TSTP Solution File: SYN467-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN467-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:55:40 EDT 2022
% Result : Unsatisfiable 1.35s 1.09s
% Output : Proof 1.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN467-1 : TPTP v8.1.0. Released v2.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 04:15:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.35/1.09 % SZS status Unsatisfiable
% 1.35/1.09 % SZS output start Proof
% 1.35/1.09 tff(c1_1_type, type, (
% 1.35/1.09 c1_1: $i > $o)).
% 1.35/1.09 tff(a249_type, type, (
% 1.35/1.09 a249: $i)).
% 1.35/1.09 tff(a238_type, type, (
% 1.35/1.09 a238: $i)).
% 1.35/1.09 tff(hskp19_type, type, (
% 1.35/1.09 hskp19: $o)).
% 1.35/1.09 tff(a239_type, type, (
% 1.35/1.09 a239: $i)).
% 1.35/1.09 tff(a256_type, type, (
% 1.35/1.09 a256: $i)).
% 1.35/1.09 tff(hskp25_type, type, (
% 1.35/1.09 hskp25: $o)).
% 1.35/1.09 tff(c3_1_type, type, (
% 1.35/1.09 c3_1: $i > $o)).
% 1.35/1.09 tff(c0_1_type, type, (
% 1.35/1.09 c0_1: $i > $o)).
% 1.35/1.09 tff(c2_1_type, type, (
% 1.35/1.09 c2_1: $i > $o)).
% 1.35/1.09 tff(ndr1_0_type, type, (
% 1.35/1.09 ndr1_0: $o)).
% 1.35/1.09 tff(hskp24_type, type, (
% 1.35/1.09 hskp24: $o)).
% 1.35/1.09 tff(a204_type, type, (
% 1.35/1.09 a204: $i)).
% 1.35/1.09 tff(hskp4_type, type, (
% 1.35/1.09 hskp4: $o)).
% 1.35/1.09 tff(a208_type, type, (
% 1.35/1.09 a208: $i)).
% 1.35/1.09 tff(hskp6_type, type, (
% 1.35/1.09 hskp6: $o)).
% 1.35/1.09 tff(a233_type, type, (
% 1.35/1.09 a233: $i)).
% 1.35/1.09 tff(hskp18_type, type, (
% 1.35/1.09 hskp18: $o)).
% 1.35/1.09 tff(hskp5_type, type, (
% 1.35/1.09 hskp5: $o)).
% 1.35/1.09 tff(a203_type, type, (
% 1.35/1.09 a203: $i)).
% 1.35/1.09 tff(a205_type, type, (
% 1.35/1.09 a205: $i)).
% 1.35/1.09 tff(a244_type, type, (
% 1.35/1.09 a244: $i)).
% 1.35/1.09 tff(hskp22_type, type, (
% 1.35/1.09 hskp22: $o)).
% 1.35/1.09 tff(hskp27_type, type, (
% 1.35/1.09 hskp27: $o)).
% 1.35/1.09 tff(a198_type, type, (
% 1.35/1.09 a198: $i)).
% 1.35/1.09 tff(a213_type, type, (
% 1.35/1.09 a213: $i)).
% 1.35/1.09 tff(hskp9_type, type, (
% 1.35/1.09 hskp9: $o)).
% 1.35/1.09 tff(a201_type, type, (
% 1.35/1.09 a201: $i)).
% 1.35/1.09 tff(hskp2_type, type, (
% 1.35/1.09 hskp2: $o)).
% 1.35/1.09 tff(hskp1_type, type, (
% 1.35/1.09 hskp1: $o)).
% 1.35/1.09 tff(a199_type, type, (
% 1.35/1.09 a199: $i)).
% 1.35/1.09 tff(hskp0_type, type, (
% 1.35/1.09 hskp0: $o)).
% 1.35/1.09 tff(a209_type, type, (
% 1.35/1.09 a209: $i)).
% 1.35/1.09 tff(hskp7_type, type, (
% 1.35/1.09 hskp7: $o)).
% 1.35/1.09 tff(a241_type, type, (
% 1.35/1.09 a241: $i)).
% 1.35/1.09 tff(hskp21_type, type, (
% 1.35/1.09 hskp21: $o)).
% 1.35/1.09 tff(a200_type, type, (
% 1.35/1.09 a200: $i)).
% 1.35/1.09 tff(a227_type, type, (
% 1.35/1.09 a227: $i)).
% 1.35/1.09 tff(hskp29_type, type, (
% 1.35/1.09 hskp29: $o)).
% 1.35/1.09 tff(hskp3_type, type, (
% 1.35/1.09 hskp3: $o)).
% 1.35/1.09 tff(a217_type, type, (
% 1.35/1.09 a217: $i)).
% 1.35/1.09 tff(hskp12_type, type, (
% 1.35/1.09 hskp12: $o)).
% 1.35/1.09 tff(a202_type, type, (
% 1.35/1.09 a202: $i)).
% 1.35/1.09 tff(hskp28_type, type, (
% 1.35/1.09 hskp28: $o)).
% 1.35/1.09 tff(a232_type, type, (
% 1.35/1.09 a232: $i)).
% 1.35/1.09 tff(hskp17_type, type, (
% 1.35/1.09 hskp17: $o)).
% 1.35/1.09 tff(a214_type, type, (
% 1.35/1.09 a214: $i)).
% 1.35/1.09 tff(hskp10_type, type, (
% 1.35/1.09 hskp10: $o)).
% 1.35/1.09 tff(hskp20_type, type, (
% 1.35/1.09 hskp20: $o)).
% 1.35/1.09 tff(a212_type, type, (
% 1.35/1.09 a212: $i)).
% 1.35/1.09 tff(hskp8_type, type, (
% 1.35/1.09 hskp8: $o)).
% 1.35/1.09 tff(a228_type, type, (
% 1.35/1.09 a228: $i)).
% 1.35/1.09 tff(hskp15_type, type, (
% 1.35/1.09 hskp15: $o)).
% 1.35/1.09 tff(1,assumption,(~hskp19), introduced(assumption)).
% 1.35/1.09 tff(2,plain,
% 1.35/1.09 (^[U: $i] : refl((hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(3,plain,
% 1.35/1.09 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.09 inference(quant_intro,[status(thm)],[2])).
% 1.35/1.09 tff(4,plain,
% 1.35/1.09 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(5,plain,
% 1.35/1.09 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp19) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp19))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp19) <=> (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp19) <=> (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(6,plain,
% 1.35/1.09 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp19) <=> ![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.09 inference(quant_intro,[status(thm)],[5])).
% 1.35/1.09 tff(7,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.35/1.09 tff(8,plain,
% 1.35/1.09 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[7, 6])).
% 1.35/1.09 tff(9,plain,
% 1.35/1.09 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.35/1.09 tff(10,plain,(
% 1.35/1.09 ![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.09 inference(skolemize,[status(sab)],[9])).
% 1.35/1.09 tff(11,plain,
% 1.35/1.09 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[10, 3])).
% 1.35/1.09 tff(12,assumption,(~hskp24), introduced(assumption)).
% 1.35/1.09 tff(13,plain,
% 1.35/1.09 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(14,plain,
% 1.35/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.35/1.09 inference(quant_intro,[status(thm)],[13])).
% 1.35/1.09 tff(15,plain,
% 1.35/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(16,plain,
% 1.35/1.09 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(17,plain,
% 1.35/1.09 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.35/1.09 inference(quant_intro,[status(thm)],[16])).
% 1.35/1.09 tff(18,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 1.35/1.09 tff(19,plain,
% 1.35/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.35/1.09 tff(20,plain,
% 1.35/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.35/1.09 tff(21,plain,(
% 1.35/1.09 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.35/1.09 inference(skolemize,[status(sab)],[20])).
% 1.35/1.09 tff(22,plain,
% 1.35/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.35/1.09 tff(23,assumption,(~hskp4), introduced(assumption)).
% 1.35/1.09 tff(24,plain,
% 1.35/1.09 ((hskp24 | hskp18 | hskp4) <=> (hskp24 | hskp18 | hskp4)),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(25,plain,
% 1.35/1.09 (((hskp24 | hskp4) | hskp18) <=> (hskp24 | hskp18 | hskp4)),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(26,axiom,((hskp24 | hskp4) | hskp18), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 1.35/1.09 tff(27,plain,
% 1.35/1.09 (hskp24 | hskp18 | hskp4),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.35/1.09 tff(28,plain,
% 1.35/1.09 (hskp24 | hskp18 | hskp4),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[27, 24])).
% 1.35/1.09 tff(29,plain,
% 1.35/1.09 (hskp24 | hskp18 | hskp4),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.35/1.09 tff(30,plain,
% 1.35/1.09 (hskp24 | hskp18 | hskp4),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[29, 24])).
% 1.35/1.09 tff(31,plain,
% 1.35/1.09 (hskp24 | hskp18 | hskp4),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[30, 24])).
% 1.35/1.09 tff(32,plain,
% 1.35/1.09 (hskp24 | hskp18 | hskp4),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[31, 24])).
% 1.35/1.09 tff(33,plain,
% 1.35/1.09 (hskp24 | hskp18 | hskp4),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[32, 24])).
% 1.35/1.09 tff(34,plain,
% 1.35/1.09 (hskp24 | hskp18 | hskp4),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[33, 24])).
% 1.35/1.09 tff(35,plain,
% 1.35/1.09 (hskp18),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[34, 23, 12])).
% 1.35/1.09 tff(36,plain,
% 1.35/1.09 (((~hskp18) | (~c3_1(a233))) <=> ((~hskp18) | (~c3_1(a233)))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(37,plain,
% 1.35/1.09 (((~c3_1(a233)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a233)))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(38,axiom,((~c3_1(a233)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.35/1.09 tff(39,plain,
% 1.35/1.09 ((~hskp18) | (~c3_1(a233))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.35/1.09 tff(40,plain,
% 1.35/1.09 ((~hskp18) | (~c3_1(a233))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[39, 36])).
% 1.35/1.09 tff(41,plain,
% 1.35/1.09 (~c3_1(a233)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[40, 35])).
% 1.35/1.09 tff(42,assumption,(hskp5), introduced(assumption)).
% 1.35/1.09 tff(43,plain,
% 1.35/1.09 (((~hskp5) | c2_1(a205)) <=> ((~hskp5) | c2_1(a205))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(44,axiom,((~hskp5) | c2_1(a205)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.35/1.09 tff(45,plain,
% 1.35/1.09 ((~hskp5) | c2_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.35/1.09 tff(46,plain,
% 1.35/1.09 ((~hskp5) | c2_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[45, 43])).
% 1.35/1.09 tff(47,plain,
% 1.35/1.09 ((~hskp5) | c2_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[46, 43])).
% 1.35/1.09 tff(48,plain,
% 1.35/1.09 ((~hskp5) | c2_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[47, 43])).
% 1.35/1.09 tff(49,plain,
% 1.35/1.09 ((~hskp5) | c2_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[48, 43])).
% 1.35/1.09 tff(50,plain,
% 1.35/1.09 ((~hskp5) | c2_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[49, 43])).
% 1.35/1.09 tff(51,plain,
% 1.35/1.09 ((~hskp5) | c2_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[50, 43])).
% 1.35/1.09 tff(52,plain,
% 1.35/1.09 ((~hskp5) | c2_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[51, 43])).
% 1.35/1.09 tff(53,plain,
% 1.35/1.09 (c2_1(a205)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[52, 42])).
% 1.35/1.09 tff(54,plain,
% 1.35/1.09 (((~hskp5) | (~c1_1(a205))) <=> ((~hskp5) | (~c1_1(a205)))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(55,plain,
% 1.35/1.09 (((~c1_1(a205)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a205)))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(56,axiom,((~c1_1(a205)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.35/1.09 tff(57,plain,
% 1.35/1.09 ((~hskp5) | (~c1_1(a205))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[56, 55])).
% 1.35/1.09 tff(58,plain,
% 1.35/1.09 ((~hskp5) | (~c1_1(a205))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[57, 54])).
% 1.35/1.09 tff(59,plain,
% 1.35/1.09 (~c1_1(a205)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[58, 42])).
% 1.35/1.09 tff(60,plain,
% 1.35/1.09 (((~hskp5) | c3_1(a205)) <=> ((~hskp5) | c3_1(a205))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(61,axiom,((~hskp5) | c3_1(a205)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.35/1.09 tff(62,plain,
% 1.35/1.09 ((~hskp5) | c3_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.35/1.09 tff(63,plain,
% 1.35/1.09 ((~hskp5) | c3_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[62, 60])).
% 1.35/1.09 tff(64,plain,
% 1.35/1.09 ((~hskp5) | c3_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[63, 60])).
% 1.35/1.09 tff(65,plain,
% 1.35/1.09 ((~hskp5) | c3_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.35/1.09 tff(66,plain,
% 1.35/1.09 ((~hskp5) | c3_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[65, 60])).
% 1.35/1.09 tff(67,plain,
% 1.35/1.09 ((~hskp5) | c3_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[66, 60])).
% 1.35/1.09 tff(68,plain,
% 1.35/1.09 ((~hskp5) | c3_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[67, 60])).
% 1.35/1.09 tff(69,plain,
% 1.35/1.09 ((~hskp5) | c3_1(a205)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[68, 60])).
% 1.35/1.09 tff(70,plain,
% 1.35/1.09 (c3_1(a205)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[69, 42])).
% 1.35/1.09 tff(71,plain,
% 1.35/1.09 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(72,plain,
% 1.35/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.35/1.09 inference(quant_intro,[status(thm)],[71])).
% 1.35/1.09 tff(73,plain,
% 1.35/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(74,plain,
% 1.35/1.09 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 1.35/1.10 inference(bind,[status(th)],[])).
% 1.35/1.10 tff(75,plain,
% 1.35/1.10 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.35/1.10 inference(quant_intro,[status(thm)],[74])).
% 1.35/1.10 tff(76,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 1.35/1.10 tff(77,plain,
% 1.35/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.35/1.10 tff(78,plain,
% 1.35/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[77, 73])).
% 1.35/1.10 tff(79,plain,(
% 1.35/1.10 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.35/1.10 inference(skolemize,[status(sab)],[78])).
% 1.35/1.10 tff(80,plain,
% 1.35/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[79, 72])).
% 1.35/1.10 tff(81,assumption,(c0_1(a205)), introduced(assumption)).
% 1.35/1.10 tff(82,plain,
% 1.35/1.10 (^[U: $i] : refl((hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 1.35/1.10 inference(bind,[status(th)],[])).
% 1.35/1.10 tff(83,plain,
% 1.35/1.10 (![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.10 inference(quant_intro,[status(thm)],[82])).
% 1.35/1.10 tff(84,plain,
% 1.35/1.10 (![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(85,plain,
% 1.35/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp24))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp22) <=> ((hskp24 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp22))), rewrite(((hskp24 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp22) <=> (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp22) <=> (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 1.35/1.10 inference(bind,[status(th)],[])).
% 1.35/1.10 tff(86,plain,
% 1.35/1.10 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp22) <=> ![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.10 inference(quant_intro,[status(thm)],[85])).
% 1.35/1.10 tff(87,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 1.35/1.10 tff(88,plain,
% 1.35/1.10 (![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.35/1.10 tff(89,plain,
% 1.35/1.10 (![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[88, 84])).
% 1.35/1.10 tff(90,plain,(
% 1.35/1.10 ![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.10 inference(skolemize,[status(sab)],[89])).
% 1.35/1.10 tff(91,plain,
% 1.35/1.10 (![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[90, 83])).
% 1.35/1.10 tff(92,assumption,(~c1_1(a205)), introduced(assumption)).
% 1.35/1.10 tff(93,assumption,(c3_1(a205)), introduced(assumption)).
% 1.35/1.10 tff(94,assumption,(~ndr1_0), introduced(assumption)).
% 1.35/1.10 tff(95,plain,
% 1.35/1.10 ((ndr1_0 | (~hskp4)) <=> (ndr1_0 | (~hskp4))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(96,plain,
% 1.35/1.10 (((~hskp4) | ndr1_0) <=> (ndr1_0 | (~hskp4))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(97,axiom,((~hskp4) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause28')).
% 1.35/1.10 tff(98,plain,
% 1.35/1.10 (ndr1_0 | (~hskp4)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.35/1.10 tff(99,plain,
% 1.35/1.10 (ndr1_0 | (~hskp4)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[98, 95])).
% 1.35/1.10 tff(100,plain,
% 1.35/1.10 (~hskp4),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[99, 94])).
% 1.35/1.10 tff(101,plain,
% 1.35/1.10 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(102,plain,
% 1.35/1.10 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(103,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 1.35/1.10 tff(104,plain,
% 1.35/1.10 (ndr1_0 | (~hskp27)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[103, 102])).
% 1.35/1.10 tff(105,plain,
% 1.35/1.10 (ndr1_0 | (~hskp27)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[104, 101])).
% 1.35/1.10 tff(106,plain,
% 1.35/1.10 (~hskp27),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[105, 94])).
% 1.35/1.10 tff(107,plain,
% 1.35/1.10 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(108,plain,
% 1.35/1.10 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(109,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 1.35/1.10 tff(110,plain,
% 1.35/1.10 (ndr1_0 | (~hskp24)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.35/1.10 tff(111,plain,
% 1.35/1.10 (ndr1_0 | (~hskp24)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[110, 107])).
% 1.35/1.10 tff(112,plain,
% 1.35/1.10 (~hskp24),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[111, 94])).
% 1.35/1.10 tff(113,plain,
% 1.35/1.10 ((hskp27 | hskp24 | hskp4) <=> (hskp27 | hskp24 | hskp4)),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(114,plain,
% 1.35/1.10 (((hskp27 | hskp24) | hskp4) <=> (hskp27 | hskp24 | hskp4)),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(115,plain,
% 1.35/1.10 ((hskp27 | hskp24) <=> (hskp27 | hskp24)),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(116,plain,
% 1.35/1.10 (((hskp27 | hskp24) | hskp4) <=> ((hskp27 | hskp24) | hskp4)),
% 1.35/1.10 inference(monotonicity,[status(thm)],[115])).
% 1.35/1.10 tff(117,plain,
% 1.35/1.10 (((hskp27 | hskp24) | hskp4) <=> (hskp27 | hskp24 | hskp4)),
% 1.35/1.10 inference(transitivity,[status(thm)],[116, 114])).
% 1.35/1.10 tff(118,axiom,((hskp27 | hskp24) | hskp4), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 1.35/1.10 tff(119,plain,
% 1.35/1.10 (hskp27 | hskp24 | hskp4),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.35/1.10 tff(120,plain,
% 1.35/1.10 (hskp27 | hskp24 | hskp4),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[119, 113])).
% 1.35/1.10 tff(121,plain,
% 1.35/1.10 (hskp27 | hskp24 | hskp4),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[120, 113])).
% 1.35/1.10 tff(122,plain,
% 1.35/1.10 (hskp27 | hskp24 | hskp4),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[121, 113])).
% 1.35/1.10 tff(123,plain,
% 1.35/1.10 (hskp27 | hskp24 | hskp4),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[122, 113])).
% 1.35/1.10 tff(124,plain,
% 1.35/1.10 (hskp27 | hskp24 | hskp4),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[123, 113])).
% 1.35/1.10 tff(125,plain,
% 1.35/1.10 (hskp27 | hskp24 | hskp4),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[124, 113])).
% 1.35/1.10 tff(126,plain,
% 1.35/1.10 (hskp27 | hskp24 | hskp4),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[125, 113])).
% 1.35/1.10 tff(127,plain,
% 1.35/1.10 ($false),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[126, 112, 106, 100])).
% 1.35/1.10 tff(128,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.35/1.10 tff(129,plain,
% 1.35/1.10 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | c1_1(a205) | (~ndr1_0) | (~c0_1(a205)) | (~c3_1(a205)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp24 | hskp22 | c1_1(a205) | (~ndr1_0) | (~c0_1(a205)) | (~c3_1(a205)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(130,plain,
% 1.35/1.10 ((hskp24 | hskp22 | (~ndr1_0) | c1_1(a205) | (~c0_1(a205)) | (~c3_1(a205))) <=> (hskp24 | hskp22 | c1_1(a205) | (~ndr1_0) | (~c0_1(a205)) | (~c3_1(a205)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(131,plain,
% 1.35/1.10 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c1_1(a205) | (~c0_1(a205)) | (~c3_1(a205)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | c1_1(a205) | (~ndr1_0) | (~c0_1(a205)) | (~c3_1(a205))))),
% 1.35/1.10 inference(monotonicity,[status(thm)],[130])).
% 1.35/1.10 tff(132,plain,
% 1.35/1.10 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c1_1(a205) | (~c0_1(a205)) | (~c3_1(a205)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp24 | hskp22 | c1_1(a205) | (~ndr1_0) | (~c0_1(a205)) | (~c3_1(a205)))),
% 1.35/1.10 inference(transitivity,[status(thm)],[131, 129])).
% 1.35/1.10 tff(133,plain,
% 1.35/1.10 ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c1_1(a205) | (~c0_1(a205)) | (~c3_1(a205)))),
% 1.35/1.10 inference(quant_inst,[status(thm)],[])).
% 1.35/1.10 tff(134,plain,
% 1.35/1.10 ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp24 | hskp22 | c1_1(a205) | (~ndr1_0) | (~c0_1(a205)) | (~c3_1(a205))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.35/1.10 tff(135,plain,
% 1.35/1.10 (hskp22 | (~c0_1(a205))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[134, 128, 12, 93, 92, 91])).
% 1.35/1.10 tff(136,plain,
% 1.35/1.10 (hskp22),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[135, 81])).
% 1.35/1.10 tff(137,plain,
% 1.35/1.10 (((~hskp22) | (~c2_1(a244))) <=> ((~hskp22) | (~c2_1(a244)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(138,plain,
% 1.35/1.10 (((~c2_1(a244)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a244)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(139,axiom,((~c2_1(a244)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.35/1.10 tff(140,plain,
% 1.35/1.10 ((~hskp22) | (~c2_1(a244))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.35/1.10 tff(141,plain,
% 1.35/1.10 ((~hskp22) | (~c2_1(a244))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[140, 137])).
% 1.35/1.10 tff(142,plain,
% 1.35/1.10 (~c2_1(a244)),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[141, 136])).
% 1.35/1.10 tff(143,plain,
% 1.35/1.10 (((~hskp22) | (~c0_1(a244))) <=> ((~hskp22) | (~c0_1(a244)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(144,plain,
% 1.35/1.10 (((~c0_1(a244)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a244)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(145,axiom,((~c0_1(a244)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.35/1.10 tff(146,plain,
% 1.35/1.10 ((~hskp22) | (~c0_1(a244))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[145, 144])).
% 1.35/1.10 tff(147,plain,
% 1.35/1.10 ((~hskp22) | (~c0_1(a244))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[146, 143])).
% 1.35/1.10 tff(148,plain,
% 1.35/1.10 (~c0_1(a244)),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[147, 136])).
% 1.35/1.10 tff(149,plain,
% 1.35/1.10 (((~hskp22) | c3_1(a244)) <=> ((~hskp22) | c3_1(a244))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(150,axiom,((~hskp22) | c3_1(a244)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.35/1.10 tff(151,plain,
% 1.35/1.10 ((~hskp22) | c3_1(a244)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.35/1.10 tff(152,plain,
% 1.35/1.10 ((~hskp22) | c3_1(a244)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[151, 149])).
% 1.35/1.10 tff(153,plain,
% 1.35/1.10 ((~hskp22) | c3_1(a244)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[152, 149])).
% 1.35/1.10 tff(154,plain,
% 1.35/1.10 ((~hskp22) | c3_1(a244)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[153, 149])).
% 1.35/1.10 tff(155,plain,
% 1.35/1.10 ((~hskp22) | c3_1(a244)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[154, 149])).
% 1.35/1.10 tff(156,plain,
% 1.35/1.10 ((~hskp22) | c3_1(a244)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[155, 149])).
% 1.35/1.10 tff(157,plain,
% 1.35/1.10 ((~hskp22) | c3_1(a244)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[156, 149])).
% 1.35/1.10 tff(158,plain,
% 1.35/1.10 ((~hskp22) | c3_1(a244)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[157, 149])).
% 1.35/1.10 tff(159,plain,
% 1.35/1.10 (c3_1(a244)),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[158, 136])).
% 1.35/1.10 tff(160,assumption,(~hskp27), introduced(assumption)).
% 1.35/1.10 tff(161,assumption,(hskp6), introduced(assumption)).
% 1.35/1.10 tff(162,plain,
% 1.35/1.10 (((~hskp6) | c0_1(a208)) <=> ((~hskp6) | c0_1(a208))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(163,axiom,((~hskp6) | c0_1(a208)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.35/1.10 tff(164,plain,
% 1.35/1.10 ((~hskp6) | c0_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.35/1.10 tff(165,plain,
% 1.35/1.10 ((~hskp6) | c0_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[164, 162])).
% 1.35/1.10 tff(166,plain,
% 1.35/1.10 ((~hskp6) | c0_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[165, 162])).
% 1.35/1.10 tff(167,plain,
% 1.35/1.10 ((~hskp6) | c0_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[166, 162])).
% 1.35/1.10 tff(168,plain,
% 1.35/1.10 ((~hskp6) | c0_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[167, 162])).
% 1.35/1.10 tff(169,plain,
% 1.35/1.10 ((~hskp6) | c0_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[168, 162])).
% 1.35/1.10 tff(170,plain,
% 1.35/1.10 ((~hskp6) | c0_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[169, 162])).
% 1.35/1.10 tff(171,plain,
% 1.35/1.10 ((~hskp6) | c0_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[170, 162])).
% 1.35/1.10 tff(172,plain,
% 1.35/1.10 (c0_1(a208)),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[171, 161])).
% 1.35/1.10 tff(173,plain,
% 1.35/1.10 (((~hskp6) | (~c2_1(a208))) <=> ((~hskp6) | (~c2_1(a208)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(174,plain,
% 1.35/1.10 (((~c2_1(a208)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a208)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(175,axiom,((~c2_1(a208)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.35/1.10 tff(176,plain,
% 1.35/1.10 ((~hskp6) | (~c2_1(a208))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.35/1.10 tff(177,plain,
% 1.35/1.10 ((~hskp6) | (~c2_1(a208))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[176, 173])).
% 1.35/1.10 tff(178,plain,
% 1.35/1.10 (~c2_1(a208)),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[177, 161])).
% 1.35/1.10 tff(179,plain,
% 1.35/1.10 (^[U: $i] : refl((hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 1.35/1.10 inference(bind,[status(th)],[])).
% 1.35/1.10 tff(180,plain,
% 1.35/1.10 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.35/1.10 inference(quant_intro,[status(thm)],[179])).
% 1.35/1.10 tff(181,plain,
% 1.35/1.10 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(182,plain,
% 1.35/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 1.35/1.10 inference(bind,[status(th)],[])).
% 1.35/1.10 tff(183,plain,
% 1.35/1.10 (![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.35/1.10 inference(quant_intro,[status(thm)],[182])).
% 1.35/1.10 tff(184,axiom,(![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.35/1.10 tff(185,plain,
% 1.35/1.10 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.35/1.10 tff(186,plain,
% 1.35/1.10 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[185, 181])).
% 1.35/1.10 tff(187,plain,(
% 1.35/1.10 ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.35/1.10 inference(skolemize,[status(sab)],[186])).
% 1.35/1.10 tff(188,plain,
% 1.35/1.10 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[187, 180])).
% 1.35/1.10 tff(189,assumption,(hskp18), introduced(assumption)).
% 1.35/1.10 tff(190,plain,
% 1.35/1.10 (~c3_1(a233)),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[40, 189])).
% 1.35/1.10 tff(191,plain,
% 1.35/1.10 (((~hskp18) | (~c2_1(a233))) <=> ((~hskp18) | (~c2_1(a233)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(192,plain,
% 1.35/1.10 (((~c2_1(a233)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a233)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(193,axiom,((~c2_1(a233)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.35/1.10 tff(194,plain,
% 1.35/1.10 ((~hskp18) | (~c2_1(a233))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.35/1.10 tff(195,plain,
% 1.35/1.10 ((~hskp18) | (~c2_1(a233))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[194, 191])).
% 1.35/1.10 tff(196,plain,
% 1.35/1.10 (~c2_1(a233)),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[195, 189])).
% 1.35/1.10 tff(197,plain,
% 1.35/1.10 (((~hskp18) | (~c1_1(a233))) <=> ((~hskp18) | (~c1_1(a233)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(198,plain,
% 1.35/1.10 (((~c1_1(a233)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a233)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(199,axiom,((~c1_1(a233)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.35/1.10 tff(200,plain,
% 1.35/1.10 ((~hskp18) | (~c1_1(a233))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.35/1.10 tff(201,plain,
% 1.35/1.10 ((~hskp18) | (~c1_1(a233))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[200, 197])).
% 1.35/1.10 tff(202,plain,
% 1.35/1.10 (~c1_1(a233)),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[201, 189])).
% 1.35/1.10 tff(203,plain,
% 1.35/1.10 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c1_1(a233) | c2_1(a233) | c3_1(a233) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a233) | c2_1(a233) | c3_1(a233) | (~ndr1_0))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(204,plain,
% 1.35/1.10 ((hskp27 | (~ndr1_0) | c3_1(a233) | c2_1(a233) | c1_1(a233)) <=> (hskp27 | c1_1(a233) | c2_1(a233) | c3_1(a233) | (~ndr1_0))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(205,plain,
% 1.35/1.10 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a233) | c2_1(a233) | c1_1(a233))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c1_1(a233) | c2_1(a233) | c3_1(a233) | (~ndr1_0)))),
% 1.35/1.10 inference(monotonicity,[status(thm)],[204])).
% 1.35/1.10 tff(206,plain,
% 1.35/1.10 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a233) | c2_1(a233) | c1_1(a233))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a233) | c2_1(a233) | c3_1(a233) | (~ndr1_0))),
% 1.35/1.10 inference(transitivity,[status(thm)],[205, 203])).
% 1.35/1.10 tff(207,plain,
% 1.35/1.10 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a233) | c2_1(a233) | c1_1(a233))),
% 1.35/1.10 inference(quant_inst,[status(thm)],[])).
% 1.35/1.10 tff(208,plain,
% 1.35/1.10 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a233) | c2_1(a233) | c3_1(a233) | (~ndr1_0)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.35/1.10 tff(209,plain,
% 1.35/1.10 ($false),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[208, 128, 160, 202, 196, 190, 188])).
% 1.35/1.10 tff(210,plain,((~hskp18) | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.35/1.10 tff(211,plain,
% 1.35/1.10 (~hskp18),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[210, 160])).
% 1.35/1.10 tff(212,plain,
% 1.35/1.10 (((~hskp6) | c1_1(a208)) <=> ((~hskp6) | c1_1(a208))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(213,axiom,((~hskp6) | c1_1(a208)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.35/1.10 tff(214,plain,
% 1.35/1.10 ((~hskp6) | c1_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.35/1.10 tff(215,plain,
% 1.35/1.10 ((~hskp6) | c1_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[214, 212])).
% 1.35/1.10 tff(216,plain,
% 1.35/1.10 ((~hskp6) | c1_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[215, 212])).
% 1.35/1.10 tff(217,plain,
% 1.35/1.10 ((~hskp6) | c1_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[216, 212])).
% 1.35/1.10 tff(218,plain,
% 1.35/1.10 ((~hskp6) | c1_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[217, 212])).
% 1.35/1.10 tff(219,plain,
% 1.35/1.10 ((~hskp6) | c1_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[218, 212])).
% 1.35/1.10 tff(220,plain,
% 1.35/1.10 ((~hskp6) | c1_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[219, 212])).
% 1.35/1.10 tff(221,plain,
% 1.35/1.10 ((~hskp6) | c1_1(a208)),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[220, 212])).
% 1.35/1.10 tff(222,plain,
% 1.35/1.10 (c1_1(a208)),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[221, 161])).
% 1.35/1.10 tff(223,assumption,(~hskp0), introduced(assumption)).
% 1.35/1.10 tff(224,plain,
% 1.35/1.10 (^[U: $i] : refl((hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 1.35/1.10 inference(bind,[status(th)],[])).
% 1.35/1.10 tff(225,plain,
% 1.35/1.10 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.35/1.10 inference(quant_intro,[status(thm)],[224])).
% 1.35/1.10 tff(226,plain,
% 1.35/1.10 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(227,plain,
% 1.35/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp0) | hskp18) <=> ((hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp18))), rewrite(((hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp18) <=> (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp0) | hskp18) <=> (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 1.35/1.10 inference(bind,[status(th)],[])).
% 1.35/1.10 tff(228,plain,
% 1.35/1.10 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp0) | hskp18) <=> ![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.35/1.10 inference(quant_intro,[status(thm)],[227])).
% 1.35/1.10 tff(229,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp0) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 1.35/1.10 tff(230,plain,
% 1.35/1.10 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[229, 228])).
% 1.35/1.10 tff(231,plain,
% 1.35/1.10 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[230, 226])).
% 1.35/1.10 tff(232,plain,(
% 1.35/1.10 ![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.35/1.10 inference(skolemize,[status(sab)],[231])).
% 1.35/1.10 tff(233,plain,
% 1.35/1.10 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[232, 225])).
% 1.35/1.10 tff(234,assumption,(~c2_1(a208)), introduced(assumption)).
% 1.35/1.10 tff(235,assumption,(c0_1(a208)), introduced(assumption)).
% 1.35/1.10 tff(236,assumption,(~hskp18), introduced(assumption)).
% 1.35/1.10 tff(237,plain,
% 1.35/1.10 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | c2_1(a208) | (~ndr1_0) | c3_1(a208) | (~c0_1(a208)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp18 | hskp0 | c2_1(a208) | (~ndr1_0) | c3_1(a208) | (~c0_1(a208)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(238,plain,
% 1.35/1.10 ((hskp18 | hskp0 | (~ndr1_0) | c3_1(a208) | c2_1(a208) | (~c0_1(a208))) <=> (hskp18 | hskp0 | c2_1(a208) | (~ndr1_0) | c3_1(a208) | (~c0_1(a208)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(239,plain,
% 1.35/1.10 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c3_1(a208) | c2_1(a208) | (~c0_1(a208)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | c2_1(a208) | (~ndr1_0) | c3_1(a208) | (~c0_1(a208))))),
% 1.35/1.10 inference(monotonicity,[status(thm)],[238])).
% 1.35/1.10 tff(240,plain,
% 1.35/1.10 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c3_1(a208) | c2_1(a208) | (~c0_1(a208)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp18 | hskp0 | c2_1(a208) | (~ndr1_0) | c3_1(a208) | (~c0_1(a208)))),
% 1.35/1.10 inference(transitivity,[status(thm)],[239, 237])).
% 1.35/1.10 tff(241,plain,
% 1.35/1.10 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c3_1(a208) | c2_1(a208) | (~c0_1(a208)))),
% 1.35/1.10 inference(quant_inst,[status(thm)],[])).
% 1.35/1.10 tff(242,plain,
% 1.35/1.10 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp18 | hskp0 | c2_1(a208) | (~ndr1_0) | c3_1(a208) | (~c0_1(a208))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[241, 240])).
% 1.35/1.10 tff(243,plain,
% 1.35/1.10 (hskp0 | c3_1(a208)),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[242, 128, 236, 235, 234, 233])).
% 1.35/1.10 tff(244,plain,
% 1.35/1.10 (c3_1(a208)),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[243, 223])).
% 1.35/1.10 tff(245,plain,
% 1.35/1.10 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))))),
% 1.35/1.10 inference(bind,[status(th)],[])).
% 1.35/1.10 tff(246,plain,
% 1.35/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.35/1.10 inference(quant_intro,[status(thm)],[245])).
% 1.35/1.10 tff(247,plain,
% 1.35/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(248,plain,
% 1.35/1.10 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))))),
% 1.35/1.10 inference(bind,[status(th)],[])).
% 1.35/1.10 tff(249,plain,
% 1.35/1.10 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.35/1.10 inference(quant_intro,[status(thm)],[248])).
% 1.35/1.10 tff(250,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 1.35/1.10 tff(251,plain,
% 1.35/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[250, 249])).
% 1.35/1.10 tff(252,plain,
% 1.35/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[251, 247])).
% 1.35/1.10 tff(253,plain,(
% 1.35/1.10 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.35/1.10 inference(skolemize,[status(sab)],[252])).
% 1.35/1.10 tff(254,plain,
% 1.35/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[253, 246])).
% 1.35/1.10 tff(255,plain,
% 1.35/1.10 (^[U: $i] : refl((hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 1.35/1.10 inference(bind,[status(th)],[])).
% 1.35/1.10 tff(256,plain,
% 1.35/1.10 (![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.10 inference(quant_intro,[status(thm)],[255])).
% 1.35/1.10 tff(257,plain,
% 1.35/1.10 (![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(258,plain,
% 1.35/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp7))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) | hskp24) <=> ((hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp24))), rewrite(((hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp24) <=> (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) | hskp24) <=> (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.35/1.11 inference(bind,[status(th)],[])).
% 1.35/1.11 tff(259,plain,
% 1.35/1.11 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) | hskp24) <=> ![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.11 inference(quant_intro,[status(thm)],[258])).
% 1.35/1.11 tff(260,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.35/1.11 tff(261,plain,
% 1.35/1.11 (![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[260, 259])).
% 1.35/1.11 tff(262,plain,
% 1.35/1.11 (![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[261, 257])).
% 1.35/1.11 tff(263,plain,(
% 1.35/1.11 ![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.11 inference(skolemize,[status(sab)],[262])).
% 1.35/1.11 tff(264,plain,
% 1.35/1.11 (![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[263, 256])).
% 1.35/1.11 tff(265,assumption,(c1_1(a208)), introduced(assumption)).
% 1.35/1.11 tff(266,plain,
% 1.35/1.11 (((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp7 | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp7 | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(267,plain,
% 1.35/1.11 ((hskp24 | hskp7 | (~ndr1_0) | (~c0_1(a208)) | (~c3_1(a208)) | (~c1_1(a208))) <=> (hskp24 | hskp7 | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(268,plain,
% 1.35/1.11 (((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(a208)) | (~c3_1(a208)) | (~c1_1(a208)))) <=> ((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp7 | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208))))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[267])).
% 1.35/1.11 tff(269,plain,
% 1.35/1.11 (((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(a208)) | (~c3_1(a208)) | (~c1_1(a208)))) <=> ((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp7 | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.35/1.11 inference(transitivity,[status(thm)],[268, 266])).
% 1.35/1.11 tff(270,plain,
% 1.35/1.11 ((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(a208)) | (~c3_1(a208)) | (~c1_1(a208)))),
% 1.35/1.11 inference(quant_inst,[status(thm)],[])).
% 1.35/1.11 tff(271,plain,
% 1.35/1.11 ((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp7 | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[270, 269])).
% 1.35/1.11 tff(272,plain,
% 1.35/1.11 (hskp7 | (~c3_1(a208))),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[271, 128, 12, 235, 265, 264])).
% 1.35/1.11 tff(273,plain,
% 1.35/1.11 (hskp7),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[272, 244])).
% 1.35/1.11 tff(274,plain,
% 1.35/1.11 (((~hskp7) | (~c3_1(a209))) <=> ((~hskp7) | (~c3_1(a209)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(275,plain,
% 1.35/1.11 (((~c3_1(a209)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a209)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(276,axiom,((~c3_1(a209)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.35/1.11 tff(277,plain,
% 1.35/1.11 ((~hskp7) | (~c3_1(a209))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.35/1.11 tff(278,plain,
% 1.35/1.11 ((~hskp7) | (~c3_1(a209))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[277, 274])).
% 1.35/1.11 tff(279,plain,
% 1.35/1.11 (~c3_1(a209)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[278, 273])).
% 1.35/1.11 tff(280,plain,
% 1.35/1.11 (^[U: $i] : refl((hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.35/1.11 inference(bind,[status(th)],[])).
% 1.35/1.11 tff(281,plain,
% 1.35/1.11 (![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.11 inference(quant_intro,[status(thm)],[280])).
% 1.35/1.11 tff(282,plain,
% 1.35/1.11 (![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(283,plain,
% 1.35/1.11 (^[U: $i] : 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)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.35/1.11 inference(bind,[status(th)],[])).
% 1.35/1.11 tff(284,plain,
% 1.35/1.11 (![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp21) <=> ![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.11 inference(quant_intro,[status(thm)],[283])).
% 1.35/1.11 tff(285,axiom,(![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 1.35/1.11 tff(286,plain,
% 1.35/1.11 (![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[285, 284])).
% 1.35/1.11 tff(287,plain,
% 1.35/1.11 (![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[286, 282])).
% 1.35/1.11 tff(288,plain,(
% 1.35/1.11 ![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.11 inference(skolemize,[status(sab)],[287])).
% 1.35/1.11 tff(289,plain,
% 1.35/1.11 (![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[288, 281])).
% 1.35/1.11 tff(290,plain,
% 1.35/1.11 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | c2_1(a208) | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | c2_1(a208) | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(291,plain,
% 1.35/1.11 ((hskp21 | (~ndr1_0) | c2_1(a208) | (~c3_1(a208)) | (~c1_1(a208))) <=> (hskp21 | c2_1(a208) | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(292,plain,
% 1.35/1.11 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a208) | (~c3_1(a208)) | (~c1_1(a208)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | c2_1(a208) | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208))))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[291])).
