/1.09 tff(159,plain,
% 1.36/1.09 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(160,plain,
% 1.36/1.09 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp20) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp20))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.36/1.09 inference(bind,[status(th)],[])).
% 1.36/1.09 tff(161,plain,
% 1.36/1.09 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.09 inference(quant_intro,[status(thm)],[160])).
% 1.36/1.09 tff(162,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 1.36/1.09 tff(163,plain,
% 1.36/1.09 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[162, 161])).
% 1.36/1.09 tff(164,plain,
% 1.36/1.09 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[163, 159])).
% 1.36/1.09 tff(165,plain,(
% 1.36/1.09 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.09 inference(skolemize,[status(sab)],[164])).
% 1.36/1.09 tff(166,plain,
% 1.36/1.09 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[165, 158])).
% 1.36/1.09 tff(167,plain,
% 1.36/1.09 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.36/1.09 inference(bind,[status(th)],[])).
% 1.36/1.09 tff(168,plain,
% 1.36/1.09 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.09 inference(quant_intro,[status(thm)],[167])).
% 1.36/1.09 tff(169,plain,
% 1.36/1.09 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(170,plain,
% 1.36/1.09 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.36/1.09 inference(bind,[status(th)],[])).
% 1.36/1.09 tff(171,plain,
% 1.36/1.09 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.09 inference(quant_intro,[status(thm)],[170])).
% 1.36/1.09 tff(172,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.36/1.09 tff(173,plain,
% 1.36/1.09 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.36/1.09 tff(174,plain,
% 1.36/1.09 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[173, 169])).
% 1.36/1.09 tff(175,plain,(
% 1.36/1.09 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.09 inference(skolemize,[status(sab)],[174])).
% 1.36/1.09 tff(176,plain,
% 1.36/1.09 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[175, 168])).
% 1.36/1.09 tff(177,assumption,(~hskp3), introduced(assumption)).
% 1.36/1.09 tff(178,plain,
% 1.36/1.09 ((hskp4 | hskp6) <=> (hskp4 | hskp6)),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(179,axiom,(hskp4 | hskp6), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.36/1.09 tff(180,plain,
% 1.36/1.09 (hskp4 | hskp6),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.36/1.09 tff(181,plain,
% 1.36/1.09 (hskp6),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[180, 145])).
% 1.36/1.09 tff(182,plain,
% 1.36/1.09 (((~hskp6) | (~c2_1(a360))) <=> ((~hskp6) | (~c2_1(a360)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(183,plain,
% 1.36/1.09 (((~c2_1(a360)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a360)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(184,axiom,((~c2_1(a360)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.36/1.09 tff(185,plain,
% 1.36/1.09 ((~hskp6) | (~c2_1(a360))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.36/1.09 tff(186,plain,
% 1.36/1.09 ((~hskp6) | (~c2_1(a360))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[185, 182])).
% 1.36/1.09 tff(187,plain,
% 1.36/1.09 (~c2_1(a360)),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[186, 181])).
% 1.36/1.09 tff(188,plain,
% 1.36/1.09 (((~hskp6) | (~c1_1(a360))) <=> ((~hskp6) | (~c1_1(a360)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(189,plain,
% 1.36/1.09 (((~c1_1(a360)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a360)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(190,axiom,((~c1_1(a360)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.36/1.09 tff(191,plain,
% 1.36/1.09 ((~hskp6) | (~c1_1(a360))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[190, 189])).
% 1.36/1.09 tff(192,plain,
% 1.36/1.09 ((~hskp6) | (~c1_1(a360))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[191, 188])).
% 1.36/1.09 tff(193,plain,
% 1.36/1.09 (~c1_1(a360)),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[192, 181])).
% 1.36/1.09 tff(194,plain,
% 1.36/1.09 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(195,plain,
% 1.36/1.09 ((hskp4 | hskp3 | (~ndr1_0) | c2_1(a360) | c1_1(a360) | c0_1(a360)) <=> (hskp4 | hskp3 | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(196,plain,
% 1.36/1.09 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360)))),
% 1.36/1.09 inference(monotonicity,[status(thm)],[195])).
% 1.36/1.09 tff(197,plain,
% 1.36/1.09 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360))),
% 1.36/1.09 inference(transitivity,[status(thm)],[196, 194])).
% 1.36/1.09 tff(198,plain,
% 1.36/1.09 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a360) | c1_1(a360) | c0_1(a360))),
% 1.36/1.09 inference(quant_inst,[status(thm)],[])).
% 1.36/1.09 tff(199,plain,
% 1.36/1.09 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360)),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[198, 197])).
% 1.36/1.09 tff(200,plain,
% 1.36/1.09 (hskp3 | c0_1(a360)),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[199, 145, 117, 193, 187, 176])).
% 1.36/1.09 tff(201,plain,
% 1.36/1.09 (c0_1(a360)),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[200, 177])).
% 1.36/1.09 tff(202,plain,
% 1.36/1.09 (^[U: $i] : refl((hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.36/1.09 inference(bind,[status(th)],[])).
% 1.36/1.09 tff(203,plain,
% 1.36/1.09 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.09 inference(quant_intro,[status(thm)],[202])).
% 1.36/1.09 tff(204,plain,
% 1.36/1.09 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(205,plain,
% 1.36/1.09 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp19) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp19) <=> (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.36/1.09 inference(bind,[status(th)],[])).
% 1.36/1.09 tff(206,plain,
% 1.36/1.09 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp19) <=> ![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.09 inference(quant_intro,[status(thm)],[205])).
% 1.36/1.09 tff(207,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.36/1.09 tff(208,plain,
% 1.36/1.09 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.36/1.09 tff(209,plain,
% 1.36/1.09 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.36/1.09 tff(210,plain,(
% 1.36/1.09 ![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.09 inference(skolemize,[status(sab)],[209])).
% 1.36/1.09 tff(211,plain,
% 1.36/1.09 (![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[210, 203])).
% 1.36/1.09 tff(212,plain,
% 1.36/1.09 (((~hskp6) | (~c3_1(a360))) <=> ((~hskp6) | (~c3_1(a360)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(213,plain,
% 1.36/1.09 (((~c3_1(a360)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a360)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(214,axiom,((~c3_1(a360)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.36/1.09 tff(215,plain,
% 1.36/1.09 ((~hskp6) | (~c3_1(a360))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.36/1.09 tff(216,plain,
% 1.36/1.09 ((~hskp6) | (~c3_1(a360))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[215, 212])).
% 1.36/1.09 tff(217,plain,
% 1.36/1.09 (~c3_1(a360)),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[216, 181])).
% 1.36/1.09 tff(218,plain,
% 1.36/1.09 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | c1_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp3 | c1_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(219,plain,
% 1.36/1.09 ((hskp19 | hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360))) <=> (hskp19 | hskp3 | c1_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(220,plain,
% 1.36/1.09 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | c1_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360))))),
% 1.36/1.09 inference(monotonicity,[status(thm)],[219])).
% 1.36/1.09 tff(221,plain,
% 1.36/1.09 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp3 | c1_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))),
% 1.36/1.09 inference(transitivity,[status(thm)],[220, 218])).
% 1.36/1.09 tff(222,plain,
% 1.36/1.09 ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)))),
% 1.36/1.09 inference(quant_inst,[status(thm)],[])).
% 1.36/1.09 tff(223,plain,
% 1.36/1.09 ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp3 | c1_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[222, 221])).
% 1.36/1.09 tff(224,plain,
% 1.36/1.09 (hskp19 | hskp3 | (~c0_1(a360))),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[223, 117, 193, 217, 211])).
% 1.36/1.09 tff(225,plain,
% 1.36/1.09 (hskp19),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[224, 201, 177])).
% 1.36/1.09 tff(226,plain,
% 1.36/1.09 (((~hskp19) | (~c2_1(a387))) <=> ((~hskp19) | (~c2_1(a387)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(227,plain,
% 1.36/1.09 (((~c2_1(a387)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a387)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(228,axiom,((~c2_1(a387)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.36/1.09 tff(229,plain,
% 1.36/1.09 ((~hskp19) | (~c2_1(a387))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[228, 227])).
% 1.36/1.09 tff(230,plain,
% 1.36/1.09 ((~hskp19) | (~c2_1(a387))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[229, 226])).
% 1.36/1.09 tff(231,plain,
% 1.36/1.09 (~c2_1(a387)),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[230, 225])).
% 1.36/1.09 tff(232,plain,
% 1.36/1.09 (((~hskp19) | (~c1_1(a387))) <=> ((~hskp19) | (~c1_1(a387)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(233,plain,
% 1.36/1.09 (((~c1_1(a387)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a387)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(234,axiom,((~c1_1(a387)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.36/1.09 tff(235,plain,
% 1.36/1.09 ((~hskp19) | (~c1_1(a387))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.36/1.09 tff(236,plain,
% 1.36/1.09 ((~hskp19) | (~c1_1(a387))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[235, 232])).
% 1.36/1.09 tff(237,plain,
% 1.36/1.09 (~c1_1(a387)),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[236, 225])).
% 1.36/1.09 tff(238,plain,
% 1.36/1.09 (((~hskp19) | (~c0_1(a387))) <=> ((~hskp19) | (~c0_1(a387)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(239,plain,
% 1.36/1.09 (((~c0_1(a387)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a387)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(240,axiom,((~c0_1(a387)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.36/1.09 tff(241,plain,
% 1.36/1.09 ((~hskp19) | (~c0_1(a387))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[240, 239])).
% 1.36/1.09 tff(242,plain,
% 1.36/1.09 ((~hskp19) | (~c0_1(a387))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[241, 238])).
% 1.36/1.09 tff(243,plain,
% 1.36/1.09 (~c0_1(a387)),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[242, 225])).
% 1.36/1.09 tff(244,plain,
% 1.36/1.09 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(245,plain,
% 1.36/1.09 ((hskp4 | hskp3 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (hskp4 | hskp3 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(246,plain,
% 1.36/1.09 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0)))),
% 1.36/1.09 inference(monotonicity,[status(thm)],[245])).
% 1.36/1.09 tff(247,plain,
% 1.36/1.09 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))),
% 1.36/1.09 inference(transitivity,[status(thm)],[246, 244])).
% 1.36/1.09 tff(248,plain,
% 1.36/1.09 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 1.36/1.09 inference(quant_inst,[status(thm)],[])).
% 1.36/1.09 tff(249,plain,
% 1.36/1.09 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0)),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[248, 247])).
% 1.36/1.09 tff(250,plain,
% 1.36/1.09 ($false),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[249, 145, 117, 177, 243, 237, 231, 176])).
% 1.36/1.09 tff(251,plain,(hskp3 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.36/1.09 tff(252,plain,
% 1.36/1.09 (hskp3),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[251, 145])).
% 1.36/1.09 tff(253,plain,
% 1.36/1.09 (((~hskp3) | (~c0_1(a357))) <=> ((~hskp3) | (~c0_1(a357)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(254,plain,
% 1.36/1.09 (((~c0_1(a357)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a357)))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(255,axiom,((~c0_1(a357)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.36/1.09 tff(256,plain,
% 1.36/1.09 ((~hskp3) | (~c0_1(a357))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[255, 254])).
% 1.36/1.09 tff(257,plain,
% 1.36/1.09 ((~hskp3) | (~c0_1(a357))),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[256, 253])).
% 1.36/1.09 tff(258,plain,
% 1.36/1.09 (~c0_1(a357)),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[257, 252])).
% 1.36/1.09 tff(259,plain,
% 1.36/1.09 (((~hskp3) | c3_1(a357)) <=> ((~hskp3) | c3_1(a357))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(260,axiom,((~hskp3) | c3_1(a357)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.36/1.09 tff(261,plain,
% 1.36/1.09 ((~hskp3) | c3_1(a357)),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[260, 259])).
% 1.36/1.09 tff(262,plain,
% 1.36/1.09 ((~hskp3) | c3_1(a357)),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[261, 259])).
% 1.36/1.09 tff(263,plain,
% 1.36/1.09 ((~hskp3) | c3_1(a357)),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[262, 259])).
% 1.36/1.09 tff(264,plain,
% 1.36/1.09 ((~hskp3) | c3_1(a357)),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[263, 259])).
% 1.36/1.09 tff(265,plain,
% 1.36/1.09 ((~hskp3) | c3_1(a357)),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[264, 259])).
% 1.36/1.09 tff(266,plain,
% 1.36/1.09 ((~hskp3) | c3_1(a357)),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[265, 259])).
% 1.36/1.09 tff(267,plain,
% 1.36/1.09 ((~hskp3) | c3_1(a357)),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[266, 259])).
% 1.36/1.09 tff(268,plain,
% 1.36/1.09 ((~hskp3) | c3_1(a357)),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[267, 259])).
% 1.36/1.09 tff(269,plain,
% 1.36/1.09 (c3_1(a357)),
% 1.36/1.09 inference(unit_resolution,[status(thm)],[268, 252])).
% 1.36/1.09 tff(270,plain,
% 1.36/1.09 (((~hskp3) | c1_1(a357)) <=> ((~hskp3) | c1_1(a357))),
% 1.36/1.09 inference(rewrite,[status(thm)],[])).
% 1.36/1.09 tff(271,axiom,((~hskp3) | c1_1(a357)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.36/1.09 tff(272,plain,
% 1.36/1.09 ((~hskp3) | c1_1(a357)),
% 1.36/1.09 inference(modus_ponens,[status(thm)],[271, 270])).
% 1.36/1.09 tff(273,plain,
% 1.36/1.10 ((~hskp3) | c1_1(a357)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[272, 270])).
% 1.36/1.10 tff(274,plain,
% 1.36/1.10 ((~hskp3) | c1_1(a357)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[273, 270])).
% 1.36/1.10 tff(275,plain,
% 1.36/1.10 ((~hskp3) | c1_1(a357)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[274, 270])).
% 1.36/1.10 tff(276,plain,
% 1.36/1.10 ((~hskp3) | c1_1(a357)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[275, 270])).
% 1.36/1.10 tff(277,plain,
% 1.36/1.10 ((~hskp3) | c1_1(a357)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[276, 270])).
% 1.36/1.10 tff(278,plain,
% 1.36/1.10 ((~hskp3) | c1_1(a357)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[277, 270])).
% 1.36/1.10 tff(279,plain,
% 1.36/1.10 ((~hskp3) | c1_1(a357)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[278, 270])).
% 1.36/1.10 tff(280,plain,
% 1.36/1.10 (c1_1(a357)),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[279, 252])).
% 1.36/1.10 tff(281,plain,
% 1.36/1.10 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(282,plain,
% 1.36/1.10 ((hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a360) | c1_1(a360) | c3_1(a360)) <=> (hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(283,plain,
% 1.36/1.10 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a360) | c1_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357))))),
% 1.36/1.10 inference(monotonicity,[status(thm)],[282])).
% 1.36/1.10 tff(284,plain,
% 1.36/1.10 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a360) | c1_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))),
% 1.36/1.10 inference(transitivity,[status(thm)],[283, 281])).
% 1.36/1.10 tff(285,plain,
% 1.36/1.10 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a360) | c1_1(a360) | c3_1(a360))),
% 1.36/1.10 inference(quant_inst,[status(thm)],[])).
% 1.36/1.10 tff(286,plain,
% 1.36/1.10 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[285, 284])).
% 1.36/1.10 tff(287,plain,
% 1.36/1.10 (hskp20),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[286, 117, 280, 269, 193, 187, 217, 258, 166])).
% 1.36/1.10 tff(288,plain,
% 1.36/1.10 (((~hskp20) | (~c3_1(a388))) <=> ((~hskp20) | (~c3_1(a388)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(289,plain,
% 1.36/1.10 (((~c3_1(a388)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a388)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(290,axiom,((~c3_1(a388)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.36/1.10 tff(291,plain,
% 1.36/1.10 ((~hskp20) | (~c3_1(a388))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[290, 289])).
% 1.36/1.10 tff(292,plain,
% 1.36/1.10 ((~hskp20) | (~c3_1(a388))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[291, 288])).
% 1.36/1.10 tff(293,plain,
% 1.36/1.10 (~c3_1(a388)),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[292, 287])).
% 1.36/1.10 tff(294,plain,
% 1.36/1.10 (((~hskp20) | (~c2_1(a388))) <=> ((~hskp20) | (~c2_1(a388)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(295,plain,
% 1.36/1.10 (((~c2_1(a388)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a388)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(296,axiom,((~c2_1(a388)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.36/1.10 tff(297,plain,
% 1.36/1.10 ((~hskp20) | (~c2_1(a388))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[296, 295])).
% 1.36/1.10 tff(298,plain,
% 1.36/1.10 ((~hskp20) | (~c2_1(a388))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[297, 294])).
% 1.36/1.10 tff(299,plain,
% 1.36/1.10 (~c2_1(a388)),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[298, 287])).
% 1.36/1.10 tff(300,plain,
% 1.36/1.10 (((~hskp20) | c1_1(a388)) <=> ((~hskp20) | c1_1(a388))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(301,axiom,((~hskp20) | c1_1(a388)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.36/1.10 tff(302,plain,
% 1.36/1.10 ((~hskp20) | c1_1(a388)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[301, 300])).
% 1.36/1.10 tff(303,plain,
% 1.36/1.10 ((~hskp20) | c1_1(a388)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[302, 300])).
% 1.36/1.10 tff(304,plain,
% 1.36/1.10 ((~hskp20) | c1_1(a388)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[303, 300])).
% 1.36/1.10 tff(305,plain,
% 1.36/1.10 ((~hskp20) | c1_1(a388)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[304, 300])).
% 1.36/1.10 tff(306,plain,
% 1.36/1.10 ((~hskp20) | c1_1(a388)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[305, 300])).
% 1.36/1.10 tff(307,plain,
% 1.36/1.10 ((~hskp20) | c1_1(a388)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[306, 300])).
% 1.36/1.10 tff(308,plain,
% 1.36/1.10 ((~hskp20) | c1_1(a388)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[307, 300])).
% 1.36/1.10 tff(309,plain,
% 1.36/1.10 ((~hskp20) | c1_1(a388)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[308, 300])).
% 1.36/1.10 tff(310,plain,
% 1.36/1.10 (c1_1(a388)),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[309, 287])).
% 1.36/1.10 tff(311,plain,
% 1.36/1.10 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | c0_1(a388))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | c0_1(a388))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(312,plain,
% 1.36/1.10 ((hskp4 | (~ndr1_0) | c0_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a388) | c0_1(a388) | (~c1_1(a388))) <=> (hskp4 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | c0_1(a388))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(313,plain,
% 1.36/1.10 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a388) | c0_1(a388) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | c0_1(a388)))),
% 1.36/1.10 inference(monotonicity,[status(thm)],[312])).
% 1.36/1.10 tff(314,plain,
% 1.36/1.10 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a388) | c0_1(a388) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | c0_1(a388))),
% 1.36/1.10 inference(transitivity,[status(thm)],[313, 311])).
% 1.36/1.10 tff(315,plain,
% 1.36/1.10 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a388) | c0_1(a388) | (~c1_1(a388)))),
% 1.36/1.10 inference(quant_inst,[status(thm)],[])).
% 1.36/1.10 tff(316,plain,
% 1.36/1.10 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | c0_1(a388)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[315, 314])).
% 1.36/1.10 tff(317,plain,
% 1.36/1.10 ($false),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[316, 145, 117, 310, 299, 293, 156, 146])).
% 1.36/1.10 tff(318,plain,(c0_1(a388) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.36/1.10 tff(319,plain,
% 1.36/1.10 (c0_1(a388)),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[318, 145])).
% 1.36/1.10 tff(320,plain,
% 1.36/1.10 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))))),
% 1.36/1.10 inference(bind,[status(th)],[])).
% 1.36/1.10 tff(321,plain,
% 1.36/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.10 inference(quant_intro,[status(thm)],[320])).
% 1.36/1.10 tff(322,plain,
% 1.36/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(323,plain,
% 1.36/1.10 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))))),
% 1.36/1.10 inference(bind,[status(th)],[])).
% 1.36/1.10 tff(324,plain,
% 1.36/1.10 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.10 inference(quant_intro,[status(thm)],[323])).
% 1.36/1.10 tff(325,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause205')).
% 1.36/1.10 tff(326,plain,
% 1.36/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[325, 324])).
% 1.36/1.10 tff(327,plain,
% 1.36/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[326, 322])).
% 1.36/1.10 tff(328,plain,(
% 1.36/1.10 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.10 inference(skolemize,[status(sab)],[327])).
% 1.36/1.10 tff(329,plain,
% 1.36/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[328, 321])).
% 1.36/1.10 tff(330,assumption,(c0_1(a388)), introduced(assumption)).
% 1.36/1.10 tff(331,assumption,(~c2_1(a357)), introduced(assumption)).
% 1.36/1.10 tff(332,assumption,(~c3_1(a388)), introduced(assumption)).
% 1.36/1.10 tff(333,assumption,(~c2_1(a388)), introduced(assumption)).
% 1.36/1.10 tff(334,assumption,(c3_1(a357)), introduced(assumption)).
% 1.36/1.10 tff(335,assumption,(c1_1(a357)), introduced(assumption)).
% 1.36/1.10 tff(336,assumption,(c1_1(a388)), introduced(assumption)).
% 1.36/1.10 tff(337,plain,
% 1.36/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a357)) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a388)) | (~c0_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a357)) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a388)) | (~c0_1(a388)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(338,plain,
% 1.36/1.10 (((~ndr1_0) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388))) <=> (c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a357)) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a388)) | (~c0_1(a388)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(339,plain,
% 1.36/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a357)) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a388)) | (~c0_1(a388))))),
% 1.36/1.10 inference(monotonicity,[status(thm)],[338])).
% 1.36/1.10 tff(340,plain,
% 1.36/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a357)) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a388)) | (~c0_1(a388)))),
% 1.36/1.10 inference(transitivity,[status(thm)],[339, 337])).
% 1.36/1.10 tff(341,plain,
% 1.36/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))),
% 1.36/1.10 inference(quant_inst,[status(thm)],[])).
% 1.36/1.10 tff(342,plain,
% 1.36/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a357)) | c2_1(a357) | (~c3_1(a357)) | (~c1_1(a388)) | (~c0_1(a388))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[341, 340])).
% 1.36/1.10 tff(343,plain,
% 1.36/1.10 ($false),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[342, 117, 336, 335, 334, 333, 332, 329, 331, 330])).
% 1.36/1.10 tff(344,plain,(c2_1(a357) | (~c1_1(a388)) | (~c1_1(a357)) | (~c3_1(a357)) | c2_1(a388) | c3_1(a388) | (~c0_1(a388))), inference(lemma,lemma(discharge,[]))).
% 1.36/1.10 tff(345,plain,
% 1.36/1.10 (c2_1(a357)),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[344, 310, 280, 269, 299, 293, 319])).
% 1.36/1.10 tff(346,plain,
% 1.36/1.10 (^[U: $i] : refl((hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.36/1.10 inference(bind,[status(th)],[])).
% 1.36/1.10 tff(347,plain,
% 1.36/1.10 (![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.10 inference(quant_intro,[status(thm)],[346])).
% 1.36/1.10 tff(348,plain,
% 1.36/1.10 (![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(349,plain,
% 1.36/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp21))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp4) <=> ((hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp4))), rewrite(((hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp4) <=> (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.36/1.10 inference(bind,[status(th)],[])).
% 1.36/1.10 tff(350,plain,
% 1.36/1.10 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp4) <=> ![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.10 inference(quant_intro,[status(thm)],[349])).
% 1.36/1.10 tff(351,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.36/1.10 tff(352,plain,
% 1.36/1.10 (![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[351, 350])).
% 1.36/1.10 tff(353,plain,
% 1.36/1.10 (![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[352, 348])).
% 1.36/1.10 tff(354,plain,(
% 1.36/1.10 ![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.10 inference(skolemize,[status(sab)],[353])).
% 1.36/1.10 tff(355,plain,
% 1.36/1.10 (![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[354, 347])).
% 1.36/1.10 tff(356,plain,
% 1.36/1.10 (((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp21 | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)))) <=> ((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp21 | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(357,plain,
% 1.36/1.10 ((hskp4 | hskp21 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357))) <=> (hskp4 | hskp21 | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(358,plain,
% 1.36/1.10 (((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp21 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357)))) <=> ((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp21 | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357))))),
% 1.36/1.10 inference(monotonicity,[status(thm)],[357])).
% 1.36/1.10 tff(359,plain,
% 1.36/1.10 (((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp21 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357)))) <=> ((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp21 | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)))),
% 1.36/1.10 inference(transitivity,[status(thm)],[358, 356])).
% 1.36/1.10 tff(360,plain,
% 1.36/1.10 ((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp21 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357)))),
% 1.36/1.10 inference(quant_inst,[status(thm)],[])).
% 1.36/1.10 tff(361,plain,
% 1.36/1.10 ((~![U: $i] : (hskp4 | hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp21 | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[360, 359])).
% 1.36/1.10 tff(362,plain,
% 1.36/1.10 (hskp21 | (~c2_1(a357))),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[361, 145, 117, 269, 258, 355])).
% 1.36/1.10 tff(363,plain,
% 1.36/1.10 (hskp21),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[362, 345])).
% 1.36/1.10 tff(364,plain,
% 1.36/1.10 (~c2_1(a395)),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[75, 363])).
% 1.36/1.10 tff(365,plain,
% 1.36/1.10 (((~hskp21) | c1_1(a395)) <=> ((~hskp21) | c1_1(a395))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(366,axiom,((~hskp21) | c1_1(a395)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.36/1.10 tff(367,plain,
% 1.36/1.10 ((~hskp21) | c1_1(a395)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[366, 365])).
% 1.36/1.10 tff(368,plain,
% 1.36/1.10 ((~hskp21) | c1_1(a395)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[367, 365])).
% 1.36/1.10 tff(369,plain,
% 1.36/1.10 ((~hskp21) | c1_1(a395)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[368, 365])).
% 1.36/1.10 tff(370,plain,
% 1.36/1.10 ((~hskp21) | c1_1(a395)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[369, 365])).
% 1.36/1.10 tff(371,plain,
% 1.36/1.10 ((~hskp21) | c1_1(a395)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[370, 365])).
% 1.36/1.10 tff(372,plain,
% 1.36/1.10 ((~hskp21) | c1_1(a395)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[371, 365])).
% 1.36/1.10 tff(373,plain,
% 1.36/1.10 ((~hskp21) | c1_1(a395)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[372, 365])).
% 1.36/1.10 tff(374,plain,
% 1.36/1.10 ((~hskp21) | c1_1(a395)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[373, 365])).
% 1.36/1.10 tff(375,plain,
% 1.36/1.10 (c1_1(a395)),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[374, 363])).
% 1.36/1.10 tff(376,plain,
% 1.36/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a395) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | (~c0_1(a388)) | (~c3_1(a395)) | (~c1_1(a395)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a395) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | (~c0_1(a388)) | (~c3_1(a395)) | (~c1_1(a395)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(377,plain,
% 1.36/1.10 (((~ndr1_0) | c2_1(a395) | (~c3_1(a395)) | (~c1_1(a395)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388))) <=> (c2_1(a395) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | (~c0_1(a388)) | (~c3_1(a395)) | (~c1_1(a395)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(378,plain,
% 1.36/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a395) | (~c3_1(a395)) | (~c1_1(a395)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a395) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | (~c0_1(a388)) | (~c3_1(a395)) | (~c1_1(a395))))),
% 1.36/1.10 inference(monotonicity,[status(thm)],[377])).
% 1.36/1.10 tff(379,plain,
% 1.36/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a395) | (~c3_1(a395)) | (~c1_1(a395)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a395) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | (~c0_1(a388)) | (~c3_1(a395)) | (~c1_1(a395)))),
% 1.36/1.10 inference(transitivity,[status(thm)],[378, 376])).
% 1.36/1.10 tff(380,plain,
% 1.36/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a395) | (~c3_1(a395)) | (~c1_1(a395)) | c2_1(a388) | (~c1_1(a388)) | (~c0_1(a388)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))),
% 1.36/1.10 inference(quant_inst,[status(thm)],[])).
% 1.36/1.10 tff(381,plain,
% 1.36/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a395) | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a388)) | (~c0_1(a388)) | (~c3_1(a395)) | (~c1_1(a395))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[380, 379])).
% 1.36/1.10 tff(382,plain,
% 1.36/1.10 (~c3_1(a395)),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[381, 117, 375, 310, 364, 299, 293, 329, 319])).
% 1.36/1.10 tff(383,plain,
% 1.36/1.10 (~c0_1(a395)),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[81, 363])).
% 1.36/1.10 tff(384,plain,
% 1.36/1.10 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | c3_1(a395) | (~c1_1(a395)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | c3_1(a395) | (~c1_1(a395)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(385,plain,
% 1.36/1.10 ((hskp4 | (~ndr1_0) | c0_1(a395) | c3_1(a395) | (~c1_1(a395)) | c2_1(a395) | c0_1(a395) | (~c1_1(a395))) <=> (hskp4 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | c3_1(a395) | (~c1_1(a395)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(386,plain,
% 1.36/1.10 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a395) | c3_1(a395) | (~c1_1(a395)) | c2_1(a395) | c0_1(a395) | (~c1_1(a395)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | c3_1(a395) | (~c1_1(a395))))),
% 1.36/1.10 inference(monotonicity,[status(thm)],[385])).
% 1.36/1.10 tff(387,plain,
% 1.36/1.10 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a395) | c3_1(a395) | (~c1_1(a395)) | c2_1(a395) | c0_1(a395) | (~c1_1(a395)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | c3_1(a395) | (~c1_1(a395)))),
% 1.36/1.10 inference(transitivity,[status(thm)],[386, 384])).
% 1.36/1.10 tff(388,plain,
% 1.36/1.10 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a395) | c3_1(a395) | (~c1_1(a395)) | c2_1(a395) | c0_1(a395) | (~c1_1(a395)))),
% 1.36/1.10 inference(quant_inst,[status(thm)],[])).
% 1.36/1.10 tff(389,plain,
% 1.36/1.10 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | c3_1(a395) | (~c1_1(a395))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[388, 387])).
% 1.36/1.10 tff(390,plain,
% 1.36/1.10 ($false),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[389, 145, 117, 375, 383, 364, 156, 382])).
% 1.36/1.10 tff(391,plain,(hskp4), inference(lemma,lemma(discharge,[]))).
% 1.36/1.10 tff(392,plain,
% 1.36/1.10 (((~hskp4) | (~c3_1(a358))) <=> ((~hskp4) | (~c3_1(a358)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(393,plain,
% 1.36/1.10 (((~c3_1(a358)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a358)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(394,axiom,((~c3_1(a358)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.36/1.10 tff(395,plain,
% 1.36/1.10 ((~hskp4) | (~c3_1(a358))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[394, 393])).
% 1.36/1.10 tff(396,plain,
% 1.36/1.10 ((~hskp4) | (~c3_1(a358))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[395, 392])).
% 1.36/1.10 tff(397,plain,
% 1.36/1.10 (~c3_1(a358)),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[396, 391])).
% 1.36/1.10 tff(398,plain,
% 1.36/1.10 (((~hskp4) | (~c0_1(a358))) <=> ((~hskp4) | (~c0_1(a358)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(399,plain,
% 1.36/1.10 (((~c0_1(a358)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a358)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(400,axiom,((~c0_1(a358)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.36/1.10 tff(401,plain,
% 1.36/1.10 ((~hskp4) | (~c0_1(a358))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[400, 399])).
% 1.36/1.10 tff(402,plain,
% 1.36/1.10 ((~hskp4) | (~c0_1(a358))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[401, 398])).
% 1.36/1.10 tff(403,plain,
% 1.36/1.10 (~c0_1(a358)),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[402, 391])).
% 1.36/1.10 tff(404,assumption,(hskp13), introduced(assumption)).
% 1.36/1.10 tff(405,plain,
% 1.36/1.10 (((~hskp13) | (~c3_1(a370))) <=> ((~hskp13) | (~c3_1(a370)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(406,plain,
% 1.36/1.10 (((~c3_1(a370)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a370)))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(407,axiom,((~c3_1(a370)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.36/1.10 tff(408,plain,
% 1.36/1.10 ((~hskp13) | (~c3_1(a370))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[407, 406])).
% 1.36/1.10 tff(409,plain,
% 1.36/1.10 ((~hskp13) | (~c3_1(a370))),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[408, 405])).
% 1.36/1.10 tff(410,plain,
% 1.36/1.10 (~c3_1(a370)),
% 1.36/1.10 inference(unit_resolution,[status(thm)],[409, 404])).
% 1.36/1.10 tff(411,plain,
% 1.36/1.10 (((~hskp4) | c2_1(a358)) <=> ((~hskp4) | c2_1(a358))),
% 1.36/1.10 inference(rewrite,[status(thm)],[])).
% 1.36/1.10 tff(412,axiom,((~hskp4) | c2_1(a358)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.36/1.10 tff(413,plain,
% 1.36/1.10 ((~hskp4) | c2_1(a358)),
% 1.36/1.10 inference(modus_ponens,[status(thm)],[412, 411])).
% 1.36/1.11 tff(414,plain,
% 1.36/1.11 ((~hskp4) | c2_1(a358)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[413, 411])).
% 1.36/1.11 tff(415,plain,
% 1.36/1.11 ((~hskp4) | c2_1(a358)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[414, 411])).
% 1.36/1.11 tff(416,plain,
% 1.36/1.11 ((~hskp4) | c2_1(a358)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[415, 411])).
% 1.36/1.11 tff(417,plain,
% 1.36/1.11 ((~hskp4) | c2_1(a358)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[416, 411])).
% 1.36/1.11 tff(418,plain,
% 1.36/1.11 ((~hskp4) | c2_1(a358)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[417, 411])).
% 1.36/1.11 tff(419,plain,
% 1.36/1.11 ((~hskp4) | c2_1(a358)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[418, 411])).
% 1.36/1.11 tff(420,plain,
% 1.36/1.11 ((~hskp4) | c2_1(a358)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[419, 411])).
% 1.36/1.11 tff(421,plain,
% 1.36/1.11 (c2_1(a358)),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[420, 391])).
% 1.36/1.11 tff(422,plain,
% 1.36/1.11 (((~hskp13) | c2_1(a370)) <=> ((~hskp13) | c2_1(a370))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(423,axiom,((~hskp13) | c2_1(a370)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.36/1.11 tff(424,plain,
% 1.36/1.11 ((~hskp13) | c2_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[423, 422])).
% 1.36/1.11 tff(425,plain,
% 1.36/1.11 ((~hskp13) | c2_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[424, 422])).
% 1.36/1.11 tff(426,plain,
% 1.36/1.11 ((~hskp13) | c2_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[425, 422])).
% 1.36/1.11 tff(427,plain,
% 1.36/1.11 ((~hskp13) | c2_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[426, 422])).
% 1.36/1.11 tff(428,plain,
% 1.36/1.11 ((~hskp13) | c2_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[427, 422])).
% 1.36/1.11 tff(429,plain,
% 1.36/1.11 ((~hskp13) | c2_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[428, 422])).
% 1.36/1.11 tff(430,plain,
% 1.36/1.11 ((~hskp13) | c2_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[429, 422])).
% 1.36/1.11 tff(431,plain,
% 1.36/1.11 ((~hskp13) | c2_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[430, 422])).
% 1.36/1.11 tff(432,plain,
% 1.36/1.11 (c2_1(a370)),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[431, 404])).
% 1.36/1.11 tff(433,plain,
% 1.36/1.11 (((~hskp13) | c0_1(a370)) <=> ((~hskp13) | c0_1(a370))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(434,axiom,((~hskp13) | c0_1(a370)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.36/1.11 tff(435,plain,
% 1.36/1.11 ((~hskp13) | c0_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[434, 433])).
% 1.36/1.11 tff(436,plain,
% 1.36/1.11 ((~hskp13) | c0_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[435, 433])).
% 1.36/1.11 tff(437,plain,
% 1.36/1.11 ((~hskp13) | c0_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[436, 433])).
% 1.36/1.11 tff(438,plain,
% 1.36/1.11 ((~hskp13) | c0_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[437, 433])).
% 1.36/1.11 tff(439,plain,
% 1.36/1.11 ((~hskp13) | c0_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[438, 433])).
% 1.36/1.11 tff(440,plain,
% 1.36/1.11 ((~hskp13) | c0_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[439, 433])).
% 1.36/1.11 tff(441,plain,
% 1.36/1.11 ((~hskp13) | c0_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[440, 433])).
% 1.36/1.11 tff(442,plain,
% 1.36/1.11 ((~hskp13) | c0_1(a370)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[441, 433])).
% 1.36/1.11 tff(443,plain,
% 1.36/1.11 (c0_1(a370)),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[442, 404])).
% 1.36/1.11 tff(444,plain,
% 1.36/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a370) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a370)) | (~c0_1(a370)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a370) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a370)) | (~c0_1(a370)))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(445,plain,
% 1.36/1.11 (((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a370) | (~c2_1(a370)) | (~c0_1(a370)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358))) <=> (c3_1(a370) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a370)) | (~c0_1(a370)))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(446,plain,
% 1.36/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a370) | (~c2_1(a370)) | (~c0_1(a370)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a370) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a370)) | (~c0_1(a370))))),
% 1.36/1.11 inference(monotonicity,[status(thm)],[445])).
% 1.36/1.11 tff(447,plain,
% 1.36/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a370) | (~c2_1(a370)) | (~c0_1(a370)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a370) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a370)) | (~c0_1(a370)))),
% 1.36/1.11 inference(transitivity,[status(thm)],[446, 444])).
% 1.36/1.11 tff(448,plain,
% 1.36/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a370) | (~c2_1(a370)) | (~c0_1(a370)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))),
% 1.36/1.11 inference(quant_inst,[status(thm)],[])).
% 1.36/1.11 tff(449,plain,
% 1.36/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a370) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a370)) | (~c0_1(a370))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[448, 447])).
% 1.36/1.11 tff(450,plain,
% 1.36/1.11 ($false),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[449, 117, 67, 69, 68, 443, 432, 421, 410, 403, 397, 144])).
% 1.36/1.11 tff(451,plain,((~hskp13) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365))), inference(lemma,lemma(discharge,[]))).
% 1.36/1.11 tff(452,plain,
% 1.36/1.11 (~hskp13),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[451, 67, 69, 68])).
% 1.36/1.11 tff(453,plain,
% 1.36/1.11 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a395))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a395))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(454,plain,
% 1.36/1.11 ((hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a395) | c0_1(a395) | c3_1(a395)) <=> (hskp13 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a395))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(455,plain,
% 1.36/1.11 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a395) | c0_1(a395) | c3_1(a395))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a395)))),
% 1.36/1.11 inference(monotonicity,[status(thm)],[454])).
% 1.36/1.11 tff(456,plain,
% 1.36/1.11 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a395) | c0_1(a395) | c3_1(a395))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a395))),
% 1.36/1.11 inference(transitivity,[status(thm)],[455, 453])).
% 1.36/1.11 tff(457,plain,
% 1.36/1.11 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a395) | c0_1(a395) | c3_1(a395))),
% 1.36/1.11 inference(quant_inst,[status(thm)],[])).
% 1.36/1.11 tff(458,plain,
% 1.36/1.11 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a395) | c2_1(a395) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a395)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[457, 456])).
% 1.36/1.11 tff(459,plain,
% 1.36/1.11 ($false),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[458, 117, 452, 67, 69, 68, 82, 76, 134, 124])).
% 1.36/1.11 tff(460,plain,((~hskp21) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365))), inference(lemma,lemma(discharge,[]))).
% 1.36/1.11 tff(461,plain,
% 1.36/1.11 (~hskp21),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[460, 56, 69, 68, 67])).
% 1.36/1.11 tff(462,plain,
% 1.36/1.11 ((hskp6 | hskp21 | hskp18) <=> (hskp6 | hskp21 | hskp18)),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(463,plain,
% 1.36/1.11 (((hskp21 | hskp18) | hskp6) <=> (hskp6 | hskp21 | hskp18)),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(464,plain,
% 1.36/1.11 ((hskp21 | hskp18) <=> (hskp21 | hskp18)),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(465,plain,
% 1.36/1.11 (((hskp21 | hskp18) | hskp6) <=> ((hskp21 | hskp18) | hskp6)),
% 1.36/1.11 inference(monotonicity,[status(thm)],[464])).
% 1.36/1.11 tff(466,plain,
% 1.36/1.11 (((hskp21 | hskp18) | hskp6) <=> (hskp6 | hskp21 | hskp18)),
% 1.36/1.11 inference(transitivity,[status(thm)],[465, 463])).
% 1.36/1.11 tff(467,axiom,((hskp21 | hskp18) | hskp6), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 1.36/1.11 tff(468,plain,
% 1.36/1.11 (hskp6 | hskp21 | hskp18),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[467, 466])).
% 1.36/1.11 tff(469,plain,
% 1.36/1.11 (hskp6 | hskp21 | hskp18),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[468, 462])).
% 1.36/1.11 tff(470,plain,
% 1.36/1.11 (hskp6 | hskp21 | hskp18),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[469, 462])).
% 1.36/1.11 tff(471,plain,
% 1.36/1.11 (hskp6 | hskp21 | hskp18),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[470, 462])).
% 1.36/1.11 tff(472,plain,
% 1.36/1.11 (hskp6 | hskp21 | hskp18),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[471, 462])).
% 1.36/1.11 tff(473,plain,
% 1.36/1.11 (hskp6 | hskp21 | hskp18),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[472, 462])).
% 1.36/1.11 tff(474,plain,
% 1.36/1.11 (hskp6 | hskp21 | hskp18),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[473, 462])).
% 1.36/1.11 tff(475,plain,
% 1.36/1.11 (hskp6 | hskp21 | hskp18),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[474, 462])).
% 1.36/1.11 tff(476,plain,
% 1.36/1.11 (hskp18),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[475, 461, 21])).
% 1.36/1.11 tff(477,plain,
% 1.36/1.11 (((~hskp18) | (~c2_1(a382))) <=> ((~hskp18) | (~c2_1(a382)))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(478,plain,
% 1.36/1.11 (((~c2_1(a382)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a382)))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(479,axiom,((~c2_1(a382)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.36/1.11 tff(480,plain,
% 1.36/1.11 ((~hskp18) | (~c2_1(a382))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[479, 478])).
% 1.36/1.11 tff(481,plain,
% 1.36/1.11 ((~hskp18) | (~c2_1(a382))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[480, 477])).
% 1.36/1.11 tff(482,plain,
% 1.36/1.11 (~c2_1(a382)),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[481, 476])).
% 1.36/1.11 tff(483,plain,
% 1.36/1.11 (((~hskp18) | (~c0_1(a382))) <=> ((~hskp18) | (~c0_1(a382)))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(484,plain,
% 1.36/1.11 (((~c0_1(a382)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a382)))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(485,axiom,((~c0_1(a382)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.36/1.11 tff(486,plain,
% 1.36/1.11 ((~hskp18) | (~c0_1(a382))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.36/1.11 tff(487,plain,
% 1.36/1.11 ((~hskp18) | (~c0_1(a382))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[486, 483])).
% 1.36/1.11 tff(488,plain,
% 1.36/1.11 (~c0_1(a382)),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[487, 476])).
% 1.36/1.11 tff(489,plain,
% 1.36/1.11 (((~hskp18) | c3_1(a382)) <=> ((~hskp18) | c3_1(a382))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(490,axiom,((~hskp18) | c3_1(a382)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.36/1.11 tff(491,plain,
% 1.36/1.11 ((~hskp18) | c3_1(a382)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[490, 489])).
% 1.36/1.11 tff(492,plain,
% 1.36/1.11 ((~hskp18) | c3_1(a382)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[491, 489])).
% 1.36/1.11 tff(493,plain,
% 1.36/1.11 ((~hskp18) | c3_1(a382)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[492, 489])).
% 1.36/1.11 tff(494,plain,
% 1.36/1.11 ((~hskp18) | c3_1(a382)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[493, 489])).
% 1.36/1.11 tff(495,plain,
% 1.36/1.11 ((~hskp18) | c3_1(a382)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[494, 489])).
% 1.36/1.11 tff(496,plain,
% 1.36/1.11 ((~hskp18) | c3_1(a382)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[495, 489])).
% 1.36/1.11 tff(497,plain,
% 1.36/1.11 ((~hskp18) | c3_1(a382)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[496, 489])).
% 1.36/1.11 tff(498,plain,
% 1.36/1.11 ((~hskp18) | c3_1(a382)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[497, 489])).
% 1.36/1.11 tff(499,plain,
% 1.36/1.11 (c3_1(a382)),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[498, 476])).
% 1.36/1.11 tff(500,plain,
% 1.36/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a382) | c2_1(a382) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a382)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a382) | c2_1(a382) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a382)))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(501,plain,
% 1.36/1.11 (((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a382) | c0_1(a382) | (~c3_1(a382))) <=> (c0_1(a382) | c2_1(a382) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a382)))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(502,plain,
% 1.36/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a382) | c0_1(a382) | (~c3_1(a382)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a382) | c2_1(a382) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a382))))),
% 1.36/1.11 inference(monotonicity,[status(thm)],[501])).
% 1.36/1.11 tff(503,plain,
% 1.36/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a382) | c0_1(a382) | (~c3_1(a382)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a382) | c2_1(a382) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a382)))),
% 1.36/1.11 inference(transitivity,[status(thm)],[502, 500])).
% 1.36/1.11 tff(504,plain,
% 1.36/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a382) | c0_1(a382) | (~c3_1(a382)))),
% 1.36/1.11 inference(quant_inst,[status(thm)],[])).
% 1.36/1.11 tff(505,plain,
% 1.36/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a382) | c2_1(a382) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a382))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[504, 503])).
% 1.36/1.11 tff(506,plain,
% 1.36/1.11 ($false),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[505, 117, 67, 69, 68, 499, 488, 482, 66, 56])).
% 1.36/1.11 tff(507,plain,((~c0_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.36/1.11 tff(508,plain,
% 1.36/1.11 (~c0_1(a365)),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[507, 55, 21, 44, 33])).
% 1.36/1.11 tff(509,plain,
% 1.36/1.11 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.36/1.11 inference(bind,[status(th)],[])).
% 1.36/1.11 tff(510,plain,
% 1.36/1.11 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.36/1.11 inference(quant_intro,[status(thm)],[509])).
% 1.36/1.11 tff(511,plain,
% 1.36/1.11 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(512,plain,
% 1.36/1.11 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.36/1.11 inference(bind,[status(th)],[])).
% 1.36/1.11 tff(513,plain,
% 1.36/1.11 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.36/1.11 inference(quant_intro,[status(thm)],[512])).
% 1.36/1.11 tff(514,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.36/1.11 tff(515,plain,
% 1.36/1.11 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[514, 513])).
% 1.36/1.11 tff(516,plain,
% 1.36/1.11 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[515, 511])).
% 1.36/1.11 tff(517,plain,(
% 1.36/1.11 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.36/1.11 inference(skolemize,[status(sab)],[516])).
% 1.36/1.11 tff(518,plain,
% 1.36/1.11 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[517, 510])).
% 1.36/1.11 tff(519,plain,
% 1.36/1.11 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.36/1.11 inference(bind,[status(th)],[])).
% 1.36/1.11 tff(520,plain,
% 1.36/1.11 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.11 inference(quant_intro,[status(thm)],[519])).
% 1.36/1.11 tff(521,plain,
% 1.36/1.11 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(522,plain,
% 1.36/1.11 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.36/1.11 inference(bind,[status(th)],[])).
% 1.36/1.11 tff(523,plain,
% 1.36/1.11 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.11 inference(quant_intro,[status(thm)],[522])).
% 1.36/1.11 tff(524,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.36/1.11 tff(525,plain,
% 1.36/1.11 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[524, 523])).
% 1.36/1.11 tff(526,plain,
% 1.36/1.11 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[525, 521])).
% 1.36/1.11 tff(527,plain,(
% 1.36/1.11 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.11 inference(skolemize,[status(sab)],[526])).
% 1.36/1.11 tff(528,plain,
% 1.36/1.11 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[527, 520])).
% 1.36/1.11 tff(529,plain,
% 1.36/1.11 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(530,plain,
% 1.36/1.11 ((hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365))) <=> (hskp16 | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(531,plain,
% 1.36/1.11 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365)))),
% 1.36/1.11 inference(monotonicity,[status(thm)],[530])).