% 1.35/1.11 tff(293,plain,
% 1.35/1.11 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a208) | (~c3_1(a208)) | (~c1_1(a208)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | c2_1(a208) | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)))),
% 1.35/1.11 inference(transitivity,[status(thm)],[292, 290])).
% 1.35/1.11 tff(294,plain,
% 1.35/1.11 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a208) | (~c3_1(a208)) | (~c1_1(a208)))),
% 1.35/1.11 inference(quant_inst,[status(thm)],[])).
% 1.35/1.11 tff(295,plain,
% 1.35/1.11 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | c2_1(a208) | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[294, 293])).
% 1.35/1.11 tff(296,plain,
% 1.35/1.11 (hskp21 | (~c3_1(a208))),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[295, 128, 265, 234, 289])).
% 1.35/1.11 tff(297,plain,
% 1.35/1.11 (hskp21),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[296, 244])).
% 1.35/1.11 tff(298,plain,
% 1.35/1.11 (((~hskp21) | (~c3_1(a241))) <=> ((~hskp21) | (~c3_1(a241)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(299,plain,
% 1.35/1.11 (((~c3_1(a241)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a241)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(300,axiom,((~c3_1(a241)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 1.35/1.11 tff(301,plain,
% 1.35/1.11 ((~hskp21) | (~c3_1(a241))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[300, 299])).
% 1.35/1.11 tff(302,plain,
% 1.35/1.11 ((~hskp21) | (~c3_1(a241))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[301, 298])).
% 1.35/1.11 tff(303,plain,
% 1.35/1.11 (~c3_1(a241)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[302, 297])).
% 1.35/1.11 tff(304,plain,
% 1.35/1.11 (((~hskp21) | (~c1_1(a241))) <=> ((~hskp21) | (~c1_1(a241)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(305,plain,
% 1.35/1.11 (((~c1_1(a241)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a241)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(306,axiom,((~c1_1(a241)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 1.35/1.11 tff(307,plain,
% 1.35/1.11 ((~hskp21) | (~c1_1(a241))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[306, 305])).
% 1.35/1.11 tff(308,plain,
% 1.35/1.11 ((~hskp21) | (~c1_1(a241))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[307, 304])).
% 1.35/1.11 tff(309,plain,
% 1.35/1.11 (~c1_1(a241)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[308, 297])).
% 1.35/1.11 tff(310,plain,
% 1.35/1.11 (((~hskp7) | c1_1(a209)) <=> ((~hskp7) | c1_1(a209))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(311,axiom,((~hskp7) | c1_1(a209)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.35/1.11 tff(312,plain,
% 1.35/1.11 ((~hskp7) | c1_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[311, 310])).
% 1.35/1.11 tff(313,plain,
% 1.35/1.11 ((~hskp7) | c1_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[312, 310])).
% 1.35/1.11 tff(314,plain,
% 1.35/1.11 ((~hskp7) | c1_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[313, 310])).
% 1.35/1.11 tff(315,plain,
% 1.35/1.11 ((~hskp7) | c1_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[314, 310])).
% 1.35/1.11 tff(316,plain,
% 1.35/1.11 ((~hskp7) | c1_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[315, 310])).
% 1.35/1.11 tff(317,plain,
% 1.35/1.11 ((~hskp7) | c1_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[316, 310])).
% 1.35/1.11 tff(318,plain,
% 1.35/1.11 ((~hskp7) | c1_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[317, 310])).
% 1.35/1.11 tff(319,plain,
% 1.35/1.11 ((~hskp7) | c1_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[318, 310])).
% 1.35/1.11 tff(320,plain,
% 1.35/1.11 (c1_1(a209)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[319, 273])).
% 1.35/1.11 tff(321,plain,
% 1.35/1.11 (((~hskp21) | c0_1(a241)) <=> ((~hskp21) | c0_1(a241))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(322,axiom,((~hskp21) | c0_1(a241)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.35/1.11 tff(323,plain,
% 1.35/1.11 ((~hskp21) | c0_1(a241)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[322, 321])).
% 1.35/1.11 tff(324,plain,
% 1.35/1.11 ((~hskp21) | c0_1(a241)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[323, 321])).
% 1.35/1.11 tff(325,plain,
% 1.35/1.11 ((~hskp21) | c0_1(a241)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[324, 321])).
% 1.35/1.11 tff(326,plain,
% 1.35/1.11 ((~hskp21) | c0_1(a241)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[325, 321])).
% 1.35/1.11 tff(327,plain,
% 1.35/1.11 ((~hskp21) | c0_1(a241)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[326, 321])).
% 1.35/1.11 tff(328,plain,
% 1.35/1.11 ((~hskp21) | c0_1(a241)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[327, 321])).
% 1.35/1.11 tff(329,plain,
% 1.35/1.11 ((~hskp21) | c0_1(a241)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[328, 321])).
% 1.35/1.11 tff(330,plain,
% 1.35/1.11 ((~hskp21) | c0_1(a241)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[329, 321])).
% 1.35/1.11 tff(331,plain,
% 1.35/1.11 (c0_1(a241)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[330, 297])).
% 1.35/1.11 tff(332,plain,
% 1.35/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a241) | c3_1(a241) | c3_1(a209) | c2_1(a208) | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)) | (~c1_1(a209)) | (~c2_1(a209)) | (~c0_1(a241)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a241) | c3_1(a241) | c3_1(a209) | c2_1(a208) | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)) | (~c1_1(a209)) | (~c2_1(a209)) | (~c0_1(a241)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(333,plain,
% 1.35/1.11 (((~ndr1_0) | c3_1(a209) | (~c2_1(a209)) | (~c1_1(a209)) | (~c3_1(a208)) | c2_1(a208) | (~c1_1(a208)) | c1_1(a241) | c3_1(a241) | (~c0_1(a241))) <=> (c1_1(a241) | c3_1(a241) | c3_1(a209) | c2_1(a208) | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)) | (~c1_1(a209)) | (~c2_1(a209)) | (~c0_1(a241)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(334,plain,
% 1.35/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a209) | (~c2_1(a209)) | (~c1_1(a209)) | (~c3_1(a208)) | c2_1(a208) | (~c1_1(a208)) | c1_1(a241) | c3_1(a241) | (~c0_1(a241)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a241) | c3_1(a241) | c3_1(a209) | c2_1(a208) | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)) | (~c1_1(a209)) | (~c2_1(a209)) | (~c0_1(a241))))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[333])).
% 1.35/1.11 tff(335,plain,
% 1.35/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a209) | (~c2_1(a209)) | (~c1_1(a209)) | (~c3_1(a208)) | c2_1(a208) | (~c1_1(a208)) | c1_1(a241) | c3_1(a241) | (~c0_1(a241)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a241) | c3_1(a241) | c3_1(a209) | c2_1(a208) | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)) | (~c1_1(a209)) | (~c2_1(a209)) | (~c0_1(a241)))),
% 1.35/1.11 inference(transitivity,[status(thm)],[334, 332])).
% 1.35/1.11 tff(336,plain,
% 1.35/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a209) | (~c2_1(a209)) | (~c1_1(a209)) | (~c3_1(a208)) | c2_1(a208) | (~c1_1(a208)) | c1_1(a241) | c3_1(a241) | (~c0_1(a241)))),
% 1.35/1.11 inference(quant_inst,[status(thm)],[])).
% 1.35/1.11 tff(337,plain,
% 1.35/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a241) | c3_1(a241) | c3_1(a209) | c2_1(a208) | (~ndr1_0) | (~c3_1(a208)) | (~c1_1(a208)) | (~c1_1(a209)) | (~c2_1(a209)) | (~c0_1(a241))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[336, 335])).
% 1.35/1.11 tff(338,plain,
% 1.35/1.11 (~c2_1(a209)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[337, 128, 331, 320, 265, 309, 303, 279, 234, 254, 244])).
% 1.35/1.11 tff(339,plain,
% 1.35/1.11 (((~hskp7) | c0_1(a209)) <=> ((~hskp7) | c0_1(a209))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(340,axiom,((~hskp7) | c0_1(a209)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.35/1.11 tff(341,plain,
% 1.35/1.11 ((~hskp7) | c0_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[340, 339])).
% 1.35/1.11 tff(342,plain,
% 1.35/1.11 ((~hskp7) | c0_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[341, 339])).
% 1.35/1.11 tff(343,plain,
% 1.35/1.11 ((~hskp7) | c0_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[342, 339])).
% 1.35/1.11 tff(344,plain,
% 1.35/1.11 ((~hskp7) | c0_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[343, 339])).
% 1.35/1.11 tff(345,plain,
% 1.35/1.11 ((~hskp7) | c0_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[344, 339])).
% 1.35/1.11 tff(346,plain,
% 1.35/1.11 ((~hskp7) | c0_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[345, 339])).
% 1.35/1.11 tff(347,plain,
% 1.35/1.11 ((~hskp7) | c0_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[346, 339])).
% 1.35/1.11 tff(348,plain,
% 1.35/1.11 ((~hskp7) | c0_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[347, 339])).
% 1.35/1.11 tff(349,plain,
% 1.35/1.11 (c0_1(a209)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[348, 273])).
% 1.35/1.11 tff(350,plain,
% 1.35/1.11 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | c3_1(a209) | (~ndr1_0) | (~c0_1(a209)) | c2_1(a209))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp18 | hskp0 | c3_1(a209) | (~ndr1_0) | (~c0_1(a209)) | c2_1(a209))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(351,plain,
% 1.35/1.11 ((hskp18 | hskp0 | (~ndr1_0) | c3_1(a209) | c2_1(a209) | (~c0_1(a209))) <=> (hskp18 | hskp0 | c3_1(a209) | (~ndr1_0) | (~c0_1(a209)) | c2_1(a209))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(352,plain,
% 1.35/1.11 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c3_1(a209) | c2_1(a209) | (~c0_1(a209)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | c3_1(a209) | (~ndr1_0) | (~c0_1(a209)) | c2_1(a209)))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[351])).
% 1.35/1.11 tff(353,plain,
% 1.35/1.11 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c3_1(a209) | c2_1(a209) | (~c0_1(a209)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp18 | hskp0 | c3_1(a209) | (~ndr1_0) | (~c0_1(a209)) | c2_1(a209))),
% 1.35/1.11 inference(transitivity,[status(thm)],[352, 350])).
% 1.35/1.11 tff(354,plain,
% 1.35/1.11 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c3_1(a209) | c2_1(a209) | (~c0_1(a209)))),
% 1.35/1.11 inference(quant_inst,[status(thm)],[])).
% 1.35/1.11 tff(355,plain,
% 1.35/1.11 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp18 | hskp0 | c3_1(a209) | (~ndr1_0) | (~c0_1(a209)) | c2_1(a209)),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[354, 353])).
% 1.35/1.11 tff(356,plain,
% 1.35/1.11 ($false),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[355, 128, 236, 223, 349, 279, 233, 338])).
% 1.35/1.11 tff(357,plain,(hskp0 | hskp18 | (~c1_1(a208)) | c2_1(a208) | hskp24 | (~c0_1(a208))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.11 tff(358,plain,
% 1.35/1.11 (hskp0),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[357, 222, 211, 178, 12, 172])).
% 1.35/1.11 tff(359,plain,
% 1.35/1.11 (((~hskp0) | (~c0_1(a199))) <=> ((~hskp0) | (~c0_1(a199)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(360,plain,
% 1.35/1.11 (((~c0_1(a199)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a199)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(361,axiom,((~c0_1(a199)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.35/1.11 tff(362,plain,
% 1.35/1.11 ((~hskp0) | (~c0_1(a199))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[361, 360])).
% 1.35/1.11 tff(363,plain,
% 1.35/1.11 ((~hskp0) | (~c0_1(a199))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[362, 359])).
% 1.35/1.11 tff(364,plain,
% 1.35/1.11 (~c0_1(a199)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[363, 358])).
% 1.35/1.11 tff(365,plain,
% 1.35/1.11 (((~hskp0) | (~c1_1(a199))) <=> ((~hskp0) | (~c1_1(a199)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(366,plain,
% 1.35/1.11 (((~c1_1(a199)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a199)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(367,axiom,((~c1_1(a199)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.35/1.11 tff(368,plain,
% 1.35/1.11 ((~hskp0) | (~c1_1(a199))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[367, 366])).
% 1.35/1.11 tff(369,plain,
% 1.35/1.11 ((~hskp0) | (~c1_1(a199))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[368, 365])).
% 1.35/1.11 tff(370,plain,
% 1.35/1.11 (~c1_1(a199)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[369, 358])).
% 1.35/1.11 tff(371,plain,
% 1.35/1.11 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.35/1.11 inference(bind,[status(th)],[])).
% 1.35/1.11 tff(372,plain,
% 1.35/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.11 inference(quant_intro,[status(thm)],[371])).
% 1.35/1.11 tff(373,plain,
% 1.35/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(374,plain,
% 1.35/1.11 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.35/1.11 inference(bind,[status(th)],[])).
% 1.35/1.11 tff(375,plain,
% 1.35/1.11 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.11 inference(quant_intro,[status(thm)],[374])).
% 1.35/1.11 tff(376,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.35/1.11 tff(377,plain,
% 1.35/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[376, 375])).
% 1.35/1.11 tff(378,plain,
% 1.35/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[377, 373])).
% 1.35/1.11 tff(379,plain,(
% 1.35/1.11 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.11 inference(skolemize,[status(sab)],[378])).
% 1.35/1.11 tff(380,plain,
% 1.35/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[379, 372])).
% 1.35/1.11 tff(381,plain,
% 1.35/1.11 (hskp4),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[126, 160, 12])).
% 1.35/1.11 tff(382,plain,
% 1.35/1.11 (((~hskp4) | (~c2_1(a204))) <=> ((~hskp4) | (~c2_1(a204)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(383,plain,
% 1.35/1.11 (((~c2_1(a204)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a204)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(384,axiom,((~c2_1(a204)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.35/1.11 tff(385,plain,
% 1.35/1.11 ((~hskp4) | (~c2_1(a204))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[384, 383])).
% 1.35/1.11 tff(386,plain,
% 1.35/1.11 ((~hskp4) | (~c2_1(a204))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[385, 382])).
% 1.35/1.11 tff(387,plain,
% 1.35/1.11 (~c2_1(a204)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[386, 381])).
% 1.35/1.11 tff(388,plain,
% 1.35/1.11 (((~hskp4) | (~c0_1(a204))) <=> ((~hskp4) | (~c0_1(a204)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(389,plain,
% 1.35/1.11 (((~c0_1(a204)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a204)))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(390,axiom,((~c0_1(a204)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.35/1.11 tff(391,plain,
% 1.35/1.11 ((~hskp4) | (~c0_1(a204))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[390, 389])).
% 1.35/1.11 tff(392,plain,
% 1.35/1.11 ((~hskp4) | (~c0_1(a204))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[391, 388])).
% 1.35/1.11 tff(393,plain,
% 1.35/1.11 (~c0_1(a204)),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[392, 381])).
% 1.35/1.11 tff(394,plain,
% 1.35/1.12 (((~hskp0) | c3_1(a199)) <=> ((~hskp0) | c3_1(a199))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(395,axiom,((~hskp0) | c3_1(a199)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.35/1.12 tff(396,plain,
% 1.35/1.12 ((~hskp0) | c3_1(a199)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[395, 394])).
% 1.35/1.12 tff(397,plain,
% 1.35/1.12 ((~hskp0) | c3_1(a199)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[396, 394])).
% 1.35/1.12 tff(398,plain,
% 1.35/1.12 ((~hskp0) | c3_1(a199)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[397, 394])).
% 1.35/1.12 tff(399,plain,
% 1.35/1.12 ((~hskp0) | c3_1(a199)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[398, 394])).
% 1.35/1.12 tff(400,plain,
% 1.35/1.12 ((~hskp0) | c3_1(a199)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[399, 394])).
% 1.35/1.12 tff(401,plain,
% 1.35/1.12 ((~hskp0) | c3_1(a199)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[400, 394])).
% 1.35/1.12 tff(402,plain,
% 1.35/1.12 ((~hskp0) | c3_1(a199)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[401, 394])).
% 1.35/1.12 tff(403,plain,
% 1.35/1.12 ((~hskp0) | c3_1(a199)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[402, 394])).
% 1.35/1.12 tff(404,plain,
% 1.35/1.12 (c3_1(a199)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[403, 358])).
% 1.35/1.12 tff(405,plain,
% 1.35/1.12 (((~hskp4) | c1_1(a204)) <=> ((~hskp4) | c1_1(a204))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(406,axiom,((~hskp4) | c1_1(a204)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.35/1.12 tff(407,plain,
% 1.35/1.12 ((~hskp4) | c1_1(a204)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[406, 405])).
% 1.35/1.12 tff(408,plain,
% 1.35/1.12 ((~hskp4) | c1_1(a204)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[407, 405])).
% 1.35/1.12 tff(409,plain,
% 1.35/1.12 ((~hskp4) | c1_1(a204)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[408, 405])).
% 1.35/1.12 tff(410,plain,
% 1.35/1.12 ((~hskp4) | c1_1(a204)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[409, 405])).
% 1.35/1.12 tff(411,plain,
% 1.35/1.12 ((~hskp4) | c1_1(a204)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[410, 405])).
% 1.35/1.12 tff(412,plain,
% 1.35/1.12 ((~hskp4) | c1_1(a204)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[411, 405])).
% 1.35/1.12 tff(413,plain,
% 1.35/1.12 ((~hskp4) | c1_1(a204)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[412, 405])).
% 1.35/1.12 tff(414,plain,
% 1.35/1.12 ((~hskp4) | c1_1(a204)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[413, 405])).
% 1.35/1.12 tff(415,plain,
% 1.35/1.12 (c1_1(a204)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[414, 381])).
% 1.35/1.12 tff(416,plain,
% 1.35/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a204) | c2_1(a204) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | (~c1_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a204) | c2_1(a204) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | (~c1_1(a204)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(417,plain,
% 1.35/1.12 (((~ndr1_0) | c0_1(a199) | (~c2_1(a199)) | (~c3_1(a199)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199))) <=> (c0_1(a204) | c2_1(a204) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | (~c1_1(a204)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(418,plain,
% 1.35/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a199) | (~c2_1(a199)) | (~c3_1(a199)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a204) | c2_1(a204) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | (~c1_1(a204))))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[417])).
% 1.35/1.12 tff(419,plain,
% 1.35/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a199) | (~c2_1(a199)) | (~c3_1(a199)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a204) | c2_1(a204) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | (~c1_1(a204)))),
% 1.35/1.12 inference(transitivity,[status(thm)],[418, 416])).
% 1.35/1.12 tff(420,plain,
% 1.35/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a199) | (~c2_1(a199)) | (~c3_1(a199)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(421,plain,
% 1.35/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a204) | c2_1(a204) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | (~c1_1(a204))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[420, 419])).
% 1.35/1.12 tff(422,plain,
% 1.35/1.12 (~c2_1(a199)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[421, 128, 415, 404, 393, 387, 364, 370, 380])).
% 1.35/1.12 tff(423,assumption,(~c2_1(a199)), introduced(assumption)).
% 1.35/1.12 tff(424,plain,
% 1.35/1.12 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.35/1.12 inference(bind,[status(th)],[])).
% 1.35/1.12 tff(425,plain,
% 1.35/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.12 inference(quant_intro,[status(thm)],[424])).
% 1.35/1.12 tff(426,plain,
% 1.35/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(427,plain,
% 1.35/1.12 (^[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))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | 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)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | 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)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.35/1.12 inference(bind,[status(th)],[])).
% 1.35/1.12 tff(428,plain,
% 1.35/1.12 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.12 inference(quant_intro,[status(thm)],[427])).
% 1.35/1.12 tff(429,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.35/1.12 tff(430,plain,
% 1.35/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[429, 428])).
% 1.35/1.12 tff(431,plain,
% 1.35/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[430, 426])).
% 1.35/1.12 tff(432,plain,(
% 1.35/1.12 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.12 inference(skolemize,[status(sab)],[431])).
% 1.35/1.12 tff(433,plain,
% 1.35/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[432, 425])).
% 1.35/1.12 tff(434,assumption,(~c1_1(a199)), introduced(assumption)).
% 1.35/1.12 tff(435,assumption,(~c0_1(a199)), introduced(assumption)).
% 1.35/1.12 tff(436,assumption,(hskp1), introduced(assumption)).
% 1.35/1.12 tff(437,plain,
% 1.35/1.12 (((~hskp1) | (~c2_1(a200))) <=> ((~hskp1) | (~c2_1(a200)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(438,plain,
% 1.35/1.12 (((~c2_1(a200)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a200)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(439,axiom,((~c2_1(a200)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.35/1.12 tff(440,plain,
% 1.35/1.12 ((~hskp1) | (~c2_1(a200))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[439, 438])).
% 1.35/1.12 tff(441,plain,
% 1.35/1.12 ((~hskp1) | (~c2_1(a200))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[440, 437])).
% 1.35/1.12 tff(442,plain,
% 1.35/1.12 (~c2_1(a200)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[441, 436])).
% 1.35/1.12 tff(443,plain,
% 1.35/1.12 (((~hskp1) | (~c1_1(a200))) <=> ((~hskp1) | (~c1_1(a200)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(444,plain,
% 1.35/1.12 (((~c1_1(a200)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a200)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(445,axiom,((~c1_1(a200)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.35/1.12 tff(446,plain,
% 1.35/1.12 ((~hskp1) | (~c1_1(a200))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[445, 444])).
% 1.35/1.12 tff(447,plain,
% 1.35/1.12 ((~hskp1) | (~c1_1(a200))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[446, 443])).
% 1.35/1.12 tff(448,plain,
% 1.35/1.12 (~c1_1(a200)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[447, 436])).
% 1.35/1.12 tff(449,plain,
% 1.35/1.12 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c1_1(a200) | c2_1(a200) | (~ndr1_0) | c3_1(a200))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a200) | c2_1(a200) | (~ndr1_0) | c3_1(a200))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(450,plain,
% 1.35/1.12 ((hskp27 | (~ndr1_0) | c3_1(a200) | c2_1(a200) | c1_1(a200)) <=> (hskp27 | c1_1(a200) | c2_1(a200) | (~ndr1_0) | c3_1(a200))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(451,plain,
% 1.35/1.12 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a200) | c2_1(a200) | c1_1(a200))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c1_1(a200) | c2_1(a200) | (~ndr1_0) | c3_1(a200)))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[450])).
% 1.35/1.12 tff(452,plain,
% 1.35/1.12 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a200) | c2_1(a200) | c1_1(a200))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a200) | c2_1(a200) | (~ndr1_0) | c3_1(a200))),
% 1.35/1.12 inference(transitivity,[status(thm)],[451, 449])).
% 1.35/1.12 tff(453,plain,
% 1.35/1.12 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a200) | c2_1(a200) | c1_1(a200))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(454,plain,
% 1.35/1.12 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a200) | c2_1(a200) | (~ndr1_0) | c3_1(a200)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[453, 452])).
% 1.35/1.12 tff(455,plain,
% 1.35/1.12 (c3_1(a200)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[454, 128, 160, 448, 442, 188])).
% 1.35/1.12 tff(456,plain,
% 1.35/1.12 (((~hskp1) | c0_1(a200)) <=> ((~hskp1) | c0_1(a200))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(457,axiom,((~hskp1) | c0_1(a200)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.35/1.12 tff(458,plain,
% 1.35/1.12 ((~hskp1) | c0_1(a200)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[457, 456])).
% 1.35/1.12 tff(459,plain,
% 1.35/1.12 ((~hskp1) | c0_1(a200)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[458, 456])).
% 1.35/1.12 tff(460,plain,
% 1.35/1.12 ((~hskp1) | c0_1(a200)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[459, 456])).
% 1.35/1.12 tff(461,plain,
% 1.35/1.12 ((~hskp1) | c0_1(a200)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[460, 456])).
% 1.35/1.12 tff(462,plain,
% 1.35/1.12 ((~hskp1) | c0_1(a200)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[461, 456])).
% 1.35/1.12 tff(463,plain,
% 1.35/1.12 ((~hskp1) | c0_1(a200)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[462, 456])).
% 1.35/1.12 tff(464,plain,
% 1.35/1.12 ((~hskp1) | c0_1(a200)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[463, 456])).
% 1.35/1.12 tff(465,plain,
% 1.35/1.12 ((~hskp1) | c0_1(a200)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[464, 456])).
% 1.35/1.12 tff(466,plain,
% 1.35/1.12 (c0_1(a200)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[465, 436])).
% 1.35/1.12 tff(467,plain,
% 1.35/1.12 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | c1_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp24 | hskp22 | c1_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(468,plain,
% 1.35/1.12 ((hskp24 | hskp22 | (~ndr1_0) | c1_1(a200) | (~c0_1(a200)) | (~c3_1(a200))) <=> (hskp24 | hskp22 | c1_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(469,plain,
% 1.35/1.12 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c1_1(a200) | (~c0_1(a200)) | (~c3_1(a200)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | c1_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200))))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[468])).
% 1.35/1.12 tff(470,plain,
% 1.35/1.12 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c1_1(a200) | (~c0_1(a200)) | (~c3_1(a200)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp24 | hskp22 | c1_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)))),
% 1.35/1.12 inference(transitivity,[status(thm)],[469, 467])).
% 1.35/1.12 tff(471,plain,
% 1.35/1.12 ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c1_1(a200) | (~c0_1(a200)) | (~c3_1(a200)))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(472,plain,
% 1.35/1.12 ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp24 | hskp22 | c1_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[471, 470])).
% 1.35/1.12 tff(473,plain,
% 1.35/1.12 (hskp22 | (~c3_1(a200))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[472, 128, 12, 466, 448, 91])).
% 1.35/1.12 tff(474,plain,
% 1.35/1.12 (hskp22),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[473, 455])).
% 1.35/1.12 tff(475,plain,
% 1.35/1.12 (~c2_1(a244)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[141, 474])).
% 1.35/1.12 tff(476,plain,
% 1.35/1.12 (~c0_1(a244)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[147, 474])).
% 1.35/1.12 tff(477,plain,
% 1.35/1.12 (^[U: $i] : refl((hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 1.35/1.12 inference(bind,[status(th)],[])).
% 1.35/1.12 tff(478,plain,
% 1.35/1.12 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.12 inference(quant_intro,[status(thm)],[477])).
% 1.35/1.12 tff(479,plain,
% 1.35/1.12 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(480,plain,
% 1.35/1.12 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp18) <=> ((hskp29 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp18))), rewrite(((hskp29 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp18) <=> (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp18) <=> (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 1.35/1.12 inference(bind,[status(th)],[])).
% 1.35/1.12 tff(481,plain,
% 1.35/1.12 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp18) <=> ![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.12 inference(quant_intro,[status(thm)],[480])).
% 1.35/1.12 tff(482,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.35/1.12 tff(483,plain,
% 1.35/1.12 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[482, 481])).
% 1.35/1.12 tff(484,plain,
% 1.35/1.12 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[483, 479])).
% 1.35/1.12 tff(485,plain,(
% 1.35/1.12 ![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.12 inference(skolemize,[status(sab)],[484])).
% 1.35/1.12 tff(486,plain,
% 1.35/1.12 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[485, 478])).
% 1.35/1.12 tff(487,plain,
% 1.35/1.12 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp29 | hskp18 | c2_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp29 | hskp18 | c2_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(488,plain,
% 1.35/1.12 ((hskp29 | hskp18 | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c3_1(a200))) <=> (hskp29 | hskp18 | c2_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(489,plain,
% 1.35/1.12 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c3_1(a200)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp29 | hskp18 | c2_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200))))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[488])).
% 1.35/1.12 tff(490,plain,
% 1.35/1.12 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c3_1(a200)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp29 | hskp18 | c2_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)))),
% 1.35/1.12 inference(transitivity,[status(thm)],[489, 487])).
% 1.35/1.12 tff(491,plain,
% 1.35/1.12 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c3_1(a200)))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(492,plain,
% 1.35/1.12 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp29 | hskp18 | c2_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[491, 490])).
% 1.35/1.12 tff(493,plain,
% 1.35/1.12 (hskp29),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[492, 128, 211, 466, 442, 486, 455])).
% 1.35/1.12 tff(494,plain,
% 1.35/1.12 (((~hskp29) | c3_1(a227)) <=> ((~hskp29) | c3_1(a227))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(495,axiom,((~hskp29) | c3_1(a227)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.35/1.12 tff(496,plain,
% 1.35/1.12 ((~hskp29) | c3_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[495, 494])).
% 1.35/1.12 tff(497,plain,
% 1.35/1.12 ((~hskp29) | c3_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[496, 494])).
% 1.35/1.12 tff(498,plain,
% 1.35/1.12 ((~hskp29) | c3_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[497, 494])).
% 1.35/1.12 tff(499,plain,
% 1.35/1.12 ((~hskp29) | c3_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[498, 494])).
% 1.35/1.12 tff(500,plain,
% 1.35/1.12 ((~hskp29) | c3_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[499, 494])).
% 1.35/1.12 tff(501,plain,
% 1.35/1.12 ((~hskp29) | c3_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[500, 494])).
% 1.35/1.12 tff(502,plain,
% 1.35/1.12 ((~hskp29) | c3_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[501, 494])).
% 1.35/1.12 tff(503,plain,
% 1.35/1.12 ((~hskp29) | c3_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[502, 494])).
% 1.35/1.12 tff(504,plain,
% 1.35/1.12 (c3_1(a227)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[503, 493])).
% 1.35/1.12 tff(505,plain,
% 1.35/1.12 (((~hskp29) | c1_1(a227)) <=> ((~hskp29) | c1_1(a227))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(506,axiom,((~hskp29) | c1_1(a227)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.35/1.12 tff(507,plain,
% 1.35/1.12 ((~hskp29) | c1_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[506, 505])).
% 1.35/1.12 tff(508,plain,
% 1.35/1.12 ((~hskp29) | c1_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[507, 505])).
% 1.35/1.12 tff(509,plain,
% 1.35/1.12 ((~hskp29) | c1_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[508, 505])).
% 1.35/1.12 tff(510,plain,
% 1.35/1.12 ((~hskp29) | c1_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[509, 505])).
% 1.35/1.12 tff(511,plain,
% 1.35/1.12 ((~hskp29) | c1_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[510, 505])).
% 1.35/1.12 tff(512,plain,
% 1.35/1.12 ((~hskp29) | c1_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[511, 505])).
% 1.35/1.12 tff(513,plain,
% 1.35/1.12 ((~hskp29) | c1_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[512, 505])).
% 1.35/1.12 tff(514,plain,
% 1.35/1.12 ((~hskp29) | c1_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[513, 505])).
% 1.35/1.12 tff(515,plain,
% 1.35/1.12 (c1_1(a227)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[514, 493])).
% 1.35/1.12 tff(516,plain,
% 1.35/1.12 (((~hskp29) | c0_1(a227)) <=> ((~hskp29) | c0_1(a227))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(517,axiom,((~hskp29) | c0_1(a227)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.35/1.12 tff(518,plain,
% 1.35/1.12 ((~hskp29) | c0_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[517, 516])).
% 1.35/1.12 tff(519,plain,
% 1.35/1.12 ((~hskp29) | c0_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[518, 516])).
% 1.35/1.12 tff(520,plain,
% 1.35/1.12 ((~hskp29) | c0_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[519, 516])).
% 1.35/1.12 tff(521,plain,
% 1.35/1.12 ((~hskp29) | c0_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[520, 516])).
% 1.35/1.12 tff(522,plain,
% 1.35/1.12 ((~hskp29) | c0_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[521, 516])).
% 1.35/1.12 tff(523,plain,
% 1.35/1.12 ((~hskp29) | c0_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[522, 516])).
% 1.35/1.12 tff(524,plain,
% 1.35/1.12 ((~hskp29) | c0_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[523, 516])).
% 1.35/1.12 tff(525,plain,
% 1.35/1.12 ((~hskp29) | c0_1(a227)),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[524, 516])).
% 1.35/1.12 tff(526,plain,
% 1.35/1.12 (c0_1(a227)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[525, 493])).
% 1.35/1.12 tff(527,plain,
% 1.35/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a244) | c2_1(a244) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)) | (~c1_1(a244)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a244) | c2_1(a244) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)) | (~c1_1(a244)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(528,plain,
% 1.35/1.12 (((~ndr1_0) | (~c0_1(a227)) | (~c3_1(a227)) | (~c1_1(a227)) | c0_1(a244) | c2_1(a244) | (~c1_1(a244)) | c2_1(a199) | c1_1(a199) | c0_1(a199)) <=> (c0_1(a244) | c2_1(a244) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)) | (~c1_1(a244)))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(529,plain,
% 1.35/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a227)) | (~c3_1(a227)) | (~c1_1(a227)) | c0_1(a244) | c2_1(a244) | (~c1_1(a244)) | c2_1(a199) | c1_1(a199) | c0_1(a199))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a244) | c2_1(a244) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)) | (~c1_1(a244))))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[528])).
% 1.35/1.12 tff(530,plain,
% 1.35/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a227)) | (~c3_1(a227)) | (~c1_1(a227)) | c0_1(a244) | c2_1(a244) | (~c1_1(a244)) | c2_1(a199) | c1_1(a199) | c0_1(a199))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a244) | c2_1(a244) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)) | (~c1_1(a244)))),
% 1.35/1.12 inference(transitivity,[status(thm)],[529, 527])).
% 1.35/1.12 tff(531,plain,
% 1.35/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a227)) | (~c3_1(a227)) | (~c1_1(a227)) | c0_1(a244) | c2_1(a244) | (~c1_1(a244)) | c2_1(a199) | c1_1(a199) | c0_1(a199))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(532,plain,
% 1.35/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a244) | c2_1(a244) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)) | (~c1_1(a244))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[531, 530])).
% 1.35/1.12 tff(533,plain,
% 1.35/1.12 (~c1_1(a244)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[532, 128, 526, 515, 504, 476, 475, 435, 434, 433, 423])).
% 1.35/1.12 tff(534,plain,
% 1.35/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a244) | c2_1(a244) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c1_1(a204)) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)) | c1_1(a244))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a244) | c2_1(a244) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c1_1(a204)) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)) | c1_1(a244))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(535,plain,
% 1.35/1.12 (((~ndr1_0) | (~c0_1(a227)) | (~c3_1(a227)) | (~c1_1(a227)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a244) | c1_1(a244) | c0_1(a244)) <=> (c0_1(a244) | c2_1(a244) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c1_1(a204)) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)) | c1_1(a244))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(536,plain,
% 1.35/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a227)) | (~c3_1(a227)) | (~c1_1(a227)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a244) | c1_1(a244) | c0_1(a244))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a244) | c2_1(a244) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c1_1(a204)) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)) | c1_1(a244)))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[535])).
% 1.35/1.12 tff(537,plain,
% 1.35/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a227)) | (~c3_1(a227)) | (~c1_1(a227)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a244) | c1_1(a244) | c0_1(a244))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a244) | c2_1(a244) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c1_1(a204)) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)) | c1_1(a244))),
% 1.35/1.12 inference(transitivity,[status(thm)],[536, 534])).
% 1.35/1.12 tff(538,plain,
% 1.35/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a227)) | (~c3_1(a227)) | (~c1_1(a227)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a244) | c1_1(a244) | c0_1(a244))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(539,plain,
% 1.35/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a244) | c2_1(a244) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c1_1(a204)) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)) | c1_1(a244)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[538, 537])).
% 1.35/1.13 tff(540,plain,
% 1.35/1.13 ($false),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[539, 128, 526, 515, 504, 415, 476, 475, 393, 387, 433, 533])).
% 1.35/1.13 tff(541,plain,((~hskp1) | c0_1(a199) | c1_1(a199) | c2_1(a199) | hskp24 | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.35/1.13 tff(542,plain,
% 1.35/1.13 (~hskp1),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[541, 422, 370, 364, 12, 160])).
% 1.35/1.13 tff(543,plain,
% 1.35/1.13 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.35/1.13 inference(bind,[status(th)],[])).
% 1.35/1.13 tff(544,plain,
% 1.35/1.13 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.35/1.13 inference(quant_intro,[status(thm)],[543])).
% 1.35/1.13 tff(545,plain,
% 1.35/1.13 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(546,plain,
% 1.35/1.13 (^[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)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.35/1.13 inference(bind,[status(th)],[])).
% 1.35/1.13 tff(547,plain,
% 1.35/1.13 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.35/1.13 inference(quant_intro,[status(thm)],[546])).
% 1.35/1.13 tff(548,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 1.35/1.13 tff(549,plain,
% 1.35/1.13 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[548, 547])).
% 1.35/1.13 tff(550,plain,
% 1.35/1.13 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[549, 545])).
% 1.35/1.13 tff(551,plain,(
% 1.35/1.13 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.35/1.13 inference(skolemize,[status(sab)],[550])).
% 1.35/1.13 tff(552,plain,
% 1.35/1.13 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[551, 544])).
% 1.35/1.13 tff(553,plain,
% 1.35/1.13 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(554,plain,
% 1.35/1.13 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a199) | c1_1(a199) | c0_1(a199)) <=> (hskp2 | hskp1 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(555,plain,
% 1.35/1.13 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a199) | c1_1(a199) | c0_1(a199))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199)))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[554])).
% 1.35/1.13 tff(556,plain,
% 1.35/1.13 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a199) | c1_1(a199) | c0_1(a199))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199))),
% 1.35/1.13 inference(transitivity,[status(thm)],[555, 553])).
% 1.35/1.13 tff(557,plain,
% 1.35/1.13 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a199) | c1_1(a199) | c0_1(a199))),
% 1.35/1.13 inference(quant_inst,[status(thm)],[])).
% 1.35/1.13 tff(558,plain,
% 1.35/1.13 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[557, 556])).
% 1.35/1.13 tff(559,plain,
% 1.35/1.13 (hskp2 | hskp1),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[558, 128, 364, 370, 552, 422])).
% 1.35/1.13 tff(560,plain,
% 1.35/1.13 (hskp2),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[559, 542])).
% 1.35/1.13 tff(561,plain,
% 1.35/1.13 (((~hskp2) | (~c1_1(a201))) <=> ((~hskp2) | (~c1_1(a201)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(562,plain,
% 1.35/1.13 (((~c1_1(a201)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a201)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(563,axiom,((~c1_1(a201)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.35/1.13 tff(564,plain,
% 1.35/1.13 ((~hskp2) | (~c1_1(a201))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[563, 562])).
% 1.35/1.13 tff(565,plain,
% 1.35/1.13 ((~hskp2) | (~c1_1(a201))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[564, 561])).
% 1.35/1.13 tff(566,plain,
% 1.35/1.13 (~c1_1(a201)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[565, 560])).
% 1.35/1.13 tff(567,plain,
% 1.35/1.13 (((~hskp2) | c2_1(a201)) <=> ((~hskp2) | c2_1(a201))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(568,axiom,((~hskp2) | c2_1(a201)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.35/1.13 tff(569,plain,
% 1.35/1.13 ((~hskp2) | c2_1(a201)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[568, 567])).
% 1.35/1.13 tff(570,plain,
% 1.35/1.13 ((~hskp2) | c2_1(a201)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[569, 567])).
% 1.35/1.13 tff(571,plain,
% 1.35/1.13 ((~hskp2) | c2_1(a201)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[570, 567])).
% 1.35/1.13 tff(572,plain,
% 1.35/1.13 ((~hskp2) | c2_1(a201)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[571, 567])).
% 1.35/1.13 tff(573,plain,
% 1.35/1.13 ((~hskp2) | c2_1(a201)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[572, 567])).
% 1.35/1.13 tff(574,plain,
% 1.35/1.13 ((~hskp2) | c2_1(a201)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[573, 567])).
% 1.35/1.13 tff(575,plain,
% 1.35/1.13 ((~hskp2) | c2_1(a201)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[574, 567])).
% 1.35/1.13 tff(576,plain,
% 1.35/1.13 ((~hskp2) | c2_1(a201)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[575, 567])).
% 1.35/1.13 tff(577,plain,
% 1.35/1.13 (c2_1(a201)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[576, 560])).
% 1.35/1.13 tff(578,plain,
% 1.35/1.13 (((~hskp2) | (~c0_1(a201))) <=> ((~hskp2) | (~c0_1(a201)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(579,plain,
% 1.35/1.13 (((~c0_1(a201)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a201)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(580,axiom,((~c0_1(a201)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.35/1.13 tff(581,plain,
% 1.35/1.13 ((~hskp2) | (~c0_1(a201))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[580, 579])).
% 1.35/1.13 tff(582,plain,
% 1.35/1.13 ((~hskp2) | (~c0_1(a201))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[581, 578])).
% 1.35/1.13 tff(583,plain,
% 1.35/1.13 (~c0_1(a201)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[582, 560])).
% 1.35/1.13 tff(584,plain,
% 1.35/1.13 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.35/1.13 inference(bind,[status(th)],[])).
% 1.35/1.13 tff(585,plain,
% 1.35/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.13 inference(quant_intro,[status(thm)],[584])).
% 1.35/1.13 tff(586,plain,
% 1.35/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(587,plain,
% 1.35/1.13 (^[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) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.35/1.13 inference(bind,[status(th)],[])).
% 1.35/1.13 tff(588,plain,
% 1.35/1.13 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.13 inference(quant_intro,[status(thm)],[587])).
% 1.35/1.13 tff(589,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.35/1.13 tff(590,plain,
% 1.35/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.35/1.13 tff(591,plain,
% 1.35/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[590, 586])).
% 1.35/1.13 tff(592,plain,(
% 1.35/1.13 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.13 inference(skolemize,[status(sab)],[591])).
% 1.35/1.13 tff(593,plain,
% 1.35/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[592, 585])).
% 1.35/1.13 tff(594,assumption,(~c1_1(a201)), introduced(assumption)).
% 1.35/1.13 tff(595,assumption,(~c0_1(a201)), introduced(assumption)).
% 1.35/1.13 tff(596,assumption,(c2_1(a201)), introduced(assumption)).
% 1.35/1.13 tff(597,plain,
% 1.35/1.13 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.35/1.13 inference(bind,[status(th)],[])).
% 1.35/1.13 tff(598,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.35/1.13 inference(quant_intro,[status(thm)],[597])).
% 1.35/1.13 tff(599,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(600,plain,
% 1.35/1.13 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.35/1.13 inference(bind,[status(th)],[])).
% 1.35/1.13 tff(601,plain,
% 1.35/1.13 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.35/1.13 inference(quant_intro,[status(thm)],[600])).
% 1.35/1.13 tff(602,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 1.35/1.13 tff(603,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[602, 601])).
% 1.35/1.13 tff(604,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[603, 599])).
% 1.35/1.13 tff(605,plain,(
% 1.35/1.13 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.35/1.13 inference(skolemize,[status(sab)],[604])).
% 1.35/1.13 tff(606,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[605, 598])).
% 1.35/1.13 tff(607,plain,
% 1.35/1.13 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c2_1(a208) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c2_1(a208) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(608,plain,
% 1.35/1.13 ((hskp3 | (~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a201) | c0_1(a201) | (~c2_1(a201))) <=> (hskp3 | c2_1(a208) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(609,plain,
% 1.35/1.13 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a201) | c0_1(a201) | (~c2_1(a201)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c2_1(a208) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c1_1(a208)) | (~c0_1(a208))))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[608])).
% 1.35/1.13 tff(610,plain,
% 1.35/1.13 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a201) | c0_1(a201) | (~c2_1(a201)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c2_1(a208) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.35/1.13 inference(transitivity,[status(thm)],[609, 607])).
% 1.35/1.13 tff(611,plain,
% 1.35/1.13 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a201) | c0_1(a201) | (~c2_1(a201)))),
% 1.35/1.13 inference(quant_inst,[status(thm)],[])).
% 1.35/1.13 tff(612,plain,
% 1.35/1.13 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c2_1(a208) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c1_1(a208)) | (~c0_1(a208))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[611, 610])).
% 1.35/1.13 tff(613,plain,
% 1.35/1.13 (hskp3 | c0_1(a201) | (~c2_1(a201))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[612, 128, 235, 265, 234, 594, 606])).
% 1.35/1.13 tff(614,plain,
% 1.35/1.13 (hskp3),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[613, 596, 595])).
% 1.35/1.13 tff(615,plain,
% 1.35/1.13 (((~hskp3) | (~c3_1(a203))) <=> ((~hskp3) | (~c3_1(a203)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(616,plain,
% 1.35/1.13 (((~c3_1(a203)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a203)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(617,axiom,((~c3_1(a203)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.35/1.13 tff(618,plain,
% 1.35/1.13 ((~hskp3) | (~c3_1(a203))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[617, 616])).
% 1.35/1.13 tff(619,plain,
% 1.35/1.13 ((~hskp3) | (~c3_1(a203))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[618, 615])).
% 1.35/1.13 tff(620,plain,
% 1.35/1.13 (~c3_1(a203)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[619, 614])).
% 1.35/1.13 tff(621,plain,
% 1.35/1.13 (((~hskp3) | (~c0_1(a203))) <=> ((~hskp3) | (~c0_1(a203)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(622,plain,
% 1.35/1.13 (((~c0_1(a203)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a203)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(623,axiom,((~c0_1(a203)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.35/1.13 tff(624,plain,
% 1.35/1.13 ((~hskp3) | (~c0_1(a203))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[623, 622])).
% 1.35/1.13 tff(625,plain,
% 1.35/1.13 ((~hskp3) | (~c0_1(a203))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[624, 621])).
% 1.35/1.13 tff(626,plain,
% 1.35/1.13 (~c0_1(a203)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[625, 614])).
% 1.35/1.13 tff(627,plain,
% 1.35/1.13 (((~hskp3) | c1_1(a203)) <=> ((~hskp3) | c1_1(a203))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(628,axiom,((~hskp3) | c1_1(a203)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.35/1.13 tff(629,plain,
% 1.35/1.13 ((~hskp3) | c1_1(a203)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[628, 627])).
% 1.35/1.13 tff(630,plain,
% 1.35/1.13 ((~hskp3) | c1_1(a203)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[629, 627])).
% 1.35/1.13 tff(631,plain,
% 1.35/1.13 ((~hskp3) | c1_1(a203)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[630, 627])).
% 1.35/1.13 tff(632,plain,
% 1.35/1.13 ((~hskp3) | c1_1(a203)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[631, 627])).
% 1.35/1.13 tff(633,plain,
% 1.35/1.13 ((~hskp3) | c1_1(a203)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[632, 627])).
% 1.35/1.13 tff(634,plain,
% 1.35/1.13 ((~hskp3) | c1_1(a203)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[633, 627])).
% 1.35/1.13 tff(635,plain,
% 1.35/1.13 ((~hskp3) | c1_1(a203)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[634, 627])).
% 1.35/1.13 tff(636,plain,
% 1.35/1.13 ((~hskp3) | c1_1(a203)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[635, 627])).
% 1.35/1.13 tff(637,plain,
% 1.35/1.13 (c1_1(a203)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[636, 614])).
% 1.35/1.13 tff(638,plain,
% 1.35/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a208) | c0_1(a203) | c3_1(a203) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c1_1(a203)) | (~c3_1(a208)) | (~c0_1(a208)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a208) | c0_1(a203) | c3_1(a203) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c1_1(a203)) | (~c3_1(a208)) | (~c0_1(a208)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(639,plain,
% 1.35/1.13 (((~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c3_1(a208)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)) | c1_1(a201) | c0_1(a201) | (~c2_1(a201))) <=> (c2_1(a208) | c0_1(a203) | c3_1(a203) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c1_1(a203)) | (~c3_1(a208)) | (~c0_1(a208)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(640,plain,
% 1.35/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c3_1(a208)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)) | c1_1(a201) | c0_1(a201) | (~c2_1(a201)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a208) | c0_1(a203) | c3_1(a203) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c1_1(a203)) | (~c3_1(a208)) | (~c0_1(a208))))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[639])).
% 1.35/1.13 tff(641,plain,
% 1.35/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c3_1(a208)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)) | c1_1(a201) | c0_1(a201) | (~c2_1(a201)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a208) | c0_1(a203) | c3_1(a203) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c1_1(a203)) | (~c3_1(a208)) | (~c0_1(a208)))),
% 1.35/1.13 inference(transitivity,[status(thm)],[640, 638])).
% 1.35/1.13 tff(642,plain,
% 1.35/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c3_1(a208)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)) | c1_1(a201) | c0_1(a201) | (~c2_1(a201)))),
% 1.35/1.13 inference(quant_inst,[status(thm)],[])).
% 1.35/1.13 tff(643,plain,
% 1.35/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a208) | c0_1(a203) | c3_1(a203) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c1_1(a203)) | (~c3_1(a208)) | (~c0_1(a208))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[642, 641])).
% 1.35/1.13 tff(644,plain,
% 1.35/1.13 (~c3_1(a208)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[643, 128, 235, 637, 596, 234, 626, 620, 595, 594, 593])).
% 1.35/1.13 tff(645,assumption,(~c2_1(a204)), introduced(assumption)).
% 1.35/1.13 tff(646,assumption,(~c0_1(a204)), introduced(assumption)).
% 1.35/1.13 tff(647,assumption,(c1_1(a204)), introduced(assumption)).
% 1.35/1.13 tff(648,plain,
% 1.35/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c3_1(a201)) | (~c1_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c3_1(a201)) | (~c1_1(a204)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(649,plain,
% 1.35/1.13 (((~ndr1_0) | c0_1(a201) | (~c2_1(a201)) | (~c3_1(a201)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c1_1(a201) | c0_1(a201) | (~c3_1(a201))) <=> (c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c3_1(a201)) | (~c1_1(a204)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(650,plain,
% 1.35/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a201) | (~c2_1(a201)) | (~c3_1(a201)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c1_1(a201) | c0_1(a201) | (~c3_1(a201)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c3_1(a201)) | (~c1_1(a204))))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[649])).
% 1.35/1.13 tff(651,plain,
% 1.35/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a201) | (~c2_1(a201)) | (~c3_1(a201)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c1_1(a201) | c0_1(a201) | (~c3_1(a201)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c3_1(a201)) | (~c1_1(a204)))),
% 1.35/1.13 inference(transitivity,[status(thm)],[650, 648])).
% 1.35/1.13 tff(652,plain,
% 1.35/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a201) | (~c2_1(a201)) | (~c3_1(a201)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c1_1(a201) | c0_1(a201) | (~c3_1(a201)))),
% 1.35/1.13 inference(quant_inst,[status(thm)],[])).
% 1.35/1.13 tff(653,plain,
% 1.35/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c3_1(a201)) | (~c1_1(a204))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[652, 651])).
% 1.35/1.13 tff(654,plain,
% 1.35/1.13 ((~c2_1(a201)) | (~c3_1(a201))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[653, 128, 647, 646, 645, 595, 594, 380])).
% 1.35/1.13 tff(655,plain,
% 1.35/1.13 (~c3_1(a201)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[654, 596])).
% 1.35/1.13 tff(656,plain,
% 1.35/1.13 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.35/1.13 inference(bind,[status(th)],[])).
% 1.35/1.13 tff(657,plain,
% 1.35/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.35/1.13 inference(quant_intro,[status(thm)],[656])).
% 1.35/1.13 tff(658,plain,
% 1.35/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(659,plain,
% 1.35/1.13 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(660,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[659])).
% 1.35/1.14 tff(661,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.35/1.14 tff(662,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[661, 660])).
% 1.35/1.14 tff(663,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[662, 658])).
% 1.35/1.14 tff(664,plain,(
% 1.35/1.14 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.35/1.14 inference(skolemize,[status(sab)],[663])).
% 1.35/1.14 tff(665,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[664, 657])).
% 1.35/1.14 tff(666,plain,
% 1.35/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a204) | c2_1(a204) | c0_1(a201) | (~ndr1_0) | (~c2_1(a201)) | c3_1(a201) | c3_1(a204) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a204) | c2_1(a204) | c0_1(a201) | (~ndr1_0) | (~c2_1(a201)) | c3_1(a201) | c3_1(a204) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(667,plain,
% 1.35/1.14 (((~ndr1_0) | c3_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c3_1(a201) | c0_1(a201) | (~c2_1(a201)) | c2_1(a204) | c0_1(a204) | c3_1(a204)) <=> (c0_1(a204) | c2_1(a204) | c0_1(a201) | (~ndr1_0) | (~c2_1(a201)) | c3_1(a201) | c3_1(a204) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(668,plain,
% 1.35/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c3_1(a201) | c0_1(a201) | (~c2_1(a201)) | c2_1(a204) | c0_1(a204) | c3_1(a204))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a204) | c2_1(a204) | c0_1(a201) | (~ndr1_0) | (~c2_1(a201)) | c3_1(a201) | c3_1(a204) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208))))),
% 1.35/1.14 inference(monotonicity,[status(thm)],[667])).
% 1.35/1.14 tff(669,plain,
% 1.35/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c3_1(a201) | c0_1(a201) | (~c2_1(a201)) | c2_1(a204) | c0_1(a204) | c3_1(a204))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a204) | c2_1(a204) | c0_1(a201) | (~ndr1_0) | (~c2_1(a201)) | c3_1(a201) | c3_1(a204) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.35/1.14 inference(transitivity,[status(thm)],[668, 666])).
% 1.35/1.14 tff(670,plain,
% 1.35/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c3_1(a201) | c0_1(a201) | (~c2_1(a201)) | c2_1(a204) | c0_1(a204) | c3_1(a204))),
% 1.35/1.14 inference(quant_inst,[status(thm)],[])).
% 1.35/1.14 tff(671,plain,
% 1.35/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a204) | c2_1(a204) | c0_1(a201) | (~ndr1_0) | (~c2_1(a201)) | c3_1(a201) | c3_1(a204) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[670, 669])).
% 1.35/1.14 tff(672,plain,
% 1.35/1.14 (c3_1(a204)),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[671, 128, 235, 265, 596, 646, 645, 595, 665, 655, 644])).
% 1.35/1.14 tff(673,plain,
% 1.35/1.14 (^[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))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(674,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~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)))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[673])).
% 1.35/1.14 tff(675,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~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)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(676,plain,
% 1.35/1.14 (^[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))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_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)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_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)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_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)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | 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)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | 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) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | 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) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_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) | (~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)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(677,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c0_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)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[676])).
% 1.35/1.14 tff(678,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 1.35/1.14 tff(679,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[678, 677])).
% 1.35/1.14 tff(680,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[679, 675])).
% 1.35/1.14 tff(681,plain,(
% 1.35/1.14 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.14 inference(skolemize,[status(sab)],[680])).
% 1.35/1.14 tff(682,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[681, 674])).
% 1.35/1.14 tff(683,plain,
% 1.35/1.14 (hskp0),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[243, 644])).
% 1.35/1.14 tff(684,plain,
% 1.35/1.14 (~c1_1(a199)),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[369, 683])).
% 1.35/1.14 tff(685,plain,
% 1.35/1.14 (~c0_1(a199)),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[363, 683])).
% 1.35/1.14 tff(686,plain,
% 1.35/1.14 (c3_1(a199)),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[403, 683])).
% 1.35/1.14 tff(687,plain,
% 1.35/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a208) | c2_1(a204) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c3_1(a204)) | (~c1_1(a204)) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![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(a208) | c2_1(a204) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c3_1(a204)) | (~c1_1(a204)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(688,plain,
% 1.35/1.14 (((~ndr1_0) | c2_1(a204) | (~c3_1(a204)) | (~c1_1(a204)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199))) <=> (c2_1(a208) | c2_1(a204) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c3_1(a204)) | (~c1_1(a204)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(689,plain,
% 1.35/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a204) | (~c3_1(a204)) | (~c1_1(a204)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))) <=> ((~![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(a208) | c2_1(a204) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c3_1(a204)) | (~c1_1(a204)) | (~c1_1(a208)) | (~c0_1(a208))))),
% 1.35/1.14 inference(monotonicity,[status(thm)],[688])).
% 1.35/1.14 tff(690,plain,
% 1.35/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a204) | (~c3_1(a204)) | (~c1_1(a204)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))) <=> ((~![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(a208) | c2_1(a204) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c3_1(a204)) | (~c1_1(a204)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.35/1.14 inference(transitivity,[status(thm)],[689, 687])).
% 1.35/1.14 tff(691,plain,
% 1.35/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a204) | (~c3_1(a204)) | (~c1_1(a204)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))),
% 1.35/1.14 inference(quant_inst,[status(thm)],[])).
% 1.35/1.14 tff(692,plain,
% 1.35/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a208) | c2_1(a204) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c3_1(a204)) | (~c1_1(a204)) | (~c1_1(a208)) | (~c0_1(a208))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[691, 690])).
% 1.35/1.14 tff(693,plain,
% 1.35/1.14 ($false),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[692, 128, 235, 265, 647, 686, 234, 645, 685, 684, 682, 672])).
% 1.35/1.14 tff(694,plain,((~c2_1(a201)) | (~c0_1(a208)) | (~c1_1(a208)) | (~c1_1(a204)) | c2_1(a208) | c2_1(a204) | c0_1(a204) | c0_1(a201) | hskp18 | c1_1(a201)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.14 tff(695,plain,
% 1.35/1.14 ($false),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[694, 583, 577, 222, 415, 178, 387, 393, 172, 211, 566])).
% 1.35/1.14 tff(696,plain,((~hskp6) | hskp24 | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.35/1.14 tff(697,plain,
% 1.35/1.14 (~hskp6),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[696, 160, 12])).
% 1.35/1.14 tff(698,plain,
% 1.35/1.14 ((hskp6 | hskp9) <=> (hskp6 | hskp9)),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(699,axiom,(hskp6 | hskp9), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.35/1.14 tff(700,plain,
% 1.35/1.14 (hskp6 | hskp9),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[699, 698])).
% 1.35/1.14 tff(701,plain,
% 1.35/1.14 (hskp9),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[700, 697])).
% 1.35/1.14 tff(702,plain,
% 1.35/1.14 (((~hskp9) | (~c1_1(a213))) <=> ((~hskp9) | (~c1_1(a213)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(703,plain,
% 1.35/1.14 (((~c1_1(a213)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a213)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(704,axiom,((~c1_1(a213)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.35/1.14 tff(705,plain,
% 1.35/1.14 ((~hskp9) | (~c1_1(a213))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[704, 703])).
% 1.35/1.14 tff(706,plain,
% 1.35/1.14 ((~hskp9) | (~c1_1(a213))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[705, 702])).
% 1.35/1.14 tff(707,plain,
% 1.35/1.14 (~c1_1(a213)),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[706, 701])).
% 1.35/1.14 tff(708,plain,
% 1.35/1.14 (((~hskp9) | (~c2_1(a213))) <=> ((~hskp9) | (~c2_1(a213)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(709,plain,
% 1.35/1.14 (((~c2_1(a213)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a213)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(710,axiom,((~c2_1(a213)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.35/1.14 tff(711,plain,
% 1.35/1.14 ((~hskp9) | (~c2_1(a213))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[710, 709])).
% 1.35/1.14 tff(712,plain,
% 1.35/1.14 ((~hskp9) | (~c2_1(a213))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[711, 708])).
% 1.35/1.14 tff(713,plain,
% 1.35/1.14 (~c2_1(a213)),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[712, 701])).
% 1.35/1.14 tff(714,assumption,(~c1_1(a213)), introduced(assumption)).
% 1.35/1.14 tff(715,assumption,(~c2_1(a213)), introduced(assumption)).
% 1.35/1.14 tff(716,plain,
% 1.35/1.14 (^[U: $i] : refl((hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(717,plain,
% 1.35/1.14 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[716])).
% 1.35/1.14 tff(718,plain,
% 1.35/1.14 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(719,plain,
% 1.35/1.14 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp12) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp12))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp12) <=> (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp12) <=> (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(720,plain,
% 1.35/1.14 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp12) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[719])).
% 1.35/1.14 tff(721,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp27) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.35/1.14 tff(722,plain,
% 1.35/1.14 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[721, 720])).
% 1.35/1.14 tff(723,plain,
% 1.35/1.14 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[722, 718])).
% 1.35/1.14 tff(724,plain,(
% 1.35/1.14 ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.14 inference(skolemize,[status(sab)],[723])).
% 1.35/1.14 tff(725,plain,
% 1.35/1.14 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[724, 717])).
% 1.35/1.14 tff(726,plain,
% 1.35/1.14 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c1_1(a213) | c2_1(a213) | (~ndr1_0) | c3_1(a213))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a213) | c2_1(a213) | (~ndr1_0) | c3_1(a213))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(727,plain,
% 1.35/1.14 ((hskp27 | (~ndr1_0) | c3_1(a213) | c2_1(a213) | c1_1(a213)) <=> (hskp27 | c1_1(a213) | c2_1(a213) | (~ndr1_0) | c3_1(a213))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(728,plain,
% 1.35/1.14 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a213) | c2_1(a213) | c1_1(a213))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c1_1(a213) | c2_1(a213) | (~ndr1_0) | c3_1(a213)))),
% 1.35/1.14 inference(monotonicity,[status(thm)],[727])).
% 1.35/1.14 tff(729,plain,
% 1.35/1.14 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a213) | c2_1(a213) | c1_1(a213))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a213) | c2_1(a213) | (~ndr1_0) | c3_1(a213))),
% 1.35/1.14 inference(transitivity,[status(thm)],[728, 726])).
% 1.35/1.14 tff(730,plain,
% 1.35/1.14 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a213) | c2_1(a213) | c1_1(a213))),
% 1.35/1.14 inference(quant_inst,[status(thm)],[])).
% 1.35/1.14 tff(731,plain,
% 1.35/1.14 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a213) | c2_1(a213) | (~ndr1_0) | c3_1(a213)),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[730, 729])).
% 1.35/1.14 tff(732,plain,
% 1.35/1.14 (c2_1(a213) | c3_1(a213)),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[731, 128, 160, 714, 188])).
% 1.35/1.14 tff(733,plain,
% 1.35/1.14 (c3_1(a213)),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[732, 715])).
% 1.35/1.14 tff(734,assumption,(~hskp12), introduced(assumption)).
% 1.35/1.14 tff(735,plain,
% 1.35/1.14 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~c0_1(a213)) | c1_1(a213) | c2_1(a213) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp12 | (~c0_1(a213)) | c1_1(a213) | c2_1(a213) | (~ndr1_0))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(736,plain,
% 1.35/1.14 ((hskp27 | hskp12 | (~ndr1_0) | c2_1(a213) | c1_1(a213) | (~c0_1(a213))) <=> (hskp27 | hskp12 | (~c0_1(a213)) | c1_1(a213) | c2_1(a213) | (~ndr1_0))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(737,plain,
% 1.35/1.14 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a213) | c1_1(a213) | (~c0_1(a213)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~c0_1(a213)) | c1_1(a213) | c2_1(a213) | (~ndr1_0)))),
% 1.35/1.14 inference(monotonicity,[status(thm)],[736])).
% 1.35/1.14 tff(738,plain,
% 1.35/1.14 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a213) | c1_1(a213) | (~c0_1(a213)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp12 | (~c0_1(a213)) | c1_1(a213) | c2_1(a213) | (~ndr1_0))),
% 1.35/1.14 inference(transitivity,[status(thm)],[737, 735])).
% 1.35/1.14 tff(739,plain,
% 1.35/1.14 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a213) | c1_1(a213) | (~c0_1(a213)))),
% 1.35/1.14 inference(quant_inst,[status(thm)],[])).
% 1.35/1.14 tff(740,plain,
% 1.35/1.14 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp12 | (~c0_1(a213)) | c1_1(a213) | c2_1(a213) | (~ndr1_0)),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[739, 738])).
% 1.35/1.14 tff(741,plain,
% 1.35/1.14 (hskp12 | (~c0_1(a213)) | c2_1(a213)),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[740, 128, 160, 714, 725])).
% 1.35/1.14 tff(742,plain,
% 1.35/1.14 (~c0_1(a213)),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[741, 734, 715])).
% 1.35/1.14 tff(743,assumption,(~c1_1(a200)), introduced(assumption)).
% 1.35/1.14 tff(744,plain,
% 1.35/1.14 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | c1_1(a200) | c2_1(a200) | (~ndr1_0) | (~c0_1(a200)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp12 | c1_1(a200) | c2_1(a200) | (~ndr1_0) | (~c0_1(a200)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(745,plain,
% 1.35/1.14 ((hskp27 | hskp12 | (~ndr1_0) | c2_1(a200) | c1_1(a200) | (~c0_1(a200))) <=> (hskp27 | hskp12 | c1_1(a200) | c2_1(a200) | (~ndr1_0) | (~c0_1(a200)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(746,plain,
% 1.35/1.14 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a200) | c1_1(a200) | (~c0_1(a200)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | c1_1(a200) | c2_1(a200) | (~ndr1_0) | (~c0_1(a200))))),
% 1.35/1.14 inference(monotonicity,[status(thm)],[745])).
% 1.35/1.14 tff(747,plain,
% 1.35/1.14 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a200) | c1_1(a200) | (~c0_1(a200)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp12 | c1_1(a200) | c2_1(a200) | (~ndr1_0) | (~c0_1(a200)))),
% 1.35/1.15 inference(transitivity,[status(thm)],[746, 744])).
% 1.35/1.15 tff(748,plain,
% 1.35/1.15 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a200) | c1_1(a200) | (~c0_1(a200)))),
% 1.35/1.15 inference(quant_inst,[status(thm)],[])).
% 1.35/1.15 tff(749,plain,
% 1.35/1.15 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp12 | c1_1(a200) | c2_1(a200) | (~ndr1_0) | (~c0_1(a200))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[748, 747])).
% 1.35/1.15 tff(750,plain,
% 1.35/1.15 (hskp12 | c2_1(a200) | (~c0_1(a200))),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[749, 128, 160, 743, 725])).
% 1.35/1.15 tff(751,plain,
% 1.35/1.15 ($false),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[750, 442, 466, 734])).
% 1.35/1.15 tff(752,plain,((~hskp1) | hskp12 | hskp27 | c1_1(a200)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.15 tff(753,plain,
% 1.35/1.15 ($false),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[752, 448, 436, 160, 734])).
% 1.35/1.15 tff(754,plain,((~hskp1) | hskp27 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.35/1.15 tff(755,plain,
% 1.35/1.15 (~hskp1),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[754, 734, 160])).
% 1.35/1.15 tff(756,plain,
% 1.35/1.15 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a213) | c1_1(a213) | c2_1(a213) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a213) | c1_1(a213) | c2_1(a213) | (~ndr1_0))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(757,plain,
% 1.35/1.15 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a213) | c1_1(a213) | c0_1(a213)) <=> (hskp2 | hskp1 | c0_1(a213) | c1_1(a213) | c2_1(a213) | (~ndr1_0))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(758,plain,
% 1.35/1.15 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a213) | c1_1(a213) | c0_1(a213))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a213) | c1_1(a213) | c2_1(a213) | (~ndr1_0)))),
% 1.35/1.15 inference(monotonicity,[status(thm)],[757])).
% 1.35/1.15 tff(759,plain,
% 1.35/1.15 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a213) | c1_1(a213) | c0_1(a213))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a213) | c1_1(a213) | c2_1(a213) | (~ndr1_0))),
% 1.35/1.15 inference(transitivity,[status(thm)],[758, 756])).
% 1.35/1.15 tff(760,plain,
% 1.35/1.15 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a213) | c1_1(a213) | c0_1(a213))),
% 1.35/1.15 inference(quant_inst,[status(thm)],[])).
% 1.35/1.15 tff(761,plain,
% 1.35/1.15 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a213) | c1_1(a213) | c2_1(a213) | (~ndr1_0)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[760, 759])).
% 1.35/1.15 tff(762,plain,
% 1.35/1.15 (hskp2 | hskp1 | c0_1(a213) | c2_1(a213)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[761, 128, 714, 552])).
% 1.35/1.15 tff(763,plain,
% 1.35/1.15 (hskp2),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[762, 755, 742, 715])).
% 1.35/1.15 tff(764,assumption,(~hskp17), introduced(assumption)).
% 1.35/1.15 tff(765,assumption,(c3_1(a213)), introduced(assumption)).
% 1.35/1.15 tff(766,assumption,(hskp2), introduced(assumption)).
% 1.35/1.15 tff(767,plain,
% 1.35/1.15 (~c1_1(a201)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[565, 766])).
% 1.35/1.15 tff(768,plain,
% 1.35/1.15 (c2_1(a201)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[576, 766])).
% 1.35/1.15 tff(769,plain,
% 1.35/1.15 (~c0_1(a201)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[582, 766])).
% 1.35/1.15 tff(770,plain,
% 1.35/1.15 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(771,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[770])).
% 1.35/1.15 tff(772,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(773,plain,
% 1.35/1.15 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(774,plain,
% 1.35/1.15 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[773])).
% 1.35/1.15 tff(775,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.35/1.15 tff(776,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[775, 774])).
% 1.35/1.15 tff(777,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[776, 772])).
% 1.35/1.15 tff(778,plain,(
% 1.35/1.15 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.35/1.15 inference(skolemize,[status(sab)],[777])).
% 1.35/1.15 tff(779,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[778, 771])).
% 1.35/1.15 tff(780,plain,
% 1.35/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp17 | c1_1(a213) | c2_1(a213) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | c3_1(a201) | (~c3_1(a213)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | hskp17 | c1_1(a213) | c2_1(a213) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | c3_1(a201) | (~c3_1(a213)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(781,plain,
% 1.35/1.15 ((hskp17 | (~ndr1_0) | c3_1(a201) | c1_1(a201) | (~c2_1(a201)) | c1_1(a213) | (~c3_1(a213)) | c2_1(a213)) <=> (hskp17 | c1_1(a213) | c2_1(a213) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | c3_1(a201) | (~c3_1(a213)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(782,plain,
% 1.35/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp17 | (~ndr1_0) | c3_1(a201) | c1_1(a201) | (~c2_1(a201)) | c1_1(a213) | (~c3_1(a213)) | c2_1(a213))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp17 | c1_1(a213) | c2_1(a213) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | c3_1(a201) | (~c3_1(a213))))),
% 1.35/1.15 inference(monotonicity,[status(thm)],[781])).
% 1.35/1.15 tff(783,plain,
% 1.35/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp17 | (~ndr1_0) | c3_1(a201) | c1_1(a201) | (~c2_1(a201)) | c1_1(a213) | (~c3_1(a213)) | c2_1(a213))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | hskp17 | c1_1(a213) | c2_1(a213) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | c3_1(a201) | (~c3_1(a213)))),
% 1.35/1.15 inference(transitivity,[status(thm)],[782, 780])).
% 1.35/1.15 tff(784,plain,
% 1.35/1.15 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp17 | (~ndr1_0) | c3_1(a201) | c1_1(a201) | (~c2_1(a201)) | c1_1(a213) | (~c3_1(a213)) | c2_1(a213))),
% 1.35/1.15 inference(quant_inst,[status(thm)],[])).
% 1.35/1.15 tff(785,plain,
% 1.35/1.15 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | hskp17 | c1_1(a213) | c2_1(a213) | c1_1(a201) | (~ndr1_0) | (~c2_1(a201)) | c3_1(a201) | (~c3_1(a213))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[784, 783])).
% 1.35/1.15 tff(786,plain,
% 1.35/1.15 ($false),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[785, 128, 764, 596, 714, 715, 594, 779, 655, 765])).
% 1.35/1.15 tff(787,plain,((~c2_1(a201)) | hskp17 | c1_1(a213) | c2_1(a213) | c1_1(a201) | (~c3_1(a213)) | (~c1_1(a204)) | c0_1(a204) | c2_1(a204) | c0_1(a201)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.15 tff(788,plain,
% 1.35/1.15 ($false),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[787, 769, 768, 714, 715, 767, 765, 647, 646, 645, 764])).
% 1.35/1.15 tff(789,plain,((~hskp2) | c1_1(a213) | c2_1(a213) | (~c3_1(a213)) | (~c1_1(a204)) | c0_1(a204) | c2_1(a204) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.35/1.15 tff(790,plain,
% 1.35/1.15 (hskp17),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[789, 763, 715, 733, 647, 646, 645, 714])).
% 1.35/1.15 tff(791,plain,
% 1.35/1.15 (((~hskp17) | (~c2_1(a232))) <=> ((~hskp17) | (~c2_1(a232)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(792,plain,
% 1.35/1.15 (((~c2_1(a232)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a232)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(793,axiom,((~c2_1(a232)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.35/1.15 tff(794,plain,
% 1.35/1.15 ((~hskp17) | (~c2_1(a232))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[793, 792])).
% 1.35/1.15 tff(795,plain,
% 1.35/1.15 ((~hskp17) | (~c2_1(a232))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[794, 791])).
% 1.35/1.15 tff(796,plain,
% 1.35/1.15 (~c2_1(a232)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[795, 790])).
% 1.35/1.15 tff(797,plain,
% 1.35/1.15 (((~hskp17) | (~c1_1(a232))) <=> ((~hskp17) | (~c1_1(a232)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(798,plain,
% 1.35/1.15 (((~c1_1(a232)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a232)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(799,axiom,((~c1_1(a232)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.35/1.15 tff(800,plain,
% 1.35/1.15 ((~hskp17) | (~c1_1(a232))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[799, 798])).
% 1.35/1.15 tff(801,plain,
% 1.35/1.15 ((~hskp17) | (~c1_1(a232))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[800, 797])).
% 1.35/1.15 tff(802,plain,
% 1.35/1.15 (~c1_1(a232)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[801, 790])).
% 1.35/1.15 tff(803,plain,
% 1.35/1.15 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a232)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp12 | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a232)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(804,plain,
% 1.35/1.15 ((hskp27 | hskp12 | (~ndr1_0) | c2_1(a232) | c1_1(a232) | (~c0_1(a232))) <=> (hskp27 | hskp12 | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a232)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(805,plain,
% 1.35/1.15 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a232) | c1_1(a232) | (~c0_1(a232)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a232))))),
% 1.35/1.15 inference(monotonicity,[status(thm)],[804])).
% 1.35/1.15 tff(806,plain,
% 1.35/1.15 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a232) | c1_1(a232) | (~c0_1(a232)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp12 | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a232)))),
% 1.35/1.15 inference(transitivity,[status(thm)],[805, 803])).
% 1.35/1.15 tff(807,plain,
% 1.35/1.15 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a232) | c1_1(a232) | (~c0_1(a232)))),
% 1.35/1.15 inference(quant_inst,[status(thm)],[])).
% 1.35/1.15 tff(808,plain,
% 1.35/1.15 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp12 | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a232))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[807, 806])).
% 1.35/1.15 tff(809,plain,
% 1.35/1.15 (~c0_1(a232)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[808, 128, 160, 734, 802, 796, 725])).
% 1.35/1.15 tff(810,plain,
% 1.35/1.15 (~c0_1(a201)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[582, 763])).
% 1.35/1.15 tff(811,plain,
% 1.35/1.15 (c2_1(a201)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[576, 763])).
% 1.35/1.15 tff(812,plain,
% 1.35/1.15 (((~hskp17) | c3_1(a232)) <=> ((~hskp17) | c3_1(a232))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(813,axiom,((~hskp17) | c3_1(a232)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.35/1.15 tff(814,plain,
% 1.35/1.15 ((~hskp17) | c3_1(a232)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[813, 812])).
% 1.35/1.15 tff(815,plain,
% 1.35/1.15 ((~hskp17) | c3_1(a232)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[814, 812])).
% 1.35/1.15 tff(816,plain,
% 1.35/1.15 ((~hskp17) | c3_1(a232)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[815, 812])).
% 1.35/1.15 tff(817,plain,
% 1.35/1.15 ((~hskp17) | c3_1(a232)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[816, 812])).
% 1.35/1.15 tff(818,plain,
% 1.35/1.15 ((~hskp17) | c3_1(a232)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[817, 812])).
% 1.35/1.15 tff(819,plain,
% 1.35/1.15 ((~hskp17) | c3_1(a232)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[818, 812])).
% 1.35/1.15 tff(820,plain,
% 1.35/1.15 ((~hskp17) | c3_1(a232)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[819, 812])).
% 1.35/1.15 tff(821,plain,
% 1.35/1.15 ((~hskp17) | c3_1(a232)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[820, 812])).
% 1.35/1.15 tff(822,plain,
% 1.35/1.15 (c3_1(a232)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[821, 790])).
% 1.35/1.15 tff(823,plain,
% 1.35/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a232) | c0_1(a204) | c2_1(a204) | c0_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c3_1(a201)) | (~c1_1(a204)) | (~c3_1(a232)) | c0_1(a232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a232) | c0_1(a204) | c2_1(a204) | c0_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c3_1(a201)) | (~c1_1(a204)) | (~c3_1(a232)) | c0_1(a232))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(824,plain,
% 1.35/1.15 (((~ndr1_0) | c0_1(a201) | (~c2_1(a201)) | (~c3_1(a201)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c1_1(a232) | c0_1(a232) | (~c3_1(a232))) <=> (c1_1(a232) | c0_1(a204) | c2_1(a204) | c0_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c3_1(a201)) | (~c1_1(a204)) | (~c3_1(a232)) | c0_1(a232))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(825,plain,
% 1.35/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a201) | (~c2_1(a201)) | (~c3_1(a201)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c1_1(a232) | c0_1(a232) | (~c3_1(a232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a232) | c0_1(a204) | c2_1(a204) | c0_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c3_1(a201)) | (~c1_1(a204)) | (~c3_1(a232)) | c0_1(a232)))),
% 1.35/1.15 inference(monotonicity,[status(thm)],[824])).
% 1.35/1.15 tff(826,plain,
% 1.35/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a201) | (~c2_1(a201)) | (~c3_1(a201)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c1_1(a232) | c0_1(a232) | (~c3_1(a232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a232) | c0_1(a204) | c2_1(a204) | c0_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c3_1(a201)) | (~c1_1(a204)) | (~c3_1(a232)) | c0_1(a232))),
% 1.35/1.15 inference(transitivity,[status(thm)],[825, 823])).
% 1.35/1.15 tff(827,plain,
% 1.35/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a201) | (~c2_1(a201)) | (~c3_1(a201)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c1_1(a232) | c0_1(a232) | (~c3_1(a232)))),
% 1.35/1.15 inference(quant_inst,[status(thm)],[])).
% 1.35/1.15 tff(828,plain,
% 1.35/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a232) | c0_1(a204) | c2_1(a204) | c0_1(a201) | (~ndr1_0) | (~c2_1(a201)) | (~c3_1(a201)) | (~c1_1(a204)) | (~c3_1(a232)) | c0_1(a232)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[827, 826])).
% 1.35/1.15 tff(829,plain,
% 1.35/1.15 (~c3_1(a201)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[828, 128, 822, 647, 811, 802, 646, 645, 810, 380, 809])).
% 1.35/1.15 tff(830,plain,
% 1.35/1.15 (~c1_1(a201)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[565, 763])).
% 1.35/1.15 tff(831,assumption,(~c0_1(a232)), introduced(assumption)).
% 1.35/1.15 tff(832,assumption,(~c2_1(a232)), introduced(assumption)).
% 1.35/1.15 tff(833,assumption,(~c1_1(a232)), introduced(assumption)).
% 1.35/1.15 tff(834,assumption,(c3_1(a232)), introduced(assumption)).
% 1.35/1.15 tff(835,assumption,(~hskp28), introduced(assumption)).
% 1.35/1.15 tff(836,assumption,(~c3_1(a201)), introduced(assumption)).
% 1.35/1.15 tff(837,assumption,(~c3_1(a204)), introduced(assumption)).
% 1.35/1.15 tff(838,plain,
% 1.35/1.15 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(839,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[838])).
% 1.35/1.15 tff(840,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(841,plain,
% 1.35/1.15 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c0_1(V))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c0_1(V)))), ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(842,plain,
% 1.35/1.15 (![V: $i, U: $i] : ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[841])).
% 1.35/1.15 tff(843,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.35/1.15 tff(844,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[843, 842])).
% 1.35/1.15 tff(845,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[844, 840])).
% 1.35/1.15 tff(846,plain,(
% 1.35/1.15 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.15 inference(skolemize,[status(sab)],[845])).
% 1.35/1.15 tff(847,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[846, 839])).
% 1.35/1.15 tff(848,plain,
% 1.35/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | c3_1(a201) | c3_1(a204))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | c3_1(a201) | c3_1(a204))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(849,plain,
% 1.35/1.15 ((hskp28 | (~ndr1_0) | c3_1(a204) | c2_1(a204) | c0_1(a204) | c3_1(a201) | c1_1(a201) | c0_1(a201)) <=> (hskp28 | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | c3_1(a201) | c3_1(a204))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(850,plain,
% 1.35/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c3_1(a204) | c2_1(a204) | c0_1(a204) | c3_1(a201) | c1_1(a201) | c0_1(a201))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | c3_1(a201) | c3_1(a204)))),
% 1.35/1.15 inference(monotonicity,[status(thm)],[849])).
% 1.35/1.15 tff(851,plain,
% 1.35/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c3_1(a204) | c2_1(a204) | c0_1(a204) | c3_1(a201) | c1_1(a201) | c0_1(a201))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | c3_1(a201) | c3_1(a204))),
% 1.35/1.15 inference(transitivity,[status(thm)],[850, 848])).
% 1.35/1.15 tff(852,plain,
% 1.35/1.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c3_1(a204) | c2_1(a204) | c0_1(a204) | c3_1(a201) | c1_1(a201) | c0_1(a201))),
% 1.35/1.15 inference(quant_inst,[status(thm)],[])).
% 1.35/1.15 tff(853,plain,
% 1.35/1.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | c3_1(a201) | c3_1(a204)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[852, 851])).
% 1.35/1.15 tff(854,plain,
% 1.35/1.15 ($false),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[853, 128, 835, 646, 645, 595, 594, 847, 837, 836])).
% 1.35/1.15 tff(855,plain,(c3_1(a204) | hskp28 | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | c3_1(a201)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.15 tff(856,plain,
% 1.35/1.15 (c3_1(a204)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[855, 835, 646, 645, 595, 594, 836])).
% 1.35/1.15 tff(857,plain,
% 1.35/1.15 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c1_1(a204)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c1_1(a204)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(858,plain,
% 1.35/1.15 ((hskp21 | (~ndr1_0) | c2_1(a204) | (~c3_1(a204)) | (~c1_1(a204))) <=> (hskp21 | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c1_1(a204)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(859,plain,
% 1.35/1.15 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a204) | (~c3_1(a204)) | (~c1_1(a204)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c1_1(a204))))),
% 1.35/1.15 inference(monotonicity,[status(thm)],[858])).