% 1.36/1.11 tff(532,plain,
% 1.36/1.11 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365))),
% 1.36/1.11 inference(transitivity,[status(thm)],[531, 529])).
% 1.36/1.11 tff(533,plain,
% 1.36/1.11 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)))),
% 1.36/1.11 inference(quant_inst,[status(thm)],[])).
% 1.36/1.11 tff(534,plain,
% 1.36/1.11 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[533, 532])).
% 1.36/1.11 tff(535,plain,
% 1.36/1.11 (hskp16),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[534, 117, 33, 55, 44, 528, 508])).
% 1.36/1.11 tff(536,plain,
% 1.36/1.11 (((~hskp16) | (~c1_1(a379))) <=> ((~hskp16) | (~c1_1(a379)))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(537,plain,
% 1.36/1.11 (((~c1_1(a379)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a379)))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(538,axiom,((~c1_1(a379)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.36/1.11 tff(539,plain,
% 1.36/1.11 ((~hskp16) | (~c1_1(a379))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[538, 537])).
% 1.36/1.11 tff(540,plain,
% 1.36/1.11 ((~hskp16) | (~c1_1(a379))),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[539, 536])).
% 1.36/1.11 tff(541,plain,
% 1.36/1.11 (~c1_1(a379)),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[540, 535])).
% 1.36/1.11 tff(542,plain,
% 1.36/1.11 (((~hskp16) | c2_1(a379)) <=> ((~hskp16) | c2_1(a379))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(543,axiom,((~hskp16) | c2_1(a379)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.36/1.11 tff(544,plain,
% 1.36/1.11 ((~hskp16) | c2_1(a379)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[543, 542])).
% 1.36/1.11 tff(545,plain,
% 1.36/1.11 ((~hskp16) | c2_1(a379)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[544, 542])).
% 1.36/1.11 tff(546,plain,
% 1.36/1.11 ((~hskp16) | c2_1(a379)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[545, 542])).
% 1.36/1.11 tff(547,plain,
% 1.36/1.11 ((~hskp16) | c2_1(a379)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[546, 542])).
% 1.36/1.11 tff(548,plain,
% 1.36/1.11 ((~hskp16) | c2_1(a379)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[547, 542])).
% 1.36/1.11 tff(549,plain,
% 1.36/1.11 ((~hskp16) | c2_1(a379)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[548, 542])).
% 1.36/1.11 tff(550,plain,
% 1.36/1.11 ((~hskp16) | c2_1(a379)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[549, 542])).
% 1.36/1.11 tff(551,plain,
% 1.36/1.11 ((~hskp16) | c2_1(a379)),
% 1.36/1.11 inference(modus_ponens,[status(thm)],[550, 542])).
% 1.36/1.11 tff(552,plain,
% 1.36/1.11 (c2_1(a379)),
% 1.36/1.11 inference(unit_resolution,[status(thm)],[551, 535])).
% 1.36/1.11 tff(553,plain,
% 1.36/1.11 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c1_1(a379) | (~ndr1_0) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365) | (~c2_1(a379)) | c0_1(a379))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c1_1(a379) | (~ndr1_0) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365) | (~c2_1(a379)) | c0_1(a379))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(554,plain,
% 1.36/1.11 ((hskp6 | (~ndr1_0) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)) | c1_1(a379) | c0_1(a379) | (~c2_1(a379))) <=> (hskp6 | c1_1(a379) | (~ndr1_0) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365) | (~c2_1(a379)) | c0_1(a379))),
% 1.36/1.11 inference(rewrite,[status(thm)],[])).
% 1.36/1.11 tff(555,plain,
% 1.36/1.11 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)) | c1_1(a379) | c0_1(a379) | (~c2_1(a379)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c1_1(a379) | (~ndr1_0) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365) | (~c2_1(a379)) | c0_1(a379)))),
% 1.36/1.11 inference(monotonicity,[status(thm)],[554])).
% 1.36/1.11 tff(556,plain,
% 1.36/1.11 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)) | c1_1(a379) | c0_1(a379) | (~c2_1(a379)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c1_1(a379) | (~ndr1_0) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365) | (~c2_1(a379)) | c0_1(a379))),
% 1.36/1.11 inference(transitivity,[status(thm)],[555, 553])).
% 1.36/1.11 tff(557,plain,
% 1.36/1.11 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a365) | (~c3_1(a365)) | (~c2_1(a365)) | c1_1(a379) | c0_1(a379) | (~c2_1(a379)))),
% 1.36/1.11 inference(quant_inst,[status(thm)],[])).
% 1.36/1.11 tff(558,plain,
% 1.36/1.11 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c1_1(a379) | (~ndr1_0) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a365) | (~c2_1(a379)) | c0_1(a379)),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[557, 556])).
% 1.36/1.12 tff(559,plain,
% 1.36/1.12 (c0_1(a379)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[558, 21, 117, 55, 44, 552, 541, 518, 508])).
% 1.36/1.12 tff(560,plain,
% 1.36/1.12 (((~hskp16) | (~c3_1(a379))) <=> ((~hskp16) | (~c3_1(a379)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(561,plain,
% 1.36/1.12 (((~c3_1(a379)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a379)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(562,axiom,((~c3_1(a379)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.36/1.12 tff(563,plain,
% 1.36/1.12 ((~hskp16) | (~c3_1(a379))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[562, 561])).
% 1.36/1.12 tff(564,plain,
% 1.36/1.12 ((~hskp16) | (~c3_1(a379))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[563, 560])).
% 1.36/1.12 tff(565,plain,
% 1.36/1.12 (~c3_1(a379)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[564, 535])).
% 1.36/1.12 tff(566,plain,
% 1.36/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a379) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a379)) | (~c0_1(a379)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a379) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a379)) | (~c0_1(a379)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(567,plain,
% 1.36/1.12 (((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a379) | (~c2_1(a379)) | (~c0_1(a379)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358))) <=> (c3_1(a379) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a379)) | (~c0_1(a379)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(568,plain,
% 1.36/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a379) | (~c2_1(a379)) | (~c0_1(a379)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a379) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a379)) | (~c0_1(a379))))),
% 1.36/1.12 inference(monotonicity,[status(thm)],[567])).
% 1.36/1.12 tff(569,plain,
% 1.36/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a379) | (~c2_1(a379)) | (~c0_1(a379)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a379) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a379)) | (~c0_1(a379)))),
% 1.36/1.12 inference(transitivity,[status(thm)],[568, 566])).
% 1.36/1.12 tff(570,plain,
% 1.36/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c3_1(a379) | (~c2_1(a379)) | (~c0_1(a379)) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))),
% 1.36/1.12 inference(quant_inst,[status(thm)],[])).
% 1.36/1.12 tff(571,plain,
% 1.36/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a379) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c2_1(a379)) | (~c0_1(a379))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[570, 569])).
% 1.36/1.12 tff(572,plain,
% 1.36/1.12 ($false),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[571, 117, 33, 55, 44, 552, 421, 565, 403, 397, 144, 559])).
% 1.36/1.12 tff(573,plain,((~hskp28) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.36/1.12 tff(574,plain,
% 1.36/1.12 (~hskp28),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[573, 21])).
% 1.36/1.12 tff(575,plain,
% 1.36/1.12 (^[U: $i] : refl((hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.36/1.12 inference(bind,[status(th)],[])).
% 1.36/1.12 tff(576,plain,
% 1.36/1.12 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.36/1.12 inference(quant_intro,[status(thm)],[575])).
% 1.36/1.12 tff(577,plain,
% 1.36/1.12 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(578,plain,
% 1.36/1.12 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp19) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp19))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp19) <=> (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp19) <=> (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.36/1.12 inference(bind,[status(th)],[])).
% 1.36/1.12 tff(579,plain,
% 1.36/1.12 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp19) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.36/1.12 inference(quant_intro,[status(thm)],[578])).
% 1.36/1.12 tff(580,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 1.36/1.12 tff(581,plain,
% 1.36/1.12 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[580, 579])).
% 1.36/1.12 tff(582,plain,
% 1.36/1.12 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[581, 577])).
% 1.36/1.12 tff(583,plain,(
% 1.36/1.12 ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.36/1.12 inference(skolemize,[status(sab)],[582])).
% 1.36/1.12 tff(584,plain,
% 1.36/1.12 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[583, 576])).
% 1.36/1.12 tff(585,plain,
% 1.36/1.12 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp19 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp19 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(586,plain,
% 1.36/1.12 ((hskp28 | hskp19 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358))) <=> (hskp28 | hskp19 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(587,plain,
% 1.36/1.12 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp19 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358))))),
% 1.36/1.12 inference(monotonicity,[status(thm)],[586])).
% 1.36/1.12 tff(588,plain,
% 1.36/1.12 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp19 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)))),
% 1.36/1.12 inference(transitivity,[status(thm)],[587, 585])).
% 1.36/1.12 tff(589,plain,
% 1.36/1.12 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))),
% 1.36/1.12 inference(quant_inst,[status(thm)],[])).
% 1.36/1.12 tff(590,plain,
% 1.36/1.12 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp19 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.36/1.12 tff(591,plain,
% 1.36/1.12 (hskp28 | hskp19),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[590, 117, 421, 403, 397, 584])).
% 1.36/1.12 tff(592,plain,
% 1.36/1.12 (hskp19),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[591, 574])).
% 1.36/1.12 tff(593,plain,
% 1.36/1.12 (~c2_1(a387)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[230, 592])).
% 1.36/1.12 tff(594,plain,
% 1.36/1.12 (~c1_1(a387)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[236, 592])).
% 1.36/1.12 tff(595,plain,
% 1.36/1.12 (~c0_1(a387)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[242, 592])).
% 1.36/1.12 tff(596,plain,
% 1.36/1.12 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp6 | hskp5 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp6 | hskp5 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(597,plain,
% 1.36/1.12 ((hskp6 | hskp5 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (hskp6 | hskp5 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(598,plain,
% 1.36/1.12 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp6 | hskp5 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0)))),
% 1.36/1.12 inference(monotonicity,[status(thm)],[597])).
% 1.36/1.12 tff(599,plain,
% 1.36/1.12 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp6 | hskp5 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0))),
% 1.36/1.12 inference(transitivity,[status(thm)],[598, 596])).
% 1.36/1.12 tff(600,plain,
% 1.36/1.12 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 1.36/1.12 inference(quant_inst,[status(thm)],[])).
% 1.36/1.12 tff(601,plain,
% 1.36/1.12 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp6 | hskp5 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0)),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[600, 599])).
% 1.36/1.12 tff(602,plain,
% 1.36/1.12 (hskp5),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[601, 21, 117, 595, 594, 593, 20])).
% 1.36/1.12 tff(603,plain,
% 1.36/1.12 (((~hskp5) | (~c3_1(a359))) <=> ((~hskp5) | (~c3_1(a359)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(604,plain,
% 1.36/1.12 (((~c3_1(a359)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a359)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(605,axiom,((~c3_1(a359)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.36/1.12 tff(606,plain,
% 1.36/1.12 ((~hskp5) | (~c3_1(a359))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[605, 604])).
% 1.36/1.12 tff(607,plain,
% 1.36/1.12 ((~hskp5) | (~c3_1(a359))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[606, 603])).
% 1.36/1.12 tff(608,plain,
% 1.36/1.12 (~c3_1(a359)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[607, 602])).
% 1.36/1.12 tff(609,plain,
% 1.36/1.12 (((~hskp5) | (~c1_1(a359))) <=> ((~hskp5) | (~c1_1(a359)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(610,plain,
% 1.36/1.12 (((~c1_1(a359)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a359)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(611,axiom,((~c1_1(a359)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.36/1.12 tff(612,plain,
% 1.36/1.12 ((~hskp5) | (~c1_1(a359))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[611, 610])).
% 1.36/1.12 tff(613,plain,
% 1.36/1.12 ((~hskp5) | (~c1_1(a359))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[612, 609])).
% 1.36/1.12 tff(614,plain,
% 1.36/1.12 (~c1_1(a359)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[613, 602])).
% 1.36/1.12 tff(615,plain,
% 1.36/1.12 (((~hskp5) | (~c0_1(a359))) <=> ((~hskp5) | (~c0_1(a359)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(616,plain,
% 1.36/1.12 (((~c0_1(a359)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a359)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(617,axiom,((~c0_1(a359)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.36/1.12 tff(618,plain,
% 1.36/1.12 ((~hskp5) | (~c0_1(a359))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[617, 616])).
% 1.36/1.12 tff(619,plain,
% 1.36/1.12 ((~hskp5) | (~c0_1(a359))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[618, 615])).
% 1.36/1.12 tff(620,plain,
% 1.36/1.12 (~c0_1(a359)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[619, 602])).
% 1.36/1.12 tff(621,plain,
% 1.36/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0) | (~c2_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0) | (~c2_1(a359)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(622,plain,
% 1.36/1.12 (((~ndr1_0) | c1_1(a359) | c0_1(a359) | (~c2_1(a359)) | c1_1(a359) | c0_1(a359) | c3_1(a359) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0) | (~c2_1(a359)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(623,plain,
% 1.36/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a359) | c0_1(a359) | (~c2_1(a359)) | c1_1(a359) | c0_1(a359) | c3_1(a359) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0) | (~c2_1(a359))))),
% 1.36/1.12 inference(monotonicity,[status(thm)],[622])).
% 1.36/1.12 tff(624,plain,
% 1.36/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a359) | c0_1(a359) | (~c2_1(a359)) | c1_1(a359) | c0_1(a359) | c3_1(a359) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0) | (~c2_1(a359)))),
% 1.36/1.12 inference(transitivity,[status(thm)],[623, 621])).
% 1.36/1.12 tff(625,plain,
% 1.36/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a359) | c0_1(a359) | (~c2_1(a359)) | c1_1(a359) | c0_1(a359) | c3_1(a359) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 1.36/1.12 inference(quant_inst,[status(thm)],[])).
% 1.36/1.12 tff(626,plain,
% 1.36/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0) | (~c2_1(a359))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[625, 624])).
% 1.36/1.12 tff(627,plain,
% 1.36/1.12 (~c2_1(a359)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[626, 117, 595, 594, 593, 620, 614, 608, 10])).
% 1.36/1.12 tff(628,plain,
% 1.36/1.12 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 1.36/1.12 inference(bind,[status(th)],[])).
% 1.36/1.12 tff(629,plain,
% 1.36/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.12 inference(quant_intro,[status(thm)],[628])).
% 1.36/1.12 tff(630,plain,
% 1.36/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(631,plain,
% 1.36/1.12 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 1.36/1.12 inference(bind,[status(th)],[])).
% 1.36/1.12 tff(632,plain,
% 1.36/1.12 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.12 inference(quant_intro,[status(thm)],[631])).
% 1.36/1.12 tff(633,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 1.36/1.12 tff(634,plain,
% 1.36/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[633, 632])).
% 1.36/1.12 tff(635,plain,
% 1.36/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[634, 630])).
% 1.36/1.12 tff(636,plain,(
% 1.36/1.12 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.12 inference(skolemize,[status(sab)],[635])).
% 1.36/1.12 tff(637,plain,
% 1.36/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[636, 629])).
% 1.36/1.12 tff(638,assumption,(~c1_1(a387)), introduced(assumption)).
% 1.36/1.12 tff(639,assumption,(~c2_1(a387)), introduced(assumption)).
% 1.36/1.12 tff(640,assumption,(~c0_1(a387)), introduced(assumption)).
% 1.36/1.12 tff(641,plain,
% 1.36/1.12 (hskp5 | c1_1(a387) | c2_1(a387)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[601, 21, 117, 640, 20])).
% 1.36/1.12 tff(642,plain,
% 1.36/1.12 (hskp5),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[641, 639, 638])).
% 1.36/1.12 tff(643,plain,
% 1.36/1.12 (~c3_1(a359)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[607, 642])).
% 1.36/1.12 tff(644,plain,
% 1.36/1.12 (~c1_1(a359)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[613, 642])).
% 1.36/1.12 tff(645,plain,
% 1.36/1.12 (~c0_1(a359)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[619, 642])).
% 1.36/1.12 tff(646,plain,
% 1.36/1.12 (~c2_1(a359)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[626, 117, 640, 638, 639, 645, 644, 643, 10])).
% 1.36/1.12 tff(647,plain,
% 1.36/1.12 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.36/1.12 inference(bind,[status(th)],[])).
% 1.36/1.12 tff(648,plain,
% 1.36/1.12 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(quant_intro,[status(thm)],[647])).
% 1.36/1.12 tff(649,plain,
% 1.36/1.12 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(650,plain,
% 1.36/1.12 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | 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))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_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)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | 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)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.36/1.12 inference(bind,[status(th)],[])).
% 1.36/1.12 tff(651,plain,
% 1.36/1.12 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(quant_intro,[status(thm)],[650])).
% 1.36/1.12 tff(652,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.36/1.12 tff(653,plain,
% 1.36/1.12 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[652, 651])).
% 1.36/1.12 tff(654,plain,
% 1.36/1.12 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[653, 649])).
% 1.36/1.12 tff(655,plain,(
% 1.36/1.12 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(skolemize,[status(sab)],[654])).
% 1.36/1.12 tff(656,plain,
% 1.36/1.12 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[655, 648])).
% 1.36/1.12 tff(657,assumption,(~hskp0), introduced(assumption)).
% 1.36/1.12 tff(658,plain,
% 1.36/1.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c3_1(a387)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(659,plain,
% 1.36/1.12 ((hskp0 | (~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c3_1(a387)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(660,plain,
% 1.36/1.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c3_1(a387))))),
% 1.36/1.12 inference(monotonicity,[status(thm)],[659])).
% 1.36/1.12 tff(661,plain,
% 1.36/1.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c3_1(a387)))),
% 1.36/1.12 inference(transitivity,[status(thm)],[660, 658])).
% 1.36/1.12 tff(662,plain,
% 1.36/1.12 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 1.36/1.12 inference(quant_inst,[status(thm)],[])).
% 1.36/1.12 tff(663,plain,
% 1.36/1.12 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c3_1(a387))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[662, 661])).
% 1.36/1.12 tff(664,plain,
% 1.36/1.12 (~c3_1(a387)),
% 1.36/1.12 inference(unit_resolution,[status(thm)],[663, 117, 657, 640, 638, 639, 656])).
% 1.36/1.12 tff(665,plain,
% 1.36/1.12 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.36/1.12 inference(bind,[status(th)],[])).
% 1.36/1.12 tff(666,plain,
% 1.36/1.12 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(quant_intro,[status(thm)],[665])).
% 1.36/1.12 tff(667,plain,
% 1.36/1.12 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(668,plain,
% 1.36/1.12 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_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) | c0_1(U) | (~c1_1(U)) | (~c2_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)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_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)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_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)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_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)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.36/1.12 inference(bind,[status(th)],[])).
% 1.36/1.12 tff(669,plain,
% 1.36/1.12 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(quant_intro,[status(thm)],[668])).
% 1.36/1.12 tff(670,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 1.36/1.12 tff(671,plain,
% 1.36/1.12 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[670, 669])).
% 1.36/1.12 tff(672,plain,
% 1.36/1.12 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[671, 667])).
% 1.36/1.12 tff(673,plain,(
% 1.36/1.12 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(skolemize,[status(sab)],[672])).
% 1.36/1.12 tff(674,plain,
% 1.36/1.12 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.12 inference(modus_ponens,[status(thm)],[673, 666])).
% 1.36/1.12 tff(675,plain,
% 1.36/1.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(676,plain,
% 1.36/1.12 ((hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)))),
% 1.36/1.12 inference(rewrite,[status(thm)],[])).
% 1.36/1.12 tff(677,plain,
% 1.36/1.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358))))),
% 1.36/1.12 inference(monotonicity,[status(thm)],[676])).
% 1.36/1.12 tff(678,plain,
% 1.36/1.12 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)))),
% 1.36/1.13 inference(transitivity,[status(thm)],[677, 675])).
% 1.36/1.13 tff(679,plain,
% 1.36/1.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(680,plain,
% 1.36/1.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[679, 678])).
% 1.36/1.13 tff(681,plain,
% 1.36/1.13 (~c1_1(a358)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[680, 117, 657, 421, 640, 638, 639, 403, 674])).
% 1.36/1.13 tff(682,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | c0_1(a359) | c1_1(a359) | c0_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c2_1(a359) | c3_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c0_1(a359) | c1_1(a359) | c0_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c2_1(a359) | c3_1(a387))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(683,plain,
% 1.36/1.13 (((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a359) | c1_1(a359) | c0_1(a359)) <=> (c0_1(a387) | c1_1(a387) | c0_1(a359) | c1_1(a359) | c0_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c2_1(a359) | c3_1(a387))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(684,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a359) | c1_1(a359) | c0_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | c0_1(a359) | c1_1(a359) | c0_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c2_1(a359) | c3_1(a387)))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[683])).
% 1.36/1.13 tff(685,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a359) | c1_1(a359) | c0_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c0_1(a359) | c1_1(a359) | c0_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c2_1(a359) | c3_1(a387))),
% 1.36/1.13 inference(transitivity,[status(thm)],[684, 682])).
% 1.36/1.13 tff(686,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a359) | c1_1(a359) | c0_1(a359))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(687,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c0_1(a359) | c1_1(a359) | c0_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c2_1(a359) | c3_1(a387)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[686, 685])).
% 1.36/1.13 tff(688,plain,
% 1.36/1.13 ($false),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[687, 117, 421, 640, 638, 645, 644, 403, 10, 681, 664, 646])).
% 1.36/1.13 tff(689,plain,(c2_1(a387) | c0_1(a387) | c1_1(a387) | hskp0 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.36/1.13 tff(690,plain,
% 1.36/1.13 (hskp0),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[689, 595, 21, 594, 593])).
% 1.36/1.13 tff(691,plain,
% 1.36/1.13 (((~hskp0) | (~c2_1(a353))) <=> ((~hskp0) | (~c2_1(a353)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(692,plain,
% 1.36/1.13 (((~c2_1(a353)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a353)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(693,axiom,((~c2_1(a353)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.36/1.13 tff(694,plain,
% 1.36/1.13 ((~hskp0) | (~c2_1(a353))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[693, 692])).
% 1.36/1.13 tff(695,plain,
% 1.36/1.13 ((~hskp0) | (~c2_1(a353))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[694, 691])).
% 1.36/1.13 tff(696,plain,
% 1.36/1.13 (~c2_1(a353)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[695, 690])).
% 1.36/1.13 tff(697,plain,
% 1.36/1.13 (((~hskp0) | c1_1(a353)) <=> ((~hskp0) | c1_1(a353))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(698,axiom,((~hskp0) | c1_1(a353)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 1.36/1.13 tff(699,plain,
% 1.36/1.13 ((~hskp0) | c1_1(a353)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[698, 697])).
% 1.36/1.13 tff(700,plain,
% 1.36/1.13 ((~hskp0) | c1_1(a353)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[699, 697])).
% 1.36/1.13 tff(701,plain,
% 1.36/1.13 ((~hskp0) | c1_1(a353)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[700, 697])).
% 1.36/1.13 tff(702,plain,
% 1.36/1.13 ((~hskp0) | c1_1(a353)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[701, 697])).
% 1.36/1.13 tff(703,plain,
% 1.36/1.13 ((~hskp0) | c1_1(a353)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[702, 697])).
% 1.36/1.13 tff(704,plain,
% 1.36/1.13 ((~hskp0) | c1_1(a353)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[703, 697])).
% 1.36/1.13 tff(705,plain,
% 1.36/1.13 ((~hskp0) | c1_1(a353)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[704, 697])).
% 1.36/1.13 tff(706,plain,
% 1.36/1.13 ((~hskp0) | c1_1(a353)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[705, 697])).
% 1.36/1.13 tff(707,plain,
% 1.36/1.13 (c1_1(a353)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[706, 690])).
% 1.36/1.13 tff(708,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(709,plain,
% 1.36/1.13 (((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359) | c1_1(a359) | c3_1(a359) | c1_1(a359) | c0_1(a359) | c3_1(a359)) <=> (c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(710,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359) | c1_1(a359) | c3_1(a359) | c1_1(a359) | c0_1(a359) | c3_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359)))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[709])).