% 1.35/1.15 tff(860,plain,
% 1.35/1.15 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a204) | (~c3_1(a204)) | (~c1_1(a204)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c1_1(a204)))),
% 1.35/1.15 inference(transitivity,[status(thm)],[859, 857])).
% 1.35/1.15 tff(861,plain,
% 1.35/1.15 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a204) | (~c3_1(a204)) | (~c1_1(a204)))),
% 1.35/1.15 inference(quant_inst,[status(thm)],[])).
% 1.35/1.15 tff(862,plain,
% 1.35/1.15 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c1_1(a204))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[861, 860])).
% 1.35/1.16 tff(863,plain,
% 1.35/1.16 (hskp21 | (~c3_1(a204))),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[862, 128, 647, 645, 289])).
% 1.35/1.16 tff(864,plain,
% 1.35/1.16 (hskp21),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[863, 856])).
% 1.35/1.16 tff(865,plain,
% 1.35/1.16 (~c1_1(a241)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[308, 864])).
% 1.35/1.16 tff(866,plain,
% 1.35/1.16 (~c3_1(a241)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[302, 864])).
% 1.35/1.16 tff(867,assumption,(~c1_1(a241)), introduced(assumption)).
% 1.35/1.16 tff(868,assumption,(~c3_1(a241)), introduced(assumption)).
% 1.35/1.16 tff(869,plain,
% 1.35/1.16 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c1_1(a241) | c3_1(a241) | (~ndr1_0) | c2_1(a241))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a241) | c3_1(a241) | (~ndr1_0) | c2_1(a241))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(870,plain,
% 1.35/1.16 ((hskp27 | (~ndr1_0) | c3_1(a241) | c2_1(a241) | c1_1(a241)) <=> (hskp27 | c1_1(a241) | c3_1(a241) | (~ndr1_0) | c2_1(a241))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(871,plain,
% 1.35/1.16 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a241) | c2_1(a241) | c1_1(a241))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c1_1(a241) | c3_1(a241) | (~ndr1_0) | c2_1(a241)))),
% 1.35/1.16 inference(monotonicity,[status(thm)],[870])).
% 1.35/1.16 tff(872,plain,
% 1.35/1.16 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a241) | c2_1(a241) | c1_1(a241))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a241) | c3_1(a241) | (~ndr1_0) | c2_1(a241))),
% 1.35/1.16 inference(transitivity,[status(thm)],[871, 869])).
% 1.35/1.16 tff(873,plain,
% 1.35/1.16 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a241) | c2_1(a241) | c1_1(a241))),
% 1.35/1.16 inference(quant_inst,[status(thm)],[])).
% 1.35/1.16 tff(874,plain,
% 1.35/1.16 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a241) | c3_1(a241) | (~ndr1_0) | c2_1(a241)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[873, 872])).
% 1.35/1.16 tff(875,plain,
% 1.35/1.16 (c1_1(a241) | c2_1(a241)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[874, 128, 160, 868, 188])).
% 1.35/1.16 tff(876,plain,
% 1.35/1.16 (c2_1(a241)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[875, 867])).
% 1.35/1.16 tff(877,plain,
% 1.35/1.16 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.35/1.16 inference(bind,[status(th)],[])).
% 1.35/1.16 tff(878,plain,
% 1.35/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.16 inference(quant_intro,[status(thm)],[877])).
% 1.35/1.16 tff(879,plain,
% 1.35/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(880,plain,
% 1.35/1.16 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.35/1.16 inference(bind,[status(th)],[])).
% 1.35/1.16 tff(881,plain,
% 1.35/1.16 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.16 inference(quant_intro,[status(thm)],[880])).
% 1.35/1.16 tff(882,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 1.35/1.16 tff(883,plain,
% 1.35/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[882, 881])).
% 1.35/1.16 tff(884,plain,
% 1.35/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[883, 879])).
% 1.35/1.16 tff(885,plain,(
% 1.35/1.16 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.16 inference(skolemize,[status(sab)],[884])).
% 1.35/1.16 tff(886,plain,
% 1.35/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[885, 878])).
% 1.35/1.16 tff(887,plain,
% 1.35/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a241) | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a232)) | c0_1(a232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a241) | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a232)) | c0_1(a232))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(888,plain,
% 1.35/1.16 (((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a232) | (~c3_1(a232)) | c2_1(a232) | c2_1(a232) | c0_1(a232) | (~c3_1(a232))) <=> (c1_1(a241) | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a232)) | c0_1(a232))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(889,plain,
% 1.35/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a232) | (~c3_1(a232)) | c2_1(a232) | c2_1(a232) | c0_1(a232) | (~c3_1(a232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a241) | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a232)) | c0_1(a232)))),
% 1.35/1.16 inference(monotonicity,[status(thm)],[888])).
% 1.35/1.16 tff(890,plain,
% 1.35/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a232) | (~c3_1(a232)) | c2_1(a232) | c2_1(a232) | c0_1(a232) | (~c3_1(a232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a241) | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a232)) | c0_1(a232))),
% 1.35/1.16 inference(transitivity,[status(thm)],[889, 887])).
% 1.35/1.16 tff(891,plain,
% 1.35/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a232) | (~c3_1(a232)) | c2_1(a232) | c2_1(a232) | c0_1(a232) | (~c3_1(a232)))),
% 1.35/1.16 inference(quant_inst,[status(thm)],[])).
% 1.35/1.16 tff(892,plain,
% 1.35/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a241) | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a232)) | c0_1(a232)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[891, 890])).
% 1.35/1.16 tff(893,plain,
% 1.35/1.16 (~c0_1(a241)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[892, 128, 834, 867, 833, 832, 886, 831, 876])).
% 1.35/1.16 tff(894,plain,
% 1.35/1.16 (~hskp21),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[330, 893])).
% 1.35/1.16 tff(895,plain,
% 1.35/1.16 (~c3_1(a204)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[863, 894])).
% 1.35/1.16 tff(896,plain,
% 1.35/1.16 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a241) | c1_1(a241) | c3_1(a241) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | c3_1(a204))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a241) | c1_1(a241) | c3_1(a241) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | c3_1(a204))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(897,plain,
% 1.35/1.16 ((hskp28 | (~ndr1_0) | c3_1(a204) | c2_1(a204) | c0_1(a204) | c3_1(a241) | c1_1(a241) | c0_1(a241)) <=> (hskp28 | c0_1(a241) | c1_1(a241) | c3_1(a241) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | c3_1(a204))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(898,plain,
% 1.35/1.16 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c3_1(a204) | c2_1(a204) | c0_1(a204) | c3_1(a241) | c1_1(a241) | c0_1(a241))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a241) | c1_1(a241) | c3_1(a241) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | c3_1(a204)))),
% 1.35/1.16 inference(monotonicity,[status(thm)],[897])).
% 1.35/1.16 tff(899,plain,
% 1.35/1.16 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c3_1(a204) | c2_1(a204) | c0_1(a204) | c3_1(a241) | c1_1(a241) | c0_1(a241))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a241) | c1_1(a241) | c3_1(a241) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | c3_1(a204))),
% 1.35/1.16 inference(transitivity,[status(thm)],[898, 896])).
% 1.35/1.16 tff(900,plain,
% 1.35/1.16 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c3_1(a204) | c2_1(a204) | c0_1(a204) | c3_1(a241) | c1_1(a241) | c0_1(a241))),
% 1.35/1.16 inference(quant_inst,[status(thm)],[])).
% 1.35/1.16 tff(901,plain,
% 1.35/1.16 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a241) | c1_1(a241) | c3_1(a241) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | c3_1(a204)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[900, 899])).
% 1.35/1.16 tff(902,plain,
% 1.35/1.16 ($false),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[901, 128, 835, 893, 867, 868, 646, 645, 847, 895])).
% 1.35/1.16 tff(903,plain,(c1_1(a241) | hskp28 | c3_1(a241) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | (~c3_1(a232)) | c1_1(a232) | c2_1(a232) | c0_1(a232) | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.35/1.16 tff(904,plain,
% 1.35/1.16 ($false),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[903, 866, 865, 835, 646, 645, 647, 834, 833, 832, 831, 160])).
% 1.35/1.16 tff(905,plain,(hskp28 | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | (~c3_1(a232)) | c1_1(a232) | c2_1(a232) | c0_1(a232) | hskp27 | c0_1(a201) | c1_1(a201) | c3_1(a201)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.16 tff(906,plain,
% 1.35/1.16 (hskp28),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[905, 822, 645, 647, 646, 802, 796, 809, 160, 810, 830, 829])).
% 1.35/1.16 tff(907,plain,
% 1.35/1.16 (((~hskp28) | c3_1(a202)) <=> ((~hskp28) | c3_1(a202))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(908,axiom,((~hskp28) | c3_1(a202)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.35/1.16 tff(909,plain,
% 1.35/1.16 ((~hskp28) | c3_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[908, 907])).
% 1.35/1.16 tff(910,plain,
% 1.35/1.16 ((~hskp28) | c3_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[909, 907])).
% 1.35/1.16 tff(911,plain,
% 1.35/1.16 ((~hskp28) | c3_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[910, 907])).
% 1.35/1.16 tff(912,plain,
% 1.35/1.16 ((~hskp28) | c3_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[911, 907])).
% 1.35/1.16 tff(913,plain,
% 1.35/1.16 ((~hskp28) | c3_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[912, 907])).
% 1.35/1.16 tff(914,plain,
% 1.35/1.16 ((~hskp28) | c3_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[913, 907])).
% 1.35/1.16 tff(915,plain,
% 1.35/1.16 ((~hskp28) | c3_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[914, 907])).
% 1.35/1.16 tff(916,plain,
% 1.35/1.16 ((~hskp28) | c3_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[915, 907])).
% 1.35/1.16 tff(917,plain,
% 1.35/1.16 (c3_1(a202)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[916, 906])).
% 1.35/1.16 tff(918,plain,
% 1.35/1.16 (((~hskp28) | c2_1(a202)) <=> ((~hskp28) | c2_1(a202))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(919,axiom,((~hskp28) | c2_1(a202)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.35/1.16 tff(920,plain,
% 1.35/1.16 ((~hskp28) | c2_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[919, 918])).
% 1.35/1.16 tff(921,plain,
% 1.35/1.16 ((~hskp28) | c2_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[920, 918])).
% 1.35/1.16 tff(922,plain,
% 1.35/1.16 ((~hskp28) | c2_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[921, 918])).
% 1.35/1.16 tff(923,plain,
% 1.35/1.16 ((~hskp28) | c2_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[922, 918])).
% 1.35/1.16 tff(924,plain,
% 1.35/1.16 ((~hskp28) | c2_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[923, 918])).
% 1.35/1.16 tff(925,plain,
% 1.35/1.16 ((~hskp28) | c2_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[924, 918])).
% 1.35/1.16 tff(926,plain,
% 1.35/1.16 ((~hskp28) | c2_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[925, 918])).
% 1.35/1.16 tff(927,plain,
% 1.35/1.16 ((~hskp28) | c2_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[926, 918])).
% 1.35/1.16 tff(928,plain,
% 1.35/1.16 (c2_1(a202)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[927, 906])).
% 1.35/1.16 tff(929,plain,
% 1.35/1.16 (((~hskp28) | c1_1(a202)) <=> ((~hskp28) | c1_1(a202))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(930,axiom,((~hskp28) | c1_1(a202)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.35/1.16 tff(931,plain,
% 1.35/1.16 ((~hskp28) | c1_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[930, 929])).
% 1.35/1.16 tff(932,plain,
% 1.35/1.16 ((~hskp28) | c1_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[931, 929])).
% 1.35/1.16 tff(933,plain,
% 1.35/1.16 ((~hskp28) | c1_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[932, 929])).
% 1.35/1.16 tff(934,plain,
% 1.35/1.16 ((~hskp28) | c1_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[933, 929])).
% 1.35/1.16 tff(935,plain,
% 1.35/1.16 ((~hskp28) | c1_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[934, 929])).
% 1.35/1.16 tff(936,plain,
% 1.35/1.16 ((~hskp28) | c1_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[935, 929])).
% 1.35/1.16 tff(937,plain,
% 1.35/1.16 ((~hskp28) | c1_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[936, 929])).
% 1.35/1.16 tff(938,plain,
% 1.35/1.16 ((~hskp28) | c1_1(a202)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[937, 929])).
% 1.35/1.16 tff(939,plain,
% 1.35/1.16 (c1_1(a202)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[938, 906])).
% 1.35/1.16 tff(940,plain,
% 1.35/1.16 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.35/1.16 inference(bind,[status(th)],[])).
% 1.35/1.16 tff(941,plain,
% 1.35/1.16 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.35/1.16 inference(quant_intro,[status(thm)],[940])).
% 1.35/1.16 tff(942,plain,
% 1.35/1.16 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(943,plain,
% 1.35/1.16 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.35/1.16 inference(bind,[status(th)],[])).
% 1.35/1.16 tff(944,plain,
% 1.35/1.16 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.35/1.16 inference(quant_intro,[status(thm)],[943])).
% 1.35/1.16 tff(945,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.35/1.16 tff(946,plain,
% 1.35/1.16 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[945, 944])).
% 1.35/1.16 tff(947,plain,
% 1.35/1.16 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[946, 942])).
% 1.35/1.16 tff(948,plain,(
% 1.35/1.16 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.35/1.16 inference(skolemize,[status(sab)],[947])).
% 1.35/1.16 tff(949,plain,
% 1.35/1.16 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[948, 941])).
% 1.35/1.16 tff(950,assumption,(c3_1(a202)), introduced(assumption)).
% 1.35/1.16 tff(951,assumption,(c2_1(a202)), introduced(assumption)).
% 1.35/1.16 tff(952,assumption,(c1_1(a202)), introduced(assumption)).
% 1.35/1.16 tff(953,plain,
% 1.35/1.16 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a204) | (~ndr1_0) | c3_1(a204) | (~c1_1(a204)) | (~c2_1(a202)) | (~c1_1(a202)) | (~c3_1(a202)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a204) | (~ndr1_0) | c3_1(a204) | (~c1_1(a204)) | (~c2_1(a202)) | (~c1_1(a202)) | (~c3_1(a202)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(954,plain,
% 1.35/1.16 ((hskp12 | (~ndr1_0) | (~c2_1(a202)) | (~c3_1(a202)) | (~c1_1(a202)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204))) <=> (hskp12 | c0_1(a204) | (~ndr1_0) | c3_1(a204) | (~c1_1(a204)) | (~c2_1(a202)) | (~c1_1(a202)) | (~c3_1(a202)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(955,plain,
% 1.35/1.16 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a202)) | (~c3_1(a202)) | (~c1_1(a202)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a204) | (~ndr1_0) | c3_1(a204) | (~c1_1(a204)) | (~c2_1(a202)) | (~c1_1(a202)) | (~c3_1(a202))))),
% 1.35/1.16 inference(monotonicity,[status(thm)],[954])).
% 1.35/1.16 tff(956,plain,
% 1.35/1.16 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a202)) | (~c3_1(a202)) | (~c1_1(a202)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a204) | (~ndr1_0) | c3_1(a204) | (~c1_1(a204)) | (~c2_1(a202)) | (~c1_1(a202)) | (~c3_1(a202)))),
% 1.35/1.16 inference(transitivity,[status(thm)],[955, 953])).
% 1.35/1.16 tff(957,plain,
% 1.35/1.16 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a202)) | (~c3_1(a202)) | (~c1_1(a202)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204)))),
% 1.35/1.16 inference(quant_inst,[status(thm)],[])).
% 1.35/1.16 tff(958,plain,
% 1.35/1.16 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a204) | (~ndr1_0) | c3_1(a204) | (~c1_1(a204)) | (~c2_1(a202)) | (~c1_1(a202)) | (~c3_1(a202))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[957, 956])).
% 1.35/1.16 tff(959,plain,
% 1.35/1.16 ($false),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[958, 128, 734, 952, 951, 950, 647, 646, 949, 837])).
% 1.35/1.16 tff(960,plain,(c3_1(a204) | hskp12 | (~c1_1(a202)) | (~c2_1(a202)) | (~c3_1(a202)) | (~c1_1(a204)) | c0_1(a204)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.16 tff(961,plain,
% 1.35/1.16 (c3_1(a204)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[960, 734, 939, 928, 917, 647, 646])).
% 1.35/1.16 tff(962,plain,
% 1.35/1.16 (hskp21),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[863, 961])).
% 1.35/1.16 tff(963,plain,
% 1.35/1.16 (~c3_1(a241)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[302, 962])).
% 1.35/1.16 tff(964,plain,
% 1.35/1.16 (~c1_1(a241)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[308, 962])).
% 1.35/1.16 tff(965,plain,
% 1.35/1.16 (c2_1(a241)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[874, 128, 160, 964, 963, 188])).
% 1.35/1.16 tff(966,plain,
% 1.35/1.16 (c0_1(a241)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[330, 962])).
% 1.35/1.16 tff(967,plain,
% 1.35/1.16 ($false),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[892, 128, 966, 822, 964, 802, 796, 886, 809, 965])).
% 1.35/1.16 tff(968,plain,(hskp12 | hskp27 | (~c1_1(a204)) | c2_1(a204) | c0_1(a204) | c2_1(a213) | c1_1(a213)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.16 tff(969,plain,
% 1.35/1.16 (hskp12),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[968, 715, 415, 387, 393, 160, 714])).
% 1.35/1.16 tff(970,plain,
% 1.35/1.16 (((~hskp12) | (~c3_1(a217))) <=> ((~hskp12) | (~c3_1(a217)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(971,plain,
% 1.35/1.16 (((~c3_1(a217)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a217)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(972,axiom,((~c3_1(a217)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.35/1.16 tff(973,plain,
% 1.35/1.16 ((~hskp12) | (~c3_1(a217))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[972, 971])).
% 1.35/1.16 tff(974,plain,
% 1.35/1.16 ((~hskp12) | (~c3_1(a217))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[973, 970])).
% 1.35/1.16 tff(975,plain,
% 1.35/1.16 (~c3_1(a217)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[974, 969])).
% 1.35/1.16 tff(976,plain,
% 1.35/1.16 (((~hskp12) | (~c2_1(a217))) <=> ((~hskp12) | (~c2_1(a217)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(977,plain,
% 1.35/1.16 (((~c2_1(a217)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a217)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(978,axiom,((~c2_1(a217)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.35/1.16 tff(979,plain,
% 1.35/1.16 ((~hskp12) | (~c2_1(a217))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[978, 977])).
% 1.35/1.16 tff(980,plain,
% 1.35/1.16 ((~hskp12) | (~c2_1(a217))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[979, 976])).
% 1.35/1.16 tff(981,plain,
% 1.35/1.16 (~c2_1(a217)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[980, 969])).
% 1.35/1.16 tff(982,plain,
% 1.35/1.16 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c1_1(a217))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c1_1(a217))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(983,plain,
% 1.35/1.16 ((hskp27 | (~ndr1_0) | c3_1(a217) | c2_1(a217) | c1_1(a217)) <=> (hskp27 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c1_1(a217))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(984,plain,
% 1.35/1.16 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a217) | c2_1(a217) | c1_1(a217))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c1_1(a217)))),
% 1.35/1.16 inference(monotonicity,[status(thm)],[983])).
% 1.35/1.16 tff(985,plain,
% 1.35/1.16 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a217) | c2_1(a217) | c1_1(a217))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c1_1(a217))),
% 1.35/1.16 inference(transitivity,[status(thm)],[984, 982])).
% 1.35/1.16 tff(986,plain,
% 1.35/1.16 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a217) | c2_1(a217) | c1_1(a217))),
% 1.35/1.16 inference(quant_inst,[status(thm)],[])).
% 1.35/1.16 tff(987,plain,
% 1.35/1.16 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c1_1(a217)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[986, 985])).
% 1.35/1.16 tff(988,plain,
% 1.35/1.16 (c1_1(a217)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[987, 128, 160, 981, 975, 188])).
% 1.35/1.16 tff(989,plain,
% 1.35/1.16 (((~hskp12) | c0_1(a217)) <=> ((~hskp12) | c0_1(a217))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(990,axiom,((~hskp12) | c0_1(a217)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.35/1.16 tff(991,plain,
% 1.35/1.16 ((~hskp12) | c0_1(a217)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[990, 989])).
% 1.35/1.16 tff(992,plain,
% 1.35/1.16 ((~hskp12) | c0_1(a217)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[991, 989])).
% 1.35/1.16 tff(993,plain,
% 1.35/1.16 ((~hskp12) | c0_1(a217)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[992, 989])).
% 1.35/1.16 tff(994,plain,
% 1.35/1.16 ((~hskp12) | c0_1(a217)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[993, 989])).
% 1.35/1.16 tff(995,plain,
% 1.35/1.16 ((~hskp12) | c0_1(a217)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[994, 989])).
% 1.35/1.16 tff(996,plain,
% 1.35/1.16 ((~hskp12) | c0_1(a217)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[995, 989])).
% 1.35/1.16 tff(997,plain,
% 1.35/1.16 ((~hskp12) | c0_1(a217)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[996, 989])).
% 1.35/1.16 tff(998,plain,
% 1.35/1.16 ((~hskp12) | c0_1(a217)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[997, 989])).
% 1.35/1.16 tff(999,plain,
% 1.35/1.16 (c0_1(a217)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[998, 969])).
% 1.35/1.16 tff(1000,plain,
% 1.35/1.16 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 1.35/1.16 inference(bind,[status(th)],[])).
% 1.35/1.16 tff(1001,plain,
% 1.35/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.35/1.16 inference(quant_intro,[status(thm)],[1000])).
% 1.35/1.16 tff(1002,plain,
% 1.35/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(1003,plain,
% 1.35/1.16 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 1.35/1.16 inference(bind,[status(th)],[])).
% 1.35/1.16 tff(1004,plain,
% 1.35/1.16 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_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) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.35/1.17 inference(quant_intro,[status(thm)],[1003])).
% 1.35/1.17 tff(1005,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.35/1.17 tff(1006,plain,
% 1.35/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 1.35/1.17 tff(1007,plain,
% 1.35/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1006, 1002])).
% 1.35/1.17 tff(1008,plain,(
% 1.35/1.17 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.35/1.17 inference(skolemize,[status(sab)],[1007])).
% 1.35/1.17 tff(1009,plain,
% 1.35/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1008, 1001])).
% 1.35/1.17 tff(1010,plain,
% 1.35/1.17 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp18 | hskp0 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1011,plain,
% 1.35/1.17 ((hskp18 | hskp0 | (~ndr1_0) | c3_1(a217) | c2_1(a217) | (~c0_1(a217))) <=> (hskp18 | hskp0 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1012,plain,
% 1.35/1.17 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c3_1(a217) | c2_1(a217) | (~c0_1(a217)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217))))),
% 1.35/1.17 inference(monotonicity,[status(thm)],[1011])).
% 1.35/1.17 tff(1013,plain,
% 1.35/1.17 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c3_1(a217) | c2_1(a217) | (~c0_1(a217)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp18 | hskp0 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)))),
% 1.35/1.17 inference(transitivity,[status(thm)],[1012, 1010])).
% 1.35/1.17 tff(1014,plain,
% 1.35/1.17 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c3_1(a217) | c2_1(a217) | (~c0_1(a217)))),
% 1.35/1.17 inference(quant_inst,[status(thm)],[])).
% 1.35/1.17 tff(1015,plain,
% 1.35/1.17 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp18 | hskp0 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217))),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 1.35/1.17 tff(1016,plain,
% 1.35/1.17 (hskp0),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1015, 128, 211, 999, 981, 975, 233])).
% 1.35/1.17 tff(1017,plain,
% 1.35/1.17 (~c1_1(a199)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[369, 1016])).
% 1.35/1.17 tff(1018,plain,
% 1.35/1.17 (c3_1(a199)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[403, 1016])).
% 1.35/1.17 tff(1019,plain,
% 1.35/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a217) | c1_1(a213) | c2_1(a213) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | (~c3_1(a213)) | (~c0_1(a217)) | (~c1_1(a217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a217) | c1_1(a213) | c2_1(a213) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | (~c3_1(a213)) | (~c0_1(a217)) | (~c1_1(a217)))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1020,plain,
% 1.35/1.17 (((~ndr1_0) | c3_1(a217) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c2_1(a213) | c1_1(a213) | (~c3_1(a213))) <=> (c3_1(a217) | c1_1(a213) | c2_1(a213) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | (~c3_1(a213)) | (~c0_1(a217)) | (~c1_1(a217)))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1021,plain,
% 1.35/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a217) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c2_1(a213) | c1_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a217) | c1_1(a213) | c2_1(a213) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | (~c3_1(a213)) | (~c0_1(a217)) | (~c1_1(a217))))),
% 1.35/1.17 inference(monotonicity,[status(thm)],[1020])).
% 1.35/1.17 tff(1022,plain,
% 1.35/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a217) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c2_1(a213) | c1_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a217) | c1_1(a213) | c2_1(a213) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | (~c3_1(a213)) | (~c0_1(a217)) | (~c1_1(a217)))),
% 1.35/1.17 inference(transitivity,[status(thm)],[1021, 1019])).
% 1.35/1.17 tff(1023,plain,
% 1.35/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a217) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c2_1(a213) | c1_1(a213) | (~c3_1(a213)))),
% 1.35/1.17 inference(quant_inst,[status(thm)],[])).
% 1.35/1.17 tff(1024,plain,
% 1.35/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a217) | c1_1(a213) | c2_1(a213) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | (~c3_1(a213)) | (~c0_1(a217)) | (~c1_1(a217))),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 1.35/1.17 tff(1025,plain,
% 1.35/1.17 (~c2_1(a199)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1024, 128, 999, 1018, 975, 714, 715, 1017, 1009, 733, 988])).
% 1.35/1.17 tff(1026,plain,
% 1.35/1.17 (~c0_1(a199)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[363, 1016])).
% 1.35/1.17 tff(1027,plain,
% 1.35/1.17 (~hskp1),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[541, 1026, 1017, 1025, 12, 160])).
% 1.35/1.17 tff(1028,plain,
% 1.35/1.17 (hskp2 | hskp1),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[558, 128, 1026, 1017, 552, 1025])).
% 1.35/1.17 tff(1029,plain,
% 1.35/1.17 (hskp2),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1028, 1027])).
% 1.35/1.17 tff(1030,plain,
% 1.35/1.17 (~c0_1(a201)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[582, 1029])).
% 1.35/1.17 tff(1031,plain,
% 1.35/1.17 (~c1_1(a201)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[565, 1029])).
% 1.35/1.17 tff(1032,assumption,(c1_1(a217)), introduced(assumption)).
% 1.35/1.17 tff(1033,plain,
% 1.35/1.17 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.35/1.17 inference(bind,[status(th)],[])).
% 1.35/1.17 tff(1034,plain,
% 1.35/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.17 inference(quant_intro,[status(thm)],[1033])).
% 1.35/1.17 tff(1035,plain,
% 1.35/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1036,plain,
% 1.35/1.17 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.35/1.17 inference(bind,[status(th)],[])).
% 1.35/1.17 tff(1037,plain,
% 1.35/1.17 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.17 inference(quant_intro,[status(thm)],[1036])).
% 1.35/1.17 tff(1038,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.35/1.17 tff(1039,plain,
% 1.35/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 1.35/1.17 tff(1040,plain,
% 1.35/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1039, 1035])).
% 1.35/1.17 tff(1041,plain,(
% 1.35/1.17 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.17 inference(skolemize,[status(sab)],[1040])).
% 1.35/1.17 tff(1042,plain,
% 1.35/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1041, 1034])).
% 1.35/1.17 tff(1043,assumption,(~c3_1(a217)), introduced(assumption)).
% 1.35/1.17 tff(1044,assumption,(c0_1(a217)), introduced(assumption)).
% 1.35/1.17 tff(1045,plain,
% 1.35/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a217) | c0_1(a201) | c1_1(a201) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199) | (~c2_1(a201)) | (~c0_1(a217)) | (~c1_1(a217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a217) | c0_1(a201) | c1_1(a201) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199) | (~c2_1(a201)) | (~c0_1(a217)) | (~c1_1(a217)))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1046,plain,
% 1.35/1.17 (((~ndr1_0) | c3_1(a217) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a201) | c0_1(a201) | (~c2_1(a201)) | c2_1(a199) | c1_1(a199) | c0_1(a199)) <=> (c3_1(a217) | c0_1(a201) | c1_1(a201) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199) | (~c2_1(a201)) | (~c0_1(a217)) | (~c1_1(a217)))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1047,plain,
% 1.35/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a217) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a201) | c0_1(a201) | (~c2_1(a201)) | c2_1(a199) | c1_1(a199) | c0_1(a199))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a217) | c0_1(a201) | c1_1(a201) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199) | (~c2_1(a201)) | (~c0_1(a217)) | (~c1_1(a217))))),
% 1.35/1.17 inference(monotonicity,[status(thm)],[1046])).
% 1.35/1.17 tff(1048,plain,
% 1.35/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a217) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a201) | c0_1(a201) | (~c2_1(a201)) | c2_1(a199) | c1_1(a199) | c0_1(a199))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a217) | c0_1(a201) | c1_1(a201) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199) | (~c2_1(a201)) | (~c0_1(a217)) | (~c1_1(a217)))),
% 1.35/1.17 inference(transitivity,[status(thm)],[1047, 1045])).
% 1.35/1.17 tff(1049,plain,
% 1.35/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a217) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a201) | c0_1(a201) | (~c2_1(a201)) | c2_1(a199) | c1_1(a199) | c0_1(a199))),
% 1.35/1.17 inference(quant_inst,[status(thm)],[])).
% 1.35/1.17 tff(1050,plain,
% 1.35/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a217) | c0_1(a201) | c1_1(a201) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c2_1(a199) | (~c2_1(a201)) | (~c0_1(a217)) | (~c1_1(a217))),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 1.35/1.17 tff(1051,plain,
% 1.35/1.17 (c0_1(a201) | (~c2_1(a201))),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1050, 128, 1044, 1043, 594, 435, 434, 1042, 1032, 423])).
% 1.35/1.17 tff(1052,plain,
% 1.35/1.17 (~c2_1(a201)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1051, 595])).
% 1.35/1.17 tff(1053,plain,
% 1.35/1.17 (~hskp2),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[576, 1052])).
% 1.35/1.17 tff(1054,plain,
% 1.35/1.17 (hskp2 | hskp1),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[558, 128, 435, 434, 552, 423])).
% 1.35/1.17 tff(1055,plain,
% 1.35/1.17 (hskp1),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1054, 1053])).
% 1.35/1.17 tff(1056,plain,
% 1.35/1.17 (~c2_1(a200)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[441, 1055])).
% 1.35/1.17 tff(1057,plain,
% 1.35/1.17 (~c1_1(a200)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[447, 1055])).
% 1.35/1.17 tff(1058,plain,
% 1.35/1.17 (c3_1(a200)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[454, 128, 160, 1057, 1056, 188])).
% 1.35/1.17 tff(1059,plain,
% 1.35/1.17 (c0_1(a200)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[465, 1055])).
% 1.35/1.17 tff(1060,plain,
% 1.35/1.17 (hskp29 | (~c3_1(a200))),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[492, 128, 211, 1059, 1056, 486])).
% 1.35/1.17 tff(1061,plain,
% 1.35/1.17 (hskp29),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1060, 1058])).
% 1.35/1.17 tff(1062,plain,
% 1.35/1.17 (c3_1(a227)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[503, 1061])).
% 1.35/1.17 tff(1063,plain,
% 1.35/1.17 (c1_1(a227)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[514, 1061])).
% 1.35/1.17 tff(1064,plain,
% 1.35/1.17 (c0_1(a227)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[525, 1061])).
% 1.35/1.17 tff(1065,plain,
% 1.35/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a201) | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c1_1(a204)) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a201) | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c1_1(a204)) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1066,plain,
% 1.35/1.17 (((~ndr1_0) | (~c0_1(a227)) | (~c3_1(a227)) | (~c1_1(a227)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a201) | c1_1(a201) | c0_1(a201)) <=> (c2_1(a201) | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c1_1(a204)) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1067,plain,
% 1.35/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a227)) | (~c3_1(a227)) | (~c1_1(a227)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a201) | c1_1(a201) | c0_1(a201))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a201) | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c1_1(a204)) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227))))),
% 1.35/1.17 inference(monotonicity,[status(thm)],[1066])).
% 1.35/1.17 tff(1068,plain,
% 1.35/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a227)) | (~c3_1(a227)) | (~c1_1(a227)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a201) | c1_1(a201) | c0_1(a201))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a201) | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c1_1(a204)) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227)))),
% 1.35/1.17 inference(transitivity,[status(thm)],[1067, 1065])).
% 1.35/1.17 tff(1069,plain,
% 1.35/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a227)) | (~c3_1(a227)) | (~c1_1(a227)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a201) | c1_1(a201) | c0_1(a201))),
% 1.35/1.17 inference(quant_inst,[status(thm)],[])).
% 1.35/1.17 tff(1070,plain,
% 1.35/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a201) | c0_1(a204) | c2_1(a204) | c0_1(a201) | c1_1(a201) | (~ndr1_0) | (~c1_1(a204)) | (~c1_1(a227)) | (~c3_1(a227)) | (~c0_1(a227))),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 1.35/1.17 tff(1071,plain,
% 1.35/1.17 ($false),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1070, 128, 1064, 1063, 1062, 647, 1052, 646, 645, 595, 594, 433])).
% 1.35/1.17 tff(1072,plain,(c0_1(a201) | (~c1_1(a204)) | c0_1(a204) | c2_1(a204) | c1_1(a201) | hskp27 | c0_1(a199) | c1_1(a199) | c2_1(a199) | (~c0_1(a217)) | c3_1(a217) | (~c1_1(a217))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.17 tff(1073,plain,
% 1.35/1.17 ($false),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1072, 1031, 1030, 393, 387, 415, 160, 1026, 1017, 1025, 999, 975, 988])).
% 1.35/1.17 tff(1074,plain,(c2_1(a213) | hskp27 | hskp24 | c1_1(a213)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.17 tff(1075,plain,
% 1.35/1.17 ($false),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1074, 713, 707, 12, 160])).
% 1.35/1.17 tff(1076,plain,(hskp27 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.35/1.17 tff(1077,plain,
% 1.35/1.17 (hskp27),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1076, 12])).
% 1.35/1.17 tff(1078,plain,
% 1.35/1.17 (((~hskp27) | c2_1(a198)) <=> ((~hskp27) | c2_1(a198))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1079,axiom,((~hskp27) | c2_1(a198)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 1.35/1.17 tff(1080,plain,
% 1.35/1.17 ((~hskp27) | c2_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 1.35/1.17 tff(1081,plain,
% 1.35/1.17 ((~hskp27) | c2_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1080, 1078])).
% 1.35/1.17 tff(1082,plain,
% 1.35/1.17 ((~hskp27) | c2_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1081, 1078])).
% 1.35/1.17 tff(1083,plain,
% 1.35/1.17 ((~hskp27) | c2_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1082, 1078])).
% 1.35/1.17 tff(1084,plain,
% 1.35/1.17 ((~hskp27) | c2_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1083, 1078])).
% 1.35/1.17 tff(1085,plain,
% 1.35/1.17 ((~hskp27) | c2_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1084, 1078])).
% 1.35/1.17 tff(1086,plain,
% 1.35/1.17 ((~hskp27) | c2_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1085, 1078])).
% 1.35/1.17 tff(1087,plain,
% 1.35/1.17 ((~hskp27) | c2_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1086, 1078])).
% 1.35/1.17 tff(1088,plain,
% 1.35/1.17 (c2_1(a198)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1087, 1077])).
% 1.35/1.17 tff(1089,plain,
% 1.35/1.17 (((~hskp27) | c1_1(a198)) <=> ((~hskp27) | c1_1(a198))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1090,axiom,((~hskp27) | c1_1(a198)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 1.35/1.17 tff(1091,plain,
% 1.35/1.17 ((~hskp27) | c1_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 1.35/1.17 tff(1092,plain,
% 1.35/1.17 ((~hskp27) | c1_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1091, 1089])).
% 1.35/1.17 tff(1093,plain,
% 1.35/1.17 ((~hskp27) | c1_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1092, 1089])).
% 1.35/1.17 tff(1094,plain,
% 1.35/1.17 ((~hskp27) | c1_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1093, 1089])).
% 1.35/1.17 tff(1095,plain,
% 1.35/1.17 ((~hskp27) | c1_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1094, 1089])).
% 1.35/1.17 tff(1096,plain,
% 1.35/1.17 ((~hskp27) | c1_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1095, 1089])).
% 1.35/1.17 tff(1097,plain,
% 1.35/1.17 ((~hskp27) | c1_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1096, 1089])).
% 1.35/1.17 tff(1098,plain,
% 1.35/1.17 ((~hskp27) | c1_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1097, 1089])).
% 1.35/1.17 tff(1099,plain,
% 1.35/1.17 (c1_1(a198)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1098, 1077])).
% 1.35/1.17 tff(1100,plain,
% 1.35/1.17 (((~hskp27) | c0_1(a198)) <=> ((~hskp27) | c0_1(a198))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1101,axiom,((~hskp27) | c0_1(a198)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.35/1.17 tff(1102,plain,
% 1.35/1.17 ((~hskp27) | c0_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 1.35/1.17 tff(1103,plain,
% 1.35/1.17 ((~hskp27) | c0_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1102, 1100])).
% 1.35/1.17 tff(1104,plain,
% 1.35/1.17 ((~hskp27) | c0_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1103, 1100])).
% 1.35/1.17 tff(1105,plain,
% 1.35/1.17 ((~hskp27) | c0_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1104, 1100])).
% 1.35/1.17 tff(1106,plain,
% 1.35/1.17 ((~hskp27) | c0_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1105, 1100])).
% 1.35/1.17 tff(1107,plain,
% 1.35/1.17 ((~hskp27) | c0_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1106, 1100])).
% 1.35/1.17 tff(1108,plain,
% 1.35/1.17 ((~hskp27) | c0_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1107, 1100])).
% 1.35/1.17 tff(1109,plain,
% 1.35/1.17 ((~hskp27) | c0_1(a198)),
% 1.35/1.17 inference(modus_ponens,[status(thm)],[1108, 1100])).
% 1.35/1.17 tff(1110,plain,
% 1.35/1.17 (c0_1(a198)),
% 1.35/1.17 inference(unit_resolution,[status(thm)],[1109, 1077])).
% 1.35/1.17 tff(1111,plain,
% 1.35/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a244) | c2_1(a244) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a244)) | (~c1_1(a244)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a244) | c2_1(a244) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a244)) | (~c1_1(a244)))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1112,plain,
% 1.35/1.17 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a244)) | c2_1(a244) | (~c1_1(a244)) | c0_1(a244) | (~c3_1(a244)) | (~c1_1(a244))) <=> (c0_1(a244) | c2_1(a244) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a244)) | (~c1_1(a244)))),
% 1.35/1.17 inference(rewrite,[status(thm)],[])).
% 1.35/1.17 tff(1113,plain,
% 1.35/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a244)) | c2_1(a244) | (~c1_1(a244)) | c0_1(a244) | (~c3_1(a244)) | (~c1_1(a244)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a244) | c2_1(a244) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a244)) | (~c1_1(a244))))),
% 1.35/1.17 inference(monotonicity,[status(thm)],[1112])).
% 1.35/1.17 tff(1114,plain,
% 1.35/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a244)) | c2_1(a244) | (~c1_1(a244)) | c0_1(a244) | (~c3_1(a244)) | (~c1_1(a244)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a244) | c2_1(a244) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a244)) | (~c1_1(a244)))),
% 1.35/1.17 inference(transitivity,[status(thm)],[1113, 1111])).
% 1.35/1.17 tff(1115,plain,
% 1.35/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a244)) | c2_1(a244) | (~c1_1(a244)) | c0_1(a244) | (~c3_1(a244)) | (~c1_1(a244)))),
% 1.35/1.17 inference(quant_inst,[status(thm)],[])).
% 1.35/1.17 tff(1116,plain,
% 1.35/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a244) | c2_1(a244) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a244)) | (~c1_1(a244))),
% 1.35/1.18 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 1.35/1.18 tff(1117,plain,
% 1.35/1.18 (~c1_1(a244)),
% 1.35/1.18 inference(unit_resolution,[status(thm)],[1116, 128, 1110, 1099, 1088, 159, 148, 142, 80])).
% 1.35/1.18 tff(1118,assumption,(c2_1(a205)), introduced(assumption)).
% 1.35/1.18 tff(1119,plain,
% 1.35/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a244) | c2_1(a244) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a244) | (~c3_1(a244)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a244) | c2_1(a244) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a244) | (~c3_1(a244)))),
% 1.35/1.18 inference(rewrite,[status(thm)],[])).
% 1.35/1.18 tff(1120,plain,
% 1.35/1.18 (((~ndr1_0) | c1_1(a205) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a244) | (~c3_1(a244)) | c2_1(a244) | c2_1(a244) | c0_1(a244) | (~c3_1(a244))) <=> (c0_1(a244) | c2_1(a244) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a244) | (~c3_1(a244)))),
% 1.35/1.18 inference(rewrite,[status(thm)],[])).
% 1.35/1.18 tff(1121,plain,
% 1.35/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a205) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a244) | (~c3_1(a244)) | c2_1(a244) | c2_1(a244) | c0_1(a244) | (~c3_1(a244)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a244) | c2_1(a244) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a244) | (~c3_1(a244))))),
% 1.35/1.18 inference(monotonicity,[status(thm)],[1120])).
% 1.35/1.18 tff(1122,plain,
% 1.35/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a205) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a244) | (~c3_1(a244)) | c2_1(a244) | c2_1(a244) | c0_1(a244) | (~c3_1(a244)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a244) | c2_1(a244) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a244) | (~c3_1(a244)))),
% 1.35/1.18 inference(transitivity,[status(thm)],[1121, 1119])).
% 1.35/1.18 tff(1123,plain,
% 1.35/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a205) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a244) | (~c3_1(a244)) | c2_1(a244) | c2_1(a244) | c0_1(a244) | (~c3_1(a244)))),
% 1.35/1.18 inference(quant_inst,[status(thm)],[])).
% 1.35/1.18 tff(1124,plain,
% 1.35/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a244) | c2_1(a244) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a244) | (~c3_1(a244))),
% 1.35/1.18 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 1.35/1.18 tff(1125,plain,
% 1.35/1.18 ($false),
% 1.35/1.18 inference(unit_resolution,[status(thm)],[1124, 128, 159, 1118, 148, 142, 92, 886, 81, 1117])).
% 1.35/1.18 tff(1126,plain,((~c0_1(a205)) | (~c2_1(a205)) | c1_1(a205) | hskp24 | (~c3_1(a205))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.18 tff(1127,plain,
% 1.35/1.18 (~c0_1(a205)),
% 1.35/1.18 inference(unit_resolution,[status(thm)],[1126, 70, 59, 12, 53])).
% 1.35/1.18 tff(1128,assumption,(~c0_1(a205)), introduced(assumption)).
% 1.35/1.18 tff(1129,assumption,(~hskp6), introduced(assumption)).
% 1.35/1.18 tff(1130,plain,
% 1.35/1.18 (^[U: $i] : refl((hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.35/1.18 inference(bind,[status(th)],[])).
% 1.35/1.18 tff(1131,plain,
% 1.35/1.18 (![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.35/1.18 inference(quant_intro,[status(thm)],[1130])).
% 1.35/1.18 tff(1132,plain,
% 1.35/1.18 (![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.35/1.18 inference(rewrite,[status(thm)],[])).
% 1.35/1.18 tff(1133,plain,
% 1.35/1.18 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp7) <=> (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.35/1.18 inference(bind,[status(th)],[])).
% 1.35/1.18 tff(1134,plain,
% 1.35/1.18 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.35/1.18 inference(quant_intro,[status(thm)],[1133])).
% 1.35/1.18 tff(1135,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.35/1.18 tff(1136,plain,
% 1.35/1.18 (![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.35/1.18 inference(modus_ponens,[status(thm)],[1135, 1134])).
% 1.35/1.18 tff(1137,plain,
% 1.35/1.18 (![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.35/1.18 inference(modus_ponens,[status(thm)],[1136, 1132])).
% 1.35/1.18 tff(1138,plain,(
% 1.35/1.18 ![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.35/1.18 inference(skolemize,[status(sab)],[1137])).
% 1.35/1.18 tff(1139,plain,
% 1.35/1.18 (![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.35/1.18 inference(modus_ponens,[status(thm)],[1138, 1131])).
% 1.35/1.18 tff(1140,plain,
% 1.35/1.18 (((~![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp7 | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205))) <=> ((~![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp7 | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205))),
% 1.35/1.18 inference(rewrite,[status(thm)],[])).
% 1.35/1.18 tff(1141,plain,
% 1.35/1.18 ((hskp6 | hskp7 | (~ndr1_0) | c1_1(a205) | c0_1(a205) | (~c2_1(a205))) <=> (hskp6 | hskp7 | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205))),
% 1.35/1.18 inference(rewrite,[status(thm)],[])).
% 1.35/1.18 tff(1142,plain,
% 1.35/1.18 (((~![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp7 | (~ndr1_0) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)))) <=> ((~![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp7 | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205)))),
% 1.35/1.18 inference(monotonicity,[status(thm)],[1141])).
% 1.35/1.18 tff(1143,plain,
% 1.35/1.18 (((~![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp7 | (~ndr1_0) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)))) <=> ((~![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp7 | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205))),
% 1.35/1.18 inference(transitivity,[status(thm)],[1142, 1140])).
% 1.35/1.18 tff(1144,plain,
% 1.35/1.18 ((~![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp7 | (~ndr1_0) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)))),
% 1.35/1.18 inference(quant_inst,[status(thm)],[])).
% 1.35/1.18 tff(1145,plain,
% 1.35/1.18 ((~![U: $i] : (hskp6 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp7 | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205)),
% 1.35/1.18 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 1.35/1.18 tff(1146,plain,
% 1.35/1.18 (hskp6 | hskp7 | c0_1(a205)),
% 1.35/1.18 inference(unit_resolution,[status(thm)],[1145, 128, 1118, 92, 1139])).
% 1.35/1.18 tff(1147,plain,
% 1.35/1.18 (hskp7),
% 1.35/1.18 inference(unit_resolution,[status(thm)],[1146, 1129, 1128])).
% 1.35/1.18 tff(1148,plain,
% 1.35/1.18 (~c3_1(a209)),
% 1.35/1.18 inference(unit_resolution,[status(thm)],[278, 1147])).
% 1.35/1.18 tff(1149,plain,
% 1.35/1.18 (hskp9),
% 1.35/1.18 inference(unit_resolution,[status(thm)],[700, 1129])).
% 1.35/1.18 tff(1150,plain,
% 1.35/1.18 (~c2_1(a213)),
% 1.35/1.18 inference(unit_resolution,[status(thm)],[712, 1149])).
% 1.35/1.18 tff(1151,plain,
% 1.35/1.18 (~c1_1(a213)),
% 1.35/1.18 inference(unit_resolution,[status(thm)],[706, 1149])).
% 1.35/1.18 tff(1152,plain,
% 1.35/1.18 (((~hskp9) | (~c0_1(a213))) <=> ((~hskp9) | (~c0_1(a213)))),
% 1.35/1.18 inference(rewrite,[status(thm)],[])).
% 1.35/1.18 tff(1153,plain,
% 1.35/1.18 (((~c0_1(a213)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a213)))),
% 1.35/1.18 inference(rewrite,[status(thm)],[])).
% 1.35/1.18 tff(1154,axiom,((~c0_1(a213)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.35/1.18 tff(1155,plain,
% 1.35/1.18 ((~hskp9) | (~c0_1(a213))),
% 1.35/1.18 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 1.35/1.18 tff(1156,plain,
% 1.35/1.18 ((~hskp9) | (~c0_1(a213))),
% 1.35/1.18 inference(modus_ponens,[status(thm)],[1155, 1152])).
% 1.35/1.18 tff(1157,plain,
% 1.35/1.18 (~c0_1(a213)),
% 1.35/1.18 inference(unit_resolution,[status(thm)],[1156, 1149])).
% 1.35/1.18 tff(1158,plain,
% 1.35/1.18 (c1_1(a209)),
% 1.35/1.18 inference(unit_resolution,[status(thm)],[319, 1147])).
% 1.35/1.18 tff(1159,plain,
% 1.35/1.18 (c0_1(a209)),
% 1.35/1.18 inference(unit_resolution,[status(thm)],[348, 1147])).
% 1.35/1.18 tff(1160,plain,
% 1.35/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a213) | c1_1(a213) | c2_1(a213) | c3_1(a209) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c0_1(a209)) | (~c1_1(a209)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a213) | c1_1(a213) | c2_1(a213) | c3_1(a209) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c0_1(a209)) | (~c1_1(a209)))),
% 1.35/1.18 inference(rewrite,[status(thm)],[])).
% 1.35/1.18 tff(1161,plain,
% 1.35/1.18 (((~ndr1_0) | c3_1(a209) | (~c0_1(a209)) | (~c1_1(a209)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)) | c2_1(a213) | c1_1(a213) | c0_1(a213)) <=> (c0_1(a213) | c1_1(a213) | c2_1(a213) | c3_1(a209) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c0_1(a209)) | (~c1_1(a209)))),
% 1.35/1.18 inference(rewrite,[status(thm)],[])).
% 1.35/1.18 tff(1162,plain,
% 1.35/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a209) | (~c0_1(a209)) | (~c1_1(a209)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)) | c2_1(a213) | c1_1(a213) | c0_1(a213))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a213) | c1_1(a213) | c2_1(a213) | c3_1(a209) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c0_1(a209)) | (~c1_1(a209))))),
% 1.35/1.18 inference(monotonicity,[status(thm)],[1161])).
% 1.35/1.18 tff(1163,plain,
% 1.35/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a209) | (~c0_1(a209)) | (~c1_1(a209)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)) | c2_1(a213) | c1_1(a213) | c0_1(a213))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a213) | c1_1(a213) | c2_1(a213) | c3_1(a209) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c0_1(a209)) | (~c1_1(a209)))),
% 1.35/1.18 inference(transitivity,[status(thm)],[1162, 1160])).
% 1.45/1.18 tff(1164,plain,
% 1.45/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a209) | (~c0_1(a209)) | (~c1_1(a209)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)) | c2_1(a213) | c1_1(a213) | c0_1(a213))),
% 1.45/1.18 inference(quant_inst,[status(thm)],[])).
% 1.45/1.18 tff(1165,plain,
% 1.45/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a213) | c1_1(a213) | c2_1(a213) | c3_1(a209) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c0_1(a209)) | (~c1_1(a209))),
% 1.45/1.18 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 1.45/1.18 tff(1166,plain,
% 1.45/1.18 ($false),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[1165, 128, 1159, 1158, 1118, 1157, 1151, 1150, 1148, 92, 1042, 1128])).
% 1.45/1.18 tff(1167,plain,(hskp6 | (~c2_1(a205)) | c1_1(a205) | c0_1(a205)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.18 tff(1168,plain,
% 1.45/1.18 (hskp6),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[1167, 1127, 59, 53])).
% 1.45/1.18 tff(1169,plain,
% 1.45/1.18 (~c2_1(a208)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[177, 1168])).
% 1.45/1.18 tff(1170,plain,
% 1.45/1.18 (c1_1(a208)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[221, 1168])).
% 1.45/1.18 tff(1171,plain,
% 1.45/1.18 (c0_1(a208)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[171, 1168])).
% 1.45/1.18 tff(1172,plain,
% 1.45/1.18 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c2_1(a208) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c2_1(a208) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.45/1.18 inference(rewrite,[status(thm)],[])).
% 1.45/1.18 tff(1173,plain,
% 1.45/1.18 ((hskp3 | (~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205))) <=> (hskp3 | c2_1(a208) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.45/1.18 inference(rewrite,[status(thm)],[])).
% 1.45/1.18 tff(1174,plain,
% 1.45/1.18 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c2_1(a208) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c1_1(a208)) | (~c0_1(a208))))),
% 1.45/1.18 inference(monotonicity,[status(thm)],[1173])).
% 1.45/1.18 tff(1175,plain,
% 1.45/1.18 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c2_1(a208) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.45/1.18 inference(transitivity,[status(thm)],[1174, 1172])).
% 1.45/1.18 tff(1176,plain,
% 1.45/1.18 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)))),
% 1.45/1.18 inference(quant_inst,[status(thm)],[])).
% 1.45/1.18 tff(1177,plain,
% 1.45/1.18 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c2_1(a208) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c1_1(a208)) | (~c0_1(a208))),
% 1.45/1.18 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 1.45/1.18 tff(1178,plain,
% 1.45/1.18 (hskp3),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[1177, 128, 1171, 1170, 53, 1169, 59, 606, 1127])).
% 1.45/1.18 tff(1179,plain,
% 1.45/1.18 (~c0_1(a203)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[625, 1178])).
% 1.45/1.18 tff(1180,plain,
% 1.45/1.18 (c1_1(a203)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[636, 1178])).
% 1.45/1.18 tff(1181,plain,
% 1.45/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a205) | c0_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c2_1(a203) | (~c2_1(a205)) | c0_1(a205) | (~c3_1(a205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a205) | c0_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c2_1(a203) | (~c2_1(a205)) | c0_1(a205) | (~c3_1(a205)))),
% 1.45/1.18 inference(rewrite,[status(thm)],[])).
% 1.45/1.18 tff(1182,plain,
% 1.45/1.18 (((~ndr1_0) | c0_1(a205) | (~c2_1(a205)) | (~c3_1(a205)) | c0_1(a203) | c2_1(a203) | (~c1_1(a203)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205))) <=> (c1_1(a205) | c0_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c2_1(a203) | (~c2_1(a205)) | c0_1(a205) | (~c3_1(a205)))),
% 1.45/1.18 inference(rewrite,[status(thm)],[])).
% 1.45/1.18 tff(1183,plain,
% 1.45/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a205) | (~c2_1(a205)) | (~c3_1(a205)) | c0_1(a203) | c2_1(a203) | (~c1_1(a203)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a205) | c0_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c2_1(a203) | (~c2_1(a205)) | c0_1(a205) | (~c3_1(a205))))),
% 1.45/1.18 inference(monotonicity,[status(thm)],[1182])).
% 1.45/1.18 tff(1184,plain,
% 1.45/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a205) | (~c2_1(a205)) | (~c3_1(a205)) | c0_1(a203) | c2_1(a203) | (~c1_1(a203)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a205) | c0_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c2_1(a203) | (~c2_1(a205)) | c0_1(a205) | (~c3_1(a205)))),
% 1.45/1.18 inference(transitivity,[status(thm)],[1183, 1181])).
% 1.45/1.18 tff(1185,plain,
% 1.45/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a205) | (~c2_1(a205)) | (~c3_1(a205)) | c0_1(a203) | c2_1(a203) | (~c1_1(a203)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205)))),
% 1.45/1.18 inference(quant_inst,[status(thm)],[])).
% 1.45/1.18 tff(1186,plain,
% 1.45/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a205) | c0_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c2_1(a203) | (~c2_1(a205)) | c0_1(a205) | (~c3_1(a205))),
% 1.45/1.18 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 1.45/1.18 tff(1187,plain,
% 1.45/1.18 (c2_1(a203)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[1186, 128, 53, 70, 1180, 59, 1179, 380, 1127])).
% 1.45/1.18 tff(1188,plain,
% 1.45/1.18 (~c3_1(a203)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[619, 1178])).
% 1.45/1.18 tff(1189,plain,
% 1.45/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a208) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c2_1(a203)) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a208) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c2_1(a203)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.45/1.18 inference(rewrite,[status(thm)],[])).
% 1.45/1.18 tff(1190,plain,
% 1.45/1.18 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c0_1(a203) | c3_1(a203) | (~c2_1(a203))) <=> (c2_1(a208) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c2_1(a203)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.45/1.18 inference(rewrite,[status(thm)],[])).
% 1.45/1.18 tff(1191,plain,
% 1.45/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c0_1(a203) | c3_1(a203) | (~c2_1(a203)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a208) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c2_1(a203)) | (~c1_1(a208)) | (~c0_1(a208))))),
% 1.45/1.18 inference(monotonicity,[status(thm)],[1190])).
% 1.45/1.18 tff(1192,plain,
% 1.45/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c0_1(a203) | c3_1(a203) | (~c2_1(a203)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a208) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c2_1(a203)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.45/1.18 inference(transitivity,[status(thm)],[1191, 1189])).
% 1.45/1.18 tff(1193,plain,
% 1.45/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c0_1(a203) | c3_1(a203) | (~c2_1(a203)))),
% 1.45/1.18 inference(quant_inst,[status(thm)],[])).
% 1.45/1.18 tff(1194,plain,
% 1.45/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a208) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c2_1(a203)) | (~c1_1(a208)) | (~c0_1(a208))),
% 1.45/1.18 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 1.45/1.18 tff(1195,plain,
% 1.45/1.18 ($false),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[1194, 128, 1110, 1099, 1088, 1171, 1170, 1169, 1179, 1188, 22, 1187])).
% 1.45/1.18 tff(1196,plain,((~hskp5) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.45/1.18 tff(1197,plain,
% 1.45/1.18 (~hskp5),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[1196, 12])).
% 1.45/1.18 tff(1198,plain,
% 1.45/1.18 (~c2_1(a233)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[195, 35])).
% 1.45/1.18 tff(1199,plain,
% 1.45/1.18 (~c1_1(a233)),
% 1.45/1.18 inference(unit_resolution,[status(thm)],[201, 35])).
% 1.45/1.18 tff(1200,plain,
% 1.45/1.18 (^[U: $i] : refl((hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.45/1.18 inference(bind,[status(th)],[])).
% 1.45/1.18 tff(1201,plain,
% 1.45/1.18 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.18 inference(quant_intro,[status(thm)],[1200])).
% 1.45/1.18 tff(1202,plain,
% 1.45/1.18 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.18 inference(rewrite,[status(thm)],[])).
% 1.45/1.18 tff(1203,plain,
% 1.45/1.18 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5) <=> ((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp5))), rewrite(((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp5) <=> (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5) <=> (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.45/1.19 inference(bind,[status(th)],[])).
% 1.45/1.19 tff(1204,plain,
% 1.45/1.19 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.19 inference(quant_intro,[status(thm)],[1203])).
% 1.45/1.19 tff(1205,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.45/1.19 tff(1206,plain,
% 1.45/1.19 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 1.45/1.19 tff(1207,plain,
% 1.45/1.19 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1206, 1202])).
% 1.45/1.19 tff(1208,plain,(
% 1.45/1.19 ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.19 inference(skolemize,[status(sab)],[1207])).
% 1.45/1.19 tff(1209,plain,
% 1.45/1.19 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1208, 1201])).
% 1.45/1.19 tff(1210,assumption,(~hskp5), introduced(assumption)).
% 1.45/1.19 tff(1211,plain,
% 1.45/1.19 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | c0_1(a213) | c1_1(a213) | (~ndr1_0) | c3_1(a213))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c0_1(a213) | c1_1(a213) | (~ndr1_0) | c3_1(a213))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1212,plain,
% 1.45/1.19 ((hskp5 | hskp4 | (~ndr1_0) | c3_1(a213) | c1_1(a213) | c0_1(a213)) <=> (hskp5 | hskp4 | c0_1(a213) | c1_1(a213) | (~ndr1_0) | c3_1(a213))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1213,plain,
% 1.45/1.19 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a213) | c1_1(a213) | c0_1(a213))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | c0_1(a213) | c1_1(a213) | (~ndr1_0) | c3_1(a213)))),
% 1.45/1.19 inference(monotonicity,[status(thm)],[1212])).
% 1.45/1.19 tff(1214,plain,
% 1.45/1.19 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a213) | c1_1(a213) | c0_1(a213))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c0_1(a213) | c1_1(a213) | (~ndr1_0) | c3_1(a213))),
% 1.45/1.19 inference(transitivity,[status(thm)],[1213, 1211])).
% 1.45/1.19 tff(1215,plain,
% 1.45/1.19 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a213) | c1_1(a213) | c0_1(a213))),
% 1.45/1.19 inference(quant_inst,[status(thm)],[])).
% 1.45/1.19 tff(1216,plain,
% 1.45/1.19 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c0_1(a213) | c1_1(a213) | (~ndr1_0) | c3_1(a213)),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 1.45/1.19 tff(1217,plain,
% 1.45/1.19 (c3_1(a213)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1216, 128, 1210, 23, 1157, 1151, 1209])).
% 1.45/1.19 tff(1218,plain,
% 1.45/1.19 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.45/1.19 inference(bind,[status(th)],[])).
% 1.45/1.19 tff(1219,plain,
% 1.45/1.19 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.19 inference(quant_intro,[status(thm)],[1218])).
% 1.45/1.19 tff(1220,plain,
% 1.45/1.19 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1221,plain,
% 1.45/1.19 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.45/1.19 inference(bind,[status(th)],[])).
% 1.45/1.19 tff(1222,plain,
% 1.45/1.19 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.19 inference(quant_intro,[status(thm)],[1221])).
% 1.45/1.19 tff(1223,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 1.45/1.19 tff(1224,plain,
% 1.45/1.19 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 1.45/1.19 tff(1225,plain,
% 1.45/1.19 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1224, 1220])).
% 1.45/1.19 tff(1226,plain,(
% 1.45/1.19 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.19 inference(skolemize,[status(sab)],[1225])).
% 1.45/1.19 tff(1227,plain,
% 1.45/1.19 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1226, 1219])).
% 1.45/1.19 tff(1228,assumption,(c0_1(a198)), introduced(assumption)).
% 1.45/1.19 tff(1229,assumption,(c2_1(a198)), introduced(assumption)).
% 1.45/1.19 tff(1230,assumption,(c1_1(a198)), introduced(assumption)).
% 1.45/1.19 tff(1231,assumption,(~hskp10), introduced(assumption)).
% 1.45/1.19 tff(1232,plain,
% 1.45/1.19 ((hskp6 | hskp20 | hskp10) <=> (hskp6 | hskp20 | hskp10)),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1233,plain,
% 1.45/1.19 (((hskp6 | hskp10) | hskp20) <=> (hskp6 | hskp20 | hskp10)),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1234,plain,
% 1.45/1.19 ((hskp6 | hskp10) <=> (hskp6 | hskp10)),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1235,plain,
% 1.45/1.19 (((hskp6 | hskp10) | hskp20) <=> ((hskp6 | hskp10) | hskp20)),
% 1.45/1.19 inference(monotonicity,[status(thm)],[1234])).
% 1.45/1.19 tff(1236,plain,
% 1.45/1.19 (((hskp6 | hskp10) | hskp20) <=> (hskp6 | hskp20 | hskp10)),
% 1.45/1.19 inference(transitivity,[status(thm)],[1235, 1233])).
% 1.45/1.19 tff(1237,axiom,((hskp6 | hskp10) | hskp20), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 1.45/1.19 tff(1238,plain,
% 1.45/1.19 (hskp6 | hskp20 | hskp10),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 1.45/1.19 tff(1239,plain,
% 1.45/1.19 (hskp6 | hskp20 | hskp10),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1238, 1232])).
% 1.45/1.19 tff(1240,plain,
% 1.45/1.19 (hskp6 | hskp20 | hskp10),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1239, 1232])).
% 1.45/1.19 tff(1241,plain,
% 1.45/1.19 (hskp6 | hskp20 | hskp10),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1240, 1232])).
% 1.45/1.19 tff(1242,plain,
% 1.45/1.19 (hskp6 | hskp20 | hskp10),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1241, 1232])).
% 1.45/1.19 tff(1243,plain,
% 1.45/1.19 (hskp6 | hskp20 | hskp10),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1242, 1232])).
% 1.45/1.19 tff(1244,plain,
% 1.45/1.19 (hskp6 | hskp20 | hskp10),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1243, 1232])).
% 1.45/1.19 tff(1245,plain,
% 1.45/1.19 (hskp6 | hskp20 | hskp10),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1244, 1232])).
% 1.45/1.19 tff(1246,plain,
% 1.45/1.19 (hskp20),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1245, 1231, 1129])).
% 1.45/1.19 tff(1247,plain,
% 1.45/1.19 (((~hskp20) | (~c3_1(a239))) <=> ((~hskp20) | (~c3_1(a239)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1248,plain,
% 1.45/1.19 (((~c3_1(a239)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a239)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1249,axiom,((~c3_1(a239)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.45/1.19 tff(1250,plain,
% 1.45/1.19 ((~hskp20) | (~c3_1(a239))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1249, 1248])).
% 1.45/1.19 tff(1251,plain,
% 1.45/1.19 ((~hskp20) | (~c3_1(a239))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1250, 1247])).
% 1.45/1.19 tff(1252,plain,
% 1.45/1.19 (~c3_1(a239)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1251, 1246])).
% 1.45/1.19 tff(1253,plain,
% 1.45/1.19 (((~hskp20) | (~c0_1(a239))) <=> ((~hskp20) | (~c0_1(a239)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1254,plain,
% 1.45/1.19 (((~c0_1(a239)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a239)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1255,axiom,((~c0_1(a239)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.45/1.19 tff(1256,plain,
% 1.45/1.19 ((~hskp20) | (~c0_1(a239))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 1.45/1.19 tff(1257,plain,
% 1.45/1.19 ((~hskp20) | (~c0_1(a239))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1256, 1253])).
% 1.45/1.19 tff(1258,plain,
% 1.45/1.19 (~c0_1(a239)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1257, 1246])).
% 1.45/1.19 tff(1259,plain,
% 1.45/1.19 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | c0_1(a239) | c3_1(a239) | (~ndr1_0) | c1_1(a239))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c0_1(a239) | c3_1(a239) | (~ndr1_0) | c1_1(a239))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1260,plain,
% 1.45/1.19 ((hskp5 | hskp4 | (~ndr1_0) | c3_1(a239) | c1_1(a239) | c0_1(a239)) <=> (hskp5 | hskp4 | c0_1(a239) | c3_1(a239) | (~ndr1_0) | c1_1(a239))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1261,plain,
% 1.45/1.19 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | c0_1(a239) | c3_1(a239) | (~ndr1_0) | c1_1(a239)))),
% 1.45/1.19 inference(monotonicity,[status(thm)],[1260])).
% 1.45/1.19 tff(1262,plain,
% 1.45/1.19 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c0_1(a239) | c3_1(a239) | (~ndr1_0) | c1_1(a239))),
% 1.45/1.19 inference(transitivity,[status(thm)],[1261, 1259])).
% 1.45/1.19 tff(1263,plain,
% 1.45/1.19 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a239) | c1_1(a239) | c0_1(a239))),
% 1.45/1.19 inference(quant_inst,[status(thm)],[])).
% 1.45/1.19 tff(1264,plain,
% 1.45/1.19 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c0_1(a239) | c3_1(a239) | (~ndr1_0) | c1_1(a239)),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1263, 1262])).
% 1.45/1.19 tff(1265,plain,
% 1.45/1.19 (c1_1(a239)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1264, 128, 1210, 23, 1258, 1252, 1209])).
% 1.45/1.19 tff(1266,plain,
% 1.45/1.19 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.45/1.19 inference(bind,[status(th)],[])).
% 1.45/1.19 tff(1267,plain,
% 1.45/1.19 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.45/1.19 inference(quant_intro,[status(thm)],[1266])).
% 1.45/1.19 tff(1268,plain,
% 1.45/1.19 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1269,plain,
% 1.45/1.19 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.45/1.19 inference(bind,[status(th)],[])).
% 1.45/1.19 tff(1270,plain,
% 1.45/1.19 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.45/1.19 inference(quant_intro,[status(thm)],[1269])).
% 1.45/1.19 tff(1271,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.45/1.19 tff(1272,plain,
% 1.45/1.19 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 1.45/1.19 tff(1273,plain,
% 1.45/1.19 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1272, 1268])).
% 1.45/1.19 tff(1274,plain,(
% 1.45/1.19 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.45/1.19 inference(skolemize,[status(sab)],[1273])).
% 1.45/1.19 tff(1275,plain,
% 1.45/1.19 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1274, 1267])).
% 1.45/1.19 tff(1276,plain,
% 1.45/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a239)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1277,plain,
% 1.45/1.19 ((hskp10 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a239) | c0_1(a239) | (~c1_1(a239))) <=> (hskp10 | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a239)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1278,plain,
% 1.45/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a239))))),
% 1.45/1.19 inference(monotonicity,[status(thm)],[1277])).
% 1.45/1.19 tff(1279,plain,
% 1.45/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a239)))),
% 1.45/1.19 inference(transitivity,[status(thm)],[1278, 1276])).
% 1.45/1.19 tff(1280,plain,
% 1.45/1.19 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)))),
% 1.45/1.19 inference(quant_inst,[status(thm)],[])).
% 1.45/1.19 tff(1281,plain,
% 1.45/1.19 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a239))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 1.45/1.19 tff(1282,plain,
% 1.45/1.19 ($false),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1281, 128, 1231, 1228, 1230, 1229, 1258, 1252, 1275, 1265])).
% 1.45/1.19 tff(1283,plain,(hskp10 | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | hskp5 | hskp4 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.45/1.19 tff(1284,plain,
% 1.45/1.19 (hskp10),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1283, 1129, 1230, 1229, 1210, 23, 1228])).
% 1.45/1.19 tff(1285,plain,
% 1.45/1.19 (((~hskp10) | c1_1(a214)) <=> ((~hskp10) | c1_1(a214))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1286,axiom,((~hskp10) | c1_1(a214)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.45/1.19 tff(1287,plain,
% 1.45/1.19 ((~hskp10) | c1_1(a214)),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 1.45/1.19 tff(1288,plain,
% 1.45/1.19 ((~hskp10) | c1_1(a214)),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1287, 1285])).
% 1.45/1.19 tff(1289,plain,
% 1.45/1.19 ((~hskp10) | c1_1(a214)),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1288, 1285])).
% 1.45/1.19 tff(1290,plain,
% 1.45/1.19 ((~hskp10) | c1_1(a214)),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1289, 1285])).
% 1.45/1.19 tff(1291,plain,
% 1.45/1.19 ((~hskp10) | c1_1(a214)),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1290, 1285])).
% 1.45/1.19 tff(1292,plain,
% 1.45/1.19 ((~hskp10) | c1_1(a214)),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1291, 1285])).
% 1.45/1.19 tff(1293,plain,
% 1.45/1.19 ((~hskp10) | c1_1(a214)),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1292, 1285])).
% 1.45/1.19 tff(1294,plain,
% 1.45/1.19 ((~hskp10) | c1_1(a214)),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1293, 1285])).
% 1.45/1.19 tff(1295,plain,
% 1.45/1.19 (c1_1(a214)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1294, 1284])).
% 1.45/1.19 tff(1296,plain,
% 1.45/1.19 (((~hskp10) | (~c3_1(a214))) <=> ((~hskp10) | (~c3_1(a214)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1297,plain,
% 1.45/1.19 (((~c3_1(a214)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a214)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1298,axiom,((~c3_1(a214)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.45/1.19 tff(1299,plain,
% 1.45/1.19 ((~hskp10) | (~c3_1(a214))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 1.45/1.19 tff(1300,plain,
% 1.45/1.19 ((~hskp10) | (~c3_1(a214))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1299, 1296])).
% 1.45/1.19 tff(1301,plain,
% 1.45/1.19 (~c3_1(a214)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1300, 1284])).
% 1.45/1.19 tff(1302,plain,
% 1.45/1.19 (((~hskp10) | (~c2_1(a214))) <=> ((~hskp10) | (~c2_1(a214)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1303,plain,
% 1.45/1.19 (((~c2_1(a214)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a214)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1304,axiom,((~c2_1(a214)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 1.45/1.19 tff(1305,plain,
% 1.45/1.19 ((~hskp10) | (~c2_1(a214))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 1.45/1.19 tff(1306,plain,
% 1.45/1.19 ((~hskp10) | (~c2_1(a214))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1305, 1302])).
% 1.45/1.19 tff(1307,plain,
% 1.45/1.19 (~c2_1(a214)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1306, 1284])).
% 1.45/1.19 tff(1308,assumption,(~c3_1(a233)), introduced(assumption)).
% 1.45/1.19 tff(1309,assumption,(~c1_1(a233)), introduced(assumption)).
% 1.45/1.19 tff(1310,plain,
% 1.45/1.19 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | c1_1(a233) | c3_1(a233) | (~ndr1_0) | c0_1(a233))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c1_1(a233) | c3_1(a233) | (~ndr1_0) | c0_1(a233))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1311,plain,
% 1.45/1.19 ((hskp5 | hskp4 | (~ndr1_0) | c3_1(a233) | c1_1(a233) | c0_1(a233)) <=> (hskp5 | hskp4 | c1_1(a233) | c3_1(a233) | (~ndr1_0) | c0_1(a233))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1312,plain,
% 1.45/1.19 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a233) | c1_1(a233) | c0_1(a233))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | c1_1(a233) | c3_1(a233) | (~ndr1_0) | c0_1(a233)))),
% 1.45/1.19 inference(monotonicity,[status(thm)],[1311])).
% 1.45/1.19 tff(1313,plain,
% 1.45/1.19 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a233) | c1_1(a233) | c0_1(a233))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c1_1(a233) | c3_1(a233) | (~ndr1_0) | c0_1(a233))),
% 1.45/1.19 inference(transitivity,[status(thm)],[1312, 1310])).
% 1.45/1.19 tff(1314,plain,
% 1.45/1.19 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a233) | c1_1(a233) | c0_1(a233))),
% 1.45/1.19 inference(quant_inst,[status(thm)],[])).
% 1.45/1.19 tff(1315,plain,
% 1.45/1.19 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c1_1(a233) | c3_1(a233) | (~ndr1_0) | c0_1(a233)),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 1.45/1.19 tff(1316,plain,
% 1.45/1.19 (c0_1(a233)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1315, 128, 1210, 23, 1309, 1308, 1209])).
% 1.45/1.19 tff(1317,assumption,(~c0_1(a213)), introduced(assumption)).
% 1.45/1.19 tff(1318,plain,
% 1.45/1.19 (c3_1(a213)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1216, 128, 1210, 23, 1317, 714, 1209])).
% 1.45/1.19 tff(1319,assumption,(hskp20), introduced(assumption)).
% 1.45/1.19 tff(1320,plain,
% 1.45/1.19 (~c3_1(a239)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1251, 1319])).
% 1.45/1.19 tff(1321,plain,
% 1.45/1.19 (~c0_1(a239)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1257, 1319])).
% 1.45/1.19 tff(1322,plain,
% 1.45/1.19 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a239) | c3_1(a239) | c0_1(a213) | c1_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c1_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a239) | c3_1(a239) | c0_1(a213) | c1_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c1_1(a239)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1323,plain,
% 1.45/1.19 ((hskp4 | (~ndr1_0) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213))) <=> (hskp4 | c0_1(a239) | c3_1(a239) | c0_1(a213) | c1_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c1_1(a239)))),
% 1.45/1.19 inference(rewrite,[status(thm)],[])).
% 1.45/1.19 tff(1324,plain,
% 1.45/1.19 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a239) | c3_1(a239) | c0_1(a213) | c1_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c1_1(a239))))),
% 1.45/1.19 inference(monotonicity,[status(thm)],[1323])).
% 1.45/1.19 tff(1325,plain,
% 1.45/1.19 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a239) | c3_1(a239) | c0_1(a213) | c1_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c1_1(a239)))),
% 1.45/1.19 inference(transitivity,[status(thm)],[1324, 1322])).
% 1.45/1.19 tff(1326,plain,
% 1.45/1.19 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213)))),
% 1.45/1.19 inference(quant_inst,[status(thm)],[])).
% 1.45/1.19 tff(1327,plain,
% 1.45/1.19 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a239) | c3_1(a239) | c0_1(a213) | c1_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c1_1(a239))),
% 1.45/1.19 inference(modus_ponens,[status(thm)],[1326, 1325])).
% 1.45/1.19 tff(1328,plain,
% 1.45/1.19 (~c1_1(a239)),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1327, 128, 23, 1321, 1320, 1317, 714, 1227, 1318])).
% 1.45/1.19 tff(1329,plain,
% 1.45/1.19 ($false),
% 1.45/1.19 inference(unit_resolution,[status(thm)],[1264, 128, 1210, 23, 1321, 1320, 1209, 1328])).
% 1.45/1.19 tff(1330,plain,((~hskp20) | hskp5 | hskp4 | c0_1(a213) | c1_1(a213)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.20 tff(1331,plain,
% 1.45/1.20 (~hskp20),
% 1.45/1.20 inference(unit_resolution,[status(thm)],[1330, 1157, 23, 1210, 1151])).
% 1.45/1.20 tff(1332,plain,
% 1.45/1.20 (^[U: $i] : refl((hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.45/1.20 inference(bind,[status(th)],[])).
% 1.45/1.20 tff(1333,plain,
% 1.45/1.20 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.20 inference(quant_intro,[status(thm)],[1332])).
% 1.45/1.20 tff(1334,plain,
% 1.45/1.20 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.20 inference(rewrite,[status(thm)],[])).
% 1.45/1.20 tff(1335,plain,
% 1.45/1.20 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp20) <=> ((hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp20))), rewrite(((hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.45/1.20 inference(bind,[status(th)],[])).
% 1.45/1.20 tff(1336,plain,
% 1.45/1.20 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp20) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.20 inference(quant_intro,[status(thm)],[1335])).
% 1.45/1.20 tff(1337,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.45/1.20 tff(1338,plain,
% 1.45/1.20 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.20 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 1.45/1.20 tff(1339,plain,
% 1.45/1.20 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.20 inference(modus_ponens,[status(thm)],[1338, 1334])).
% 1.45/1.20 tff(1340,plain,(
% 1.45/1.20 ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.20 inference(skolemize,[status(sab)],[1339])).
% 1.45/1.20 tff(1341,plain,
% 1.45/1.20 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.45/1.20 inference(modus_ponens,[status(thm)],[1340, 1333])).
% 1.45/1.20 tff(1342,assumption,(~c2_1(a233)), introduced(assumption)).
% 1.45/1.20 tff(1343,plain,
% 1.45/1.20 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c1_1(a233) | c2_1(a233) | (~ndr1_0) | (~c0_1(a233)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a233) | c2_1(a233) | (~ndr1_0) | (~c0_1(a233)))),
% 1.45/1.20 inference(rewrite,[status(thm)],[])).
% 1.45/1.20 tff(1344,plain,
% 1.45/1.20 ((hskp20 | hskp19 | (~ndr1_0) | c2_1(a233) | c1_1(a233) | (~c0_1(a233))) <=> (hskp20 | hskp19 | c1_1(a233) | c2_1(a233) | (~ndr1_0) | (~c0_1(a233)))),
% 1.45/1.20 inference(rewrite,[status(thm)],[])).
% 1.45/1.20 tff(1345,plain,
% 1.45/1.20 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c2_1(a233) | c1_1(a233) | (~c0_1(a233)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c1_1(a233) | c2_1(a233) | (~ndr1_0) | (~c0_1(a233))))),
% 1.45/1.20 inference(monotonicity,[status(thm)],[1344])).
% 1.45/1.20 tff(1346,plain,
% 1.45/1.20 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c2_1(a233) | c1_1(a233) | (~c0_1(a233)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a233) | c2_1(a233) | (~ndr1_0) | (~c0_1(a233)))),
% 1.45/1.20 inference(transitivity,[status(thm)],[1345, 1343])).
% 1.45/1.20 tff(1347,plain,
% 1.45/1.20 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c2_1(a233) | c1_1(a233) | (~c0_1(a233)))),
% 1.45/1.20 inference(quant_inst,[status(thm)],[])).
% 1.45/1.20 tff(1348,plain,
% 1.45/1.20 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a233) | c2_1(a233) | (~ndr1_0) | (~c0_1(a233))),
% 1.45/1.20 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 1.45/1.20 tff(1349,plain,
% 1.45/1.20 (hskp20 | hskp19 | (~c0_1(a233))),
% 1.45/1.20 inference(unit_resolution,[status(thm)],[1348, 128, 1309, 1342, 1341])).
% 1.45/1.20 tff(1350,plain,
% 1.45/1.20 (hskp19),
% 1.45/1.20 inference(unit_resolution,[status(thm)],[1349, 1331, 1316])).
% 1.45/1.20 tff(1351,assumption,(~c3_1(a198)), introduced(assumption)).
% 1.45/1.20 tff(1352,plain,
% 1.45/1.20 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))))),
% 1.45/1.20 inference(bind,[status(th)],[])).
% 1.45/1.20 tff(1353,plain,
% 1.45/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.45/1.20 inference(quant_intro,[status(thm)],[1352])).
% 1.45/1.20 tff(1354,plain,
% 1.45/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.45/1.20 inference(rewrite,[status(thm)],[])).
% 1.45/1.20 tff(1355,plain,
% 1.45/1.20 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(1356,plain,
% 1.47/1.20 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[1355])).
% 1.47/1.20 tff(1357,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 1.47/1.20 tff(1358,plain,
% 1.47/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1357, 1356])).
% 1.47/1.20 tff(1359,plain,
% 1.47/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1358, 1354])).
% 1.47/1.20 tff(1360,plain,(
% 1.47/1.20 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.20 inference(skolemize,[status(sab)],[1359])).
% 1.47/1.20 tff(1361,plain,
% 1.47/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1360, 1353])).
% 1.47/1.20 tff(1362,assumption,(~c3_1(a214)), introduced(assumption)).
% 1.47/1.20 tff(1363,assumption,(~c2_1(a214)), introduced(assumption)).
% 1.47/1.20 tff(1364,assumption,(hskp19), introduced(assumption)).
% 1.47/1.20 tff(1365,plain,
% 1.47/1.20 (((~hskp19) | (~c2_1(a238))) <=> ((~hskp19) | (~c2_1(a238)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(1366,plain,
% 1.47/1.20 (((~c2_1(a238)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a238)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(1367,axiom,((~c2_1(a238)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.47/1.20 tff(1368,plain,
% 1.47/1.20 ((~hskp19) | (~c2_1(a238))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 1.47/1.20 tff(1369,plain,
% 1.47/1.20 ((~hskp19) | (~c2_1(a238))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1368, 1365])).
% 1.47/1.20 tff(1370,plain,
% 1.47/1.20 (~c2_1(a238)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[1369, 1364])).