% 1.36/1.13 tff(711,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359) | c1_1(a359) | c3_1(a359) | c1_1(a359) | c0_1(a359) | c3_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359))),
% 1.36/1.13 inference(transitivity,[status(thm)],[710, 708])).
% 1.36/1.13 tff(712,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359) | c1_1(a359) | c3_1(a359) | c1_1(a359) | c0_1(a359) | c3_1(a359))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(713,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a359)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[712, 711])).
% 1.36/1.13 tff(714,plain,
% 1.36/1.13 (~c3_1(a353)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[713, 117, 707, 620, 614, 608, 696, 637, 627])).
% 1.36/1.13 tff(715,plain,
% 1.36/1.13 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.36/1.13 inference(bind,[status(th)],[])).
% 1.36/1.13 tff(716,plain,
% 1.36/1.13 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.13 inference(quant_intro,[status(thm)],[715])).
% 1.36/1.13 tff(717,plain,
% 1.36/1.13 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(718,plain,
% 1.36/1.13 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.36/1.13 inference(bind,[status(th)],[])).
% 1.36/1.13 tff(719,plain,
% 1.36/1.13 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.13 inference(quant_intro,[status(thm)],[718])).
% 1.36/1.13 tff(720,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 1.36/1.13 tff(721,plain,
% 1.36/1.13 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[720, 719])).
% 1.36/1.13 tff(722,plain,
% 1.36/1.13 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[721, 717])).
% 1.36/1.13 tff(723,plain,(
% 1.36/1.13 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.13 inference(skolemize,[status(sab)],[722])).
% 1.36/1.13 tff(724,plain,
% 1.36/1.13 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[723, 716])).
% 1.36/1.13 tff(725,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c0_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c0_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(726,plain,
% 1.36/1.13 ((hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359) | c0_1(a359) | c3_1(a359)) <=> (hskp12 | c0_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(727,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359) | c0_1(a359) | c3_1(a359))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c0_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359)))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[726])).
% 1.36/1.13 tff(728,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359) | c0_1(a359) | c3_1(a359))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c0_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359))),
% 1.36/1.13 inference(transitivity,[status(thm)],[727, 725])).
% 1.36/1.13 tff(729,plain,
% 1.36/1.13 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359) | c0_1(a359) | c3_1(a359))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(730,plain,
% 1.36/1.13 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c0_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c2_1(a359)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[729, 728])).
% 1.36/1.13 tff(731,plain,
% 1.36/1.13 (hskp12),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[730, 117, 707, 620, 608, 696, 724, 714, 627])).
% 1.36/1.13 tff(732,plain,
% 1.36/1.13 (((~hskp12) | (~c2_1(a369))) <=> ((~hskp12) | (~c2_1(a369)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(733,plain,
% 1.36/1.13 (((~c2_1(a369)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a369)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(734,axiom,((~c2_1(a369)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.36/1.13 tff(735,plain,
% 1.36/1.13 ((~hskp12) | (~c2_1(a369))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[734, 733])).
% 1.36/1.13 tff(736,plain,
% 1.36/1.13 ((~hskp12) | (~c2_1(a369))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[735, 732])).
% 1.36/1.13 tff(737,plain,
% 1.36/1.13 (~c2_1(a369)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[736, 731])).
% 1.36/1.13 tff(738,plain,
% 1.36/1.13 (((~hskp12) | c3_1(a369)) <=> ((~hskp12) | c3_1(a369))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(739,axiom,((~hskp12) | c3_1(a369)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.36/1.13 tff(740,plain,
% 1.36/1.13 ((~hskp12) | c3_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[739, 738])).
% 1.36/1.13 tff(741,plain,
% 1.36/1.13 ((~hskp12) | c3_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[740, 738])).
% 1.36/1.13 tff(742,plain,
% 1.36/1.13 ((~hskp12) | c3_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[741, 738])).
% 1.36/1.13 tff(743,plain,
% 1.36/1.13 ((~hskp12) | c3_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[742, 738])).
% 1.36/1.13 tff(744,plain,
% 1.36/1.13 ((~hskp12) | c3_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[743, 738])).
% 1.36/1.13 tff(745,plain,
% 1.36/1.13 ((~hskp12) | c3_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[744, 738])).
% 1.36/1.13 tff(746,plain,
% 1.36/1.13 ((~hskp12) | c3_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[745, 738])).
% 1.36/1.13 tff(747,plain,
% 1.36/1.13 ((~hskp12) | c3_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[746, 738])).
% 1.36/1.13 tff(748,plain,
% 1.36/1.13 (c3_1(a369)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[747, 731])).
% 1.36/1.13 tff(749,plain,
% 1.36/1.13 (((~hskp12) | c0_1(a369)) <=> ((~hskp12) | c0_1(a369))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(750,axiom,((~hskp12) | c0_1(a369)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.36/1.13 tff(751,plain,
% 1.36/1.13 ((~hskp12) | c0_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[750, 749])).
% 1.36/1.13 tff(752,plain,
% 1.36/1.13 ((~hskp12) | c0_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[751, 749])).
% 1.36/1.13 tff(753,plain,
% 1.36/1.13 ((~hskp12) | c0_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[752, 749])).
% 1.36/1.13 tff(754,plain,
% 1.36/1.13 ((~hskp12) | c0_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[753, 749])).
% 1.36/1.13 tff(755,plain,
% 1.36/1.13 ((~hskp12) | c0_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[754, 749])).
% 1.36/1.13 tff(756,plain,
% 1.36/1.13 ((~hskp12) | c0_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[755, 749])).
% 1.36/1.13 tff(757,plain,
% 1.36/1.13 ((~hskp12) | c0_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[756, 749])).
% 1.36/1.13 tff(758,plain,
% 1.36/1.13 ((~hskp12) | c0_1(a369)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[757, 749])).
% 1.36/1.13 tff(759,plain,
% 1.36/1.13 (c0_1(a369)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[758, 731])).
% 1.36/1.13 tff(760,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | (~c3_1(a369)) | (~c1_1(a369)) | (~c0_1(a369)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | (~c3_1(a369)) | (~c1_1(a369)) | (~c0_1(a369)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(761,plain,
% 1.36/1.13 (((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a369) | (~c1_1(a369)) | (~c0_1(a369)) | c2_1(a353) | c3_1(a353) | (~c1_1(a353))) <=> (c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | (~c3_1(a369)) | (~c1_1(a369)) | (~c0_1(a369)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(762,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a369) | (~c1_1(a369)) | (~c0_1(a369)) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | (~c3_1(a369)) | (~c1_1(a369)) | (~c0_1(a369))))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[761])).
% 1.36/1.13 tff(763,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a369) | (~c1_1(a369)) | (~c0_1(a369)) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | (~c3_1(a369)) | (~c1_1(a369)) | (~c0_1(a369)))),
% 1.36/1.13 inference(transitivity,[status(thm)],[762, 760])).
% 1.36/1.13 tff(764,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a369) | (~c1_1(a369)) | (~c0_1(a369)) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(765,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | (~c3_1(a369)) | (~c1_1(a369)) | (~c0_1(a369))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[764, 763])).
% 1.36/1.13 tff(766,plain,
% 1.36/1.13 (~c1_1(a369)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[765, 117, 759, 748, 707, 737, 696, 329, 714])).
% 1.36/1.13 tff(767,plain,
% 1.36/1.13 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 1.36/1.13 inference(bind,[status(th)],[])).
% 1.36/1.13 tff(768,plain,
% 1.36/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.13 inference(quant_intro,[status(thm)],[767])).
% 1.36/1.13 tff(769,plain,
% 1.36/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(770,plain,
% 1.36/1.13 (^[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(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 1.36/1.13 inference(bind,[status(th)],[])).
% 1.36/1.13 tff(771,plain,
% 1.36/1.13 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.13 inference(quant_intro,[status(thm)],[770])).
% 1.36/1.13 tff(772,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 1.36/1.13 tff(773,plain,
% 1.36/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[772, 771])).
% 1.36/1.13 tff(774,plain,
% 1.36/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[773, 769])).
% 1.36/1.13 tff(775,plain,(
% 1.36/1.13 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.13 inference(skolemize,[status(sab)],[774])).
% 1.36/1.13 tff(776,plain,
% 1.36/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[775, 768])).
% 1.36/1.13 tff(777,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a369) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(778,plain,
% 1.36/1.13 (((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a359) | c0_1(a359) | c3_1(a359)) <=> (c2_1(a369) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(779,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a359) | c0_1(a359) | c3_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a369) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369))))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[778])).
% 1.36/1.13 tff(780,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a359) | c0_1(a359) | c3_1(a359))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)))),
% 1.36/1.13 inference(transitivity,[status(thm)],[779, 777])).
% 1.36/1.13 tff(781,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a359) | c0_1(a359) | c3_1(a359))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(782,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c0_1(a359) | c1_1(a359) | c3_1(a359) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[781, 780])).
% 1.36/1.13 tff(783,plain,
% 1.36/1.13 ($false),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[782, 117, 759, 707, 737, 620, 614, 608, 696, 776, 714, 766])).
% 1.36/1.13 tff(784,plain,(hskp6), inference(lemma,lemma(discharge,[]))).
% 1.36/1.13 tff(785,plain,
% 1.36/1.13 (~c3_1(a360)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[216, 784])).
% 1.36/1.13 tff(786,plain,
% 1.36/1.13 (~c1_1(a360)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[192, 784])).
% 1.36/1.13 tff(787,plain,
% 1.36/1.13 (~c2_1(a360)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[186, 784])).
% 1.36/1.13 tff(788,assumption,(~c2_1(a360)), introduced(assumption)).
% 1.36/1.13 tff(789,assumption,(~c3_1(a360)), introduced(assumption)).
% 1.36/1.13 tff(790,assumption,(~c1_1(a360)), introduced(assumption)).
% 1.36/1.13 tff(791,assumption,(~c0_1(a360)), introduced(assumption)).
% 1.36/1.13 tff(792,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a360) | c2_1(a360) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a360))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a360) | c2_1(a360) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a360))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(793,plain,
% 1.36/1.13 ((hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a360) | c1_1(a360) | c0_1(a360)) <=> (hskp0 | c1_1(a360) | c2_1(a360) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a360))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(794,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a360) | c2_1(a360) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a360)))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[793])).
% 1.36/1.14 tff(795,plain,
% 1.36/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a360) | c2_1(a360) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a360))),
% 1.36/1.14 inference(transitivity,[status(thm)],[794, 792])).
% 1.36/1.14 tff(796,plain,
% 1.36/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a360) | c1_1(a360) | c0_1(a360))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(797,plain,
% 1.36/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a360) | c2_1(a360) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a360)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[796, 795])).
% 1.36/1.14 tff(798,plain,
% 1.36/1.14 (hskp0 | c1_1(a360) | (~c1_1(a358)) | c0_1(a360)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[797, 117, 421, 788, 403, 674])).
% 1.36/1.14 tff(799,plain,
% 1.36/1.14 (~c1_1(a358)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[798, 791, 790, 657])).
% 1.36/1.14 tff(800,assumption,(~c1_1(a388)), introduced(assumption)).
% 1.36/1.14 tff(801,assumption,(hskp3), introduced(assumption)).
% 1.36/1.14 tff(802,plain,
% 1.36/1.14 (~c0_1(a357)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[257, 801])).
% 1.36/1.14 tff(803,plain,
% 1.36/1.14 (c3_1(a357)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[268, 801])).
% 1.36/1.14 tff(804,plain,
% 1.36/1.14 (c1_1(a357)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[279, 801])).
% 1.36/1.14 tff(805,plain,
% 1.36/1.14 (~hskp20),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[309, 800])).
% 1.36/1.14 tff(806,plain,
% 1.36/1.14 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | c1_1(a388) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a388) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(807,plain,
% 1.36/1.14 ((hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | c1_1(a388) | c3_1(a388)) <=> (hskp20 | c1_1(a388) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(808,plain,
% 1.36/1.14 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | c1_1(a388) | c3_1(a388))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | c1_1(a388) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357))))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[807])).
% 1.36/1.14 tff(809,plain,
% 1.36/1.14 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | c1_1(a388) | c3_1(a388))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a388) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357)))),
% 1.36/1.14 inference(transitivity,[status(thm)],[808, 806])).
% 1.36/1.14 tff(810,plain,
% 1.36/1.14 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c0_1(a357) | (~c3_1(a357)) | (~c1_1(a357)) | c2_1(a388) | c1_1(a388) | c3_1(a388))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(811,plain,
% 1.36/1.14 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a388) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c1_1(a357)) | (~c3_1(a357))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[810, 809])).
% 1.36/1.14 tff(812,plain,
% 1.36/1.14 ($false),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[811, 117, 805, 800, 804, 803, 333, 332, 802, 166])).
% 1.36/1.14 tff(813,plain,((~hskp3) | c1_1(a388) | c2_1(a388) | c3_1(a388)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.14 tff(814,plain,
% 1.36/1.14 (~hskp3),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[813, 800, 333, 332])).
% 1.36/1.14 tff(815,plain,
% 1.36/1.14 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.36/1.14 inference(bind,[status(th)],[])).
% 1.36/1.14 tff(816,plain,
% 1.36/1.14 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.14 inference(quant_intro,[status(thm)],[815])).
% 1.36/1.14 tff(817,plain,
% 1.36/1.14 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(818,plain,
% 1.36/1.14 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.36/1.14 inference(bind,[status(th)],[])).
% 1.36/1.14 tff(819,plain,
% 1.36/1.14 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.14 inference(quant_intro,[status(thm)],[818])).
% 1.36/1.14 tff(820,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.36/1.14 tff(821,plain,
% 1.36/1.14 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[820, 819])).
% 1.36/1.14 tff(822,plain,
% 1.36/1.14 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[821, 817])).
% 1.36/1.14 tff(823,plain,(
% 1.36/1.14 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.14 inference(skolemize,[status(sab)],[822])).
% 1.36/1.14 tff(824,plain,
% 1.36/1.14 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[823, 816])).
% 1.36/1.14 tff(825,plain,
% 1.36/1.14 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c1_1(a388) | c3_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c1_1(a388) | c3_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a388)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(826,plain,
% 1.36/1.14 ((hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358))) <=> (hskp3 | c1_1(a388) | c3_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a388)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(827,plain,
% 1.36/1.14 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c1_1(a388) | c3_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a388))))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[826])).
% 1.36/1.14 tff(828,plain,
% 1.36/1.14 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c1_1(a388) | c3_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a388)))),
% 1.36/1.14 inference(transitivity,[status(thm)],[827, 825])).
% 1.36/1.14 tff(829,plain,
% 1.36/1.14 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358)))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(830,plain,
% 1.36/1.14 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c1_1(a388) | c3_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a388))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[829, 828])).
% 1.36/1.14 tff(831,plain,
% 1.36/1.14 (hskp3 | (~c1_1(a358)) | (~c0_1(a388))),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[830, 117, 800, 332, 403, 397, 824])).
% 1.36/1.14 tff(832,plain,
% 1.36/1.14 (~c1_1(a358)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[831, 177, 330])).
% 1.36/1.14 tff(833,plain,
% 1.36/1.14 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | c1_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a388)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp3 | c1_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a388)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(834,plain,
% 1.36/1.14 ((hskp19 | hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388))) <=> (hskp19 | hskp3 | c1_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a388)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(835,plain,
% 1.36/1.14 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | c1_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a388))))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[834])).
% 1.36/1.14 tff(836,plain,
% 1.36/1.14 (((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)))) <=> ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp3 | c1_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a388)))),
% 1.36/1.14 inference(transitivity,[status(thm)],[835, 833])).
% 1.36/1.14 tff(837,plain,
% 1.36/1.14 ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp3 | (~ndr1_0) | c1_1(a388) | c3_1(a388) | (~c0_1(a388)))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(838,plain,
% 1.36/1.14 ((~![U: $i] : (hskp19 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp3 | c1_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a388))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[837, 836])).
% 1.36/1.14 tff(839,plain,
% 1.36/1.14 (hskp19 | hskp3 | c1_1(a388) | (~c0_1(a388))),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[838, 117, 332, 211])).
% 1.36/1.14 tff(840,plain,
% 1.36/1.14 (hskp19),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[839, 177, 800, 330])).
% 1.36/1.14 tff(841,plain,
% 1.36/1.14 (~c2_1(a387)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[230, 840])).
% 1.36/1.14 tff(842,plain,
% 1.36/1.14 (~c1_1(a387)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[236, 840])).
% 1.36/1.14 tff(843,plain,
% 1.36/1.14 (~c0_1(a387)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[242, 840])).
% 1.36/1.14 tff(844,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(845,plain,
% 1.36/1.14 (((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(846,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358))))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[845])).
% 1.36/1.14 tff(847,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)))),
% 1.36/1.14 inference(transitivity,[status(thm)],[846, 844])).
% 1.36/1.14 tff(848,plain,
% 1.36/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(849,plain,
% 1.36/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[848, 847])).
% 1.36/1.14 tff(850,plain,
% 1.36/1.14 ($false),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[849, 117, 421, 843, 842, 841, 403, 397, 10, 832])).
% 1.36/1.14 tff(851,plain,(hskp3 | c1_1(a388) | (~c0_1(a388)) | c3_1(a388)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.14 tff(852,plain,
% 1.36/1.14 (~c0_1(a388)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[851, 814, 800, 332])).
% 1.36/1.14 tff(853,plain,
% 1.36/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a388) | c2_1(a388) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a388))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a388) | c2_1(a388) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a388))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(854,plain,
% 1.36/1.14 ((hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a388) | c1_1(a388) | c0_1(a388)) <=> (hskp0 | c1_1(a388) | c2_1(a388) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a388))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(855,plain,
% 1.36/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a388) | c1_1(a388) | c0_1(a388))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a388) | c2_1(a388) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a388)))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[854])).
% 1.36/1.14 tff(856,plain,
% 1.36/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a388) | c1_1(a388) | c0_1(a388))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a388) | c2_1(a388) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a388))),
% 1.36/1.14 inference(transitivity,[status(thm)],[855, 853])).
% 1.36/1.14 tff(857,plain,
% 1.36/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a388) | c1_1(a388) | c0_1(a388))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(858,plain,
% 1.36/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a388) | c2_1(a388) | c0_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | c0_1(a388)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[857, 856])).
% 1.36/1.14 tff(859,plain,
% 1.36/1.14 (hskp0 | c1_1(a388) | (~c1_1(a358)) | c0_1(a388)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[858, 117, 421, 333, 403, 674])).
% 1.36/1.14 tff(860,plain,
% 1.36/1.14 (~c1_1(a358)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[859, 146, 800, 657])).
% 1.36/1.14 tff(861,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a388) | c2_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c0_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a388) | c2_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c0_1(a388))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(862,plain,
% 1.36/1.14 (((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a388) | c1_1(a388) | c0_1(a388)) <=> (c1_1(a388) | c2_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c0_1(a388))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(863,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a388) | c1_1(a388) | c0_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a388) | c2_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c0_1(a388)))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[862])).
% 1.36/1.14 tff(864,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a388) | c1_1(a388) | c0_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a388) | c2_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c0_1(a388))),
% 1.36/1.14 inference(transitivity,[status(thm)],[863, 861])).
% 1.36/1.14 tff(865,plain,
% 1.36/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a358) | c0_1(a358) | (~c2_1(a358)) | c1_1(a358) | c0_1(a358) | c3_1(a358) | c2_1(a388) | c1_1(a388) | c0_1(a388))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(866,plain,
% 1.36/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a388) | c2_1(a388) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c2_1(a358)) | c0_1(a388)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[865, 864])).
% 1.36/1.14 tff(867,plain,
% 1.36/1.14 ($false),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[866, 117, 800, 421, 333, 403, 397, 10, 146, 860])).
% 1.36/1.14 tff(868,plain,(c0_1(a388) | c1_1(a388) | c2_1(a388) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.36/1.14 tff(869,plain,
% 1.36/1.14 (hskp0),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[868, 852, 333, 800])).
% 1.36/1.14 tff(870,plain,
% 1.36/1.14 (~c2_1(a353)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[695, 869])).
% 1.36/1.14 tff(871,plain,
% 1.36/1.14 (c1_1(a353)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[706, 869])).
% 1.36/1.14 tff(872,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a388) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a388) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a388))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(873,plain,
% 1.36/1.14 (((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a388) | c1_1(a388) | c3_1(a388) | c1_1(a388) | c0_1(a388) | c3_1(a388)) <=> (c1_1(a388) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a388))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(874,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a388) | c1_1(a388) | c3_1(a388) | c1_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a388) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a388)))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[873])).
% 1.36/1.15 tff(875,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a388) | c1_1(a388) | c3_1(a388) | c1_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a388) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a388))),
% 1.36/1.15 inference(transitivity,[status(thm)],[874, 872])).
% 1.36/1.15 tff(876,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a388) | c1_1(a388) | c3_1(a388) | c1_1(a388) | c0_1(a388) | c3_1(a388))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(877,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a388) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a388)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[876, 875])).
% 1.36/1.15 tff(878,plain,
% 1.36/1.15 (~c3_1(a353)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[877, 117, 800, 871, 333, 332, 870, 637, 852])).
% 1.36/1.15 tff(879,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a388))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a388))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(880,plain,
% 1.36/1.15 ((hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a388) | c0_1(a388) | c3_1(a388)) <=> (hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a388))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(881,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a388)))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[880])).
% 1.36/1.15 tff(882,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a388))),
% 1.36/1.15 inference(transitivity,[status(thm)],[881, 879])).
% 1.36/1.15 tff(883,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a388) | c0_1(a388) | c3_1(a388))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(884,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a388)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[883, 882])).
% 1.36/1.15 tff(885,plain,
% 1.36/1.15 (hskp12),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[884, 117, 871, 333, 332, 870, 724, 852, 878])).
% 1.36/1.15 tff(886,plain,
% 1.36/1.15 (~c2_1(a369)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[736, 885])).
% 1.36/1.15 tff(887,plain,
% 1.36/1.15 (c3_1(a369)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[747, 885])).
% 1.36/1.15 tff(888,plain,
% 1.36/1.15 (c0_1(a369)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[758, 885])).
% 1.36/1.15 tff(889,plain,
% 1.36/1.15 (~c1_1(a369)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[765, 117, 888, 887, 871, 886, 870, 329, 878])).
% 1.36/1.15 tff(890,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a388) | c3_1(a388) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)) | c0_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a388) | c3_1(a388) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)) | c0_1(a388))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(891,plain,
% 1.36/1.15 (((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a388) | c0_1(a388) | c3_1(a388)) <=> (c1_1(a388) | c3_1(a388) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)) | c0_1(a388))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(892,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a388) | c3_1(a388) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)) | c0_1(a388)))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[891])).
% 1.36/1.15 tff(893,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a388) | c3_1(a388) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)) | c0_1(a388))),
% 1.36/1.15 inference(transitivity,[status(thm)],[892, 890])).
% 1.36/1.15 tff(894,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a388) | c0_1(a388) | c3_1(a388))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(895,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a388) | c3_1(a388) | c2_1(a369) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a369) | (~c0_1(a369)) | c0_1(a388)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[894, 893])).
% 1.36/1.15 tff(896,plain,
% 1.36/1.15 ($false),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[895, 117, 800, 888, 871, 332, 886, 870, 776, 852, 878, 889])).
% 1.36/1.15 tff(897,plain,(c1_1(a388) | c3_1(a388) | c2_1(a388)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.15 tff(898,plain,
% 1.36/1.15 (c1_1(a388)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[897, 332, 333])).
% 1.36/1.15 tff(899,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(900,plain,
% 1.36/1.15 ((hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c0_1(a360) | c3_1(a360)) <=> (hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(901,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388))))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[900])).
% 1.36/1.15 tff(902,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))),
% 1.36/1.15 inference(transitivity,[status(thm)],[901, 899])).
% 1.36/1.15 tff(903,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c0_1(a360) | c3_1(a360))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(904,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[903, 902])).
% 1.36/1.15 tff(905,plain,
% 1.36/1.15 (hskp12 | c3_1(a388) | c0_1(a360) | (~c1_1(a388))),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[904, 117, 333, 788, 789, 724])).
% 1.36/1.15 tff(906,plain,
% 1.36/1.15 (hskp12),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[905, 791, 332, 898])).