% 1.47/1.20 tff(1371,assumption,(c1_1(a214)), introduced(assumption)).
% 1.47/1.20 tff(1372,plain,
% 1.47/1.20 (((~hskp19) | c3_1(a238)) <=> ((~hskp19) | c3_1(a238))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(1373,axiom,((~hskp19) | c3_1(a238)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 1.47/1.20 tff(1374,plain,
% 1.47/1.20 ((~hskp19) | c3_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 1.47/1.20 tff(1375,plain,
% 1.47/1.20 ((~hskp19) | c3_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1374, 1372])).
% 1.47/1.20 tff(1376,plain,
% 1.47/1.20 ((~hskp19) | c3_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1375, 1372])).
% 1.47/1.20 tff(1377,plain,
% 1.47/1.20 ((~hskp19) | c3_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1376, 1372])).
% 1.47/1.20 tff(1378,plain,
% 1.47/1.20 ((~hskp19) | c3_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1377, 1372])).
% 1.47/1.20 tff(1379,plain,
% 1.47/1.20 ((~hskp19) | c3_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1378, 1372])).
% 1.47/1.20 tff(1380,plain,
% 1.47/1.20 ((~hskp19) | c3_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1379, 1372])).
% 1.47/1.20 tff(1381,plain,
% 1.47/1.20 ((~hskp19) | c3_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1380, 1372])).
% 1.47/1.20 tff(1382,plain,
% 1.47/1.20 (c3_1(a238)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[1381, 1364])).
% 1.47/1.20 tff(1383,plain,
% 1.47/1.20 (((~hskp19) | c1_1(a238)) <=> ((~hskp19) | c1_1(a238))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(1384,axiom,((~hskp19) | c1_1(a238)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.47/1.20 tff(1385,plain,
% 1.47/1.20 ((~hskp19) | c1_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 1.47/1.20 tff(1386,plain,
% 1.47/1.20 ((~hskp19) | c1_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1385, 1383])).
% 1.47/1.20 tff(1387,plain,
% 1.47/1.20 ((~hskp19) | c1_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1386, 1383])).
% 1.47/1.20 tff(1388,plain,
% 1.47/1.20 ((~hskp19) | c1_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1387, 1383])).
% 1.47/1.20 tff(1389,plain,
% 1.47/1.20 ((~hskp19) | c1_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1388, 1383])).
% 1.47/1.20 tff(1390,plain,
% 1.47/1.20 ((~hskp19) | c1_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1389, 1383])).
% 1.47/1.20 tff(1391,plain,
% 1.47/1.20 ((~hskp19) | c1_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1390, 1383])).
% 1.47/1.20 tff(1392,plain,
% 1.47/1.20 ((~hskp19) | c1_1(a238)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1391, 1383])).
% 1.47/1.20 tff(1393,plain,
% 1.47/1.20 (c1_1(a238)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[1392, 1364])).
% 1.47/1.20 tff(1394,plain,
% 1.47/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a238) | c2_1(a214) | c3_1(a214) | (~ndr1_0) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a214)) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a238) | c2_1(a214) | c3_1(a214) | (~ndr1_0) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a214)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(1395,plain,
% 1.47/1.20 (((~ndr1_0) | c3_1(a198) | (~c2_1(a198)) | (~c1_1(a198)) | (~c3_1(a238)) | c2_1(a238) | (~c1_1(a238)) | c2_1(a214) | c3_1(a214) | (~c1_1(a214))) <=> (c2_1(a238) | c2_1(a214) | c3_1(a214) | (~ndr1_0) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a214)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(1396,plain,
% 1.47/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a198) | (~c2_1(a198)) | (~c1_1(a198)) | (~c3_1(a238)) | c2_1(a238) | (~c1_1(a238)) | c2_1(a214) | c3_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a238) | c2_1(a214) | c3_1(a214) | (~ndr1_0) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a214)) | (~c3_1(a238)) | (~c1_1(a238))))),
% 1.47/1.20 inference(monotonicity,[status(thm)],[1395])).
% 1.47/1.20 tff(1397,plain,
% 1.47/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a198) | (~c2_1(a198)) | (~c1_1(a198)) | (~c3_1(a238)) | c2_1(a238) | (~c1_1(a238)) | c2_1(a214) | c3_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a238) | c2_1(a214) | c3_1(a214) | (~ndr1_0) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a214)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.20 inference(transitivity,[status(thm)],[1396, 1394])).
% 1.47/1.20 tff(1398,plain,
% 1.47/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a198) | (~c2_1(a198)) | (~c1_1(a198)) | (~c3_1(a238)) | c2_1(a238) | (~c1_1(a238)) | c2_1(a214) | c3_1(a214) | (~c1_1(a214)))),
% 1.47/1.20 inference(quant_inst,[status(thm)],[])).
% 1.47/1.20 tff(1399,plain,
% 1.47/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a238) | c2_1(a214) | c3_1(a214) | (~ndr1_0) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a214)) | (~c3_1(a238)) | (~c1_1(a238))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 1.47/1.20 tff(1400,plain,
% 1.47/1.20 ($false),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[1399, 128, 1230, 1229, 1393, 1382, 1371, 1370, 1363, 1362, 1361, 1351])).
% 1.47/1.20 tff(1401,plain,((~hskp19) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a214)) | c2_1(a214) | c3_1(a214) | c3_1(a198)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.20 tff(1402,plain,
% 1.47/1.20 (c3_1(a198)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[1401, 1350, 1229, 1230, 1307, 1301, 1295])).
% 1.47/1.20 tff(1403,plain,
% 1.47/1.20 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(1404,plain,
% 1.47/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[1403])).
% 1.47/1.20 tff(1405,plain,
% 1.47/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(1406,plain,
% 1.47/1.20 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(1407,plain,
% 1.47/1.20 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[1406])).
% 1.47/1.20 tff(1408,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.47/1.20 tff(1409,plain,
% 1.47/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 1.47/1.20 tff(1410,plain,
% 1.47/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1409, 1405])).
% 1.47/1.20 tff(1411,plain,(
% 1.47/1.20 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.47/1.20 inference(skolemize,[status(sab)],[1410])).
% 1.47/1.20 tff(1412,plain,
% 1.47/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1411, 1404])).
% 1.47/1.20 tff(1413,plain,
% 1.47/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a233) | c3_1(a233) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a233)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a233) | c3_1(a233) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a233)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(1414,plain,
% 1.47/1.20 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a233) | c2_1(a233) | (~c0_1(a233)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214))) <=> (c2_1(a233) | c3_1(a233) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a233)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(1415,plain,
% 1.47/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a233) | c2_1(a233) | (~c0_1(a233)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a233) | c3_1(a233) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a233))))),
% 1.47/1.20 inference(monotonicity,[status(thm)],[1414])).
% 1.47/1.20 tff(1416,plain,
% 1.47/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a233) | c2_1(a233) | (~c0_1(a233)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a233) | c3_1(a233) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a233)))),
% 1.47/1.20 inference(transitivity,[status(thm)],[1415, 1413])).
% 1.47/1.20 tff(1417,plain,
% 1.47/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a233) | c2_1(a233) | (~c0_1(a233)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214)))),
% 1.47/1.20 inference(quant_inst,[status(thm)],[])).
% 1.47/1.20 tff(1418,plain,
% 1.47/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a233) | c3_1(a233) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a233))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 1.47/1.20 tff(1419,plain,
% 1.47/1.20 (c0_1(a214)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[1418, 128, 1228, 1230, 1229, 1295, 1342, 1308, 1307, 1412, 1316])).
% 1.47/1.20 tff(1420,plain,
% 1.47/1.20 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(1421,plain,
% 1.47/1.20 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[1420])).
% 1.47/1.20 tff(1422,plain,
% 1.47/1.20 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(1423,plain,
% 1.47/1.20 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_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))) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(1424,plain,
% 1.47/1.20 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[1423])).
% 1.47/1.20 tff(1425,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.47/1.20 tff(1426,plain,
% 1.47/1.20 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1425, 1424])).
% 1.47/1.20 tff(1427,plain,
% 1.47/1.20 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[1426, 1422])).
% 1.47/1.20 tff(1428,plain,(
% 1.47/1.20 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.21 inference(skolemize,[status(sab)],[1427])).
% 1.47/1.21 tff(1429,plain,
% 1.47/1.21 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1428, 1421])).
% 1.47/1.21 tff(1430,plain,
% 1.47/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c0_1(a214)) | (~c1_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c0_1(a214)) | (~c1_1(a214)))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1431,plain,
% 1.47/1.21 ((hskp3 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c2_1(a214) | (~c1_1(a214)) | (~c0_1(a214))) <=> (hskp3 | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c0_1(a214)) | (~c1_1(a214)))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1432,plain,
% 1.47/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c2_1(a214) | (~c1_1(a214)) | (~c0_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c0_1(a214)) | (~c1_1(a214))))),
% 1.47/1.21 inference(monotonicity,[status(thm)],[1431])).
% 1.47/1.21 tff(1433,plain,
% 1.47/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c2_1(a214) | (~c1_1(a214)) | (~c0_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c0_1(a214)) | (~c1_1(a214)))),
% 1.47/1.21 inference(transitivity,[status(thm)],[1432, 1430])).
% 1.47/1.21 tff(1434,plain,
% 1.47/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c2_1(a214) | (~c1_1(a214)) | (~c0_1(a214)))),
% 1.47/1.21 inference(quant_inst,[status(thm)],[])).
% 1.47/1.21 tff(1435,plain,
% 1.47/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c0_1(a214)) | (~c1_1(a214))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 1.47/1.21 tff(1436,plain,
% 1.47/1.21 (hskp3 | (~c3_1(a198))),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[1435, 128, 1228, 1229, 1295, 1307, 1429, 1419])).
% 1.47/1.21 tff(1437,plain,
% 1.47/1.21 (hskp3),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[1436, 1402])).
% 1.47/1.21 tff(1438,plain,
% 1.47/1.21 (~c3_1(a203)),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[619, 1437])).
% 1.47/1.21 tff(1439,plain,
% 1.47/1.21 (~c0_1(a203)),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[625, 1437])).
% 1.47/1.21 tff(1440,plain,
% 1.47/1.21 (c1_1(a203)),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[636, 1437])).
% 1.47/1.21 tff(1441,plain,
% 1.47/1.21 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a213) | c1_1(a213) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c3_1(a213)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a213) | c1_1(a213) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c3_1(a213)))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1442,plain,
% 1.47/1.21 ((hskp4 | (~ndr1_0) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213))) <=> (hskp4 | c0_1(a213) | c1_1(a213) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c3_1(a213)))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1443,plain,
% 1.47/1.21 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a213) | c1_1(a213) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c3_1(a213))))),
% 1.47/1.21 inference(monotonicity,[status(thm)],[1442])).
% 1.47/1.21 tff(1444,plain,
% 1.47/1.21 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a213) | c1_1(a213) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c3_1(a213)))),
% 1.47/1.21 inference(transitivity,[status(thm)],[1443, 1441])).
% 1.47/1.21 tff(1445,plain,
% 1.47/1.21 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213)))),
% 1.47/1.21 inference(quant_inst,[status(thm)],[])).
% 1.47/1.21 tff(1446,plain,
% 1.47/1.21 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a213) | c1_1(a213) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c3_1(a213))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 1.47/1.21 tff(1447,plain,
% 1.47/1.21 ($false),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[1446, 128, 23, 1440, 1157, 1151, 1439, 1438, 1227, 1217])).
% 1.47/1.21 tff(1448,plain,(hskp6 | hskp4 | (~c0_1(a198)) | (~c2_1(a198)) | (~c1_1(a198)) | c1_1(a233) | c2_1(a233) | hskp5 | c3_1(a233)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.21 tff(1449,plain,
% 1.47/1.21 (hskp6),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[1448, 23, 1110, 1088, 1099, 1199, 1198, 1197, 41])).
% 1.47/1.21 tff(1450,plain,
% 1.47/1.21 (~c2_1(a208)),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[177, 1449])).
% 1.47/1.21 tff(1451,plain,
% 1.47/1.21 (c0_1(a233)),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[1315, 128, 1197, 23, 1199, 41, 1209])).
% 1.47/1.21 tff(1452,plain,
% 1.47/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a238) | c2_1(a233) | c3_1(a233) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a233)) | (~c1_1(a238)) | c0_1(a238))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a238) | c2_1(a233) | c3_1(a233) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a233)) | (~c1_1(a238)) | c0_1(a238))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1453,plain,
% 1.47/1.21 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a233) | c2_1(a233) | (~c0_1(a233)) | c2_1(a238) | c0_1(a238) | (~c1_1(a238))) <=> (c2_1(a238) | c2_1(a233) | c3_1(a233) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a233)) | (~c1_1(a238)) | c0_1(a238))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1454,plain,
% 1.47/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a233) | c2_1(a233) | (~c0_1(a233)) | c2_1(a238) | c0_1(a238) | (~c1_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a238) | c2_1(a233) | c3_1(a233) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a233)) | (~c1_1(a238)) | c0_1(a238)))),
% 1.47/1.21 inference(monotonicity,[status(thm)],[1453])).
% 1.47/1.21 tff(1455,plain,
% 1.47/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a233) | c2_1(a233) | (~c0_1(a233)) | c2_1(a238) | c0_1(a238) | (~c1_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a238) | c2_1(a233) | c3_1(a233) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a233)) | (~c1_1(a238)) | c0_1(a238))),
% 1.47/1.21 inference(transitivity,[status(thm)],[1454, 1452])).
% 1.47/1.21 tff(1456,plain,
% 1.47/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a233) | c2_1(a233) | (~c0_1(a233)) | c2_1(a238) | c0_1(a238) | (~c1_1(a238)))),
% 1.47/1.21 inference(quant_inst,[status(thm)],[])).
% 1.47/1.21 tff(1457,plain,
% 1.47/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a238) | c2_1(a233) | c3_1(a233) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a233)) | (~c1_1(a238)) | c0_1(a238)),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 1.47/1.21 tff(1458,plain,
% 1.47/1.21 (c0_1(a238)),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[1457, 128, 1110, 1099, 1088, 1393, 1370, 1198, 41, 1412, 1451])).
% 1.47/1.21 tff(1459,plain,
% 1.47/1.21 (((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp7 | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))) <=> ((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp7 | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1460,plain,
% 1.47/1.21 ((hskp24 | hskp7 | (~ndr1_0) | (~c0_1(a238)) | (~c3_1(a238)) | (~c1_1(a238))) <=> (hskp24 | hskp7 | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1461,plain,
% 1.47/1.21 (((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(a238)) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp7 | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238))))),
% 1.47/1.21 inference(monotonicity,[status(thm)],[1460])).
% 1.47/1.21 tff(1462,plain,
% 1.47/1.21 (((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(a238)) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp7 | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.47/1.21 inference(transitivity,[status(thm)],[1461, 1459])).
% 1.47/1.21 tff(1463,plain,
% 1.47/1.21 ((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(a238)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.21 inference(quant_inst,[status(thm)],[])).
% 1.47/1.21 tff(1464,plain,
% 1.47/1.21 ((~![U: $i] : (hskp24 | hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp7 | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1463, 1462])).
% 1.47/1.21 tff(1465,plain,
% 1.47/1.21 (hskp7 | (~c0_1(a238))),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[1464, 128, 12, 1393, 1382, 264])).
% 1.47/1.21 tff(1466,plain,
% 1.47/1.21 (hskp7),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[1465, 1458])).
% 1.47/1.21 tff(1467,plain,
% 1.47/1.21 (~c3_1(a209)),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[278, 1466])).
% 1.47/1.21 tff(1468,plain,
% 1.47/1.21 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | c2_1(a238) | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | c2_1(a238) | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1469,plain,
% 1.47/1.21 ((hskp21 | (~ndr1_0) | c2_1(a238) | (~c3_1(a238)) | (~c1_1(a238))) <=> (hskp21 | c2_1(a238) | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1470,plain,
% 1.47/1.21 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a238) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | c2_1(a238) | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238))))),
% 1.47/1.21 inference(monotonicity,[status(thm)],[1469])).
% 1.47/1.21 tff(1471,plain,
% 1.47/1.21 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a238) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | c2_1(a238) | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.21 inference(transitivity,[status(thm)],[1470, 1468])).
% 1.47/1.21 tff(1472,plain,
% 1.47/1.21 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a238) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.21 inference(quant_inst,[status(thm)],[])).
% 1.47/1.21 tff(1473,plain,
% 1.47/1.21 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | c2_1(a238) | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 1.47/1.21 tff(1474,plain,
% 1.47/1.21 (hskp21),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[1473, 128, 1393, 1382, 1370, 289])).
% 1.47/1.21 tff(1475,plain,
% 1.47/1.21 (~c3_1(a241)),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[302, 1474])).
% 1.47/1.21 tff(1476,plain,
% 1.47/1.21 (~c1_1(a241)),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[308, 1474])).
% 1.47/1.21 tff(1477,plain,
% 1.47/1.21 (c1_1(a209)),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[319, 1466])).
% 1.47/1.21 tff(1478,plain,
% 1.47/1.21 (c0_1(a241)),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[330, 1474])).
% 1.47/1.21 tff(1479,plain,
% 1.47/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a241) | c3_1(a241) | c2_1(a238) | c3_1(a209) | (~ndr1_0) | (~c1_1(a209)) | (~c2_1(a209)) | (~c0_1(a241)) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a241) | c3_1(a241) | c2_1(a238) | c3_1(a209) | (~ndr1_0) | (~c1_1(a209)) | (~c2_1(a209)) | (~c0_1(a241)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1480,plain,
% 1.47/1.21 (((~ndr1_0) | c3_1(a209) | (~c2_1(a209)) | (~c1_1(a209)) | (~c3_1(a238)) | c2_1(a238) | (~c1_1(a238)) | c1_1(a241) | c3_1(a241) | (~c0_1(a241))) <=> (c1_1(a241) | c3_1(a241) | c2_1(a238) | c3_1(a209) | (~ndr1_0) | (~c1_1(a209)) | (~c2_1(a209)) | (~c0_1(a241)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1481,plain,
% 1.47/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a209) | (~c2_1(a209)) | (~c1_1(a209)) | (~c3_1(a238)) | c2_1(a238) | (~c1_1(a238)) | c1_1(a241) | c3_1(a241) | (~c0_1(a241)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a241) | c3_1(a241) | c2_1(a238) | c3_1(a209) | (~ndr1_0) | (~c1_1(a209)) | (~c2_1(a209)) | (~c0_1(a241)) | (~c3_1(a238)) | (~c1_1(a238))))),
% 1.47/1.21 inference(monotonicity,[status(thm)],[1480])).
% 1.47/1.21 tff(1482,plain,
% 1.47/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a209) | (~c2_1(a209)) | (~c1_1(a209)) | (~c3_1(a238)) | c2_1(a238) | (~c1_1(a238)) | c1_1(a241) | c3_1(a241) | (~c0_1(a241)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a241) | c3_1(a241) | c2_1(a238) | c3_1(a209) | (~ndr1_0) | (~c1_1(a209)) | (~c2_1(a209)) | (~c0_1(a241)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.21 inference(transitivity,[status(thm)],[1481, 1479])).
% 1.47/1.21 tff(1483,plain,
% 1.47/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a209) | (~c2_1(a209)) | (~c1_1(a209)) | (~c3_1(a238)) | c2_1(a238) | (~c1_1(a238)) | c1_1(a241) | c3_1(a241) | (~c0_1(a241)))),
% 1.47/1.21 inference(quant_inst,[status(thm)],[])).
% 1.47/1.21 tff(1484,plain,
% 1.47/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a241) | c3_1(a241) | c2_1(a238) | c3_1(a209) | (~ndr1_0) | (~c1_1(a209)) | (~c2_1(a209)) | (~c0_1(a241)) | (~c3_1(a238)) | (~c1_1(a238))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 1.47/1.21 tff(1485,plain,
% 1.47/1.21 (~c2_1(a209)),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[1484, 128, 1478, 1393, 1382, 1477, 1476, 1475, 1370, 1467, 254])).
% 1.47/1.21 tff(1486,assumption,(~c2_1(a209)), introduced(assumption)).
% 1.47/1.21 tff(1487,plain,
% 1.47/1.21 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V)) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V)))),
% 1.47/1.21 inference(bind,[status(th)],[])).
% 1.47/1.21 tff(1488,plain,
% 1.47/1.21 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.47/1.21 inference(quant_intro,[status(thm)],[1487])).
% 1.47/1.21 tff(1489,plain,
% 1.47/1.21 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1490,plain,
% 1.47/1.21 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V)) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))))),
% 1.47/1.21 inference(bind,[status(th)],[])).
% 1.47/1.21 tff(1491,plain,
% 1.47/1.21 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.47/1.21 inference(quant_intro,[status(thm)],[1490])).
% 1.47/1.21 tff(1492,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 1.47/1.21 tff(1493,plain,
% 1.47/1.21 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 1.47/1.21 tff(1494,plain,
% 1.47/1.21 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1493, 1489])).
% 1.47/1.21 tff(1495,plain,(
% 1.47/1.21 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.47/1.21 inference(skolemize,[status(sab)],[1494])).
% 1.47/1.21 tff(1496,plain,
% 1.47/1.21 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1495, 1488])).
% 1.47/1.21 tff(1497,assumption,(~c3_1(a209)), introduced(assumption)).
% 1.47/1.21 tff(1498,assumption,(c0_1(a238)), introduced(assumption)).
% 1.47/1.21 tff(1499,plain,
% 1.47/1.21 (^[U: $i] : refl((hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 1.47/1.21 inference(bind,[status(th)],[])).
% 1.47/1.21 tff(1500,plain,
% 1.47/1.21 (![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.47/1.21 inference(quant_intro,[status(thm)],[1499])).
% 1.47/1.21 tff(1501,plain,
% 1.47/1.21 (![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1502,plain,
% 1.47/1.21 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp10))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp9) <=> ((hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp9))), rewrite(((hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp9) <=> (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp9) <=> (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.47/1.21 inference(bind,[status(th)],[])).
% 1.47/1.21 tff(1503,plain,
% 1.47/1.21 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp9) <=> ![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.47/1.21 inference(quant_intro,[status(thm)],[1502])).
% 1.47/1.21 tff(1504,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 1.47/1.21 tff(1505,plain,
% 1.47/1.21 (![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 1.47/1.21 tff(1506,plain,
% 1.47/1.21 (![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1505, 1501])).
% 1.47/1.21 tff(1507,plain,(
% 1.47/1.21 ![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.47/1.21 inference(skolemize,[status(sab)],[1506])).
% 1.47/1.21 tff(1508,plain,
% 1.47/1.21 (![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1507, 1500])).
% 1.47/1.21 tff(1509,assumption,(c3_1(a238)), introduced(assumption)).
% 1.47/1.21 tff(1510,assumption,(c1_1(a238)), introduced(assumption)).
% 1.47/1.21 tff(1511,plain,
% 1.47/1.21 (((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp10 | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))) <=> ((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp10 | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1512,plain,
% 1.47/1.21 ((hskp9 | hskp10 | (~ndr1_0) | (~c0_1(a238)) | (~c3_1(a238)) | (~c1_1(a238))) <=> (hskp9 | hskp10 | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(1513,plain,
% 1.47/1.21 (((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(a238)) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp10 | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238))))),
% 1.47/1.21 inference(monotonicity,[status(thm)],[1512])).
% 1.47/1.21 tff(1514,plain,
% 1.47/1.21 (((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(a238)) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp10 | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.47/1.21 inference(transitivity,[status(thm)],[1513, 1511])).
% 1.47/1.21 tff(1515,plain,
% 1.47/1.21 ((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(a238)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.21 inference(quant_inst,[status(thm)],[])).
% 1.47/1.21 tff(1516,plain,
% 1.47/1.21 ((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp10 | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 1.47/1.21 tff(1517,plain,
% 1.47/1.21 (hskp9 | hskp10 | (~c0_1(a238))),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[1516, 128, 1510, 1509, 1508])).
% 1.47/1.21 tff(1518,plain,
% 1.47/1.21 (hskp9),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[1517, 1231, 1498])).
% 1.47/1.21 tff(1519,plain,
% 1.47/1.21 (~c2_1(a213)),
% 1.47/1.21 inference(unit_resolution,[status(thm)],[712, 1518])).
% 1.47/1.22 tff(1520,plain,
% 1.47/1.22 (~c0_1(a213)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1156, 1518])).
% 1.47/1.22 tff(1521,assumption,(c1_1(a209)), introduced(assumption)).
% 1.47/1.22 tff(1522,plain,
% 1.47/1.22 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp10 | c0_1(a213) | c2_1(a213) | c3_1(a209) | (~ndr1_0) | (~c1_1(a209)) | c2_1(a209) | (~c3_1(a213)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))) | hskp10 | c0_1(a213) | c2_1(a213) | c3_1(a209) | (~ndr1_0) | (~c1_1(a209)) | c2_1(a209) | (~c3_1(a213)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1523,plain,
% 1.47/1.22 ((hskp10 | (~ndr1_0) | c3_1(a209) | c2_1(a209) | (~c1_1(a209)) | c0_1(a213) | (~c3_1(a213)) | c2_1(a213)) <=> (hskp10 | c0_1(a213) | c2_1(a213) | c3_1(a209) | (~ndr1_0) | (~c1_1(a209)) | c2_1(a209) | (~c3_1(a213)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1524,plain,
% 1.47/1.22 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp10 | (~ndr1_0) | c3_1(a209) | c2_1(a209) | (~c1_1(a209)) | c0_1(a213) | (~c3_1(a213)) | c2_1(a213))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp10 | c0_1(a213) | c2_1(a213) | c3_1(a209) | (~ndr1_0) | (~c1_1(a209)) | c2_1(a209) | (~c3_1(a213))))),
% 1.47/1.22 inference(monotonicity,[status(thm)],[1523])).
% 1.47/1.22 tff(1525,plain,
% 1.47/1.22 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp10 | (~ndr1_0) | c3_1(a209) | c2_1(a209) | (~c1_1(a209)) | c0_1(a213) | (~c3_1(a213)) | c2_1(a213))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))) | hskp10 | c0_1(a213) | c2_1(a213) | c3_1(a209) | (~ndr1_0) | (~c1_1(a209)) | c2_1(a209) | (~c3_1(a213)))),
% 1.47/1.22 inference(transitivity,[status(thm)],[1524, 1522])).
% 1.47/1.22 tff(1526,plain,
% 1.47/1.22 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp10 | (~ndr1_0) | c3_1(a209) | c2_1(a209) | (~c1_1(a209)) | c0_1(a213) | (~c3_1(a213)) | c2_1(a213))),
% 1.47/1.22 inference(quant_inst,[status(thm)],[])).
% 1.47/1.22 tff(1527,plain,
% 1.47/1.22 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(V))) | hskp10 | c0_1(a213) | c2_1(a213) | c3_1(a209) | (~ndr1_0) | (~c1_1(a209)) | c2_1(a209) | (~c3_1(a213))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1526, 1525])).
% 1.47/1.22 tff(1528,plain,
% 1.47/1.22 (~c3_1(a213)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1527, 128, 1231, 1521, 1520, 1519, 1497, 1496, 1486])).
% 1.47/1.22 tff(1529,plain,
% 1.47/1.22 (~c1_1(a213)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[706, 1518])).
% 1.47/1.22 tff(1530,plain,
% 1.47/1.22 ($false),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1216, 128, 1210, 23, 1520, 1529, 1209, 1528])).
% 1.47/1.22 tff(1531,plain,(hskp10 | hskp5 | hskp4 | (~c1_1(a209)) | c3_1(a209) | c2_1(a209) | (~c0_1(a238)) | (~c1_1(a238)) | (~c3_1(a238))), inference(lemma,lemma(discharge,[]))).
% 1.47/1.22 tff(1532,plain,
% 1.47/1.22 (hskp10),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1531, 1477, 23, 1197, 1467, 1485, 1458, 1393, 1382])).
% 1.47/1.22 tff(1533,plain,
% 1.47/1.22 (c1_1(a214)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1294, 1532])).
% 1.47/1.22 tff(1534,plain,
% 1.47/1.22 (~c3_1(a214)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1300, 1532])).
% 1.47/1.22 tff(1535,plain,
% 1.47/1.22 (~c2_1(a214)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1306, 1532])).
% 1.47/1.22 tff(1536,plain,
% 1.47/1.22 (c3_1(a198)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1401, 1535, 1088, 1099, 1364, 1534, 1533])).
% 1.47/1.22 tff(1537,plain,
% 1.47/1.22 (c1_1(a208)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[221, 1449])).
% 1.47/1.22 tff(1538,plain,
% 1.47/1.22 (c0_1(a208)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[171, 1449])).
% 1.47/1.22 tff(1539,plain,
% 1.47/1.22 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1540,plain,
% 1.47/1.22 ((hskp3 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208))) <=> (hskp3 | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1541,plain,
% 1.47/1.22 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a208)) | (~c0_1(a208))))),
% 1.47/1.22 inference(monotonicity,[status(thm)],[1540])).
% 1.47/1.22 tff(1542,plain,
% 1.47/1.22 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.47/1.22 inference(transitivity,[status(thm)],[1541, 1539])).
% 1.47/1.22 tff(1543,plain,
% 1.47/1.22 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.47/1.22 inference(quant_inst,[status(thm)],[])).
% 1.47/1.22 tff(1544,plain,
% 1.47/1.22 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a208)) | (~c0_1(a208))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 1.47/1.22 tff(1545,plain,
% 1.47/1.22 (hskp3 | (~c3_1(a198))),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1544, 128, 1110, 1088, 1538, 1537, 1450, 1429])).
% 1.47/1.22 tff(1546,plain,
% 1.47/1.22 (hskp3),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1545, 1536])).
% 1.47/1.22 tff(1547,plain,
% 1.47/1.22 (~c3_1(a203)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[619, 1546])).
% 1.47/1.22 tff(1548,plain,
% 1.47/1.22 (c1_1(a203)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[636, 1546])).
% 1.47/1.22 tff(1549,plain,
% 1.47/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a238) | c2_1(a214) | c3_1(a214) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c2_1(a203)) | (~c1_1(a214)) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a238) | c2_1(a214) | c3_1(a214) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c2_1(a203)) | (~c1_1(a214)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1550,plain,
% 1.47/1.22 (((~ndr1_0) | c3_1(a203) | (~c2_1(a203)) | (~c1_1(a203)) | (~c3_1(a238)) | c2_1(a238) | (~c1_1(a238)) | c2_1(a214) | c3_1(a214) | (~c1_1(a214))) <=> (c2_1(a238) | c2_1(a214) | c3_1(a214) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c2_1(a203)) | (~c1_1(a214)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1551,plain,
% 1.47/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a203) | (~c2_1(a203)) | (~c1_1(a203)) | (~c3_1(a238)) | c2_1(a238) | (~c1_1(a238)) | c2_1(a214) | c3_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a238) | c2_1(a214) | c3_1(a214) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c2_1(a203)) | (~c1_1(a214)) | (~c3_1(a238)) | (~c1_1(a238))))),
% 1.47/1.22 inference(monotonicity,[status(thm)],[1550])).
% 1.47/1.22 tff(1552,plain,
% 1.47/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a203) | (~c2_1(a203)) | (~c1_1(a203)) | (~c3_1(a238)) | c2_1(a238) | (~c1_1(a238)) | c2_1(a214) | c3_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a238) | c2_1(a214) | c3_1(a214) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c2_1(a203)) | (~c1_1(a214)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.47/1.22 inference(transitivity,[status(thm)],[1551, 1549])).
% 1.47/1.22 tff(1553,plain,
% 1.47/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a203) | (~c2_1(a203)) | (~c1_1(a203)) | (~c3_1(a238)) | c2_1(a238) | (~c1_1(a238)) | c2_1(a214) | c3_1(a214) | (~c1_1(a214)))),
% 1.47/1.22 inference(quant_inst,[status(thm)],[])).
% 1.47/1.22 tff(1554,plain,
% 1.47/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a238) | c2_1(a214) | c3_1(a214) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c2_1(a203)) | (~c1_1(a214)) | (~c3_1(a238)) | (~c1_1(a238))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1553, 1552])).
% 1.47/1.22 tff(1555,plain,
% 1.47/1.22 (~c2_1(a203)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1554, 128, 1393, 1382, 1533, 1548, 1370, 1535, 1534, 1547, 1361])).
% 1.47/1.22 tff(1556,plain,
% 1.47/1.22 (~c0_1(a203)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[625, 1546])).
% 1.47/1.22 tff(1557,plain,
% 1.47/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a233) | c3_1(a233) | c0_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)) | c2_1(a203) | (~c0_1(a233)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a233) | c3_1(a233) | c0_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)) | c2_1(a203) | (~c0_1(a233)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1558,plain,
% 1.47/1.22 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a233) | c2_1(a233) | (~c0_1(a233)) | c2_1(a203) | c0_1(a203) | (~c1_1(a203))) <=> (c2_1(a233) | c3_1(a233) | c0_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)) | c2_1(a203) | (~c0_1(a233)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1559,plain,
% 1.47/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a233) | c2_1(a233) | (~c0_1(a233)) | c2_1(a203) | c0_1(a203) | (~c1_1(a203)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a233) | c3_1(a233) | c0_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)) | c2_1(a203) | (~c0_1(a233))))),
% 1.47/1.22 inference(monotonicity,[status(thm)],[1558])).
% 1.47/1.22 tff(1560,plain,
% 1.47/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a233) | c2_1(a233) | (~c0_1(a233)) | c2_1(a203) | c0_1(a203) | (~c1_1(a203)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a233) | c3_1(a233) | c0_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)) | c2_1(a203) | (~c0_1(a233)))),
% 1.47/1.22 inference(transitivity,[status(thm)],[1559, 1557])).
% 1.47/1.22 tff(1561,plain,
% 1.47/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a233) | c2_1(a233) | (~c0_1(a233)) | c2_1(a203) | c0_1(a203) | (~c1_1(a203)))),
% 1.47/1.22 inference(quant_inst,[status(thm)],[])).
% 1.47/1.22 tff(1562,plain,
% 1.47/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a233) | c3_1(a233) | c0_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)) | c2_1(a203) | (~c0_1(a233))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 1.47/1.22 tff(1563,plain,
% 1.47/1.22 ($false),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1562, 128, 1110, 1099, 1088, 1548, 1198, 41, 1556, 1412, 1451, 1555])).
% 1.47/1.22 tff(1564,plain,((~hskp19) | hskp4 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.47/1.22 tff(1565,plain,
% 1.47/1.22 (~hskp19),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1564, 23, 12])).
% 1.47/1.22 tff(1566,plain,
% 1.47/1.22 (hskp20 | hskp19 | (~c0_1(a233))),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1348, 128, 1199, 1198, 1341])).
% 1.47/1.22 tff(1567,plain,
% 1.47/1.22 (hskp20),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1566, 1565, 1451])).
% 1.47/1.22 tff(1568,plain,
% 1.47/1.22 (~c3_1(a239)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1251, 1567])).
% 1.47/1.22 tff(1569,plain,
% 1.47/1.22 (~c0_1(a239)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1257, 1567])).
% 1.47/1.22 tff(1570,plain,
% 1.47/1.22 (((~hskp20) | c2_1(a239)) <=> ((~hskp20) | c2_1(a239))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1571,axiom,((~hskp20) | c2_1(a239)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.47/1.22 tff(1572,plain,
% 1.47/1.22 ((~hskp20) | c2_1(a239)),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 1.47/1.22 tff(1573,plain,
% 1.47/1.22 ((~hskp20) | c2_1(a239)),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1572, 1570])).
% 1.47/1.22 tff(1574,plain,
% 1.47/1.22 ((~hskp20) | c2_1(a239)),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1573, 1570])).
% 1.47/1.22 tff(1575,plain,
% 1.47/1.22 ((~hskp20) | c2_1(a239)),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1574, 1570])).
% 1.47/1.22 tff(1576,plain,
% 1.47/1.22 ((~hskp20) | c2_1(a239)),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1575, 1570])).
% 1.47/1.22 tff(1577,plain,
% 1.47/1.22 ((~hskp20) | c2_1(a239)),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1576, 1570])).
% 1.47/1.22 tff(1578,plain,
% 1.47/1.22 ((~hskp20) | c2_1(a239)),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1577, 1570])).
% 1.47/1.22 tff(1579,plain,
% 1.47/1.22 ((~hskp20) | c2_1(a239)),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1578, 1570])).
% 1.47/1.22 tff(1580,plain,
% 1.47/1.22 (c2_1(a239)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1579, 1567])).
% 1.47/1.22 tff(1581,plain,
% 1.47/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a239) | c3_1(a239) | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a208)) | (~c0_1(a208)) | (~c2_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a239) | c3_1(a239) | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a208)) | (~c0_1(a208)) | (~c2_1(a239)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1582,plain,
% 1.47/1.22 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c0_1(a239) | c3_1(a239) | (~c2_1(a239))) <=> (c0_1(a239) | c3_1(a239) | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a208)) | (~c0_1(a208)) | (~c2_1(a239)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1583,plain,
% 1.47/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c0_1(a239) | c3_1(a239) | (~c2_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a239) | c3_1(a239) | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a208)) | (~c0_1(a208)) | (~c2_1(a239))))),
% 1.47/1.22 inference(monotonicity,[status(thm)],[1582])).
% 1.47/1.22 tff(1584,plain,
% 1.47/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c0_1(a239) | c3_1(a239) | (~c2_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a239) | c3_1(a239) | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a208)) | (~c0_1(a208)) | (~c2_1(a239)))),
% 1.47/1.22 inference(transitivity,[status(thm)],[1583, 1581])).
% 1.47/1.22 tff(1585,plain,
% 1.47/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c0_1(a239) | c3_1(a239) | (~c2_1(a239)))),
% 1.47/1.22 inference(quant_inst,[status(thm)],[])).
% 1.47/1.22 tff(1586,plain,
% 1.47/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a239) | c3_1(a239) | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a208)) | (~c0_1(a208)) | (~c2_1(a239))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1585, 1584])).
% 1.47/1.22 tff(1587,plain,
% 1.47/1.22 ($false),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1586, 128, 1110, 1099, 1088, 1580, 1538, 1537, 1569, 1568, 1450, 22])).
% 1.47/1.22 tff(1588,plain,(hskp4 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.47/1.22 tff(1589,plain,
% 1.47/1.22 (hskp4),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1588, 12])).
% 1.47/1.22 tff(1590,plain,
% 1.47/1.22 (~c0_1(a204)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[392, 1589])).
% 1.47/1.22 tff(1591,assumption,(~c1_1(a204)), introduced(assumption)).
% 1.47/1.22 tff(1592,plain,
% 1.47/1.22 (~hskp4),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[414, 1591])).
% 1.47/1.22 tff(1593,plain,
% 1.47/1.22 (hskp18),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[34, 1592, 12])).
% 1.47/1.22 tff(1594,plain,
% 1.47/1.22 (~c1_1(a233)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[201, 1593])).
% 1.47/1.22 tff(1595,plain,
% 1.47/1.22 (~c3_1(a233)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[40, 1593])).
% 1.47/1.22 tff(1596,plain,
% 1.47/1.22 (~c2_1(a233)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[195, 1593])).
% 1.47/1.22 tff(1597,assumption,(c3_1(a204)), introduced(assumption)).
% 1.47/1.22 tff(1598,plain,
% 1.47/1.22 (hskp5 | c0_1(a233)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1315, 128, 1592, 1309, 1308, 1209])).
% 1.47/1.22 tff(1599,plain,
% 1.47/1.22 (c0_1(a233)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1598, 1210])).
% 1.47/1.22 tff(1600,plain,
% 1.47/1.22 (c1_1(a239)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1264, 128, 1210, 1592, 1321, 1320, 1209])).
% 1.47/1.22 tff(1601,plain,
% 1.47/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c1_1(a204) | c0_1(a239) | c3_1(a239) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c1_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a204) | c0_1(a239) | c3_1(a239) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c1_1(a239)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1602,plain,
% 1.47/1.22 ((hskp4 | (~ndr1_0) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204))) <=> (hskp4 | c1_1(a204) | c0_1(a239) | c3_1(a239) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c1_1(a239)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1603,plain,
% 1.47/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c1_1(a204) | c0_1(a239) | c3_1(a239) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c1_1(a239))))),
% 1.47/1.22 inference(monotonicity,[status(thm)],[1602])).
% 1.47/1.22 tff(1604,plain,
% 1.47/1.22 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a204) | c0_1(a239) | c3_1(a239) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c1_1(a239)))),
% 1.47/1.22 inference(transitivity,[status(thm)],[1603, 1601])).
% 1.47/1.22 tff(1605,plain,
% 1.47/1.22 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204)))),
% 1.47/1.22 inference(quant_inst,[status(thm)],[])).
% 1.47/1.22 tff(1606,plain,
% 1.47/1.22 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a204) | c0_1(a239) | c3_1(a239) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c1_1(a239))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1605, 1604])).
% 1.47/1.22 tff(1607,plain,
% 1.47/1.22 ($false),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1606, 128, 1592, 1591, 1321, 1320, 646, 1227, 1597, 1600])).
% 1.47/1.22 tff(1608,plain,((~hskp20) | c1_1(a204) | c0_1(a204) | (~c3_1(a204)) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.47/1.22 tff(1609,plain,
% 1.47/1.22 (~hskp20),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1608, 1210, 646, 1597, 1591])).
% 1.47/1.22 tff(1610,plain,
% 1.47/1.22 (hskp19),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1349, 1609, 1599])).
% 1.47/1.22 tff(1611,plain,
% 1.47/1.22 (~c2_1(a238)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1369, 1610])).
% 1.47/1.22 tff(1612,plain,
% 1.47/1.22 (c1_1(a238)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1392, 1610])).
% 1.47/1.22 tff(1613,plain,
% 1.47/1.22 (c0_1(a238)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1457, 128, 1228, 1230, 1229, 1612, 1611, 1342, 1308, 1412, 1599])).
% 1.47/1.22 tff(1614,plain,
% 1.47/1.22 (c3_1(a238)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1381, 1610])).
% 1.47/1.22 tff(1615,plain,
% 1.47/1.22 (((~![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(a204) | c2_1(a238) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))) <=> ((~![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(a204) | c2_1(a238) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1616,plain,
% 1.47/1.22 (((~ndr1_0) | c2_1(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204))) <=> (c1_1(a204) | c2_1(a238) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1617,plain,
% 1.47/1.22 (((~![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(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204)))) <=> ((~![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(a204) | c2_1(a238) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238))))),
% 1.47/1.22 inference(monotonicity,[status(thm)],[1616])).
% 1.47/1.22 tff(1618,plain,
% 1.47/1.22 (((~![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(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204)))) <=> ((~![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(a204) | c2_1(a238) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.47/1.22 inference(transitivity,[status(thm)],[1617, 1615])).
% 1.47/1.22 tff(1619,plain,
% 1.47/1.22 ((~![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(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204)))),
% 1.47/1.22 inference(quant_inst,[status(thm)],[])).
% 1.47/1.22 tff(1620,plain,
% 1.47/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a204) | c2_1(a238) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[1619, 1618])).
% 1.47/1.22 tff(1621,plain,
% 1.47/1.22 ($false),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1620, 128, 1612, 1614, 1591, 1611, 646, 682, 1597, 1613])).
% 1.47/1.22 tff(1622,plain,(hskp5 | c1_1(a204) | c0_1(a204) | (~c3_1(a204)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c2_1(a233) | c3_1(a233) | c1_1(a233)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.22 tff(1623,plain,
% 1.47/1.22 (hskp5),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[1622, 1597, 646, 1591, 1228, 1230, 1229, 1342, 1308, 1309])).
% 1.47/1.22 tff(1624,plain,
% 1.47/1.22 (~c1_1(a205)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[58, 1623])).
% 1.47/1.22 tff(1625,plain,
% 1.47/1.22 (c2_1(a205)),
% 1.47/1.22 inference(unit_resolution,[status(thm)],[52, 1623])).
% 1.47/1.22 tff(1626,plain,
% 1.47/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a204) | c1_1(a205) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c2_1(a205)) | (~c0_1(a205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a204) | c1_1(a205) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c2_1(a205)) | (~c0_1(a205)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1627,plain,
% 1.47/1.22 (((~ndr1_0) | c1_1(a205) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a204) | (~c3_1(a204)) | c2_1(a204) | c2_1(a204) | c0_1(a204) | (~c3_1(a204))) <=> (c1_1(a204) | c1_1(a205) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c2_1(a205)) | (~c0_1(a205)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(1628,plain,
% 1.47/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a205) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a204) | (~c3_1(a204)) | c2_1(a204) | c2_1(a204) | c0_1(a204) | (~c3_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a204) | c1_1(a205) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c2_1(a205)) | (~c0_1(a205))))),
% 1.47/1.22 inference(monotonicity,[status(thm)],[1627])).
% 1.47/1.22 tff(1629,plain,
% 1.47/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a205) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a204) | (~c3_1(a204)) | c2_1(a204) | c2_1(a204) | c0_1(a204) | (~c3_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a204) | c1_1(a205) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c2_1(a205)) | (~c0_1(a205)))),
% 1.47/1.22 inference(transitivity,[status(thm)],[1628, 1626])).
% 1.47/1.22 tff(1630,plain,
% 1.47/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a205) | (~c2_1(a205)) | (~c0_1(a205)) | c1_1(a204) | (~c3_1(a204)) | c2_1(a204) | c2_1(a204) | c0_1(a204) | (~c3_1(a204)))),
% 1.47/1.23 inference(quant_inst,[status(thm)],[])).
% 1.47/1.23 tff(1631,plain,
% 1.47/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a204) | c1_1(a205) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c2_1(a205)) | (~c0_1(a205))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 1.47/1.23 tff(1632,plain,
% 1.47/1.23 (~c0_1(a205)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[1631, 128, 1625, 1591, 1624, 646, 645, 886, 1597])).
% 1.47/1.23 tff(1633,plain,
% 1.47/1.23 (hskp6),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[1167, 1625, 1624, 1632])).
% 1.47/1.23 tff(1634,plain,
% 1.47/1.23 (~c2_1(a208)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[177, 1633])).
% 1.47/1.23 tff(1635,plain,
% 1.47/1.23 (c1_1(a208)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[221, 1633])).
% 1.47/1.23 tff(1636,plain,
% 1.47/1.23 (c0_1(a208)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[171, 1633])).
% 1.47/1.23 tff(1637,plain,
% 1.47/1.23 (((~![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(a204) | c2_1(a208) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![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(a204) | c2_1(a208) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(1638,plain,
% 1.47/1.23 (((~ndr1_0) | c2_1(a208) | (~c3_1(a208)) | (~c1_1(a208)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204))) <=> (c1_1(a204) | c2_1(a208) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(1639,plain,
% 1.47/1.23 (((~![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(a208) | (~c3_1(a208)) | (~c1_1(a208)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204)))) <=> ((~![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(a204) | c2_1(a208) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208))))),
% 1.47/1.23 inference(monotonicity,[status(thm)],[1638])).
% 1.47/1.23 tff(1640,plain,
% 1.47/1.23 (((~![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(a208) | (~c3_1(a208)) | (~c1_1(a208)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204)))) <=> ((~![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(a204) | c2_1(a208) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.47/1.23 inference(transitivity,[status(thm)],[1639, 1637])).
% 1.47/1.23 tff(1641,plain,
% 1.47/1.23 ((~![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(a208) | (~c3_1(a208)) | (~c1_1(a208)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204)))),
% 1.47/1.23 inference(quant_inst,[status(thm)],[])).
% 1.47/1.23 tff(1642,plain,
% 1.47/1.23 ((~![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(a204) | c2_1(a208) | c0_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 1.47/1.23 tff(1643,plain,
% 1.47/1.23 (~c3_1(a208)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[1642, 128, 1636, 1635, 1591, 1634, 646, 682, 1597])).
% 1.47/1.23 tff(1644,plain,
% 1.47/1.23 (c3_1(a205)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[69, 1623])).
% 1.47/1.23 tff(1645,plain,
% 1.47/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a204) | c1_1(a205) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c2_1(a205)) | (~c3_1(a205)) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a204) | c1_1(a205) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c2_1(a205)) | (~c3_1(a205)) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(1646,plain,
% 1.47/1.23 (((~ndr1_0) | c3_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a205) | (~c3_1(a205)) | (~c2_1(a205)) | c2_1(a204) | c1_1(a204) | (~c3_1(a204))) <=> (c1_1(a204) | c1_1(a205) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c2_1(a205)) | (~c3_1(a205)) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(1647,plain,
% 1.47/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a205) | (~c3_1(a205)) | (~c2_1(a205)) | c2_1(a204) | c1_1(a204) | (~c3_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a204) | c1_1(a205) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c2_1(a205)) | (~c3_1(a205)) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208))))),
% 1.47/1.23 inference(monotonicity,[status(thm)],[1646])).
% 1.47/1.23 tff(1648,plain,
% 1.47/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a205) | (~c3_1(a205)) | (~c2_1(a205)) | c2_1(a204) | c1_1(a204) | (~c3_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a204) | c1_1(a205) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c2_1(a205)) | (~c3_1(a205)) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.47/1.23 inference(transitivity,[status(thm)],[1647, 1645])).
% 1.47/1.23 tff(1649,plain,
% 1.47/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a205) | (~c3_1(a205)) | (~c2_1(a205)) | c2_1(a204) | c1_1(a204) | (~c3_1(a204)))),
% 1.47/1.23 inference(quant_inst,[status(thm)],[])).
% 1.47/1.23 tff(1650,plain,
% 1.47/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a204) | c1_1(a205) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | (~c2_1(a205)) | (~c3_1(a205)) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 1.47/1.23 tff(1651,plain,
% 1.47/1.23 ($false),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[1650, 128, 1636, 1635, 1625, 1644, 1591, 1624, 645, 1009, 1597, 1643])).
% 1.47/1.23 tff(1652,plain,((~c3_1(a204)) | c1_1(a204) | c2_1(a204) | c0_1(a204) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c2_1(a233) | c3_1(a233) | c1_1(a233)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.23 tff(1653,plain,
% 1.47/1.23 (~c3_1(a204)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[1652, 645, 1591, 646, 1110, 1099, 1088, 1596, 1595, 1594])).
% 1.47/1.23 tff(1654,plain,
% 1.47/1.23 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | c1_1(a204) | c0_1(a204) | (~ndr1_0) | c3_1(a204))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c1_1(a204) | c0_1(a204) | (~ndr1_0) | c3_1(a204))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(1655,plain,
% 1.47/1.23 ((hskp5 | hskp4 | (~ndr1_0) | c3_1(a204) | c1_1(a204) | c0_1(a204)) <=> (hskp5 | hskp4 | c1_1(a204) | c0_1(a204) | (~ndr1_0) | c3_1(a204))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(1656,plain,
% 1.50/1.23 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a204) | c1_1(a204) | c0_1(a204))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | c1_1(a204) | c0_1(a204) | (~ndr1_0) | c3_1(a204)))),
% 1.50/1.23 inference(monotonicity,[status(thm)],[1655])).
% 1.50/1.23 tff(1657,plain,
% 1.50/1.23 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a204) | c1_1(a204) | c0_1(a204))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c1_1(a204) | c0_1(a204) | (~ndr1_0) | c3_1(a204))),
% 1.50/1.23 inference(transitivity,[status(thm)],[1656, 1654])).
% 1.50/1.23 tff(1658,plain,
% 1.50/1.23 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a204) | c1_1(a204) | c0_1(a204))),
% 1.50/1.23 inference(quant_inst,[status(thm)],[])).
% 1.50/1.23 tff(1659,plain,
% 1.50/1.23 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c1_1(a204) | c0_1(a204) | (~ndr1_0) | c3_1(a204)),
% 1.50/1.23 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 1.50/1.23 tff(1660,plain,
% 1.50/1.23 (hskp5 | hskp4 | c1_1(a204) | c3_1(a204)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1659, 128, 646, 1209])).
% 1.50/1.23 tff(1661,plain,
% 1.50/1.23 (hskp5),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1660, 1653, 1591, 1592])).
% 1.50/1.23 tff(1662,plain,
% 1.50/1.23 (c3_1(a205)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[69, 1661])).
% 1.50/1.23 tff(1663,plain,
% 1.50/1.23 (~c1_1(a205)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[58, 1661])).
% 1.50/1.23 tff(1664,plain,
% 1.50/1.23 (c2_1(a205)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[52, 1661])).
% 1.50/1.23 tff(1665,plain,
% 1.50/1.23 (~c0_1(a205)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1126, 1664, 1663, 12, 1662])).
% 1.50/1.23 tff(1666,plain,
% 1.50/1.23 (hskp6),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1167, 1665, 1663, 1664])).
% 1.50/1.23 tff(1667,plain,
% 1.50/1.23 (~c2_1(a208)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[177, 1666])).
% 1.50/1.23 tff(1668,plain,
% 1.50/1.23 (c1_1(a208)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[221, 1666])).
% 1.50/1.23 tff(1669,plain,
% 1.50/1.23 (c0_1(a208)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[171, 1666])).
% 1.50/1.23 tff(1670,plain,
% 1.50/1.23 (((~![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(a208) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![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(a208) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.50/1.23 inference(rewrite,[status(thm)],[])).
% 1.50/1.23 tff(1671,plain,
% 1.50/1.23 (((~ndr1_0) | c2_1(a208) | (~c3_1(a208)) | (~c1_1(a208)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205))) <=> (c2_1(a208) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.50/1.23 inference(rewrite,[status(thm)],[])).
% 1.50/1.23 tff(1672,plain,
% 1.50/1.23 (((~![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(a208) | (~c3_1(a208)) | (~c1_1(a208)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205)))) <=> ((~![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(a208) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208))))),
% 1.50/1.23 inference(monotonicity,[status(thm)],[1671])).
% 1.50/1.23 tff(1673,plain,
% 1.50/1.23 (((~![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(a208) | (~c3_1(a208)) | (~c1_1(a208)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205)))) <=> ((~![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(a208) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.50/1.23 inference(transitivity,[status(thm)],[1672, 1670])).
% 1.50/1.23 tff(1674,plain,
% 1.50/1.23 ((~![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(a208) | (~c3_1(a208)) | (~c1_1(a208)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205)))),
% 1.50/1.23 inference(quant_inst,[status(thm)],[])).
% 1.50/1.23 tff(1675,plain,
% 1.50/1.23 ((~![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(a208) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208))),
% 1.50/1.23 inference(modus_ponens,[status(thm)],[1674, 1673])).
% 1.50/1.23 tff(1676,plain,
% 1.50/1.23 (~c3_1(a208)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1675, 128, 1669, 1668, 1662, 1667, 1663, 682, 1665])).
% 1.50/1.23 tff(1677,plain,
% 1.50/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a204) | c1_1(a205) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a204) | c1_1(a205) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.50/1.23 inference(rewrite,[status(thm)],[])).
% 1.50/1.23 tff(1678,plain,
% 1.50/1.23 (((~ndr1_0) | c3_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)) | c2_1(a204) | c1_1(a204) | c0_1(a204)) <=> (c1_1(a204) | c1_1(a205) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.50/1.23 inference(rewrite,[status(thm)],[])).
% 1.50/1.23 tff(1679,plain,
% 1.50/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)) | c2_1(a204) | c1_1(a204) | c0_1(a204))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a204) | c1_1(a205) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208))))),
% 1.50/1.23 inference(monotonicity,[status(thm)],[1678])).
% 1.50/1.23 tff(1680,plain,
% 1.50/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)) | c2_1(a204) | c1_1(a204) | c0_1(a204))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a204) | c1_1(a205) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.50/1.23 inference(transitivity,[status(thm)],[1679, 1677])).
% 1.50/1.23 tff(1681,plain,
% 1.50/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)) | c2_1(a204) | c1_1(a204) | c0_1(a204))),
% 1.50/1.23 inference(quant_inst,[status(thm)],[])).
% 1.50/1.23 tff(1682,plain,
% 1.50/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a204) | c1_1(a205) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | c3_1(a208) | (~c1_1(a208)) | (~c0_1(a208))),
% 1.50/1.23 inference(modus_ponens,[status(thm)],[1681, 1680])).
% 1.50/1.23 tff(1683,plain,
% 1.50/1.23 ($false),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1682, 128, 1669, 1668, 1664, 1591, 1663, 646, 645, 1042, 1665, 1676])).
% 1.50/1.23 tff(1684,plain,(c2_1(a204) | c1_1(a204) | c0_1(a204) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.50/1.23 tff(1685,plain,
% 1.50/1.23 (c2_1(a204)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1684, 1591, 646, 12])).
% 1.50/1.23 tff(1686,plain,
% 1.50/1.23 (hskp5),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1660, 837, 1591, 1592])).
% 1.50/1.23 tff(1687,plain,
% 1.50/1.23 (c2_1(a205)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[52, 1686])).
% 1.50/1.23 tff(1688,plain,
% 1.50/1.23 (~c1_1(a205)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[58, 1686])).
% 1.50/1.23 tff(1689,plain,
% 1.50/1.23 (c3_1(a205)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[69, 1686])).
% 1.50/1.23 tff(1690,plain,
% 1.50/1.23 (~c0_1(a205)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1126, 1689, 1688, 12, 1687])).
% 1.50/1.23 tff(1691,plain,
% 1.50/1.23 (hskp6),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1167, 1690, 1688, 1687])).
% 1.50/1.23 tff(1692,plain,
% 1.50/1.23 (~c2_1(a208)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[177, 1691])).
% 1.50/1.23 tff(1693,plain,
% 1.50/1.23 (c1_1(a208)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[221, 1691])).
% 1.50/1.23 tff(1694,plain,
% 1.50/1.23 (c0_1(a208)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[171, 1691])).
% 1.50/1.23 tff(1695,plain,
% 1.50/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a208) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a208) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.50/1.23 inference(rewrite,[status(thm)],[])).
% 1.50/1.23 tff(1696,plain,
% 1.50/1.23 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c0_1(a204) | c3_1(a204) | (~c2_1(a204))) <=> (c2_1(a208) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.50/1.23 inference(rewrite,[status(thm)],[])).
% 1.50/1.23 tff(1697,plain,
% 1.50/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c0_1(a204) | c3_1(a204) | (~c2_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a208) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a208)) | (~c0_1(a208))))),
% 1.50/1.23 inference(monotonicity,[status(thm)],[1696])).
% 1.50/1.23 tff(1698,plain,
% 1.50/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c0_1(a204) | c3_1(a204) | (~c2_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a208) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.50/1.23 inference(transitivity,[status(thm)],[1697, 1695])).
% 1.50/1.23 tff(1699,plain,
% 1.50/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c0_1(a204) | c3_1(a204) | (~c2_1(a204)))),
% 1.50/1.23 inference(quant_inst,[status(thm)],[])).
% 1.50/1.23 tff(1700,plain,
% 1.50/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a208) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a208)) | (~c0_1(a208))),
% 1.50/1.23 inference(modus_ponens,[status(thm)],[1699, 1698])).
% 1.50/1.23 tff(1701,plain,
% 1.50/1.23 ($false),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1700, 128, 1110, 1099, 1088, 1694, 1693, 1692, 646, 1685, 22, 837])).
% 1.50/1.23 tff(1702,plain,(c3_1(a204) | c0_1(a204) | hskp24 | c1_1(a204)), inference(lemma,lemma(discharge,[]))).
% 1.50/1.23 tff(1703,plain,
% 1.50/1.23 (c3_1(a204)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1702, 1591, 12, 646])).
% 1.50/1.23 tff(1704,plain,
% 1.50/1.23 (hskp5),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1622, 1703, 646, 1591, 1110, 1099, 1088, 1596, 1595, 1594])).
% 1.50/1.23 tff(1705,plain,
% 1.50/1.23 (c2_1(a205)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[52, 1704])).
% 1.50/1.23 tff(1706,plain,
% 1.50/1.23 (~c1_1(a205)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[58, 1704])).
% 1.50/1.23 tff(1707,plain,
% 1.50/1.23 (c3_1(a205)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[69, 1704])).
% 1.50/1.23 tff(1708,plain,
% 1.50/1.23 (~c0_1(a205)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1126, 1707, 1706, 12, 1705])).
% 1.50/1.23 tff(1709,plain,
% 1.50/1.23 (hskp6),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1167, 1708, 1706, 1705])).
% 1.50/1.23 tff(1710,plain,
% 1.50/1.23 (~c2_1(a208)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[177, 1709])).
% 1.50/1.23 tff(1711,plain,
% 1.50/1.23 (c1_1(a208)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[221, 1709])).
% 1.50/1.23 tff(1712,plain,
% 1.50/1.23 (c0_1(a208)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[171, 1709])).
% 1.50/1.23 tff(1713,plain,
% 1.50/1.23 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a204) | c2_1(a208) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c1_1(a208)) | (~c0_1(a208)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a204) | c2_1(a208) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.50/1.23 inference(rewrite,[status(thm)],[])).
% 1.50/1.23 tff(1714,plain,
% 1.50/1.23 ((hskp3 | (~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a204) | c0_1(a204) | (~c2_1(a204))) <=> (hskp3 | c1_1(a204) | c2_1(a208) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.50/1.23 inference(rewrite,[status(thm)],[])).
% 1.50/1.23 tff(1715,plain,
% 1.50/1.23 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a204) | c0_1(a204) | (~c2_1(a204)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a204) | c2_1(a208) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c1_1(a208)) | (~c0_1(a208))))),
% 1.50/1.23 inference(monotonicity,[status(thm)],[1714])).
% 1.50/1.23 tff(1716,plain,
% 1.50/1.23 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a204) | c0_1(a204) | (~c2_1(a204)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a204) | c2_1(a208) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c1_1(a208)) | (~c0_1(a208)))),
% 1.50/1.23 inference(transitivity,[status(thm)],[1715, 1713])).
% 1.50/1.23 tff(1717,plain,
% 1.50/1.23 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a208) | (~c0_1(a208)) | (~c1_1(a208)) | c1_1(a204) | c0_1(a204) | (~c2_1(a204)))),
% 1.50/1.23 inference(quant_inst,[status(thm)],[])).
% 1.50/1.23 tff(1718,plain,
% 1.50/1.23 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a204) | c2_1(a208) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c1_1(a208)) | (~c0_1(a208))),
% 1.50/1.23 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 1.50/1.23 tff(1719,plain,
% 1.50/1.23 (hskp3),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[1718, 128, 1712, 1711, 1591, 1710, 646, 1685, 606])).
% 1.50/1.23 tff(1720,plain,
% 1.50/1.23 (~c0_1(a203)),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[625, 1719])).
% 1.50/1.24 tff(1721,plain,
% 1.50/1.24 (c1_1(a203)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[636, 1719])).
% 1.50/1.24 tff(1722,plain,
% 1.50/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a204) | c0_1(a204) | c0_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c2_1(a203) | (~c3_1(a204)) | (~c2_1(a205)) | c0_1(a205) | (~c3_1(a205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a204) | c0_1(a204) | c0_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c2_1(a203) | (~c3_1(a204)) | (~c2_1(a205)) | c0_1(a205) | (~c3_1(a205)))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1723,plain,
% 1.50/1.24 (((~ndr1_0) | c0_1(a205) | (~c2_1(a205)) | (~c3_1(a205)) | c0_1(a203) | c2_1(a203) | (~c1_1(a203)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204))) <=> (c1_1(a204) | c0_1(a204) | c0_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c2_1(a203) | (~c3_1(a204)) | (~c2_1(a205)) | c0_1(a205) | (~c3_1(a205)))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1724,plain,
% 1.50/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a205) | (~c2_1(a205)) | (~c3_1(a205)) | c0_1(a203) | c2_1(a203) | (~c1_1(a203)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a204) | c0_1(a204) | c0_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c2_1(a203) | (~c3_1(a204)) | (~c2_1(a205)) | c0_1(a205) | (~c3_1(a205))))),
% 1.50/1.24 inference(monotonicity,[status(thm)],[1723])).
% 1.50/1.24 tff(1725,plain,
% 1.50/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a205) | (~c2_1(a205)) | (~c3_1(a205)) | c0_1(a203) | c2_1(a203) | (~c1_1(a203)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a204) | c0_1(a204) | c0_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c2_1(a203) | (~c3_1(a204)) | (~c2_1(a205)) | c0_1(a205) | (~c3_1(a205)))),
% 1.50/1.24 inference(transitivity,[status(thm)],[1724, 1722])).
% 1.50/1.24 tff(1726,plain,
% 1.50/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a205) | (~c2_1(a205)) | (~c3_1(a205)) | c0_1(a203) | c2_1(a203) | (~c1_1(a203)) | c1_1(a204) | c0_1(a204) | (~c3_1(a204)))),
% 1.50/1.24 inference(quant_inst,[status(thm)],[])).
% 1.50/1.24 tff(1727,plain,
% 1.50/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a204) | c0_1(a204) | c0_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c2_1(a203) | (~c3_1(a204)) | (~c2_1(a205)) | c0_1(a205) | (~c3_1(a205))),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1726, 1725])).
% 1.50/1.24 tff(1728,plain,
% 1.50/1.24 (c2_1(a203)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1727, 128, 1705, 1707, 1591, 1721, 646, 1720, 380, 1703, 1708])).
% 1.50/1.24 tff(1729,plain,
% 1.50/1.24 (~c3_1(a203)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[619, 1719])).
% 1.50/1.24 tff(1730,plain,
% 1.50/1.24 ($false),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1194, 128, 1110, 1099, 1088, 1712, 1711, 1710, 1720, 1729, 22, 1728])).
% 1.50/1.24 tff(1731,plain,(c1_1(a204) | c0_1(a204) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.50/1.24 tff(1732,plain,
% 1.50/1.24 (c1_1(a204)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1731, 646, 12])).
% 1.50/1.24 tff(1733,assumption,(~hskp9), introduced(assumption)).
% 1.50/1.24 tff(1734,plain,
% 1.50/1.24 (hskp6),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[700, 1733])).
% 1.50/1.24 tff(1735,plain,
% 1.50/1.24 (~c2_1(a208)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[177, 1734])).
% 1.50/1.24 tff(1736,plain,
% 1.50/1.24 (c1_1(a208)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[221, 1734])).
% 1.50/1.24 tff(1737,plain,
% 1.50/1.24 (c0_1(a208)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[171, 1734])).
% 1.50/1.24 tff(1738,plain,
% 1.50/1.24 (~c2_1(a204)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1700, 128, 1110, 1099, 1088, 1737, 1736, 1735, 646, 22, 837])).
% 1.50/1.24 tff(1739,plain,
% 1.50/1.24 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))),
% 1.50/1.24 inference(bind,[status(th)],[])).
% 1.50/1.24 tff(1740,plain,
% 1.50/1.24 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.50/1.24 inference(quant_intro,[status(thm)],[1739])).
% 1.50/1.24 tff(1741,plain,
% 1.50/1.24 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1742,plain,
% 1.50/1.24 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))))),
% 1.50/1.24 inference(bind,[status(th)],[])).
% 1.50/1.24 tff(1743,plain,
% 1.50/1.24 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.50/1.24 inference(quant_intro,[status(thm)],[1742])).
% 1.50/1.24 tff(1744,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.50/1.24 tff(1745,plain,
% 1.50/1.24 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1744, 1743])).
% 1.50/1.24 tff(1746,plain,
% 1.50/1.24 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1745, 1741])).
% 1.50/1.24 tff(1747,plain,(
% 1.50/1.24 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.50/1.24 inference(skolemize,[status(sab)],[1746])).
% 1.50/1.24 tff(1748,plain,
% 1.50/1.24 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1747, 1740])).
% 1.50/1.24 tff(1749,plain,
% 1.50/1.24 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp9 | hskp8 | c0_1(a204) | c2_1(a204) | (~ndr1_0) | c3_1(a204))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp9 | hskp8 | c0_1(a204) | c2_1(a204) | (~ndr1_0) | c3_1(a204))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1750,plain,
% 1.50/1.24 ((hskp9 | hskp8 | (~ndr1_0) | c3_1(a204) | c2_1(a204) | c0_1(a204)) <=> (hskp9 | hskp8 | c0_1(a204) | c2_1(a204) | (~ndr1_0) | c3_1(a204))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1751,plain,
% 1.50/1.24 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp9 | hskp8 | (~ndr1_0) | c3_1(a204) | c2_1(a204) | c0_1(a204))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp9 | hskp8 | c0_1(a204) | c2_1(a204) | (~ndr1_0) | c3_1(a204)))),
% 1.50/1.24 inference(monotonicity,[status(thm)],[1750])).
% 1.50/1.24 tff(1752,plain,
% 1.50/1.24 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp9 | hskp8 | (~ndr1_0) | c3_1(a204) | c2_1(a204) | c0_1(a204))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp9 | hskp8 | c0_1(a204) | c2_1(a204) | (~ndr1_0) | c3_1(a204))),
% 1.50/1.24 inference(transitivity,[status(thm)],[1751, 1749])).
% 1.50/1.24 tff(1753,plain,
% 1.50/1.24 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp9 | hskp8 | (~ndr1_0) | c3_1(a204) | c2_1(a204) | c0_1(a204))),
% 1.50/1.24 inference(quant_inst,[status(thm)],[])).
% 1.50/1.24 tff(1754,plain,
% 1.50/1.24 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp9 | hskp8 | c0_1(a204) | c2_1(a204) | (~ndr1_0) | c3_1(a204)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 1.50/1.24 tff(1755,plain,
% 1.50/1.24 (hskp9 | hskp8 | c2_1(a204) | c3_1(a204)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1754, 128, 646, 1748])).
% 1.50/1.24 tff(1756,plain,
% 1.50/1.24 (hskp8),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1755, 1738, 1733, 837])).
% 1.50/1.24 tff(1757,plain,
% 1.50/1.24 (((~hskp8) | (~c1_1(a212))) <=> ((~hskp8) | (~c1_1(a212)))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1758,plain,
% 1.50/1.24 (((~c1_1(a212)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a212)))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1759,axiom,((~c1_1(a212)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.50/1.24 tff(1760,plain,
% 1.50/1.24 ((~hskp8) | (~c1_1(a212))),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 1.50/1.24 tff(1761,plain,
% 1.50/1.24 ((~hskp8) | (~c1_1(a212))),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1760, 1757])).
% 1.50/1.24 tff(1762,plain,
% 1.50/1.24 (~c1_1(a212)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1761, 1756])).
% 1.50/1.24 tff(1763,plain,
% 1.50/1.24 (((~hskp8) | c3_1(a212)) <=> ((~hskp8) | c3_1(a212))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1764,axiom,((~hskp8) | c3_1(a212)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.50/1.24 tff(1765,plain,
% 1.50/1.24 ((~hskp8) | c3_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 1.50/1.24 tff(1766,plain,
% 1.50/1.24 ((~hskp8) | c3_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1765, 1763])).
% 1.50/1.24 tff(1767,plain,
% 1.50/1.24 ((~hskp8) | c3_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1766, 1763])).
% 1.50/1.24 tff(1768,plain,
% 1.50/1.24 ((~hskp8) | c3_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1767, 1763])).
% 1.50/1.24 tff(1769,plain,
% 1.50/1.24 ((~hskp8) | c3_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1768, 1763])).
% 1.50/1.24 tff(1770,plain,
% 1.50/1.24 ((~hskp8) | c3_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1769, 1763])).
% 1.50/1.24 tff(1771,plain,
% 1.50/1.24 ((~hskp8) | c3_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1770, 1763])).
% 1.50/1.24 tff(1772,plain,
% 1.50/1.24 ((~hskp8) | c3_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1771, 1763])).
% 1.50/1.24 tff(1773,plain,
% 1.50/1.24 (c3_1(a212)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1772, 1756])).
% 1.50/1.24 tff(1774,plain,
% 1.50/1.24 (((~hskp8) | c0_1(a212)) <=> ((~hskp8) | c0_1(a212))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1775,axiom,((~hskp8) | c0_1(a212)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.50/1.24 tff(1776,plain,
% 1.50/1.24 ((~hskp8) | c0_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 1.50/1.24 tff(1777,plain,
% 1.50/1.24 ((~hskp8) | c0_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1776, 1774])).
% 1.50/1.24 tff(1778,plain,
% 1.50/1.24 ((~hskp8) | c0_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1777, 1774])).
% 1.50/1.24 tff(1779,plain,
% 1.50/1.24 ((~hskp8) | c0_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1778, 1774])).
% 1.50/1.24 tff(1780,plain,
% 1.50/1.24 ((~hskp8) | c0_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1779, 1774])).
% 1.50/1.24 tff(1781,plain,
% 1.50/1.24 ((~hskp8) | c0_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1780, 1774])).
% 1.50/1.24 tff(1782,plain,
% 1.50/1.24 ((~hskp8) | c0_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1781, 1774])).
% 1.50/1.24 tff(1783,plain,
% 1.50/1.24 ((~hskp8) | c0_1(a212)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1782, 1774])).
% 1.50/1.24 tff(1784,plain,
% 1.50/1.24 (c0_1(a212)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1783, 1756])).
% 1.50/1.24 tff(1785,plain,
% 1.50/1.24 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | c1_1(a212) | (~ndr1_0) | (~c3_1(a212)) | (~c0_1(a212)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp24 | hskp22 | c1_1(a212) | (~ndr1_0) | (~c3_1(a212)) | (~c0_1(a212)))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1786,plain,
% 1.50/1.24 ((hskp24 | hskp22 | (~ndr1_0) | c1_1(a212) | (~c0_1(a212)) | (~c3_1(a212))) <=> (hskp24 | hskp22 | c1_1(a212) | (~ndr1_0) | (~c3_1(a212)) | (~c0_1(a212)))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1787,plain,
% 1.50/1.24 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c1_1(a212) | (~c0_1(a212)) | (~c3_1(a212)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | c1_1(a212) | (~ndr1_0) | (~c3_1(a212)) | (~c0_1(a212))))),
% 1.50/1.24 inference(monotonicity,[status(thm)],[1786])).
% 1.50/1.24 tff(1788,plain,
% 1.50/1.24 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c1_1(a212) | (~c0_1(a212)) | (~c3_1(a212)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp24 | hskp22 | c1_1(a212) | (~ndr1_0) | (~c3_1(a212)) | (~c0_1(a212)))),
% 1.50/1.24 inference(transitivity,[status(thm)],[1787, 1785])).
% 1.50/1.24 tff(1789,plain,
% 1.50/1.24 ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c1_1(a212) | (~c0_1(a212)) | (~c3_1(a212)))),
% 1.50/1.24 inference(quant_inst,[status(thm)],[])).
% 1.50/1.24 tff(1790,plain,
% 1.50/1.24 ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp24 | hskp22 | c1_1(a212) | (~ndr1_0) | (~c3_1(a212)) | (~c0_1(a212))),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 1.50/1.24 tff(1791,plain,
% 1.50/1.24 (hskp22),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1790, 128, 12, 1784, 1773, 1762, 91])).
% 1.50/1.24 tff(1792,plain,
% 1.50/1.24 (~c2_1(a244)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[141, 1791])).
% 1.50/1.24 tff(1793,plain,
% 1.50/1.24 (~c0_1(a244)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[147, 1791])).
% 1.50/1.24 tff(1794,plain,
% 1.50/1.24 (c3_1(a244)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[158, 1791])).
% 1.50/1.24 tff(1795,plain,
% 1.50/1.24 (~c1_1(a244)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1116, 128, 1110, 1099, 1088, 1794, 1793, 1792, 80])).
% 1.50/1.24 tff(1796,plain,
% 1.50/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a244) | c2_1(a244) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c1_1(a204)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a244))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a244) | c2_1(a244) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c1_1(a204)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a244))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1797,plain,
% 1.50/1.24 (((~ndr1_0) | (~c0_1(a208)) | (~c3_1(a208)) | (~c1_1(a208)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a244) | c1_1(a244) | c0_1(a244)) <=> (c0_1(a244) | c2_1(a244) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c1_1(a204)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a244))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1798,plain,
% 1.50/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a208)) | (~c3_1(a208)) | (~c1_1(a208)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a244) | c1_1(a244) | c0_1(a244))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a244) | c2_1(a244) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c1_1(a204)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a244)))),
% 1.50/1.24 inference(monotonicity,[status(thm)],[1797])).
% 1.50/1.24 tff(1799,plain,
% 1.50/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a208)) | (~c3_1(a208)) | (~c1_1(a208)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a244) | c1_1(a244) | c0_1(a244))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a244) | c2_1(a244) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c1_1(a204)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a244))),
% 1.50/1.24 inference(transitivity,[status(thm)],[1798, 1796])).
% 1.50/1.24 tff(1800,plain,
% 1.50/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a208)) | (~c3_1(a208)) | (~c1_1(a208)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a244) | c1_1(a244) | c0_1(a244))),
% 1.50/1.24 inference(quant_inst,[status(thm)],[])).
% 1.50/1.24 tff(1801,plain,
% 1.50/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a244) | c2_1(a244) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c1_1(a204)) | (~c3_1(a208)) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a244)),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.50/1.24 tff(1802,plain,
% 1.50/1.24 (~c3_1(a208)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1801, 128, 1737, 1736, 1732, 1793, 1792, 646, 1738, 433, 1795])).
% 1.50/1.24 tff(1803,plain,
% 1.50/1.24 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1804,plain,
% 1.50/1.24 ((hskp10 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204))) <=> (hskp10 | c0_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1805,plain,
% 1.50/1.24 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204))))),
% 1.50/1.24 inference(monotonicity,[status(thm)],[1804])).
% 1.50/1.24 tff(1806,plain,
% 1.50/1.24 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)))),
% 1.50/1.24 inference(transitivity,[status(thm)],[1805, 1803])).
% 1.50/1.24 tff(1807,plain,
% 1.50/1.24 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204)))),
% 1.50/1.24 inference(quant_inst,[status(thm)],[])).
% 1.50/1.24 tff(1808,plain,
% 1.50/1.24 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204))),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 1.50/1.24 tff(1809,plain,
% 1.50/1.24 (hskp10),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1808, 128, 1110, 1099, 1088, 1732, 646, 1275, 837])).
% 1.50/1.24 tff(1810,plain,
% 1.50/1.24 (~c3_1(a214)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1300, 1809])).
% 1.50/1.24 tff(1811,plain,
% 1.50/1.24 (~c2_1(a214)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1306, 1809])).
% 1.50/1.24 tff(1812,plain,
% 1.50/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a214) | c3_1(a214) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a204)) | (~c0_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a214) | c3_1(a214) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a204)) | (~c0_1(a214)))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1813,plain,
% 1.50/1.24 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a214) | c2_1(a214) | (~c0_1(a214)) | c2_1(a204) | c0_1(a204) | (~c1_1(a204))) <=> (c2_1(a214) | c3_1(a214) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a204)) | (~c0_1(a214)))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1814,plain,
% 1.50/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a214) | c2_1(a214) | (~c0_1(a214)) | c2_1(a204) | c0_1(a204) | (~c1_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a214) | c3_1(a214) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a204)) | (~c0_1(a214))))),
% 1.50/1.24 inference(monotonicity,[status(thm)],[1813])).
% 1.50/1.24 tff(1815,plain,
% 1.50/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a214) | c2_1(a214) | (~c0_1(a214)) | c2_1(a204) | c0_1(a204) | (~c1_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a214) | c3_1(a214) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a204)) | (~c0_1(a214)))),
% 1.50/1.24 inference(transitivity,[status(thm)],[1814, 1812])).
% 1.50/1.24 tff(1816,plain,
% 1.50/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a214) | c2_1(a214) | (~c0_1(a214)) | c2_1(a204) | c0_1(a204) | (~c1_1(a204)))),
% 1.50/1.24 inference(quant_inst,[status(thm)],[])).
% 1.50/1.24 tff(1817,plain,
% 1.50/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a214) | c3_1(a214) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a204)) | (~c0_1(a214))),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[1816, 1815])).
% 1.50/1.24 tff(1818,plain,
% 1.50/1.24 (~c0_1(a214)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1817, 128, 1110, 1099, 1088, 1732, 1811, 1810, 646, 1738, 1412])).
% 1.50/1.24 tff(1819,plain,
% 1.50/1.24 (c1_1(a214)),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[1294, 1809])).
% 1.50/1.24 tff(1820,plain,
% 1.50/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a214) | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a208) | (~c0_1(a208)) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a214) | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a208) | (~c0_1(a208)) | c0_1(a214) | (~c1_1(a214)))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(1821,plain,
% 1.50/1.24 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a208) | c2_1(a208) | (~c0_1(a208)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214))) <=> (c2_1(a214) | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a208) | (~c0_1(a208)) | c0_1(a214) | (~c1_1(a214)))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1822,plain,
% 1.50/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a208) | c2_1(a208) | (~c0_1(a208)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a214) | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a208) | (~c0_1(a208)) | c0_1(a214) | (~c1_1(a214))))),
% 1.50/1.25 inference(monotonicity,[status(thm)],[1821])).
% 1.50/1.25 tff(1823,plain,
% 1.50/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a208) | c2_1(a208) | (~c0_1(a208)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a214) | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a208) | (~c0_1(a208)) | c0_1(a214) | (~c1_1(a214)))),
% 1.50/1.25 inference(transitivity,[status(thm)],[1822, 1820])).
% 1.50/1.25 tff(1824,plain,
% 1.50/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a208) | c2_1(a208) | (~c0_1(a208)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214)))),
% 1.50/1.25 inference(quant_inst,[status(thm)],[])).
% 1.50/1.25 tff(1825,plain,
% 1.50/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a214) | c2_1(a208) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a208) | (~c0_1(a208)) | c0_1(a214) | (~c1_1(a214))),
% 1.50/1.25 inference(modus_ponens,[status(thm)],[1824, 1823])).
% 1.50/1.25 tff(1826,plain,
% 1.50/1.25 ($false),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[1825, 128, 1110, 1099, 1088, 1819, 1737, 1811, 1735, 1412, 1818, 1802])).
% 1.50/1.25 tff(1827,plain,(hskp9 | c0_1(a204) | hskp24 | c3_1(a204)), inference(lemma,lemma(discharge,[]))).
% 1.50/1.25 tff(1828,plain,
% 1.50/1.25 (hskp9),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[1827, 837, 12, 646])).
% 1.50/1.25 tff(1829,plain,
% 1.50/1.25 (~c2_1(a213)),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[712, 1828])).
% 1.50/1.25 tff(1830,plain,
% 1.50/1.25 (~c0_1(a213)),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[1156, 1828])).
% 1.50/1.25 tff(1831,plain,
% 1.50/1.25 (~c1_1(a213)),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[706, 1828])).