% 1.36/1.15 tff(907,plain,
% 1.36/1.15 (~c2_1(a369)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[736, 906])).
% 1.36/1.15 tff(908,plain,
% 1.36/1.15 (c0_1(a369)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[758, 906])).
% 1.36/1.15 tff(909,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a388) | c3_1(a388) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | c1_1(a369) | (~c0_1(a369)) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | c3_1(a388) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | c1_1(a369) | (~c0_1(a369)) | (~c1_1(a388)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(910,plain,
% 1.36/1.15 (((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c2_1(a388) | c3_1(a388) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | c1_1(a369) | (~c0_1(a369)) | (~c1_1(a388)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(911,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a388) | c3_1(a388) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | c1_1(a369) | (~c0_1(a369)) | (~c1_1(a388))))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[910])).
% 1.36/1.15 tff(912,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | c3_1(a388) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | c1_1(a369) | (~c0_1(a369)) | (~c1_1(a388)))),
% 1.36/1.15 inference(transitivity,[status(thm)],[911, 909])).
% 1.36/1.15 tff(913,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(914,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | c3_1(a388) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | c1_1(a369) | (~c0_1(a369)) | (~c1_1(a388))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[913, 912])).
% 1.36/1.15 tff(915,plain,
% 1.36/1.15 (c1_1(a369)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[914, 117, 898, 908, 333, 332, 907, 403, 397, 776, 799])).
% 1.36/1.15 tff(916,plain,
% 1.36/1.15 (c3_1(a369)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[747, 906])).
% 1.36/1.15 tff(917,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a369) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(918,plain,
% 1.36/1.15 (((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c2_1(a369) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(919,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a369) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369))))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[918])).
% 1.36/1.15 tff(920,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)))),
% 1.36/1.15 inference(transitivity,[status(thm)],[919, 917])).
% 1.36/1.15 tff(921,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(922,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[921, 920])).
% 1.36/1.15 tff(923,plain,
% 1.36/1.15 ($false),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[922, 117, 916, 907, 790, 788, 789, 403, 397, 637, 799, 915])).
% 1.36/1.15 tff(924,plain,(c0_1(a360) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a388) | c3_1(a388) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.36/1.15 tff(925,plain,
% 1.36/1.15 (c0_1(a360)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[924, 657, 788, 789, 333, 332, 790])).
% 1.36/1.15 tff(926,plain,
% 1.36/1.15 (hskp19 | hskp3 | c1_1(a360) | (~c0_1(a360))),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[223, 117, 789, 211])).
% 1.36/1.15 tff(927,plain,
% 1.36/1.15 (hskp19),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[926, 925, 790, 177])).
% 1.36/1.15 tff(928,plain,
% 1.36/1.15 (~c0_1(a387)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[242, 927])).
% 1.36/1.15 tff(929,plain,
% 1.36/1.15 (~c1_1(a387)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[236, 927])).
% 1.36/1.15 tff(930,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a388) | c3_1(a388) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c1_1(a388)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(931,plain,
% 1.36/1.15 ((hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387)) <=> (hskp12 | c2_1(a388) | c3_1(a388) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c1_1(a388)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(932,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a388) | c3_1(a388) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c1_1(a388))))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[931])).
% 1.36/1.15 tff(933,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c1_1(a388)))),
% 1.36/1.15 inference(transitivity,[status(thm)],[932, 930])).
% 1.36/1.15 tff(934,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(935,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a388) | c3_1(a388) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c1_1(a388))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[934, 933])).
% 1.36/1.15 tff(936,plain,
% 1.36/1.15 (hskp12 | c3_1(a387)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[935, 117, 898, 333, 332, 640, 639, 724])).
% 1.36/1.15 tff(937,plain,
% 1.36/1.15 (hskp12),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[936, 664])).
% 1.36/1.15 tff(938,plain,
% 1.36/1.15 (~c2_1(a369)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[736, 937])).
% 1.36/1.15 tff(939,plain,
% 1.36/1.15 (c0_1(a369)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[758, 937])).
% 1.36/1.15 tff(940,plain,
% 1.36/1.15 (c1_1(a369)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[914, 117, 898, 939, 333, 332, 938, 403, 397, 776, 681])).
% 1.36/1.15 tff(941,plain,
% 1.36/1.15 (c3_1(a369)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[747, 937])).
% 1.36/1.15 tff(942,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a387) | c2_1(a387) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)) | c3_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a387) | c2_1(a387) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)) | c3_1(a387))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(943,plain,
% 1.36/1.15 (((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a387) | c1_1(a387) | c3_1(a387) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c1_1(a387) | c2_1(a387) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)) | c3_1(a387))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(944,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a387) | c1_1(a387) | c3_1(a387) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a387) | c2_1(a387) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)) | c3_1(a387)))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[943])).
% 1.36/1.15 tff(945,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a387) | c1_1(a387) | c3_1(a387) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a387) | c2_1(a387) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)) | c3_1(a387))),
% 1.36/1.15 inference(transitivity,[status(thm)],[944, 942])).
% 1.36/1.15 tff(946,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a369) | (~c3_1(a369)) | (~c1_1(a369)) | c2_1(a387) | c1_1(a387) | c3_1(a387) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(947,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a387) | c2_1(a387) | c2_1(a369) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c3_1(a369)) | (~c1_1(a369)) | c3_1(a387)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[946, 945])).
% 1.36/1.15 tff(948,plain,
% 1.36/1.15 ($false),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[947, 117, 941, 638, 639, 938, 403, 397, 637, 681, 664, 940])).
% 1.36/1.15 tff(949,plain,(c2_1(a387) | c1_1(a387) | c2_1(a388) | c3_1(a388) | c0_1(a387) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.36/1.15 tff(950,plain,
% 1.36/1.15 (c2_1(a387)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[949, 638, 333, 332, 640, 657])).
% 1.36/1.15 tff(951,plain,
% 1.36/1.15 (~hskp19),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[230, 950])).
% 1.36/1.15 tff(952,plain,
% 1.36/1.15 (^[U: $i] : refl((hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.36/1.15 inference(bind,[status(th)],[])).
% 1.36/1.15 tff(953,plain,
% 1.36/1.15 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.15 inference(quant_intro,[status(thm)],[952])).
% 1.36/1.15 tff(954,plain,
% 1.36/1.15 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(955,plain,
% 1.36/1.15 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.36/1.15 inference(bind,[status(th)],[])).
% 1.36/1.15 tff(956,plain,
% 1.36/1.15 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.15 inference(quant_intro,[status(thm)],[955])).
% 1.36/1.15 tff(957,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.36/1.15 tff(958,plain,
% 1.36/1.15 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[957, 956])).
% 1.36/1.15 tff(959,plain,
% 1.36/1.15 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[958, 954])).
% 1.36/1.15 tff(960,plain,(
% 1.36/1.15 ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.15 inference(skolemize,[status(sab)],[959])).
% 1.36/1.15 tff(961,plain,
% 1.36/1.15 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[960, 953])).
% 1.36/1.15 tff(962,plain,
% 1.36/1.15 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp0 | c0_1(a387) | (~c2_1(a387)) | (~ndr1_0) | (~c3_1(a387)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp0 | c0_1(a387) | (~c2_1(a387)) | (~ndr1_0) | (~c3_1(a387)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(963,plain,
% 1.36/1.15 ((hskp0 | (~ndr1_0) | c0_1(a387) | (~c3_1(a387)) | (~c2_1(a387))) <=> (hskp0 | c0_1(a387) | (~c2_1(a387)) | (~ndr1_0) | (~c3_1(a387)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(964,plain,
% 1.36/1.15 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a387) | (~c3_1(a387)) | (~c2_1(a387)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp0 | c0_1(a387) | (~c2_1(a387)) | (~ndr1_0) | (~c3_1(a387))))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[963])).
% 1.36/1.15 tff(965,plain,
% 1.36/1.15 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a387) | (~c3_1(a387)) | (~c2_1(a387)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp0 | c0_1(a387) | (~c2_1(a387)) | (~ndr1_0) | (~c3_1(a387)))),
% 1.36/1.15 inference(transitivity,[status(thm)],[964, 962])).
% 1.36/1.15 tff(966,plain,
% 1.36/1.15 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a387) | (~c3_1(a387)) | (~c2_1(a387)))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(967,plain,
% 1.36/1.15 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp0 | c0_1(a387) | (~c2_1(a387)) | (~ndr1_0) | (~c3_1(a387))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[966, 965])).
% 1.36/1.15 tff(968,plain,
% 1.36/1.15 ((~c2_1(a387)) | (~c3_1(a387))),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[967, 117, 657, 640, 961])).
% 1.36/1.15 tff(969,plain,
% 1.36/1.15 (~c3_1(a387)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[968, 950])).
% 1.36/1.15 tff(970,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360) | c3_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360) | c3_1(a387))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(971,plain,
% 1.36/1.15 (((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a360) | c1_1(a360) | c0_1(a360)) <=> (c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360) | c3_1(a387))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(972,plain,
% 1.36/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360) | c3_1(a387)))),
% 1.36/1.16 inference(monotonicity,[status(thm)],[971])).
% 1.36/1.16 tff(973,plain,
% 1.36/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360) | c3_1(a387))),
% 1.36/1.16 inference(transitivity,[status(thm)],[972, 970])).
% 1.36/1.16 tff(974,plain,
% 1.36/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a360) | c1_1(a360) | c0_1(a360))),
% 1.36/1.16 inference(quant_inst,[status(thm)],[])).
% 1.36/1.16 tff(975,plain,
% 1.36/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | c0_1(a360) | c3_1(a387)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[974, 973])).
% 1.36/1.16 tff(976,plain,
% 1.36/1.16 ((~c2_1(a387)) | c0_1(a360) | c3_1(a387)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[975, 117, 640, 638, 790, 788, 10])).
% 1.36/1.16 tff(977,plain,
% 1.36/1.16 (c0_1(a360)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[976, 950, 969])).
% 1.36/1.16 tff(978,plain,
% 1.36/1.16 ($false),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[926, 977, 951, 790, 177])).
% 1.36/1.16 tff(979,plain,(c1_1(a387) | c1_1(a360) | hskp3 | c3_1(a360) | c0_1(a387) | c2_1(a360) | hskp0 | c2_1(a388) | c3_1(a388)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.16 tff(980,plain,
% 1.36/1.16 ($false),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[979, 929, 928, 177, 789, 790, 788, 657, 333, 332])).
% 1.36/1.16 tff(981,plain,(hskp0 | hskp3 | c3_1(a360) | c1_1(a360) | c2_1(a360) | c2_1(a388) | c3_1(a388)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.16 tff(982,plain,
% 1.36/1.16 (hskp0),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[981, 177, 789, 790, 788, 333, 332])).
% 1.36/1.16 tff(983,plain,
% 1.36/1.16 (~c2_1(a353)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[695, 982])).
% 1.36/1.16 tff(984,plain,
% 1.36/1.16 (c1_1(a353)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[706, 982])).
% 1.36/1.16 tff(985,plain,
% 1.36/1.16 (((~hskp0) | c0_1(a353)) <=> ((~hskp0) | c0_1(a353))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(986,axiom,((~hskp0) | c0_1(a353)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 1.36/1.16 tff(987,plain,
% 1.36/1.16 ((~hskp0) | c0_1(a353)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[986, 985])).
% 1.36/1.16 tff(988,plain,
% 1.36/1.16 ((~hskp0) | c0_1(a353)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[987, 985])).
% 1.36/1.16 tff(989,plain,
% 1.36/1.16 ((~hskp0) | c0_1(a353)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[988, 985])).
% 1.36/1.16 tff(990,plain,
% 1.36/1.16 ((~hskp0) | c0_1(a353)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[989, 985])).
% 1.36/1.16 tff(991,plain,
% 1.36/1.16 ((~hskp0) | c0_1(a353)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[990, 985])).
% 1.36/1.16 tff(992,plain,
% 1.36/1.16 ((~hskp0) | c0_1(a353)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[991, 985])).
% 1.36/1.16 tff(993,plain,
% 1.36/1.16 ((~hskp0) | c0_1(a353)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[992, 985])).
% 1.36/1.16 tff(994,plain,
% 1.36/1.16 ((~hskp0) | c0_1(a353)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[993, 985])).
% 1.36/1.16 tff(995,plain,
% 1.36/1.16 (c0_1(a353)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[994, 982])).
% 1.36/1.16 tff(996,plain,
% 1.36/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | (~c0_1(a353)) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | (~c0_1(a353)) | (~c1_1(a388)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(997,plain,
% 1.36/1.16 (((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a353) | (~c1_1(a353)) | (~c0_1(a353)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388))) <=> (c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | (~c0_1(a353)) | (~c1_1(a388)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(998,plain,
% 1.36/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a353) | (~c1_1(a353)) | (~c0_1(a353)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | (~c0_1(a353)) | (~c1_1(a388))))),
% 1.36/1.16 inference(monotonicity,[status(thm)],[997])).
% 1.36/1.16 tff(999,plain,
% 1.36/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a353) | (~c1_1(a353)) | (~c0_1(a353)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | (~c0_1(a353)) | (~c1_1(a388)))),
% 1.36/1.16 inference(transitivity,[status(thm)],[998, 996])).
% 1.36/1.16 tff(1000,plain,
% 1.36/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a353) | (~c1_1(a353)) | (~c0_1(a353)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))),
% 1.36/1.16 inference(quant_inst,[status(thm)],[])).
% 1.36/1.16 tff(1001,plain,
% 1.36/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a388) | c3_1(a388) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | (~c0_1(a353)) | (~c1_1(a388))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1000, 999])).
% 1.36/1.16 tff(1002,plain,
% 1.36/1.16 (~c3_1(a353)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1001, 117, 898, 995, 984, 333, 332, 983, 329])).
% 1.36/1.16 tff(1003,plain,
% 1.36/1.16 (^[U: $i] : refl((hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.36/1.16 inference(bind,[status(th)],[])).
% 1.36/1.16 tff(1004,plain,
% 1.36/1.16 (![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.16 inference(quant_intro,[status(thm)],[1003])).
% 1.36/1.16 tff(1005,plain,
% 1.36/1.16 (![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1006,plain,
% 1.36/1.16 (^[U: $i] : 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) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.36/1.16 inference(bind,[status(th)],[])).
% 1.36/1.16 tff(1007,plain,
% 1.36/1.16 (![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) <=> ![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.16 inference(quant_intro,[status(thm)],[1006])).
% 1.36/1.16 tff(1008,axiom,(![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.36/1.16 tff(1009,plain,
% 1.36/1.16 (![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 1.36/1.16 tff(1010,plain,
% 1.36/1.16 (![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1009, 1005])).
% 1.36/1.16 tff(1011,plain,(
% 1.36/1.16 ![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.16 inference(skolemize,[status(sab)],[1010])).
% 1.36/1.16 tff(1012,plain,
% 1.36/1.16 (![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1011, 1004])).
% 1.36/1.16 tff(1013,plain,
% 1.36/1.16 (((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c0_1(a353)))) <=> ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp26 | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c0_1(a353)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1014,plain,
% 1.36/1.16 ((hskp26 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c0_1(a353))) <=> (hskp26 | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c0_1(a353)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1015,plain,
% 1.36/1.16 (((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c0_1(a353)))) <=> ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c0_1(a353))))),
% 1.36/1.16 inference(monotonicity,[status(thm)],[1014])).
% 1.36/1.16 tff(1016,plain,
% 1.36/1.16 (((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c0_1(a353)))) <=> ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp26 | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c0_1(a353)))),
% 1.36/1.16 inference(transitivity,[status(thm)],[1015, 1013])).
% 1.36/1.16 tff(1017,plain,
% 1.36/1.16 ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c0_1(a353)))),
% 1.36/1.16 inference(quant_inst,[status(thm)],[])).
% 1.36/1.16 tff(1018,plain,
% 1.36/1.16 ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp26 | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c0_1(a353))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 1.36/1.16 tff(1019,plain,
% 1.36/1.16 (hskp26 | c3_1(a353)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1018, 117, 995, 983, 1012])).
% 1.36/1.16 tff(1020,plain,
% 1.36/1.16 (hskp26),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1019, 1002])).
% 1.36/1.16 tff(1021,plain,
% 1.36/1.16 (((~hskp26) | (~c3_1(a418))) <=> ((~hskp26) | (~c3_1(a418)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1022,plain,
% 1.36/1.16 (((~c3_1(a418)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a418)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1023,axiom,((~c3_1(a418)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.36/1.16 tff(1024,plain,
% 1.36/1.16 ((~hskp26) | (~c3_1(a418))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 1.36/1.16 tff(1025,plain,
% 1.36/1.16 ((~hskp26) | (~c3_1(a418))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1024, 1021])).
% 1.36/1.16 tff(1026,plain,
% 1.36/1.16 (~c3_1(a418)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1025, 1020])).
% 1.36/1.16 tff(1027,plain,
% 1.36/1.16 (((~hskp26) | (~c2_1(a418))) <=> ((~hskp26) | (~c2_1(a418)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1028,plain,
% 1.36/1.16 (((~c2_1(a418)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a418)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1029,axiom,((~c2_1(a418)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 1.36/1.16 tff(1030,plain,
% 1.36/1.16 ((~hskp26) | (~c2_1(a418))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 1.36/1.16 tff(1031,plain,
% 1.36/1.16 ((~hskp26) | (~c2_1(a418))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1030, 1027])).
% 1.36/1.16 tff(1032,plain,
% 1.36/1.16 (~c2_1(a418)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1031, 1020])).
% 1.36/1.16 tff(1033,plain,
% 1.36/1.16 (((~hskp26) | c0_1(a418)) <=> ((~hskp26) | c0_1(a418))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1034,axiom,((~hskp26) | c0_1(a418)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 1.36/1.16 tff(1035,plain,
% 1.36/1.16 ((~hskp26) | c0_1(a418)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 1.36/1.16 tff(1036,plain,
% 1.36/1.16 ((~hskp26) | c0_1(a418)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1035, 1033])).
% 1.36/1.16 tff(1037,plain,
% 1.36/1.16 ((~hskp26) | c0_1(a418)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1036, 1033])).
% 1.36/1.16 tff(1038,plain,
% 1.36/1.16 ((~hskp26) | c0_1(a418)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1037, 1033])).
% 1.36/1.16 tff(1039,plain,
% 1.36/1.16 ((~hskp26) | c0_1(a418)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1038, 1033])).
% 1.36/1.16 tff(1040,plain,
% 1.36/1.16 ((~hskp26) | c0_1(a418)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1039, 1033])).
% 1.36/1.16 tff(1041,plain,
% 1.36/1.16 ((~hskp26) | c0_1(a418)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1040, 1033])).
% 1.36/1.16 tff(1042,plain,
% 1.36/1.16 ((~hskp26) | c0_1(a418)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1041, 1033])).
% 1.36/1.16 tff(1043,plain,
% 1.36/1.16 (c0_1(a418)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1042, 1020])).
% 1.36/1.16 tff(1044,assumption,(~hskp19), introduced(assumption)).
% 1.36/1.16 tff(1045,plain,
% 1.36/1.16 (~c0_1(a360)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[926, 1044, 790, 177])).
% 1.36/1.16 tff(1046,plain,
% 1.36/1.16 (hskp28),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[591, 1044])).
% 1.36/1.16 tff(1047,plain,
% 1.36/1.16 (c3_1(a365)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[43, 1046])).
% 1.36/1.16 tff(1048,plain,
% 1.36/1.16 (c2_1(a365)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[54, 1046])).
% 1.36/1.16 tff(1049,plain,
% 1.36/1.16 (c1_1(a365)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[32, 1046])).
% 1.36/1.16 tff(1050,plain,
% 1.36/1.16 (~hskp13),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[451, 1049, 1048, 1047])).
% 1.36/1.16 tff(1051,plain,
% 1.36/1.16 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a360))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a360))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1052,plain,
% 1.36/1.16 ((hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a360) | c0_1(a360) | c3_1(a360)) <=> (hskp13 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a360))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1053,plain,
% 1.36/1.16 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a360)))),
% 1.36/1.16 inference(monotonicity,[status(thm)],[1052])).
% 1.36/1.16 tff(1054,plain,
% 1.36/1.16 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a360))),
% 1.36/1.16 inference(transitivity,[status(thm)],[1053, 1051])).
% 1.36/1.16 tff(1055,plain,
% 1.36/1.16 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a360) | c0_1(a360) | c3_1(a360))),
% 1.36/1.16 inference(quant_inst,[status(thm)],[])).
% 1.36/1.16 tff(1056,plain,
% 1.36/1.16 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a360)),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1055, 1054])).
% 1.36/1.16 tff(1057,plain,
% 1.36/1.16 ($false),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1056, 117, 1050, 1049, 1048, 1047, 788, 789, 134, 1045])).
% 1.36/1.16 tff(1058,plain,(hskp19 | c2_1(a360) | c3_1(a360) | c1_1(a360) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.36/1.16 tff(1059,plain,
% 1.36/1.16 (hskp19),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1058, 177, 789, 790, 788])).
% 1.36/1.16 tff(1060,plain,
% 1.36/1.16 (~c1_1(a387)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[236, 1059])).
% 1.36/1.16 tff(1061,plain,
% 1.36/1.16 (~c0_1(a387)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[242, 1059])).
% 1.36/1.16 tff(1062,plain,
% 1.36/1.16 (~c2_1(a387)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[230, 1059])).
% 1.36/1.16 tff(1063,plain,
% 1.36/1.16 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.36/1.16 inference(bind,[status(th)],[])).
% 1.36/1.16 tff(1064,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.16 inference(quant_intro,[status(thm)],[1063])).
% 1.36/1.16 tff(1065,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1066,plain,
% 1.36/1.16 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.36/1.16 inference(bind,[status(th)],[])).
% 1.36/1.16 tff(1067,plain,
% 1.36/1.16 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.16 inference(quant_intro,[status(thm)],[1066])).
% 1.36/1.16 tff(1068,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.36/1.16 tff(1069,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 1.36/1.16 tff(1070,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1069, 1065])).
% 1.36/1.16 tff(1071,plain,(
% 1.36/1.16 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.16 inference(skolemize,[status(sab)],[1070])).
% 1.36/1.16 tff(1072,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1071, 1064])).
% 1.36/1.16 tff(1073,plain,
% 1.36/1.16 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.36/1.16 inference(bind,[status(th)],[])).
% 1.36/1.16 tff(1074,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.16 inference(quant_intro,[status(thm)],[1073])).
% 1.36/1.16 tff(1075,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1076,plain,
% 1.36/1.16 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp31) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp31))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp31) <=> (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.36/1.16 inference(bind,[status(th)],[])).
% 1.36/1.16 tff(1077,plain,
% 1.36/1.16 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.16 inference(quant_intro,[status(thm)],[1076])).
% 1.36/1.16 tff(1078,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.36/1.16 tff(1079,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 1.36/1.16 tff(1080,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1079, 1075])).
% 1.36/1.16 tff(1081,plain,(
% 1.36/1.16 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.16 inference(skolemize,[status(sab)],[1080])).
% 1.36/1.16 tff(1082,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1081, 1074])).
% 1.36/1.16 tff(1083,plain,
% 1.36/1.16 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.36/1.16 inference(bind,[status(th)],[])).
% 1.36/1.16 tff(1084,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.16 inference(quant_intro,[status(thm)],[1083])).
% 1.36/1.16 tff(1085,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1086,plain,
% 1.36/1.16 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(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) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.36/1.16 inference(bind,[status(th)],[])).
% 1.36/1.16 tff(1087,plain,
% 1.36/1.16 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.16 inference(quant_intro,[status(thm)],[1086])).
% 1.36/1.16 tff(1088,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 1.36/1.16 tff(1089,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 1.36/1.16 tff(1090,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1089, 1085])).
% 1.36/1.16 tff(1091,plain,(
% 1.36/1.16 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.16 inference(skolemize,[status(sab)],[1090])).
% 1.36/1.16 tff(1092,plain,
% 1.36/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1091, 1084])).
% 1.36/1.16 tff(1093,assumption,(~c3_1(a418)), introduced(assumption)).
% 1.36/1.16 tff(1094,assumption,(~c2_1(a418)), introduced(assumption)).
% 1.36/1.16 tff(1095,assumption,(c0_1(a418)), introduced(assumption)).
% 1.36/1.16 tff(1096,plain,
% 1.36/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c2_1(a418) | c3_1(a418) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c0_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a418) | c3_1(a418) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c0_1(a418)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1097,plain,
% 1.36/1.16 ((hskp1 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (hskp1 | c2_1(a418) | c3_1(a418) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c0_1(a418)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1098,plain,
% 1.36/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c2_1(a418) | c3_1(a418) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c0_1(a418))))),
% 1.36/1.16 inference(monotonicity,[status(thm)],[1097])).
% 1.36/1.16 tff(1099,plain,
% 1.36/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a418) | c3_1(a418) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c0_1(a418)))),
% 1.36/1.16 inference(transitivity,[status(thm)],[1098, 1096])).
% 1.36/1.16 tff(1100,plain,
% 1.36/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 1.36/1.16 inference(quant_inst,[status(thm)],[])).
% 1.36/1.16 tff(1101,plain,
% 1.36/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a418) | c3_1(a418) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | (~c0_1(a418))),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1100, 1099])).
% 1.36/1.17 tff(1102,plain,
% 1.36/1.17 (hskp1),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[1101, 117, 1095, 1094, 1093, 640, 638, 639, 1092])).
% 1.36/1.17 tff(1103,plain,
% 1.36/1.17 (((~hskp1) | (~c1_1(a355))) <=> ((~hskp1) | (~c1_1(a355)))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1104,plain,
% 1.36/1.17 (((~c1_1(a355)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a355)))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1105,axiom,((~c1_1(a355)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.36/1.17 tff(1106,plain,
% 1.36/1.17 ((~hskp1) | (~c1_1(a355))),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 1.36/1.17 tff(1107,plain,
% 1.36/1.17 ((~hskp1) | (~c1_1(a355))),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1106, 1103])).
% 1.36/1.17 tff(1108,plain,
% 1.36/1.17 (~c1_1(a355)),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[1107, 1102])).
% 1.36/1.17 tff(1109,plain,
% 1.36/1.17 (((~hskp1) | c3_1(a355)) <=> ((~hskp1) | c3_1(a355))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1110,axiom,((~hskp1) | c3_1(a355)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.36/1.17 tff(1111,plain,
% 1.36/1.17 ((~hskp1) | c3_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 1.36/1.17 tff(1112,plain,
% 1.36/1.17 ((~hskp1) | c3_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1111, 1109])).
% 1.36/1.17 tff(1113,plain,
% 1.36/1.17 ((~hskp1) | c3_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1112, 1109])).
% 1.36/1.17 tff(1114,plain,
% 1.36/1.17 ((~hskp1) | c3_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1113, 1109])).
% 1.36/1.17 tff(1115,plain,
% 1.36/1.17 ((~hskp1) | c3_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1114, 1109])).
% 1.36/1.17 tff(1116,plain,
% 1.36/1.17 ((~hskp1) | c3_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1115, 1109])).
% 1.36/1.17 tff(1117,plain,
% 1.36/1.17 ((~hskp1) | c3_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1116, 1109])).
% 1.36/1.17 tff(1118,plain,
% 1.36/1.17 ((~hskp1) | c3_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1117, 1109])).
% 1.36/1.17 tff(1119,plain,
% 1.36/1.17 (c3_1(a355)),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[1118, 1102])).
% 1.36/1.17 tff(1120,plain,
% 1.36/1.17 (((~hskp1) | c0_1(a355)) <=> ((~hskp1) | c0_1(a355))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1121,axiom,((~hskp1) | c0_1(a355)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.36/1.17 tff(1122,plain,
% 1.36/1.17 ((~hskp1) | c0_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 1.36/1.17 tff(1123,plain,
% 1.36/1.17 ((~hskp1) | c0_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1122, 1120])).
% 1.36/1.17 tff(1124,plain,
% 1.36/1.17 ((~hskp1) | c0_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1123, 1120])).
% 1.36/1.17 tff(1125,plain,
% 1.36/1.17 ((~hskp1) | c0_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1124, 1120])).
% 1.36/1.17 tff(1126,plain,
% 1.36/1.17 ((~hskp1) | c0_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1125, 1120])).
% 1.36/1.17 tff(1127,plain,
% 1.36/1.17 ((~hskp1) | c0_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1126, 1120])).
% 1.36/1.17 tff(1128,plain,
% 1.36/1.17 ((~hskp1) | c0_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1127, 1120])).
% 1.36/1.17 tff(1129,plain,
% 1.36/1.17 ((~hskp1) | c0_1(a355)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1128, 1120])).
% 1.36/1.17 tff(1130,plain,
% 1.36/1.17 (c0_1(a355)),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[1129, 1102])).
% 1.36/1.17 tff(1131,plain,
% 1.36/1.17 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp31 | c2_1(a418) | c3_1(a418) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c0_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp31 | c2_1(a418) | c3_1(a418) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c0_1(a418)))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1132,plain,
% 1.36/1.17 ((hskp31 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355))) <=> (hskp31 | c2_1(a418) | c3_1(a418) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c0_1(a418)))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1133,plain,
% 1.36/1.17 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp31 | c2_1(a418) | c3_1(a418) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c0_1(a418))))),
% 1.36/1.17 inference(monotonicity,[status(thm)],[1132])).
% 1.36/1.17 tff(1134,plain,
% 1.36/1.17 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp31 | c2_1(a418) | c3_1(a418) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c0_1(a418)))),
% 1.36/1.17 inference(transitivity,[status(thm)],[1133, 1131])).
% 1.36/1.17 tff(1135,plain,
% 1.36/1.17 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c0_1(a418)) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)))),
% 1.36/1.17 inference(quant_inst,[status(thm)],[])).
% 1.36/1.17 tff(1136,plain,
% 1.36/1.17 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp31 | c2_1(a418) | c3_1(a418) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c0_1(a418))),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1135, 1134])).
% 1.36/1.17 tff(1137,plain,
% 1.36/1.17 (hskp31),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[1136, 117, 1095, 1130, 1119, 1094, 1093, 1108, 1082])).
% 1.36/1.17 tff(1138,plain,
% 1.36/1.17 (((~hskp31) | c3_1(a410)) <=> ((~hskp31) | c3_1(a410))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1139,axiom,((~hskp31) | c3_1(a410)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.36/1.17 tff(1140,plain,
% 1.36/1.17 ((~hskp31) | c3_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 1.36/1.17 tff(1141,plain,
% 1.36/1.17 ((~hskp31) | c3_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1140, 1138])).
% 1.36/1.17 tff(1142,plain,
% 1.36/1.17 ((~hskp31) | c3_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1141, 1138])).
% 1.36/1.17 tff(1143,plain,
% 1.36/1.17 ((~hskp31) | c3_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1142, 1138])).
% 1.36/1.17 tff(1144,plain,
% 1.36/1.17 ((~hskp31) | c3_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1143, 1138])).
% 1.36/1.17 tff(1145,plain,
% 1.36/1.17 ((~hskp31) | c3_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1144, 1138])).
% 1.36/1.17 tff(1146,plain,
% 1.36/1.17 ((~hskp31) | c3_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1145, 1138])).
% 1.36/1.17 tff(1147,plain,
% 1.36/1.17 ((~hskp31) | c3_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1146, 1138])).
% 1.36/1.17 tff(1148,plain,
% 1.36/1.17 (c3_1(a410)),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[1147, 1137])).
% 1.36/1.17 tff(1149,plain,
% 1.36/1.17 (((~hskp31) | c2_1(a410)) <=> ((~hskp31) | c2_1(a410))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1150,axiom,((~hskp31) | c2_1(a410)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.36/1.17 tff(1151,plain,
% 1.36/1.17 ((~hskp31) | c2_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 1.36/1.17 tff(1152,plain,
% 1.36/1.17 ((~hskp31) | c2_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1151, 1149])).
% 1.36/1.17 tff(1153,plain,
% 1.36/1.17 ((~hskp31) | c2_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1152, 1149])).
% 1.36/1.17 tff(1154,plain,
% 1.36/1.17 ((~hskp31) | c2_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1153, 1149])).
% 1.36/1.17 tff(1155,plain,
% 1.36/1.17 ((~hskp31) | c2_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1154, 1149])).
% 1.36/1.17 tff(1156,plain,
% 1.36/1.17 ((~hskp31) | c2_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1155, 1149])).
% 1.36/1.17 tff(1157,plain,
% 1.36/1.17 ((~hskp31) | c2_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1156, 1149])).
% 1.36/1.17 tff(1158,plain,
% 1.36/1.17 ((~hskp31) | c2_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1157, 1149])).
% 1.36/1.17 tff(1159,plain,
% 1.36/1.17 (c2_1(a410)),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[1158, 1137])).
% 1.36/1.17 tff(1160,plain,
% 1.36/1.17 (((~hskp31) | c0_1(a410)) <=> ((~hskp31) | c0_1(a410))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1161,axiom,((~hskp31) | c0_1(a410)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 1.36/1.17 tff(1162,plain,
% 1.36/1.17 ((~hskp31) | c0_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 1.36/1.17 tff(1163,plain,
% 1.36/1.17 ((~hskp31) | c0_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1162, 1160])).
% 1.36/1.17 tff(1164,plain,
% 1.36/1.17 ((~hskp31) | c0_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1163, 1160])).
% 1.36/1.17 tff(1165,plain,
% 1.36/1.17 ((~hskp31) | c0_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1164, 1160])).
% 1.36/1.17 tff(1166,plain,
% 1.36/1.17 ((~hskp31) | c0_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1165, 1160])).
% 1.36/1.17 tff(1167,plain,
% 1.36/1.17 ((~hskp31) | c0_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1166, 1160])).
% 1.36/1.17 tff(1168,plain,
% 1.36/1.17 ((~hskp31) | c0_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1167, 1160])).
% 1.36/1.17 tff(1169,plain,
% 1.36/1.17 ((~hskp31) | c0_1(a410)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1168, 1160])).
% 1.36/1.17 tff(1170,plain,
% 1.36/1.17 (c0_1(a410)),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[1169, 1137])).
% 1.36/1.17 tff(1171,plain,
% 1.36/1.17 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c1_1(a388)))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1172,plain,
% 1.36/1.17 ((hskp28 | (~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388))) <=> (hskp28 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c1_1(a388)))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1173,plain,
% 1.36/1.17 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c1_1(a388))))),
% 1.36/1.17 inference(monotonicity,[status(thm)],[1172])).
% 1.36/1.17 tff(1174,plain,
% 1.36/1.17 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c1_1(a388)))),
% 1.36/1.17 inference(transitivity,[status(thm)],[1173, 1171])).
% 1.36/1.17 tff(1175,plain,
% 1.36/1.17 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)))),
% 1.36/1.17 inference(quant_inst,[status(thm)],[])).
% 1.36/1.17 tff(1176,plain,
% 1.36/1.17 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c1_1(a388))),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 1.36/1.17 tff(1177,plain,
% 1.36/1.17 (hskp28),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[1176, 117, 1170, 1159, 1148, 898, 333, 332, 1072])).
% 1.36/1.17 tff(1178,plain,
% 1.36/1.17 (c3_1(a365)),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[43, 1177])).
% 1.36/1.17 tff(1179,plain,
% 1.36/1.17 (c2_1(a365)),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[54, 1177])).
% 1.36/1.17 tff(1180,plain,
% 1.36/1.17 (c1_1(a365)),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[32, 1177])).
% 1.36/1.17 tff(1181,plain,
% 1.36/1.17 (~hskp13),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[451, 1180, 1179, 1178])).
% 1.36/1.17 tff(1182,plain,
% 1.36/1.17 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a387))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a387))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1183,plain,
% 1.36/1.17 ((hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | c3_1(a387)) <=> (hskp13 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a387))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1184,plain,
% 1.36/1.17 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | c3_1(a387))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a387)))),
% 1.36/1.17 inference(monotonicity,[status(thm)],[1183])).
% 1.36/1.17 tff(1185,plain,
% 1.36/1.17 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | c3_1(a387))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a387))),
% 1.36/1.17 inference(transitivity,[status(thm)],[1184, 1182])).
% 1.36/1.17 tff(1186,plain,
% 1.36/1.17 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | c3_1(a387))),
% 1.36/1.17 inference(quant_inst,[status(thm)],[])).
% 1.36/1.17 tff(1187,plain,
% 1.36/1.17 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c3_1(a387)),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 1.36/1.17 tff(1188,plain,
% 1.36/1.17 (hskp13 | c3_1(a387)),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[1187, 117, 1180, 1179, 1178, 640, 639, 134])).
% 1.36/1.17 tff(1189,plain,
% 1.36/1.17 (c3_1(a387)),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[1188, 1181])).
% 1.36/1.17 tff(1190,plain,
% 1.36/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a387)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a387)))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1191,plain,
% 1.36/1.17 (((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387))) <=> (c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a387)))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1192,plain,
% 1.36/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a387))))),
% 1.36/1.17 inference(monotonicity,[status(thm)],[1191])).
% 1.36/1.17 tff(1193,plain,
% 1.36/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a387)))),
% 1.36/1.17 inference(transitivity,[status(thm)],[1192, 1190])).
% 1.36/1.17 tff(1194,plain,
% 1.36/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a365)) | (~c0_1(a365)) | (~c1_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | (~c0_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387)))),
% 1.36/1.17 inference(quant_inst,[status(thm)],[])).
% 1.36/1.17 tff(1195,plain,
% 1.36/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c0_1(a365)) | (~c3_1(a387))),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1194, 1193])).
% 1.36/1.17 tff(1196,plain,
% 1.36/1.17 ((~c0_1(a365)) | (~c3_1(a387))),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[1195, 117, 1180, 1179, 1178, 640, 639, 66])).
% 1.36/1.17 tff(1197,plain,
% 1.36/1.17 (~c0_1(a365)),
% 1.36/1.17 inference(unit_resolution,[status(thm)],[1196, 1189])).
% 1.36/1.17 tff(1198,plain,
% 1.36/1.17 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.36/1.17 inference(bind,[status(th)],[])).
% 1.36/1.17 tff(1199,plain,
% 1.36/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.36/1.17 inference(quant_intro,[status(thm)],[1198])).
% 1.36/1.17 tff(1200,plain,
% 1.36/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1201,plain,
% 1.36/1.17 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.36/1.17 inference(bind,[status(th)],[])).
% 1.36/1.17 tff(1202,plain,
% 1.36/1.17 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.36/1.17 inference(quant_intro,[status(thm)],[1201])).
% 1.36/1.17 tff(1203,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 1.36/1.17 tff(1204,plain,
% 1.36/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 1.36/1.17 tff(1205,plain,
% 1.36/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1204, 1200])).
% 1.36/1.17 tff(1206,plain,(
% 1.36/1.17 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.36/1.17 inference(skolemize,[status(sab)],[1205])).
% 1.36/1.17 tff(1207,plain,
% 1.36/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1206, 1199])).
% 1.36/1.17 tff(1208,plain,
% 1.36/1.17 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.36/1.17 inference(bind,[status(th)],[])).
% 1.36/1.17 tff(1209,plain,
% 1.36/1.17 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.36/1.17 inference(quant_intro,[status(thm)],[1208])).
% 1.36/1.17 tff(1210,plain,
% 1.36/1.17 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1211,plain,
% 1.36/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp23))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.36/1.17 inference(bind,[status(th)],[])).
% 1.36/1.17 tff(1212,plain,
% 1.36/1.17 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.36/1.17 inference(quant_intro,[status(thm)],[1211])).
% 1.36/1.17 tff(1213,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 1.36/1.17 tff(1214,plain,
% 1.36/1.17 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 1.36/1.17 tff(1215,plain,
% 1.36/1.17 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1214, 1210])).
% 1.36/1.17 tff(1216,plain,(
% 1.36/1.17 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.36/1.17 inference(skolemize,[status(sab)],[1215])).
% 1.36/1.17 tff(1217,plain,
% 1.36/1.17 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.36/1.17 inference(modus_ponens,[status(thm)],[1216, 1209])).
% 1.36/1.17 tff(1218,plain,
% 1.36/1.17 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a387) | c2_1(a387) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a387) | c2_1(a387) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c3_1(a387)))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1219,plain,
% 1.36/1.17 ((hskp23 | (~ndr1_0) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)) | c2_1(a387) | c1_1(a387) | (~c3_1(a387))) <=> (hskp23 | c1_1(a387) | c2_1(a387) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c3_1(a387)))),
% 1.36/1.17 inference(rewrite,[status(thm)],[])).
% 1.36/1.17 tff(1220,plain,
% 1.36/1.17 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)) | c2_1(a387) | c1_1(a387) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a387) | c2_1(a387) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c3_1(a387))))),
% 1.36/1.17 inference(monotonicity,[status(thm)],[1219])).
% 1.36/1.17 tff(1221,plain,
% 1.36/1.17 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)) | c2_1(a387) | c1_1(a387) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a387) | c2_1(a387) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c3_1(a387)))),
% 1.36/1.17 inference(transitivity,[status(thm)],[1220, 1218])).
% 1.36/1.17 tff(1222,plain,
% 1.36/1.17 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c1_1(a355) | (~c3_1(a355)) | (~c0_1(a355)) | c2_1(a387) | c1_1(a387) | (~c3_1(a387)))),
% 1.36/1.18 inference(quant_inst,[status(thm)],[])).
% 1.36/1.18 tff(1223,plain,
% 1.36/1.18 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a387) | c2_1(a387) | c1_1(a355) | (~ndr1_0) | (~c3_1(a355)) | (~c0_1(a355)) | (~c3_1(a387))),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 1.36/1.18 tff(1224,plain,
% 1.36/1.18 (hskp23 | (~c3_1(a387))),
% 1.36/1.18 inference(unit_resolution,[status(thm)],[1223, 117, 1130, 1119, 638, 639, 1108, 1217])).
% 1.36/1.18 tff(1225,plain,
% 1.36/1.18 (hskp23),
% 1.36/1.18 inference(unit_resolution,[status(thm)],[1224, 1189])).
% 1.36/1.18 tff(1226,plain,
% 1.36/1.18 (((~hskp23) | (~c2_1(a398))) <=> ((~hskp23) | (~c2_1(a398)))),
% 1.36/1.18 inference(rewrite,[status(thm)],[])).
% 1.36/1.18 tff(1227,plain,
% 1.36/1.18 (((~c2_1(a398)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a398)))),
% 1.36/1.18 inference(rewrite,[status(thm)],[])).
% 1.36/1.18 tff(1228,axiom,((~c2_1(a398)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.36/1.18 tff(1229,plain,
% 1.36/1.18 ((~hskp23) | (~c2_1(a398))),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 1.36/1.18 tff(1230,plain,
% 1.36/1.18 ((~hskp23) | (~c2_1(a398))),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1229, 1226])).
% 1.36/1.18 tff(1231,plain,
% 1.36/1.18 (~c2_1(a398)),
% 1.36/1.18 inference(unit_resolution,[status(thm)],[1230, 1225])).
% 1.36/1.18 tff(1232,plain,
% 1.36/1.18 (((~hskp23) | c3_1(a398)) <=> ((~hskp23) | c3_1(a398))),
% 1.36/1.18 inference(rewrite,[status(thm)],[])).
% 1.36/1.18 tff(1233,axiom,((~hskp23) | c3_1(a398)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.36/1.18 tff(1234,plain,
% 1.36/1.18 ((~hskp23) | c3_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 1.36/1.18 tff(1235,plain,
% 1.36/1.18 ((~hskp23) | c3_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1234, 1232])).
% 1.36/1.18 tff(1236,plain,
% 1.36/1.18 ((~hskp23) | c3_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1235, 1232])).
% 1.36/1.18 tff(1237,plain,
% 1.36/1.18 ((~hskp23) | c3_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1236, 1232])).
% 1.36/1.18 tff(1238,plain,
% 1.36/1.18 ((~hskp23) | c3_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1237, 1232])).
% 1.36/1.18 tff(1239,plain,
% 1.36/1.18 ((~hskp23) | c3_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1238, 1232])).
% 1.36/1.18 tff(1240,plain,
% 1.36/1.18 ((~hskp23) | c3_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1239, 1232])).
% 1.36/1.18 tff(1241,plain,
% 1.36/1.18 ((~hskp23) | c3_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1240, 1232])).
% 1.36/1.18 tff(1242,plain,
% 1.36/1.18 (c3_1(a398)),
% 1.36/1.18 inference(unit_resolution,[status(thm)],[1241, 1225])).
% 1.36/1.18 tff(1243,plain,
% 1.36/1.18 (((~hskp23) | c1_1(a398)) <=> ((~hskp23) | c1_1(a398))),
% 1.36/1.18 inference(rewrite,[status(thm)],[])).
% 1.36/1.18 tff(1244,axiom,((~hskp23) | c1_1(a398)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.36/1.18 tff(1245,plain,
% 1.36/1.18 ((~hskp23) | c1_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 1.36/1.18 tff(1246,plain,
% 1.36/1.18 ((~hskp23) | c1_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1245, 1243])).
% 1.36/1.18 tff(1247,plain,
% 1.36/1.18 ((~hskp23) | c1_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1246, 1243])).
% 1.36/1.18 tff(1248,plain,
% 1.36/1.18 ((~hskp23) | c1_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1247, 1243])).
% 1.36/1.18 tff(1249,plain,
% 1.36/1.18 ((~hskp23) | c1_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1248, 1243])).
% 1.36/1.18 tff(1250,plain,
% 1.36/1.18 ((~hskp23) | c1_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1249, 1243])).
% 1.36/1.18 tff(1251,plain,
% 1.36/1.18 ((~hskp23) | c1_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1250, 1243])).
% 1.36/1.18 tff(1252,plain,
% 1.36/1.18 ((~hskp23) | c1_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1251, 1243])).
% 1.36/1.18 tff(1253,plain,
% 1.36/1.18 (c1_1(a398)),
% 1.36/1.18 inference(unit_resolution,[status(thm)],[1252, 1225])).
% 1.36/1.18 tff(1254,plain,
% 1.36/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a398) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a398))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a398) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a398))),
% 1.36/1.18 inference(rewrite,[status(thm)],[])).
% 1.36/1.18 tff(1255,plain,
% 1.36/1.18 (((~ndr1_0) | c2_1(a398) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a365) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a398) | c0_1(a398) | (~c1_1(a398))) <=> (c2_1(a398) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a398))),
% 1.36/1.18 inference(rewrite,[status(thm)],[])).
% 1.36/1.18 tff(1256,plain,
% 1.36/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a398) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a365) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a398) | c0_1(a398) | (~c1_1(a398)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a398) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a398)))),
% 1.36/1.18 inference(monotonicity,[status(thm)],[1255])).
% 1.36/1.18 tff(1257,plain,
% 1.36/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a398) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a365) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a398) | c0_1(a398) | (~c1_1(a398)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a398) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a398))),
% 1.36/1.18 inference(transitivity,[status(thm)],[1256, 1254])).
% 1.36/1.18 tff(1258,plain,
% 1.36/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a398) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a365) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a398) | c0_1(a398) | (~c1_1(a398)))),
% 1.36/1.18 inference(quant_inst,[status(thm)],[])).
% 1.36/1.18 tff(1259,plain,
% 1.36/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a398) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | c0_1(a365) | (~c3_1(a398)) | (~c1_1(a398)) | c0_1(a398)),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 1.36/1.18 tff(1260,plain,
% 1.36/1.18 (c0_1(a398)),
% 1.36/1.18 inference(unit_resolution,[status(thm)],[1259, 117, 1180, 1179, 1253, 1242, 1231, 1207, 1197])).
% 1.36/1.18 tff(1261,plain,
% 1.36/1.18 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))))),
% 1.36/1.18 inference(bind,[status(th)],[])).
% 1.36/1.18 tff(1262,plain,
% 1.36/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.36/1.18 inference(quant_intro,[status(thm)],[1261])).
% 1.36/1.18 tff(1263,plain,
% 1.36/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.36/1.18 inference(rewrite,[status(thm)],[])).
% 1.36/1.18 tff(1264,plain,
% 1.36/1.18 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))))),
% 1.36/1.18 inference(bind,[status(th)],[])).
% 1.36/1.18 tff(1265,plain,
% 1.36/1.18 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.36/1.18 inference(quant_intro,[status(thm)],[1264])).
% 1.36/1.18 tff(1266,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause208')).
% 1.36/1.18 tff(1267,plain,
% 1.36/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 1.36/1.18 tff(1268,plain,
% 1.36/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1267, 1263])).
% 1.36/1.18 tff(1269,plain,(
% 1.36/1.18 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.36/1.18 inference(skolemize,[status(sab)],[1268])).
% 1.36/1.18 tff(1270,plain,
% 1.36/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1269, 1262])).
% 1.36/1.18 tff(1271,plain,
% 1.36/1.18 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.36/1.18 inference(bind,[status(th)],[])).
% 1.36/1.18 tff(1272,plain,
% 1.36/1.18 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.18 inference(quant_intro,[status(thm)],[1271])).
% 1.36/1.18 tff(1273,plain,
% 1.36/1.18 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.18 inference(rewrite,[status(thm)],[])).
% 1.36/1.18 tff(1274,plain,
% 1.36/1.18 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_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) | (~c3_1(U)) | (~c1_1(U)) | (~c2_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) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.36/1.18 inference(bind,[status(th)],[])).
% 1.36/1.18 tff(1275,plain,
% 1.36/1.18 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.18 inference(quant_intro,[status(thm)],[1274])).
% 1.36/1.18 tff(1276,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)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 1.36/1.18 tff(1277,plain,
% 1.36/1.18 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 1.36/1.18 tff(1278,plain,
% 1.36/1.18 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1277, 1273])).
% 1.36/1.18 tff(1279,plain,(
% 1.36/1.18 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.18 inference(skolemize,[status(sab)],[1278])).
% 1.36/1.18 tff(1280,plain,
% 1.36/1.18 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.36/1.18 inference(modus_ponens,[status(thm)],[1279, 1272])).
% 1.36/1.18 tff(1281,plain,
% 1.36/1.18 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c3_1(a387)))),
% 1.36/1.18 inference(rewrite,[status(thm)],[])).
% 1.36/1.18 tff(1282,plain,
% 1.36/1.18 ((hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387))) <=> (hskp16 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c3_1(a387)))),
% 1.36/1.18 inference(rewrite,[status(thm)],[])).
% 1.36/1.18 tff(1283,plain,
% 1.36/1.18 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c3_1(a387))))),
% 1.45/1.18 inference(monotonicity,[status(thm)],[1282])).
% 1.45/1.18 tff(1284,plain,
% 1.45/1.18 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c3_1(a387)))),
% 1.45/1.18 inference(transitivity,[status(thm)],[1283, 1281])).
% 1.45/1.18 tff(1285,plain,
% 1.45/1.18 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a387) | c0_1(a387) | (~c3_1(a387)))),
% 1.45/1.18 inference(quant_inst,[status(thm)],[])).
% 1.45/1.18 tff(1286,plain,
% 1.45/1.18 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a387) | c2_1(a387) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | (~c3_1(a387))),
% 1.45/1.18 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 1.45/1.18 tff(1287,plain,
% 1.45/1.18 (hskp16 | (~c3_1(a387))),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[1286, 117, 1180, 1179, 1178, 640, 639, 1280])).
% 1.45/1.18 tff(1288,plain,
% 1.45/1.18 (hskp16),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[1287, 1189])).
% 1.45/1.18 tff(1289,plain,
% 1.45/1.18 (~c3_1(a379)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[564, 1288])).
% 1.45/1.18 tff(1290,plain,
% 1.45/1.18 (~c1_1(a379)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[540, 1288])).
% 1.45/1.18 tff(1291,plain,
% 1.45/1.18 (c2_1(a379)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[551, 1288])).
% 1.45/1.18 tff(1292,plain,
% 1.45/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a379) | c3_1(a379) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c2_1(a379)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a379) | c3_1(a379) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c2_1(a379)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)))),
% 1.45/1.18 inference(rewrite,[status(thm)],[])).
% 1.45/1.18 tff(1293,plain,
% 1.45/1.18 (((~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)) | c1_1(a379) | c3_1(a379) | (~c2_1(a379))) <=> (c1_1(a379) | c3_1(a379) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c2_1(a379)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)))),
% 1.45/1.18 inference(rewrite,[status(thm)],[])).
% 1.45/1.18 tff(1294,plain,
% 1.45/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)) | c1_1(a379) | c3_1(a379) | (~c2_1(a379)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a379) | c3_1(a379) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c2_1(a379)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398))))),
% 1.45/1.18 inference(monotonicity,[status(thm)],[1293])).
% 1.45/1.18 tff(1295,plain,
% 1.45/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)) | c1_1(a379) | c3_1(a379) | (~c2_1(a379)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a379) | c3_1(a379) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c2_1(a379)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)))),
% 1.45/1.18 inference(transitivity,[status(thm)],[1294, 1292])).
% 1.45/1.18 tff(1296,plain,
% 1.45/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a410)) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398)) | c1_1(a379) | c3_1(a379) | (~c2_1(a379)))),
% 1.45/1.18 inference(quant_inst,[status(thm)],[])).
% 1.45/1.18 tff(1297,plain,
% 1.45/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a379) | c3_1(a379) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c3_1(a410)) | (~c2_1(a379)) | (~c3_1(a398)) | (~c1_1(a398)) | (~c0_1(a398))),
% 1.45/1.18 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 1.45/1.18 tff(1298,plain,
% 1.45/1.18 ($false),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[1297, 117, 1170, 1159, 1148, 1253, 1242, 1291, 1290, 1289, 1270, 1260])).
% 1.45/1.18 tff(1299,plain,(c2_1(a387) | c0_1(a387) | c1_1(a387) | c2_1(a388) | c3_1(a388) | (~c0_1(a418)) | c2_1(a418) | c3_1(a418)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.18 tff(1300,plain,
% 1.45/1.18 ($false),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[1299, 1062, 1061, 1060, 333, 332, 1043, 1032, 1026])).
% 1.45/1.18 tff(1301,plain,(hskp3 | c2_1(a388) | c3_1(a388) | c3_1(a360) | c1_1(a360) | c2_1(a360)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.18 tff(1302,plain,
% 1.45/1.18 (hskp3),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[1301, 332, 333, 789, 790, 788])).
% 1.45/1.18 tff(1303,plain,
% 1.45/1.18 (c1_1(a357)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[279, 1302])).
% 1.45/1.18 tff(1304,plain,
% 1.45/1.18 (~c0_1(a357)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[257, 1302])).
% 1.45/1.18 tff(1305,plain,
% 1.45/1.18 (c3_1(a357)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[268, 1302])).
% 1.45/1.18 tff(1306,plain,
% 1.45/1.18 (~hskp13),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[451, 33, 55, 44])).
% 1.45/1.18 tff(1307,plain,
% 1.45/1.18 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a388))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a388))),
% 1.45/1.18 inference(rewrite,[status(thm)],[])).
% 1.45/1.18 tff(1308,plain,
% 1.45/1.18 ((hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a388) | c0_1(a388) | c3_1(a388)) <=> (hskp13 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a388))),
% 1.45/1.18 inference(rewrite,[status(thm)],[])).
% 1.45/1.18 tff(1309,plain,
% 1.45/1.18 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a388)))),
% 1.45/1.18 inference(monotonicity,[status(thm)],[1308])).
% 1.45/1.18 tff(1310,plain,
% 1.45/1.18 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a388) | c0_1(a388) | c3_1(a388))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a388))),
% 1.45/1.18 inference(transitivity,[status(thm)],[1309, 1307])).
% 1.45/1.18 tff(1311,plain,
% 1.45/1.18 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a388) | c0_1(a388) | c3_1(a388))),
% 1.45/1.18 inference(quant_inst,[status(thm)],[])).
% 1.45/1.18 tff(1312,plain,
% 1.45/1.18 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a388) | c3_1(a388) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)) | c0_1(a388)),
% 1.45/1.18 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 1.45/1.18 tff(1313,plain,
% 1.45/1.18 (c0_1(a388)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[1312, 117, 1306, 33, 55, 44, 333, 332, 134])).
% 1.45/1.18 tff(1314,plain,
% 1.45/1.18 (c2_1(a357)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[344, 1313, 898, 334, 333, 332, 335])).
% 1.45/1.18 tff(1315,plain,
% 1.45/1.18 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.45/1.18 inference(bind,[status(th)],[])).
% 1.45/1.18 tff(1316,plain,
% 1.45/1.18 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.45/1.18 inference(quant_intro,[status(thm)],[1315])).
% 1.45/1.18 tff(1317,plain,
% 1.45/1.18 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.45/1.18 inference(rewrite,[status(thm)],[])).
% 1.45/1.18 tff(1318,plain,
% 1.45/1.18 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.45/1.19 inference(bind,[status(th)],[])).
% 1.45/1.19 tff(1319,plain,
% 1.45/1.19 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.45/1.19 inference(quant_intro,[status(thm)],[1318])).
% 1.45/1.19 tff(1320,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.45/1.19 tff(1321,plain,
% 1.45/1.19 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 1.45/1.19 tff(1322,plain,
% 1.45/1.19 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1321, 1317])).
% 1.45/1.19 tff(1323,plain,(
% 1.45/1.19 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.45/1.19 inference(skolemize,[status(sab)],[1322])).
% 1.45/1.19 tff(1324,plain,
% 1.45/1.19 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1323, 1316])).
% 1.45/1.19 tff(1325,assumption,(~c0_1(a357)), introduced(assumption)).
% 1.45/1.19 tff(1326,plain,
% 1.45/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)) | (~c1_1(a388)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)) | (~c1_1(a388)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1327,plain,
% 1.45/1.19 ((hskp10 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357))) <=> (hskp10 | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)) | (~c1_1(a388)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1328,plain,
% 1.45/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)) | (~c1_1(a388))))),
% 1.45/1.19 inference(monotonicity,[status(thm)],[1327])).
% 1.45/1.19 tff(1329,plain,
% 1.45/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)) | (~c1_1(a388)))),
% 1.45/1.19 inference(transitivity,[status(thm)],[1328, 1326])).
% 1.45/1.19 tff(1330,plain,
% 1.45/1.19 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c0_1(a357) | (~c3_1(a357)) | (~c2_1(a357)))),
% 1.45/1.19 inference(quant_inst,[status(thm)],[])).
% 1.45/1.19 tff(1331,plain,
% 1.45/1.19 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~ndr1_0) | (~c2_1(a357)) | (~c3_1(a357)) | (~c1_1(a388))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 1.45/1.19 tff(1332,plain,
% 1.45/1.19 (hskp10 | (~c2_1(a357))),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1331, 117, 898, 334, 333, 332, 1325, 1324])).
% 1.45/1.19 tff(1333,plain,
% 1.45/1.19 (hskp10),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1332, 1314])).
% 1.45/1.19 tff(1334,plain,
% 1.45/1.19 (((~hskp10) | (~c3_1(a366))) <=> ((~hskp10) | (~c3_1(a366)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1335,plain,
% 1.45/1.19 (((~c3_1(a366)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a366)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1336,axiom,((~c3_1(a366)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.45/1.19 tff(1337,plain,
% 1.45/1.19 ((~hskp10) | (~c3_1(a366))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 1.45/1.19 tff(1338,plain,
% 1.45/1.19 ((~hskp10) | (~c3_1(a366))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1337, 1334])).
% 1.45/1.19 tff(1339,plain,
% 1.45/1.19 (~c3_1(a366)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1338, 1333])).
% 1.45/1.19 tff(1340,plain,
% 1.45/1.19 (((~hskp10) | (~c2_1(a366))) <=> ((~hskp10) | (~c2_1(a366)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1341,plain,
% 1.45/1.19 (((~c2_1(a366)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a366)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1342,axiom,((~c2_1(a366)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.45/1.19 tff(1343,plain,
% 1.45/1.19 ((~hskp10) | (~c2_1(a366))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 1.45/1.19 tff(1344,plain,
% 1.45/1.19 ((~hskp10) | (~c2_1(a366))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1343, 1340])).
% 1.45/1.19 tff(1345,plain,
% 1.45/1.19 (~c2_1(a366)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1344, 1333])).
% 1.45/1.19 tff(1346,plain,
% 1.45/1.19 (((~hskp10) | (~c0_1(a366))) <=> ((~hskp10) | (~c0_1(a366)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1347,plain,
% 1.45/1.19 (((~c0_1(a366)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a366)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1348,axiom,((~c0_1(a366)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.45/1.19 tff(1349,plain,
% 1.45/1.19 ((~hskp10) | (~c0_1(a366))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 1.45/1.19 tff(1350,plain,
% 1.45/1.19 ((~hskp10) | (~c0_1(a366))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1349, 1346])).
% 1.45/1.19 tff(1351,plain,
% 1.45/1.19 (~c0_1(a366)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1350, 1333])).
% 1.45/1.19 tff(1352,plain,
% 1.45/1.19 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a366) | c2_1(a366) | c3_1(a366) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a366) | c2_1(a366) | c3_1(a366) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1353,plain,
% 1.45/1.19 ((hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a366) | c0_1(a366) | c3_1(a366)) <=> (hskp13 | c0_1(a366) | c2_1(a366) | c3_1(a366) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1354,plain,
% 1.45/1.19 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a366) | c0_1(a366) | c3_1(a366))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a366) | c2_1(a366) | c3_1(a366) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365))))),
% 1.45/1.19 inference(monotonicity,[status(thm)],[1353])).
% 1.45/1.19 tff(1355,plain,
% 1.45/1.19 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a366) | c0_1(a366) | c3_1(a366))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a366) | c2_1(a366) | c3_1(a366) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365)))),
% 1.45/1.19 inference(transitivity,[status(thm)],[1354, 1352])).
% 1.45/1.19 tff(1356,plain,
% 1.45/1.19 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c3_1(a365)) | (~c1_1(a365)) | (~c2_1(a365)) | c2_1(a366) | c0_1(a366) | c3_1(a366))),
% 1.45/1.19 inference(quant_inst,[status(thm)],[])).
% 1.45/1.19 tff(1357,plain,
% 1.45/1.19 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a366) | c2_1(a366) | c3_1(a366) | (~ndr1_0) | (~c1_1(a365)) | (~c2_1(a365)) | (~c3_1(a365))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 1.45/1.19 tff(1358,plain,
% 1.45/1.19 ($false),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1357, 117, 1306, 33, 55, 44, 1351, 1345, 1339, 134])).
% 1.45/1.19 tff(1359,plain,((~hskp28) | (~c3_1(a357)) | c2_1(a388) | c3_1(a388) | c0_1(a357) | (~c1_1(a357))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.19 tff(1360,plain,
% 1.45/1.19 (~hskp28),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1359, 1305, 333, 332, 1304, 1303])).
% 1.45/1.19 tff(1361,plain,
% 1.45/1.19 (hskp19),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[591, 1360])).
% 1.45/1.19 tff(1362,plain,
% 1.45/1.19 (~c0_1(a387)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[242, 1361])).
% 1.45/1.19 tff(1363,plain,
% 1.45/1.19 (~c1_1(a387)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[236, 1361])).
% 1.45/1.19 tff(1364,plain,
% 1.45/1.19 (c2_1(a387)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[949, 657, 333, 332, 638, 640])).
% 1.45/1.19 tff(1365,plain,
% 1.45/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a388) | c3_1(a388) | c0_1(a387) | c1_1(a387) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | (~c0_1(a360)) | c3_1(a387) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | c3_1(a388) | c0_1(a387) | c1_1(a387) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | (~c0_1(a360)) | c3_1(a387) | (~c1_1(a388)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1366,plain,
% 1.45/1.19 (((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a387) | c0_1(a387) | c3_1(a387)) <=> (c2_1(a388) | c3_1(a388) | c0_1(a387) | c1_1(a387) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | (~c0_1(a360)) | c3_1(a387) | (~c1_1(a388)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1367,plain,
% 1.45/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a387) | c0_1(a387) | c3_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a388) | c3_1(a388) | c0_1(a387) | c1_1(a387) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | (~c0_1(a360)) | c3_1(a387) | (~c1_1(a388))))),
% 1.45/1.19 inference(monotonicity,[status(thm)],[1366])).
% 1.45/1.19 tff(1368,plain,
% 1.45/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a387) | c0_1(a387) | c3_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | c3_1(a388) | c0_1(a387) | c1_1(a387) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | (~c0_1(a360)) | c3_1(a387) | (~c1_1(a388)))),
% 1.45/1.19 inference(transitivity,[status(thm)],[1367, 1365])).
% 1.45/1.19 tff(1369,plain,
% 1.45/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | c3_1(a388) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a387) | c0_1(a387) | c3_1(a387))),
% 1.45/1.19 inference(quant_inst,[status(thm)],[])).
% 1.45/1.19 tff(1370,plain,
% 1.46/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | c3_1(a388) | c0_1(a387) | c1_1(a387) | c1_1(a360) | c2_1(a360) | (~ndr1_0) | (~c0_1(a360)) | c3_1(a387) | (~c1_1(a388))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 1.46/1.19 tff(1371,plain,
% 1.46/1.19 ((~c0_1(a360)) | c3_1(a387)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1370, 117, 898, 333, 332, 640, 638, 790, 788, 776])).
% 1.46/1.19 tff(1372,plain,
% 1.46/1.19 (c3_1(a387)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1371, 925])).
% 1.46/1.19 tff(1373,plain,
% 1.46/1.19 (hskp0 | (~c2_1(a387)) | (~c3_1(a387))),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[967, 117, 640, 961])).
% 1.46/1.19 tff(1374,plain,
% 1.46/1.19 ($false),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1373, 1372, 1364, 657])).
% 1.46/1.19 tff(1375,plain,(hskp0 | c0_1(a387) | c2_1(a388) | c3_1(a388) | c1_1(a387) | c1_1(a360) | c2_1(a360) | c3_1(a360)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.19 tff(1376,plain,
% 1.46/1.19 (hskp0),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1375, 638, 333, 332, 640, 790, 788, 789])).
% 1.46/1.19 tff(1377,plain,
% 1.46/1.19 (~c2_1(a353)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[695, 1376])).
% 1.46/1.19 tff(1378,plain,
% 1.46/1.19 (c1_1(a353)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[706, 1376])).
% 1.46/1.19 tff(1379,plain,
% 1.46/1.19 (c0_1(a353)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[994, 1376])).
% 1.46/1.19 tff(1380,plain,
% 1.46/1.19 (~c3_1(a353)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1001, 117, 898, 1379, 1378, 333, 332, 1377, 329])).
% 1.46/1.19 tff(1381,plain,
% 1.46/1.19 (hskp26 | c3_1(a353)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1018, 117, 1379, 1377, 1012])).
% 1.46/1.19 tff(1382,plain,
% 1.46/1.19 (hskp26),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1381, 1380])).
% 1.46/1.19 tff(1383,plain,
% 1.46/1.19 (~c3_1(a418)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1025, 1382])).
% 1.46/1.19 tff(1384,plain,
% 1.46/1.19 (~c2_1(a418)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1031, 1382])).
% 1.46/1.19 tff(1385,plain,
% 1.46/1.19 (c0_1(a418)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1042, 1382])).
% 1.46/1.19 tff(1386,plain,
% 1.46/1.19 (c2_1(a387)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1299, 1385, 640, 333, 332, 638, 1384, 1383])).
% 1.46/1.19 tff(1387,plain,
% 1.46/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360))),
% 1.46/1.19 inference(rewrite,[status(thm)],[])).
% 1.46/1.19 tff(1388,plain,
% 1.46/1.19 (((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a360) | c0_1(a360) | c3_1(a360) | c2_1(a360) | c1_1(a360) | c0_1(a360)) <=> (c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360))),
% 1.46/1.19 inference(rewrite,[status(thm)],[])).
% 1.46/1.19 tff(1389,plain,
% 1.46/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a360) | c0_1(a360) | c3_1(a360) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360)))),
% 1.46/1.19 inference(monotonicity,[status(thm)],[1388])).
% 1.46/1.19 tff(1390,plain,
% 1.46/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a360) | c0_1(a360) | c3_1(a360) | c2_1(a360) | c1_1(a360) | c0_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360))),
% 1.46/1.19 inference(transitivity,[status(thm)],[1389, 1387])).
% 1.46/1.19 tff(1391,plain,
% 1.46/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a387) | c0_1(a387) | (~c2_1(a387)) | c1_1(a360) | c0_1(a360) | c3_1(a360) | c2_1(a360) | c1_1(a360) | c0_1(a360))),
% 1.46/1.19 inference(quant_inst,[status(thm)],[])).
% 1.46/1.19 tff(1392,plain,
% 1.46/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a387) | c1_1(a387) | (~c2_1(a387)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360)),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 1.46/1.19 tff(1393,plain,
% 1.46/1.19 ((~c2_1(a387)) | c0_1(a360)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1392, 117, 640, 638, 790, 788, 789, 10])).
% 1.46/1.19 tff(1394,plain,
% 1.46/1.19 (c0_1(a360)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1393, 1386])).
% 1.46/1.19 tff(1395,plain,
% 1.46/1.19 (c3_1(a387)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1371, 1394])).
% 1.46/1.19 tff(1396,plain,
% 1.46/1.19 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.46/1.19 inference(bind,[status(th)],[])).
% 1.46/1.19 tff(1397,plain,
% 1.46/1.19 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.46/1.19 inference(quant_intro,[status(thm)],[1396])).
% 1.46/1.19 tff(1398,plain,
% 1.46/1.19 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.46/1.19 inference(rewrite,[status(thm)],[])).
% 1.46/1.19 tff(1399,plain,
% 1.46/1.19 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.46/1.19 inference(bind,[status(th)],[])).
% 1.46/1.19 tff(1400,plain,
% 1.46/1.19 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.46/1.19 inference(quant_intro,[status(thm)],[1399])).
% 1.46/1.19 tff(1401,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 1.46/1.19 tff(1402,plain,
% 1.46/1.19 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 1.46/1.19 tff(1403,plain,
% 1.46/1.19 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[1402, 1398])).
% 1.46/1.19 tff(1404,plain,(
% 1.46/1.19 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.46/1.19 inference(skolemize,[status(sab)],[1403])).
% 1.46/1.19 tff(1405,plain,
% 1.46/1.19 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[1404, 1397])).
% 1.46/1.19 tff(1406,plain,
% 1.46/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a387) | c1_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a387) | c1_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c3_1(a387)))),
% 1.46/1.19 inference(rewrite,[status(thm)],[])).
% 1.46/1.19 tff(1407,plain,
% 1.46/1.19 ((hskp10 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | (~c3_1(a387))) <=> (hskp10 | c0_1(a387) | c1_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c3_1(a387)))),
% 1.46/1.19 inference(rewrite,[status(thm)],[])).
% 1.46/1.19 tff(1408,plain,
% 1.46/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a387) | c1_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c3_1(a387))))),
% 1.46/1.19 inference(monotonicity,[status(thm)],[1407])).
% 1.46/1.19 tff(1409,plain,
% 1.46/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a387) | c1_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c3_1(a387)))),
% 1.46/1.19 inference(transitivity,[status(thm)],[1408, 1406])).
% 1.46/1.19 tff(1410,plain,
% 1.46/1.19 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)) | c1_1(a387) | c0_1(a387) | (~c3_1(a387)))),
% 1.46/1.19 inference(quant_inst,[status(thm)],[])).
% 1.46/1.19 tff(1411,plain,
% 1.46/1.19 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a387) | c1_1(a387) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)) | (~c3_1(a387))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 1.46/1.19 tff(1412,plain,
% 1.46/1.19 (hskp10 | (~c3_1(a387))),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1411, 117, 421, 640, 638, 403, 397, 1405])).
% 1.46/1.19 tff(1413,plain,
% 1.46/1.19 (hskp10),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1412, 1395])).
% 1.46/1.19 tff(1414,plain,
% 1.46/1.19 (~c3_1(a366)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1338, 1413])).
% 1.46/1.19 tff(1415,plain,
% 1.46/1.19 (~c2_1(a366)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1344, 1413])).
% 1.46/1.19 tff(1416,plain,
% 1.46/1.19 (~c0_1(a366)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1350, 1413])).
% 1.46/1.19 tff(1417,plain,
% 1.46/1.19 (~hskp19),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[230, 1386])).
% 1.46/1.19 tff(1418,plain,
% 1.46/1.19 (hskp28),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[591, 1417])).
% 1.46/1.19 tff(1419,plain,
% 1.46/1.19 (c3_1(a365)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[43, 1418])).
% 1.46/1.19 tff(1420,plain,
% 1.46/1.19 (c2_1(a365)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[54, 1418])).
% 1.46/1.19 tff(1421,plain,
% 1.46/1.19 (c1_1(a365)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[32, 1418])).
% 1.46/1.19 tff(1422,plain,
% 1.46/1.19 (~hskp13),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[451, 1421, 1420, 1419])).
% 1.46/1.19 tff(1423,plain,
% 1.46/1.19 ($false),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1357, 117, 1422, 1421, 1420, 1419, 1416, 1415, 1414, 134])).
% 1.46/1.19 tff(1424,plain,(c1_1(a387) | c0_1(a387) | c2_1(a388) | c3_1(a388) | c1_1(a360) | c2_1(a360) | c3_1(a360)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.19 tff(1425,plain,
% 1.46/1.19 ($false),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1424, 1363, 1362, 333, 332, 790, 788, 789])).
% 1.46/1.19 tff(1426,plain,(c3_1(a388) | c2_1(a388) | c1_1(a360) | c2_1(a360) | c3_1(a360)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.19 tff(1427,plain,
% 1.46/1.19 (c3_1(a388)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1426, 333, 790, 788, 789])).
% 1.46/1.19 tff(1428,plain,
% 1.46/1.19 (~hskp20),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[292, 1427])).
% 1.46/1.19 tff(1429,assumption,(~hskp20), introduced(assumption)).
% 1.46/1.19 tff(1430,plain,
% 1.46/1.19 ($false),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[286, 117, 1429, 804, 803, 790, 788, 789, 802, 166])).
% 1.46/1.19 tff(1431,plain,((~hskp3) | hskp20 | c1_1(a360) | c2_1(a360) | c3_1(a360)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.19 tff(1432,plain,
% 1.46/1.19 (~hskp3),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1431, 1428, 790, 788, 789])).
% 1.46/1.19 tff(1433,plain,
% 1.46/1.19 (hskp19),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1058, 1432, 789, 790, 788])).
% 1.46/1.19 tff(1434,plain,
% 1.46/1.19 (~c0_1(a387)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[242, 1433])).
% 1.46/1.19 tff(1435,plain,
% 1.46/1.19 (~c1_1(a387)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[236, 1433])).
% 1.46/1.19 tff(1436,plain,
% 1.46/1.19 (c0_1(a388)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[868, 657, 333, 800])).
% 1.46/1.19 tff(1437,plain,
% 1.46/1.19 (hskp0 | (~c3_1(a387))),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[663, 117, 640, 638, 639, 656])).
% 1.46/1.19 tff(1438,plain,
% 1.46/1.19 (~c3_1(a387)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1437, 657])).
% 1.46/1.19 tff(1439,plain,
% 1.46/1.19 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.46/1.19 inference(bind,[status(th)],[])).
% 1.46/1.19 tff(1440,plain,
% 1.46/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.46/1.19 inference(quant_intro,[status(thm)],[1439])).
% 1.46/1.19 tff(1441,plain,
% 1.46/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.46/1.19 inference(rewrite,[status(thm)],[])).
% 1.46/1.19 tff(1442,plain,
% 1.46/1.19 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.46/1.19 inference(bind,[status(th)],[])).
% 1.46/1.19 tff(1443,plain,
% 1.46/1.19 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.46/1.19 inference(quant_intro,[status(thm)],[1442])).
% 1.46/1.19 tff(1444,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 1.46/1.19 tff(1445,plain,
% 1.46/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[1444, 1443])).
% 1.46/1.19 tff(1446,plain,
% 1.46/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[1445, 1441])).
% 1.46/1.19 tff(1447,plain,(
% 1.46/1.19 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.46/1.19 inference(skolemize,[status(sab)],[1446])).
% 1.46/1.19 tff(1448,plain,
% 1.46/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[1447, 1440])).
% 1.46/1.19 tff(1449,assumption,(c3_1(a388)), introduced(assumption)).
% 1.46/1.19 tff(1450,plain,
% 1.46/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c0_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c0_1(a388)))),
% 1.46/1.19 inference(rewrite,[status(thm)],[])).
% 1.46/1.19 tff(1451,plain,
% 1.46/1.19 (((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c0_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a387) | c1_1(a387) | c0_1(a387)) <=> (c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c0_1(a388)))),
% 1.46/1.19 inference(rewrite,[status(thm)],[])).
% 1.46/1.19 tff(1452,plain,
% 1.46/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c0_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c0_1(a388))))),
% 1.46/1.19 inference(monotonicity,[status(thm)],[1451])).
% 1.46/1.19 tff(1453,plain,
% 1.46/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c0_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a387) | c1_1(a387) | c0_1(a387))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c0_1(a388)))),
% 1.46/1.19 inference(transitivity,[status(thm)],[1452, 1450])).
% 1.46/1.19 tff(1454,plain,
% 1.46/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c0_1(a388)) | c2_1(a387) | c0_1(a387) | c3_1(a387) | c2_1(a387) | c1_1(a387) | c0_1(a387))),
% 1.46/1.19 inference(quant_inst,[status(thm)],[])).
% 1.46/1.19 tff(1455,plain,
% 1.46/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | (~ndr1_0) | c3_1(a387) | (~c0_1(a388))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 1.46/1.19 tff(1456,plain,
% 1.46/1.19 (c3_1(a387) | (~c0_1(a388))),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[1455, 117, 333, 1449, 640, 638, 639, 1448])).
% 1.46/1.19 tff(1457,plain,
% 1.46/1.19 ($false),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1456, 1438, 1436])).
% 1.46/1.20 tff(1458,plain,(hskp0 | c2_1(a388) | (~c3_1(a388)) | c0_1(a387) | c1_1(a387) | c2_1(a387) | c1_1(a388)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.20 tff(1459,plain,
% 1.46/1.20 (hskp0),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1458, 1062, 1427, 640, 638, 333, 800])).
% 1.46/1.20 tff(1460,plain,
% 1.46/1.20 (~c2_1(a353)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[695, 1459])).
% 1.46/1.20 tff(1461,plain,
% 1.46/1.20 (c1_1(a353)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[706, 1459])).
% 1.46/1.20 tff(1462,assumption,(~c2_1(a353)), introduced(assumption)).
% 1.46/1.20 tff(1463,assumption,(c1_1(a353)), introduced(assumption)).
% 1.46/1.20 tff(1464,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a360))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1465,plain,
% 1.46/1.20 (((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360)) <=> (c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a360))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1466,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a360)))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[1465])).
% 1.46/1.20 tff(1467,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a360))),
% 1.46/1.20 inference(transitivity,[status(thm)],[1466, 1464])).
% 1.46/1.20 tff(1468,plain,
% 1.46/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360))),
% 1.46/1.20 inference(quant_inst,[status(thm)],[])).
% 1.46/1.20 tff(1469,plain,
% 1.46/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a360) | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c0_1(a360)),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[1468, 1467])).
% 1.46/1.20 tff(1470,plain,
% 1.46/1.20 ((~c3_1(a353)) | c0_1(a360)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1469, 117, 1463, 790, 788, 789, 1462, 637])).
% 1.46/1.20 tff(1471,plain,
% 1.46/1.20 (~c3_1(a353)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1470, 791])).
% 1.46/1.20 tff(1472,plain,
% 1.46/1.20 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1473,plain,
% 1.46/1.20 ((hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a360) | c0_1(a360) | c3_1(a360)) <=> (hskp12 | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1474,plain,
% 1.46/1.20 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360)))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[1473])).
% 1.46/1.20 tff(1475,plain,
% 1.46/1.20 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360))),
% 1.46/1.20 inference(transitivity,[status(thm)],[1474, 1472])).
% 1.46/1.20 tff(1476,plain,
% 1.46/1.20 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a360) | c0_1(a360) | c3_1(a360))),
% 1.46/1.20 inference(quant_inst,[status(thm)],[])).
% 1.46/1.20 tff(1477,plain,
% 1.46/1.20 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp12 | c2_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360)),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 1.46/1.20 tff(1478,plain,
% 1.46/1.20 (hskp12 | c3_1(a353) | c0_1(a360)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1477, 117, 1463, 788, 789, 1462, 724])).
% 1.46/1.20 tff(1479,plain,
% 1.46/1.20 (hskp12),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1478, 791, 1471])).
% 1.46/1.20 tff(1480,plain,
% 1.46/1.20 (~c2_1(a369)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[736, 1479])).
% 1.46/1.20 tff(1481,plain,
% 1.46/1.20 (c3_1(a369)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[747, 1479])).
% 1.46/1.20 tff(1482,plain,
% 1.46/1.20 (c0_1(a369)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[758, 1479])).
% 1.46/1.20 tff(1483,plain,
% 1.46/1.20 (~c1_1(a369)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[765, 117, 1482, 1481, 1463, 1480, 1462, 329, 1471])).
% 1.46/1.20 tff(1484,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a369) | c1_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360) | c1_1(a369) | (~c0_1(a369)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c1_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360) | c1_1(a369) | (~c0_1(a369)))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1485,plain,
% 1.46/1.20 (((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a360) | c0_1(a360) | c3_1(a360)) <=> (c2_1(a369) | c1_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360) | c1_1(a369) | (~c0_1(a369)))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1486,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a369) | c1_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360) | c1_1(a369) | (~c0_1(a369))))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[1485])).
% 1.46/1.20 tff(1487,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c1_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360) | c1_1(a369) | (~c0_1(a369)))),
% 1.46/1.20 inference(transitivity,[status(thm)],[1486, 1484])).
% 1.46/1.20 tff(1488,plain,
% 1.46/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a369) | c1_1(a369) | (~c0_1(a369)) | c1_1(a360) | c0_1(a360) | c3_1(a360))),
% 1.46/1.20 inference(quant_inst,[status(thm)],[])).
% 1.46/1.20 tff(1489,plain,
% 1.46/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a369) | c1_1(a360) | c3_1(a360) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c0_1(a360) | c1_1(a369) | (~c0_1(a369))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[1488, 1487])).
% 1.46/1.20 tff(1490,plain,
% 1.46/1.20 ($false),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1489, 117, 1482, 1463, 1480, 790, 789, 1462, 776, 791, 1471, 1483])).
% 1.46/1.20 tff(1491,plain,(c0_1(a360) | (~c1_1(a353)) | c1_1(a360) | c3_1(a360) | c2_1(a353) | c2_1(a360)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.20 tff(1492,plain,
% 1.46/1.20 (c0_1(a360)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1491, 1461, 790, 789, 1460, 788])).
% 1.46/1.20 tff(1493,plain,
% 1.46/1.20 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c1_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a360)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c1_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a360)))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1494,plain,
% 1.46/1.20 ((hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358))) <=> (hskp3 | c1_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a360)))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1495,plain,
% 1.46/1.20 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c1_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a360))))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[1494])).
% 1.46/1.20 tff(1496,plain,
% 1.46/1.20 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c1_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a360)))),
% 1.46/1.20 inference(transitivity,[status(thm)],[1495, 1493])).
% 1.46/1.20 tff(1497,plain,
% 1.46/1.20 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a360) | c3_1(a360) | (~c0_1(a360)) | c0_1(a358) | c3_1(a358) | (~c1_1(a358)))),
% 1.46/1.20 inference(quant_inst,[status(thm)],[])).
% 1.46/1.20 tff(1498,plain,
% 1.46/1.20 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c1_1(a360) | c3_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c0_1(a360))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[1497, 1496])).
% 1.46/1.20 tff(1499,plain,
% 1.46/1.20 (hskp3 | (~c1_1(a358)) | (~c0_1(a360))),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1498, 117, 790, 789, 403, 397, 824])).
% 1.46/1.20 tff(1500,plain,
% 1.46/1.20 (~c1_1(a358)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1499, 1492, 177])).
% 1.46/1.20 tff(1501,plain,
% 1.46/1.20 (((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))) <=> ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp26 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1502,plain,
% 1.46/1.20 ((hskp26 | (~ndr1_0) | c2_1(a360) | c3_1(a360) | (~c0_1(a360))) <=> (hskp26 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1503,plain,
% 1.46/1.20 (((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | (~ndr1_0) | c2_1(a360) | c3_1(a360) | (~c0_1(a360)))) <=> ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360))))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[1502])).
% 1.46/1.20 tff(1504,plain,
% 1.46/1.20 (((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | (~ndr1_0) | c2_1(a360) | c3_1(a360) | (~c0_1(a360)))) <=> ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp26 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360)))),
% 1.46/1.20 inference(transitivity,[status(thm)],[1503, 1501])).
% 1.46/1.20 tff(1505,plain,
% 1.46/1.20 ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp26 | (~ndr1_0) | c2_1(a360) | c3_1(a360) | (~c0_1(a360)))),
% 1.46/1.20 inference(quant_inst,[status(thm)],[])).
% 1.46/1.20 tff(1506,plain,
% 1.46/1.20 ((~![U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp26 | c2_1(a360) | c3_1(a360) | (~ndr1_0) | (~c0_1(a360))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 1.46/1.20 tff(1507,plain,
% 1.46/1.20 (hskp26 | c2_1(a360) | (~c0_1(a360))),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1506, 117, 789, 1012])).
% 1.46/1.20 tff(1508,plain,
% 1.46/1.20 (hskp26),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1507, 1492, 788])).
% 1.46/1.20 tff(1509,plain,
% 1.46/1.20 (~c3_1(a418)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1025, 1508])).
% 1.46/1.20 tff(1510,plain,
% 1.46/1.20 (~c2_1(a418)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1031, 1508])).
% 1.46/1.20 tff(1511,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c3_1(a418) | c1_1(a360) | c2_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a360)) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c1_1(a360) | c2_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a360)) | (~c1_1(a418)))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1512,plain,
% 1.46/1.20 (((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c2_1(a418) | c3_1(a418) | c1_1(a360) | c2_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a360)) | (~c1_1(a418)))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1513,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c3_1(a418) | c1_1(a360) | c2_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a360)) | (~c1_1(a418))))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[1512])).
% 1.46/1.20 tff(1514,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c1_1(a360) | c2_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a360)) | (~c1_1(a418)))),
% 1.46/1.20 inference(transitivity,[status(thm)],[1513, 1511])).
% 1.46/1.20 tff(1515,plain,
% 1.46/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c2_1(a360) | c1_1(a360) | (~c0_1(a360)) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 1.46/1.20 inference(quant_inst,[status(thm)],[])).
% 1.46/1.20 tff(1516,plain,
% 1.46/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c1_1(a360) | c2_1(a360) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a360)) | (~c1_1(a418))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 1.46/1.20 tff(1517,plain,
% 1.46/1.20 (~c1_1(a418)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1516, 117, 1510, 1509, 790, 788, 403, 397, 776, 1492, 1500])).
% 1.46/1.20 tff(1518,plain,
% 1.46/1.20 (c0_1(a418)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1042, 1508])).
% 1.46/1.20 tff(1519,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418) | (~c0_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418) | (~c0_1(a418)))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1520,plain,
% 1.46/1.20 (((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | (~c0_1(a418)) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c2_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418) | (~c0_1(a418)))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1521,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | (~c0_1(a418)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418) | (~c0_1(a418))))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[1520])).
% 1.46/1.20 tff(1522,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | (~c0_1(a418)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418) | (~c0_1(a418)))),
% 1.46/1.20 inference(transitivity,[status(thm)],[1521, 1519])).
% 1.46/1.20 tff(1523,plain,
% 1.46/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | c3_1(a353) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | (~c0_1(a418)) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 1.46/1.20 inference(quant_inst,[status(thm)],[])).
% 1.46/1.20 tff(1524,plain,
% 1.46/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | c3_1(a353) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418) | (~c0_1(a418))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 1.46/1.20 tff(1525,plain,
% 1.46/1.20 (c3_1(a353)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1524, 117, 1518, 1461, 1510, 403, 397, 1460, 776, 1500, 1517])).
% 1.46/1.20 tff(1526,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c3_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1527,plain,
% 1.46/1.20 (((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c2_1(a418) | c3_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(1528,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c3_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418)))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[1527])).
% 1.46/1.20 tff(1529,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418))),
% 1.46/1.20 inference(transitivity,[status(thm)],[1528, 1526])).
% 1.46/1.20 tff(1530,plain,
% 1.46/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a353) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 1.46/1.20 inference(quant_inst,[status(thm)],[])).
% 1.46/1.20 tff(1531,plain,
% 1.46/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c0_1(a358) | c3_1(a358) | c2_1(a353) | (~ndr1_0) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a358) | c1_1(a418)),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[1530, 1529])).
% 1.46/1.20 tff(1532,plain,
% 1.46/1.20 ($false),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1531, 117, 1461, 1510, 1509, 403, 397, 1460, 637, 1500, 1525, 1517])).
% 1.46/1.20 tff(1533,plain,(hskp3 | c1_1(a360) | c2_1(a360) | c3_1(a360) | c0_1(a387) | c1_1(a387) | c2_1(a388) | c1_1(a388)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.20 tff(1534,plain,
% 1.46/1.20 (c1_1(a388)),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[1533, 1435, 788, 789, 1432, 790, 333, 1434])).
% 1.46/1.20 tff(1535,plain,
% 1.46/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a388) | (~c3_1(a388)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | (~c3_1(a388)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))),
% 1.46/1.21 inference(rewrite,[status(thm)],[])).
% 1.46/1.21 tff(1536,plain,
% 1.46/1.21 (((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360)) <=> (c2_1(a388) | (~c3_1(a388)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))),
% 1.46/1.21 inference(rewrite,[status(thm)],[])).
% 1.46/1.21 tff(1537,plain,
% 1.46/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a388) | (~c3_1(a388)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388))))),
% 1.46/1.21 inference(monotonicity,[status(thm)],[1536])).
% 1.46/1.21 tff(1538,plain,
% 1.46/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | (~c3_1(a388)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388)))),
% 1.46/1.21 inference(transitivity,[status(thm)],[1537, 1535])).
% 1.46/1.21 tff(1539,plain,
% 1.46/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a360) | c1_1(a360) | c3_1(a360) | c1_1(a360) | c0_1(a360) | c3_1(a360))),
% 1.46/1.21 inference(quant_inst,[status(thm)],[])).
% 1.46/1.21 tff(1540,plain,
% 1.46/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a388) | (~c3_1(a388)) | c1_1(a360) | c2_1(a360) | c3_1(a360) | (~ndr1_0) | c0_1(a360) | (~c1_1(a388))),
% 1.46/1.21 inference(modus_ponens,[status(thm)],[1539, 1538])).
% 1.46/1.21 tff(1541,plain,
% 1.46/1.21 ((~c3_1(a388)) | c0_1(a360) | (~c1_1(a388))),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1540, 117, 333, 790, 788, 789, 637])).
% 1.46/1.21 tff(1542,plain,
% 1.46/1.21 (c0_1(a360)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1541, 1534, 1427])).
% 1.46/1.21 tff(1543,plain,
% 1.46/1.21 (~c1_1(a358)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1499, 1542, 1432])).
% 1.46/1.21 tff(1544,plain,
% 1.46/1.21 (hskp26),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1507, 1542, 788])).
% 1.46/1.21 tff(1545,plain,
% 1.46/1.21 (~c3_1(a418)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1025, 1544])).
% 1.46/1.21 tff(1546,plain,
% 1.46/1.21 (~c2_1(a418)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1031, 1544])).
% 1.46/1.21 tff(1547,plain,
% 1.46/1.21 (~c1_1(a418)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1516, 117, 1546, 1545, 790, 788, 403, 397, 776, 1542, 1543])).
% 1.46/1.21 tff(1548,plain,
% 1.46/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c3_1(a418) | c2_1(a388) | (~c3_1(a388)) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c1_1(a388)) | c1_1(a418))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c2_1(a388) | (~c3_1(a388)) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c1_1(a388)) | c1_1(a418))),
% 1.46/1.21 inference(rewrite,[status(thm)],[])).
% 1.46/1.21 tff(1549,plain,
% 1.46/1.21 (((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (c2_1(a418) | c3_1(a418) | c2_1(a388) | (~c3_1(a388)) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c1_1(a388)) | c1_1(a418))),
% 1.46/1.21 inference(rewrite,[status(thm)],[])).
% 1.46/1.21 tff(1550,plain,
% 1.46/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a418) | c3_1(a418) | c2_1(a388) | (~c3_1(a388)) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c1_1(a388)) | c1_1(a418)))),
% 1.46/1.21 inference(monotonicity,[status(thm)],[1549])).
% 1.46/1.21 tff(1551,plain,
% 1.46/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c2_1(a388) | (~c3_1(a388)) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c1_1(a388)) | c1_1(a418))),
% 1.46/1.21 inference(transitivity,[status(thm)],[1550, 1548])).
% 1.46/1.21 tff(1552,plain,
% 1.46/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a388) | (~c3_1(a388)) | (~c1_1(a388)) | c2_1(a418) | c1_1(a418) | c3_1(a418) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 1.46/1.21 inference(quant_inst,[status(thm)],[])).
% 1.46/1.21 tff(1553,plain,
% 1.46/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a418) | c3_1(a418) | c2_1(a388) | (~c3_1(a388)) | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c1_1(a388)) | c1_1(a418)),
% 1.46/1.21 inference(modus_ponens,[status(thm)],[1552, 1551])).
% 1.46/1.21 tff(1554,plain,
% 1.46/1.21 ($false),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1553, 117, 1534, 1546, 1545, 333, 1427, 403, 397, 637, 1543, 1547])).
% 1.46/1.21 tff(1555,plain,(c2_1(a388) | c1_1(a360) | c2_1(a360) | c3_1(a360)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.21 tff(1556,plain,
% 1.46/1.21 (c2_1(a388)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1555, 790, 788, 789])).
% 1.46/1.21 tff(1557,plain,
% 1.46/1.21 (~hskp20),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[298, 1556])).
% 1.46/1.21 tff(1558,plain,
% 1.46/1.21 (~hskp3),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1431, 1557, 790, 788, 789])).
% 1.46/1.21 tff(1559,plain,
% 1.46/1.21 (hskp19),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1058, 1558, 789, 790, 788])).
% 1.46/1.21 tff(1560,plain,
% 1.46/1.21 (~c2_1(a387)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[230, 1559])).
% 1.46/1.21 tff(1561,plain,
% 1.46/1.21 (~c1_1(a387)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[236, 1559])).
% 1.46/1.21 tff(1562,plain,
% 1.46/1.21 (~c0_1(a387)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[242, 1559])).
% 1.46/1.21 tff(1563,assumption,(~c1_1(a358)), introduced(assumption)).
% 1.46/1.21 tff(1564,plain,
% 1.46/1.21 ($false),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[849, 117, 421, 640, 638, 639, 403, 397, 10, 1563])).
% 1.46/1.21 tff(1565,plain,(c1_1(a358) | c0_1(a387) | c1_1(a387) | c2_1(a387)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.21 tff(1566,plain,
% 1.46/1.21 (c1_1(a358)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1565, 1562, 1561, 1560])).
% 1.46/1.21 tff(1567,plain,
% 1.46/1.21 (~c0_1(a360)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1499, 1566, 1558])).
% 1.46/1.21 tff(1568,plain,
% 1.46/1.21 (hskp0 | (~c1_1(a358))),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[680, 117, 421, 1562, 1561, 1560, 403, 674])).
% 1.46/1.21 tff(1569,plain,
% 1.46/1.21 (hskp0),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1568, 1566])).
% 1.46/1.21 tff(1570,plain,
% 1.46/1.21 (c1_1(a353)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[706, 1569])).
% 1.46/1.21 tff(1571,plain,
% 1.46/1.21 (~c2_1(a353)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[695, 1569])).
% 1.46/1.21 tff(1572,plain,
% 1.46/1.21 ($false),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1491, 1571, 1570, 790, 789, 1567, 788])).
% 1.46/1.21 tff(1573,plain,(c1_1(a360) | c3_1(a360) | c2_1(a360)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.21 tff(1574,plain,
% 1.46/1.21 ($false),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[1573, 787, 786, 785])).
% 1.46/1.21 % SZS output end Proof
%------------------------------------------------------------------------------