% 1.50/1.25 tff(1832,plain,
% 1.50/1.25 (~c0_1(a214)),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[1817, 128, 1228, 1230, 1229, 647, 1363, 1362, 646, 645, 1412])).
% 1.50/1.25 tff(1833,plain,
% 1.50/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a213) | c1_1(a213) | c2_1(a213) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a198)) | (~c1_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a213) | c1_1(a213) | c2_1(a213) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a198)) | (~c1_1(a204)))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1834,plain,
% 1.50/1.25 (((~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c1_1(a198)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a213) | c1_1(a213) | c0_1(a213)) <=> (c0_1(a213) | c1_1(a213) | c2_1(a213) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a198)) | (~c1_1(a204)))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1835,plain,
% 1.50/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c1_1(a198)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a213) | c1_1(a213) | c0_1(a213))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a213) | c1_1(a213) | c2_1(a213) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a198)) | (~c1_1(a204))))),
% 1.50/1.25 inference(monotonicity,[status(thm)],[1834])).
% 1.50/1.25 tff(1836,plain,
% 1.50/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c1_1(a198)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a213) | c1_1(a213) | c0_1(a213))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a213) | c1_1(a213) | c2_1(a213) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a198)) | (~c1_1(a204)))),
% 1.50/1.25 inference(transitivity,[status(thm)],[1835, 1833])).
% 1.50/1.25 tff(1837,plain,
% 1.50/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c1_1(a198)) | c0_1(a204) | c2_1(a204) | (~c1_1(a204)) | c2_1(a213) | c1_1(a213) | c0_1(a213))),
% 1.50/1.25 inference(quant_inst,[status(thm)],[])).
% 1.50/1.25 tff(1838,plain,
% 1.50/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a213) | c1_1(a213) | c2_1(a213) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a198)) | (~c1_1(a204))),
% 1.50/1.25 inference(modus_ponens,[status(thm)],[1837, 1836])).
% 1.50/1.25 tff(1839,plain,
% 1.50/1.25 (c2_1(a204) | (~c3_1(a198))),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[1838, 128, 1228, 1230, 647, 1317, 714, 715, 646, 433])).
% 1.50/1.25 tff(1840,plain,
% 1.50/1.25 (~c3_1(a198)),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[1839, 645])).
% 1.50/1.25 tff(1841,plain,
% 1.50/1.25 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 1.50/1.25 inference(bind,[status(th)],[])).
% 1.50/1.25 tff(1842,plain,
% 1.50/1.25 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.50/1.25 inference(quant_intro,[status(thm)],[1841])).
% 1.50/1.25 tff(1843,plain,
% 1.50/1.25 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1844,plain,
% 1.50/1.25 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 1.50/1.25 inference(bind,[status(th)],[])).
% 1.50/1.25 tff(1845,plain,
% 1.50/1.25 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.50/1.25 inference(quant_intro,[status(thm)],[1844])).
% 1.50/1.25 tff(1846,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 1.50/1.25 tff(1847,plain,
% 1.50/1.25 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.50/1.25 inference(modus_ponens,[status(thm)],[1846, 1845])).
% 1.50/1.25 tff(1848,plain,
% 1.50/1.25 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.50/1.25 inference(modus_ponens,[status(thm)],[1847, 1843])).
% 1.50/1.25 tff(1849,plain,(
% 1.50/1.25 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.50/1.25 inference(skolemize,[status(sab)],[1848])).
% 1.50/1.25 tff(1850,plain,
% 1.50/1.25 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.50/1.25 inference(modus_ponens,[status(thm)],[1849, 1842])).
% 1.50/1.25 tff(1851,plain,
% 1.50/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c2_1(a214) | c3_1(a214) | (~ndr1_0) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a214) | c3_1(a214) | (~ndr1_0) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1852,plain,
% 1.50/1.25 ((hskp0 | (~ndr1_0) | c3_1(a198) | (~c2_1(a198)) | (~c1_1(a198)) | c3_1(a214) | c0_1(a214) | c2_1(a214)) <=> (hskp0 | c2_1(a214) | c3_1(a214) | (~ndr1_0) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1853,plain,
% 1.50/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a198) | (~c2_1(a198)) | (~c1_1(a198)) | c3_1(a214) | c0_1(a214) | c2_1(a214))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c2_1(a214) | c3_1(a214) | (~ndr1_0) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214)))),
% 1.50/1.25 inference(monotonicity,[status(thm)],[1852])).
% 1.50/1.25 tff(1854,plain,
% 1.50/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a198) | (~c2_1(a198)) | (~c1_1(a198)) | c3_1(a214) | c0_1(a214) | c2_1(a214))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a214) | c3_1(a214) | (~ndr1_0) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214))),
% 1.50/1.25 inference(transitivity,[status(thm)],[1853, 1851])).
% 1.50/1.25 tff(1855,plain,
% 1.50/1.25 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a198) | (~c2_1(a198)) | (~c1_1(a198)) | c3_1(a214) | c0_1(a214) | c2_1(a214))),
% 1.50/1.25 inference(quant_inst,[status(thm)],[])).
% 1.50/1.25 tff(1856,plain,
% 1.50/1.25 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a214) | c3_1(a214) | (~ndr1_0) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214)),
% 1.50/1.25 inference(modus_ponens,[status(thm)],[1855, 1854])).
% 1.50/1.25 tff(1857,plain,
% 1.50/1.25 (hskp0),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[1856, 128, 1230, 1229, 1363, 1362, 1850, 1840, 1832])).
% 1.50/1.25 tff(1858,plain,
% 1.50/1.25 (~c1_1(a199)),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[369, 1857])).
% 1.50/1.25 tff(1859,plain,
% 1.50/1.25 (~c0_1(a199)),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[363, 1857])).
% 1.50/1.25 tff(1860,plain,
% 1.50/1.25 (c3_1(a199)),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[403, 1857])).
% 1.50/1.25 tff(1861,plain,
% 1.50/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a214) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a214) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | c0_1(a214) | (~c1_1(a214)))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1862,plain,
% 1.50/1.25 (((~ndr1_0) | c0_1(a199) | (~c2_1(a199)) | (~c3_1(a199)) | c0_1(a214) | c2_1(a214) | (~c1_1(a214)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199))) <=> (c2_1(a214) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | c0_1(a214) | (~c1_1(a214)))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1863,plain,
% 1.50/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a199) | (~c2_1(a199)) | (~c3_1(a199)) | c0_1(a214) | c2_1(a214) | (~c1_1(a214)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a214) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | c0_1(a214) | (~c1_1(a214))))),
% 1.50/1.25 inference(monotonicity,[status(thm)],[1862])).
% 1.50/1.25 tff(1864,plain,
% 1.50/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a199) | (~c2_1(a199)) | (~c3_1(a199)) | c0_1(a214) | c2_1(a214) | (~c1_1(a214)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a214) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | c0_1(a214) | (~c1_1(a214)))),
% 1.50/1.25 inference(transitivity,[status(thm)],[1863, 1861])).
% 1.50/1.25 tff(1865,plain,
% 1.50/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a199) | (~c2_1(a199)) | (~c3_1(a199)) | c0_1(a214) | c2_1(a214) | (~c1_1(a214)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))),
% 1.50/1.25 inference(quant_inst,[status(thm)],[])).
% 1.50/1.25 tff(1866,plain,
% 1.50/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a214) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c2_1(a199)) | c0_1(a214) | (~c1_1(a214))),
% 1.50/1.25 inference(modus_ponens,[status(thm)],[1865, 1864])).
% 1.50/1.25 tff(1867,plain,
% 1.50/1.25 (~c2_1(a199)),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[1866, 128, 1371, 1860, 1363, 1859, 1858, 380, 1832])).
% 1.50/1.25 tff(1868,plain,
% 1.50/1.25 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)))),
% 1.50/1.25 inference(bind,[status(th)],[])).
% 1.50/1.25 tff(1869,plain,
% 1.50/1.25 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.50/1.25 inference(quant_intro,[status(thm)],[1868])).
% 1.50/1.25 tff(1870,plain,
% 1.50/1.25 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1871,plain,
% 1.50/1.25 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))))),
% 1.50/1.25 inference(bind,[status(th)],[])).
% 1.50/1.25 tff(1872,plain,
% 1.50/1.25 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.50/1.25 inference(quant_intro,[status(thm)],[1871])).
% 1.50/1.25 tff(1873,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 1.50/1.25 tff(1874,plain,
% 1.50/1.25 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.50/1.25 inference(modus_ponens,[status(thm)],[1873, 1872])).
% 1.50/1.25 tff(1875,plain,
% 1.50/1.25 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.50/1.25 inference(modus_ponens,[status(thm)],[1874, 1870])).
% 1.50/1.25 tff(1876,plain,(
% 1.50/1.25 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.50/1.25 inference(skolemize,[status(sab)],[1875])).
% 1.50/1.25 tff(1877,plain,
% 1.50/1.25 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))),
% 1.50/1.25 inference(modus_ponens,[status(thm)],[1876, 1869])).
% 1.50/1.25 tff(1878,plain,
% 1.50/1.25 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp21 | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | c3_1(a198) | (~c1_1(a198)) | c2_1(a199) | (~c2_1(a198)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | hskp21 | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | c3_1(a198) | (~c1_1(a198)) | c2_1(a199) | (~c2_1(a198)))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1879,plain,
% 1.50/1.25 ((hskp21 | (~ndr1_0) | c3_1(a198) | (~c2_1(a198)) | (~c1_1(a198)) | c1_1(a199) | (~c3_1(a199)) | c2_1(a199)) <=> (hskp21 | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | c3_1(a198) | (~c1_1(a198)) | c2_1(a199) | (~c2_1(a198)))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1880,plain,
% 1.50/1.25 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a198) | (~c2_1(a198)) | (~c1_1(a198)) | c1_1(a199) | (~c3_1(a199)) | c2_1(a199))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp21 | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | c3_1(a198) | (~c1_1(a198)) | c2_1(a199) | (~c2_1(a198))))),
% 1.50/1.25 inference(monotonicity,[status(thm)],[1879])).
% 1.50/1.25 tff(1881,plain,
% 1.50/1.25 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a198) | (~c2_1(a198)) | (~c1_1(a198)) | c1_1(a199) | (~c3_1(a199)) | c2_1(a199))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | hskp21 | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | c3_1(a198) | (~c1_1(a198)) | c2_1(a199) | (~c2_1(a198)))),
% 1.50/1.25 inference(transitivity,[status(thm)],[1880, 1878])).
% 1.50/1.25 tff(1882,plain,
% 1.50/1.25 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a198) | (~c2_1(a198)) | (~c1_1(a198)) | c1_1(a199) | (~c3_1(a199)) | c2_1(a199))),
% 1.50/1.25 inference(quant_inst,[status(thm)],[])).
% 1.50/1.25 tff(1883,plain,
% 1.50/1.25 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | hskp21 | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | c3_1(a198) | (~c1_1(a198)) | c2_1(a199) | (~c2_1(a198))),
% 1.50/1.25 inference(modus_ponens,[status(thm)],[1882, 1881])).
% 1.50/1.25 tff(1884,plain,
% 1.50/1.25 (hskp21),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[1883, 128, 1230, 1229, 1860, 1858, 1877, 1867, 1840])).
% 1.50/1.25 tff(1885,plain,
% 1.50/1.25 (~c1_1(a241)),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[308, 1884])).
% 1.50/1.25 tff(1886,plain,
% 1.50/1.25 (c0_1(a241)),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[330, 1884])).
% 1.50/1.25 tff(1887,plain,
% 1.50/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a241) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | c2_1(a199) | (~c0_1(a241)) | (~c2_1(a241)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a241) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | c2_1(a199) | (~c0_1(a241)) | (~c2_1(a241)))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1888,plain,
% 1.50/1.25 (((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a199) | (~c3_1(a199)) | c2_1(a199) | c2_1(a199) | c0_1(a199) | (~c3_1(a199))) <=> (c1_1(a241) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | c2_1(a199) | (~c0_1(a241)) | (~c2_1(a241)))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1889,plain,
% 1.50/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a199) | (~c3_1(a199)) | c2_1(a199) | c2_1(a199) | c0_1(a199) | (~c3_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a241) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | c2_1(a199) | (~c0_1(a241)) | (~c2_1(a241))))),
% 1.50/1.25 inference(monotonicity,[status(thm)],[1888])).
% 1.50/1.25 tff(1890,plain,
% 1.50/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a199) | (~c3_1(a199)) | c2_1(a199) | c2_1(a199) | c0_1(a199) | (~c3_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a241) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | c2_1(a199) | (~c0_1(a241)) | (~c2_1(a241)))),
% 1.50/1.25 inference(transitivity,[status(thm)],[1889, 1887])).
% 1.50/1.25 tff(1891,plain,
% 1.50/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a199) | (~c3_1(a199)) | c2_1(a199) | c2_1(a199) | c0_1(a199) | (~c3_1(a199)))),
% 1.50/1.25 inference(quant_inst,[status(thm)],[])).
% 1.50/1.25 tff(1892,plain,
% 1.50/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a241) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | c2_1(a199) | (~c0_1(a241)) | (~c2_1(a241))),
% 1.50/1.25 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 1.50/1.25 tff(1893,plain,
% 1.50/1.25 (~c2_1(a241)),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[1892, 128, 1886, 1860, 1885, 1859, 1858, 886, 1867])).
% 1.50/1.25 tff(1894,plain,
% 1.50/1.25 (~c3_1(a241)),
% 1.50/1.25 inference(unit_resolution,[status(thm)],[302, 1884])).
% 1.50/1.25 tff(1895,plain,
% 1.50/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a241) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a241)) | c2_1(a241))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a241) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a241)) | c2_1(a241))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1896,plain,
% 1.50/1.25 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a241) | c2_1(a241) | (~c0_1(a241)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214))) <=> (c3_1(a241) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a241)) | c2_1(a241))),
% 1.50/1.25 inference(rewrite,[status(thm)],[])).
% 1.50/1.25 tff(1897,plain,
% 1.50/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a241) | c2_1(a241) | (~c0_1(a241)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a241) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a241)) | c2_1(a241)))),
% 1.50/1.26 inference(monotonicity,[status(thm)],[1896])).
% 1.50/1.26 tff(1898,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a241) | c2_1(a241) | (~c0_1(a241)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a241) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a241)) | c2_1(a241))),
% 1.50/1.26 inference(transitivity,[status(thm)],[1897, 1895])).
% 1.50/1.26 tff(1899,plain,
% 1.50/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a241) | c2_1(a241) | (~c0_1(a241)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214)))),
% 1.50/1.26 inference(quant_inst,[status(thm)],[])).
% 1.50/1.26 tff(1900,plain,
% 1.50/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a241) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a241)) | c2_1(a241)),
% 1.50/1.26 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 1.50/1.26 tff(1901,plain,
% 1.50/1.26 ($false),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1900, 128, 1228, 1230, 1229, 1886, 1371, 1894, 1363, 1412, 1893, 1832])).
% 1.50/1.26 tff(1902,plain,(c2_1(a204) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a214)) | c2_1(a214) | c3_1(a214) | (~c1_1(a204)) | c0_1(a204) | c0_1(a213) | c1_1(a213) | c2_1(a213)), inference(lemma,lemma(discharge,[]))).
% 1.50/1.26 tff(1903,plain,
% 1.50/1.26 (c2_1(a204)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1902, 1831, 1099, 1088, 1819, 1811, 1810, 1732, 646, 1110, 1830, 1829])).
% 1.50/1.26 tff(1904,plain,
% 1.50/1.26 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 1.50/1.26 inference(bind,[status(th)],[])).
% 1.50/1.26 tff(1905,plain,
% 1.50/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.50/1.26 inference(quant_intro,[status(thm)],[1904])).
% 1.50/1.26 tff(1906,plain,
% 1.50/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.50/1.26 inference(rewrite,[status(thm)],[])).
% 1.50/1.26 tff(1907,plain,
% 1.50/1.26 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 1.50/1.26 inference(bind,[status(th)],[])).
% 1.50/1.26 tff(1908,plain,
% 1.50/1.26 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.50/1.26 inference(quant_intro,[status(thm)],[1907])).
% 1.50/1.26 tff(1909,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.50/1.26 tff(1910,plain,
% 1.50/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.50/1.26 inference(modus_ponens,[status(thm)],[1909, 1908])).
% 1.50/1.26 tff(1911,plain,
% 1.50/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.50/1.26 inference(modus_ponens,[status(thm)],[1910, 1906])).
% 1.50/1.26 tff(1912,plain,(
% 1.50/1.26 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.50/1.26 inference(skolemize,[status(sab)],[1911])).
% 1.50/1.26 tff(1913,plain,
% 1.50/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.50/1.26 inference(modus_ponens,[status(thm)],[1912, 1905])).
% 1.50/1.26 tff(1914,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)))),
% 1.50/1.26 inference(rewrite,[status(thm)],[])).
% 1.50/1.26 tff(1915,plain,
% 1.50/1.26 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c0_1(a204) | (~c2_1(a204)) | (~c1_1(a204)) | c0_1(a204) | c3_1(a204) | (~c1_1(a204))) <=> (c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)))),
% 1.50/1.26 inference(rewrite,[status(thm)],[])).
% 1.50/1.26 tff(1916,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c0_1(a204) | (~c2_1(a204)) | (~c1_1(a204)) | c0_1(a204) | c3_1(a204) | (~c1_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204))))),
% 1.50/1.26 inference(monotonicity,[status(thm)],[1915])).
% 1.50/1.26 tff(1917,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c0_1(a204) | (~c2_1(a204)) | (~c1_1(a204)) | c0_1(a204) | c3_1(a204) | (~c1_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)))),
% 1.50/1.26 inference(transitivity,[status(thm)],[1916, 1914])).
% 1.50/1.26 tff(1918,plain,
% 1.50/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c0_1(a204) | (~c2_1(a204)) | (~c1_1(a204)) | c0_1(a204) | c3_1(a204) | (~c1_1(a204)))),
% 1.50/1.26 inference(quant_inst,[status(thm)],[])).
% 1.50/1.26 tff(1919,plain,
% 1.50/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204))),
% 1.50/1.26 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.50/1.26 tff(1920,plain,
% 1.50/1.26 ((~c2_1(a204)) | (~c3_1(a198)) | c3_1(a204) | (~c1_1(a204))),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1919, 128, 1110, 1088, 646, 1913])).
% 1.50/1.26 tff(1921,plain,
% 1.50/1.26 (~c3_1(a198)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1920, 1903, 1732, 837])).
% 1.50/1.26 tff(1922,assumption,(hskp9), introduced(assumption)).
% 1.50/1.26 tff(1923,plain,
% 1.50/1.26 (~c2_1(a213)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[712, 1922])).
% 1.50/1.26 tff(1924,plain,
% 1.50/1.26 (~c1_1(a213)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[706, 1922])).
% 1.50/1.26 tff(1925,plain,
% 1.50/1.26 (hskp10),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1808, 128, 1228, 1230, 1229, 647, 646, 1275, 837])).
% 1.50/1.26 tff(1926,plain,
% 1.50/1.26 (~c3_1(a214)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1300, 1925])).
% 1.50/1.26 tff(1927,plain,
% 1.50/1.26 (~c2_1(a214)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1306, 1925])).
% 1.50/1.26 tff(1928,plain,
% 1.50/1.26 (c1_1(a214)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1294, 1925])).
% 1.50/1.26 tff(1929,plain,
% 1.50/1.26 (~c0_1(a213)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1156, 1922])).
% 1.50/1.26 tff(1930,plain,
% 1.50/1.26 (c2_1(a204)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1902, 1929, 1230, 1229, 1928, 1927, 1926, 647, 646, 1228, 1924, 1923])).
% 1.50/1.26 tff(1931,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a214) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c0_1(a214)) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a214) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c0_1(a214)) | (~c1_1(a214)))),
% 1.50/1.26 inference(rewrite,[status(thm)],[])).
% 1.50/1.26 tff(1932,plain,
% 1.50/1.26 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a214) | (~c1_1(a214)) | (~c0_1(a214)) | c0_1(a204) | c3_1(a204) | (~c2_1(a204))) <=> (c2_1(a214) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c0_1(a214)) | (~c1_1(a214)))),
% 1.50/1.26 inference(rewrite,[status(thm)],[])).
% 1.50/1.26 tff(1933,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a214) | (~c1_1(a214)) | (~c0_1(a214)) | c0_1(a204) | c3_1(a204) | (~c2_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a214) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c0_1(a214)) | (~c1_1(a214))))),
% 1.50/1.26 inference(monotonicity,[status(thm)],[1932])).
% 1.50/1.26 tff(1934,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a214) | (~c1_1(a214)) | (~c0_1(a214)) | c0_1(a204) | c3_1(a204) | (~c2_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a214) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c0_1(a214)) | (~c1_1(a214)))),
% 1.50/1.26 inference(transitivity,[status(thm)],[1933, 1931])).
% 1.50/1.26 tff(1935,plain,
% 1.50/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a214) | (~c1_1(a214)) | (~c0_1(a214)) | c0_1(a204) | c3_1(a204) | (~c2_1(a204)))),
% 1.50/1.26 inference(quant_inst,[status(thm)],[])).
% 1.50/1.26 tff(1936,plain,
% 1.50/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a214) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c0_1(a214)) | (~c1_1(a214))),
% 1.50/1.26 inference(modus_ponens,[status(thm)],[1935, 1934])).
% 1.50/1.26 tff(1937,plain,
% 1.50/1.26 ((~c2_1(a204)) | (~c0_1(a214))),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1936, 128, 1228, 1230, 1229, 1928, 1927, 646, 22, 837])).
% 1.50/1.26 tff(1938,plain,
% 1.50/1.26 (~c0_1(a214)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1937, 1930])).
% 1.50/1.26 tff(1939,plain,
% 1.50/1.26 (~hskp4),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[386, 1930])).
% 1.50/1.26 tff(1940,plain,
% 1.50/1.26 (hskp4 | c3_1(a213)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1216, 128, 1210, 1929, 1924, 1209])).
% 1.50/1.26 tff(1941,plain,
% 1.50/1.26 (c3_1(a213)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1940, 1939])).
% 1.50/1.26 tff(1942,plain,
% 1.50/1.26 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c3_1(a214) | c0_1(a213) | c1_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c3_1(a214) | c0_1(a213) | c1_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a214) | (~c1_1(a214)))),
% 1.50/1.26 inference(rewrite,[status(thm)],[])).
% 1.50/1.26 tff(1943,plain,
% 1.50/1.26 ((hskp4 | (~ndr1_0) | c3_1(a214) | c0_1(a214) | (~c1_1(a214)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213))) <=> (hskp4 | c3_1(a214) | c0_1(a213) | c1_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a214) | (~c1_1(a214)))),
% 1.50/1.26 inference(rewrite,[status(thm)],[])).
% 1.50/1.26 tff(1944,plain,
% 1.50/1.26 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a214) | c0_1(a214) | (~c1_1(a214)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c3_1(a214) | c0_1(a213) | c1_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a214) | (~c1_1(a214))))),
% 1.50/1.26 inference(monotonicity,[status(thm)],[1943])).
% 1.50/1.26 tff(1945,plain,
% 1.50/1.26 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a214) | c0_1(a214) | (~c1_1(a214)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c3_1(a214) | c0_1(a213) | c1_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a214) | (~c1_1(a214)))),
% 1.50/1.26 inference(transitivity,[status(thm)],[1944, 1942])).
% 1.50/1.26 tff(1946,plain,
% 1.50/1.26 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a214) | c0_1(a214) | (~c1_1(a214)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213)))),
% 1.50/1.26 inference(quant_inst,[status(thm)],[])).
% 1.50/1.26 tff(1947,plain,
% 1.50/1.26 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c3_1(a214) | c0_1(a213) | c1_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a214) | (~c1_1(a214))),
% 1.50/1.26 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 1.50/1.26 tff(1948,plain,
% 1.50/1.26 (hskp4 | (~c3_1(a213)) | c0_1(a214)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1947, 128, 1928, 1926, 1929, 1924, 1227])).
% 1.50/1.26 tff(1949,plain,
% 1.50/1.26 ($false),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1948, 1941, 1939, 1938])).
% 1.50/1.26 tff(1950,plain,((~hskp9) | hskp5 | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a204) | c3_1(a204) | (~c1_1(a204))), inference(lemma,lemma(discharge,[]))).
% 1.50/1.26 tff(1951,plain,
% 1.50/1.26 (hskp5),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1950, 1828, 1110, 1099, 1088, 646, 837, 1732])).
% 1.50/1.26 tff(1952,plain,
% 1.50/1.26 (~c1_1(a205)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[58, 1951])).
% 1.50/1.26 tff(1953,plain,
% 1.50/1.26 (c3_1(a205)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[69, 1951])).
% 1.50/1.26 tff(1954,plain,
% 1.50/1.26 (c2_1(a205)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[52, 1951])).
% 1.50/1.26 tff(1955,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a213) | c2_1(a213) | c1_1(a205) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a205)) | (~c3_1(a205)) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a213) | c2_1(a213) | c1_1(a205) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a205)) | (~c3_1(a205)) | (~c3_1(a213)))),
% 1.50/1.26 inference(rewrite,[status(thm)],[])).
% 1.50/1.26 tff(1956,plain,
% 1.50/1.26 (((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c1_1(a205) | (~c3_1(a205)) | (~c2_1(a205)) | c2_1(a213) | c1_1(a213) | (~c3_1(a213))) <=> (c1_1(a213) | c2_1(a213) | c1_1(a205) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a205)) | (~c3_1(a205)) | (~c3_1(a213)))),
% 1.50/1.26 inference(rewrite,[status(thm)],[])).
% 1.50/1.26 tff(1957,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c1_1(a205) | (~c3_1(a205)) | (~c2_1(a205)) | c2_1(a213) | c1_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a213) | c2_1(a213) | c1_1(a205) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a205)) | (~c3_1(a205)) | (~c3_1(a213))))),
% 1.50/1.26 inference(monotonicity,[status(thm)],[1956])).
% 1.50/1.26 tff(1958,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c1_1(a205) | (~c3_1(a205)) | (~c2_1(a205)) | c2_1(a213) | c1_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a213) | c2_1(a213) | c1_1(a205) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a205)) | (~c3_1(a205)) | (~c3_1(a213)))),
% 1.50/1.26 inference(transitivity,[status(thm)],[1957, 1955])).
% 1.50/1.26 tff(1959,plain,
% 1.50/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c1_1(a205) | (~c3_1(a205)) | (~c2_1(a205)) | c2_1(a213) | c1_1(a213) | (~c3_1(a213)))),
% 1.50/1.26 inference(quant_inst,[status(thm)],[])).
% 1.50/1.26 tff(1960,plain,
% 1.50/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a213) | c2_1(a213) | c1_1(a205) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | (~c2_1(a205)) | (~c3_1(a205)) | (~c3_1(a213))),
% 1.50/1.26 inference(modus_ponens,[status(thm)],[1959, 1958])).
% 1.50/1.26 tff(1961,plain,
% 1.50/1.26 (~c3_1(a213)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1960, 128, 1110, 1099, 1954, 1953, 1831, 1829, 1952, 1009, 1921])).
% 1.50/1.26 tff(1962,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a213) | c2_1(a213) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c3_1(a204) | c3_1(a213))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a213) | c2_1(a213) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c3_1(a204) | c3_1(a213))),
% 1.50/1.26 inference(rewrite,[status(thm)],[])).
% 1.50/1.26 tff(1963,plain,
% 1.50/1.26 (((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a204) | c0_1(a204) | (~c2_1(a204)) | c2_1(a213) | c0_1(a213) | c3_1(a213)) <=> (c0_1(a213) | c2_1(a213) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c3_1(a204) | c3_1(a213))),
% 1.50/1.26 inference(rewrite,[status(thm)],[])).
% 1.50/1.26 tff(1964,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a204) | c0_1(a204) | (~c2_1(a204)) | c2_1(a213) | c0_1(a213) | c3_1(a213))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a213) | c2_1(a213) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c3_1(a204) | c3_1(a213)))),
% 1.50/1.26 inference(monotonicity,[status(thm)],[1963])).
% 1.50/1.26 tff(1965,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a204) | c0_1(a204) | (~c2_1(a204)) | c2_1(a213) | c0_1(a213) | c3_1(a213))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a213) | c2_1(a213) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c3_1(a204) | c3_1(a213))),
% 1.50/1.26 inference(transitivity,[status(thm)],[1964, 1962])).
% 1.50/1.26 tff(1966,plain,
% 1.50/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a204) | c0_1(a204) | (~c2_1(a204)) | c2_1(a213) | c0_1(a213) | c3_1(a213))),
% 1.50/1.26 inference(quant_inst,[status(thm)],[])).
% 1.50/1.26 tff(1967,plain,
% 1.50/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a213) | c2_1(a213) | c0_1(a204) | (~c2_1(a204)) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c3_1(a204) | c3_1(a213)),
% 1.50/1.26 inference(modus_ponens,[status(thm)],[1966, 1965])).
% 1.50/1.26 tff(1968,plain,
% 1.50/1.26 ($false),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1967, 128, 1110, 1099, 1830, 1829, 646, 1903, 665, 1961, 837, 1921])).
% 1.50/1.26 tff(1969,plain,(c3_1(a204) | c0_1(a204) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.50/1.26 tff(1970,plain,
% 1.50/1.26 (c3_1(a204)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[1969, 1590, 12])).
% 1.50/1.26 tff(1971,plain,
% 1.50/1.26 (~c2_1(a204)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[386, 1589])).
% 1.50/1.26 tff(1972,plain,
% 1.50/1.26 (c1_1(a204)),
% 1.50/1.26 inference(unit_resolution,[status(thm)],[414, 1589])).
% 1.50/1.26 tff(1973,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a204)) | (~c1_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a204)) | (~c1_1(a204)))),
% 1.50/1.26 inference(rewrite,[status(thm)],[])).
% 1.50/1.26 tff(1974,plain,
% 1.50/1.26 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a204)) | c2_1(a204) | (~c1_1(a204)) | c0_1(a204) | (~c3_1(a204)) | (~c1_1(a204))) <=> (c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a204)) | (~c1_1(a204)))),
% 1.50/1.26 inference(rewrite,[status(thm)],[])).
% 1.50/1.26 tff(1975,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a204)) | c2_1(a204) | (~c1_1(a204)) | c0_1(a204) | (~c3_1(a204)) | (~c1_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a204)) | (~c1_1(a204))))),
% 1.50/1.26 inference(monotonicity,[status(thm)],[1974])).
% 1.50/1.26 tff(1976,plain,
% 1.50/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a204)) | c2_1(a204) | (~c1_1(a204)) | c0_1(a204) | (~c3_1(a204)) | (~c1_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a204)) | (~c1_1(a204)))),
% 1.50/1.27 inference(transitivity,[status(thm)],[1975, 1973])).
% 1.50/1.27 tff(1977,plain,
% 1.50/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a204)) | c2_1(a204) | (~c1_1(a204)) | c0_1(a204) | (~c3_1(a204)) | (~c1_1(a204)))),
% 1.50/1.27 inference(quant_inst,[status(thm)],[])).
% 1.50/1.27 tff(1978,plain,
% 1.50/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a204)) | (~c1_1(a204))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[1977, 1976])).
% 1.50/1.27 tff(1979,plain,
% 1.50/1.27 ($false),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[1978, 128, 1110, 1099, 1088, 1972, 1590, 1971, 80, 1970])).
% 1.50/1.27 tff(1980,plain,(hskp24), inference(lemma,lemma(discharge,[]))).
% 1.50/1.27 tff(1981,plain,
% 1.50/1.27 (((~hskp24) | (~c2_1(a249))) <=> ((~hskp24) | (~c2_1(a249)))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(1982,plain,
% 1.50/1.27 (((~c2_1(a249)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a249)))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(1983,axiom,((~c2_1(a249)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 1.50/1.27 tff(1984,plain,
% 1.50/1.27 ((~hskp24) | (~c2_1(a249))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[1983, 1982])).
% 1.50/1.27 tff(1985,plain,
% 1.50/1.27 ((~hskp24) | (~c2_1(a249))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[1984, 1981])).
% 1.50/1.27 tff(1986,plain,
% 1.50/1.27 (~c2_1(a249)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[1985, 1980])).
% 1.50/1.27 tff(1987,plain,
% 1.50/1.27 (((~hskp24) | c3_1(a249)) <=> ((~hskp24) | c3_1(a249))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(1988,axiom,((~hskp24) | c3_1(a249)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.50/1.27 tff(1989,plain,
% 1.50/1.27 ((~hskp24) | c3_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[1988, 1987])).
% 1.50/1.27 tff(1990,plain,
% 1.50/1.27 ((~hskp24) | c3_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[1989, 1987])).
% 1.50/1.27 tff(1991,plain,
% 1.50/1.27 ((~hskp24) | c3_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[1990, 1987])).
% 1.50/1.27 tff(1992,plain,
% 1.50/1.27 ((~hskp24) | c3_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[1991, 1987])).
% 1.50/1.27 tff(1993,plain,
% 1.50/1.27 ((~hskp24) | c3_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[1992, 1987])).
% 1.50/1.27 tff(1994,plain,
% 1.50/1.27 ((~hskp24) | c3_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[1993, 1987])).
% 1.50/1.27 tff(1995,plain,
% 1.50/1.27 ((~hskp24) | c3_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[1994, 1987])).
% 1.50/1.27 tff(1996,plain,
% 1.50/1.27 ((~hskp24) | c3_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[1995, 1987])).
% 1.50/1.27 tff(1997,plain,
% 1.50/1.27 (c3_1(a249)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[1996, 1980])).
% 1.50/1.27 tff(1998,plain,
% 1.50/1.27 (((~hskp24) | c0_1(a249)) <=> ((~hskp24) | c0_1(a249))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(1999,axiom,((~hskp24) | c0_1(a249)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 1.50/1.27 tff(2000,plain,
% 1.50/1.27 ((~hskp24) | c0_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 1.50/1.27 tff(2001,plain,
% 1.50/1.27 ((~hskp24) | c0_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2000, 1998])).
% 1.50/1.27 tff(2002,plain,
% 1.50/1.27 ((~hskp24) | c0_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2001, 1998])).
% 1.50/1.27 tff(2003,plain,
% 1.50/1.27 ((~hskp24) | c0_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2002, 1998])).
% 1.50/1.27 tff(2004,plain,
% 1.50/1.27 ((~hskp24) | c0_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2003, 1998])).
% 1.50/1.27 tff(2005,plain,
% 1.50/1.27 ((~hskp24) | c0_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2004, 1998])).
% 1.50/1.27 tff(2006,plain,
% 1.50/1.27 ((~hskp24) | c0_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2005, 1998])).
% 1.50/1.27 tff(2007,plain,
% 1.50/1.27 ((~hskp24) | c0_1(a249)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2006, 1998])).
% 1.50/1.27 tff(2008,plain,
% 1.50/1.27 (c0_1(a249)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[2007, 1980])).
% 1.50/1.27 tff(2009,plain,
% 1.50/1.27 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp25 | hskp19 | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | (~c0_1(a249)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp25 | hskp19 | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2010,plain,
% 1.50/1.27 ((hskp25 | hskp19 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249))) <=> (hskp25 | hskp19 | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2011,plain,
% 1.50/1.27 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp25 | hskp19 | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | (~c0_1(a249))))),
% 1.50/1.27 inference(monotonicity,[status(thm)],[2010])).
% 1.50/1.27 tff(2012,plain,
% 1.50/1.27 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp25 | hskp19 | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.27 inference(transitivity,[status(thm)],[2011, 2009])).
% 1.50/1.27 tff(2013,plain,
% 1.50/1.27 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)))),
% 1.50/1.27 inference(quant_inst,[status(thm)],[])).
% 1.50/1.27 tff(2014,plain,
% 1.50/1.27 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp25 | hskp19 | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | (~c0_1(a249))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 1.50/1.27 tff(2015,plain,
% 1.50/1.27 (hskp25 | hskp19),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[2014, 128, 2008, 1997, 1986, 11])).
% 1.50/1.27 tff(2016,plain,
% 1.50/1.27 (hskp25),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[2015, 1])).
% 1.50/1.27 tff(2017,plain,
% 1.50/1.27 (((~hskp25) | c1_1(a256)) <=> ((~hskp25) | c1_1(a256))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2018,axiom,((~hskp25) | c1_1(a256)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 1.50/1.27 tff(2019,plain,
% 1.50/1.27 ((~hskp25) | c1_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 1.50/1.27 tff(2020,plain,
% 1.50/1.27 ((~hskp25) | c1_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2019, 2017])).
% 1.50/1.27 tff(2021,plain,
% 1.50/1.27 ((~hskp25) | c1_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2020, 2017])).
% 1.50/1.27 tff(2022,plain,
% 1.50/1.27 ((~hskp25) | c1_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2021, 2017])).
% 1.50/1.27 tff(2023,plain,
% 1.50/1.27 ((~hskp25) | c1_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2022, 2017])).
% 1.50/1.27 tff(2024,plain,
% 1.50/1.27 ((~hskp25) | c1_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2023, 2017])).
% 1.50/1.27 tff(2025,plain,
% 1.50/1.27 ((~hskp25) | c1_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2024, 2017])).
% 1.50/1.27 tff(2026,plain,
% 1.50/1.27 ((~hskp25) | c1_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2025, 2017])).
% 1.50/1.27 tff(2027,plain,
% 1.50/1.27 (c1_1(a256)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[2026, 2016])).
% 1.50/1.27 tff(2028,plain,
% 1.50/1.27 (((~hskp25) | (~c0_1(a256))) <=> ((~hskp25) | (~c0_1(a256)))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2029,plain,
% 1.50/1.27 (((~c0_1(a256)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a256)))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2030,axiom,((~c0_1(a256)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.50/1.27 tff(2031,plain,
% 1.50/1.27 ((~hskp25) | (~c0_1(a256))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2030, 2029])).
% 1.50/1.27 tff(2032,plain,
% 1.50/1.27 ((~hskp25) | (~c0_1(a256))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2031, 2028])).
% 1.50/1.27 tff(2033,plain,
% 1.50/1.27 (~c0_1(a256)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[2032, 2016])).
% 1.50/1.27 tff(2034,plain,
% 1.50/1.27 (((~hskp25) | c2_1(a256)) <=> ((~hskp25) | c2_1(a256))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2035,axiom,((~hskp25) | c2_1(a256)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 1.50/1.27 tff(2036,plain,
% 1.50/1.27 ((~hskp25) | c2_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2035, 2034])).
% 1.50/1.27 tff(2037,plain,
% 1.50/1.27 ((~hskp25) | c2_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2036, 2034])).
% 1.50/1.27 tff(2038,plain,
% 1.50/1.27 ((~hskp25) | c2_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2037, 2034])).
% 1.50/1.27 tff(2039,plain,
% 1.50/1.27 ((~hskp25) | c2_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2038, 2034])).
% 1.50/1.27 tff(2040,plain,
% 1.50/1.27 ((~hskp25) | c2_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2039, 2034])).
% 1.50/1.27 tff(2041,plain,
% 1.50/1.27 ((~hskp25) | c2_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2040, 2034])).
% 1.50/1.27 tff(2042,plain,
% 1.50/1.27 ((~hskp25) | c2_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2041, 2034])).
% 1.50/1.27 tff(2043,plain,
% 1.50/1.27 ((~hskp25) | c2_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2042, 2034])).
% 1.50/1.27 tff(2044,plain,
% 1.50/1.27 (c2_1(a256)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[2043, 2016])).
% 1.50/1.27 tff(2045,assumption,(c1_1(a249)), introduced(assumption)).
% 1.50/1.27 tff(2046,assumption,(~c0_1(a256)), introduced(assumption)).
% 1.50/1.27 tff(2047,assumption,(c1_1(a256)), introduced(assumption)).
% 1.50/1.27 tff(2048,plain,
% 1.50/1.27 (^[U: $i] : refl((hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.50/1.27 inference(bind,[status(th)],[])).
% 1.50/1.27 tff(2049,plain,
% 1.50/1.27 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.50/1.27 inference(quant_intro,[status(thm)],[2048])).
% 1.50/1.27 tff(2050,plain,
% 1.50/1.27 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2051,plain,
% 1.50/1.27 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp19) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp19))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.50/1.27 inference(bind,[status(th)],[])).
% 1.50/1.27 tff(2052,plain,
% 1.50/1.27 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp19) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.50/1.27 inference(quant_intro,[status(thm)],[2051])).
% 1.50/1.27 tff(2053,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.50/1.27 tff(2054,plain,
% 1.50/1.27 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2053, 2052])).
% 1.50/1.27 tff(2055,plain,
% 1.50/1.27 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2054, 2050])).
% 1.50/1.27 tff(2056,plain,(
% 1.50/1.27 ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.50/1.27 inference(skolemize,[status(sab)],[2055])).
% 1.50/1.27 tff(2057,plain,
% 1.50/1.27 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2056, 2049])).
% 1.50/1.27 tff(2058,plain,
% 1.50/1.27 (c2_1(a241)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[874, 128, 160, 1476, 1475, 188])).
% 1.50/1.27 tff(2059,plain,
% 1.50/1.27 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.50/1.27 inference(bind,[status(th)],[])).
% 1.50/1.27 tff(2060,plain,
% 1.50/1.27 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.50/1.27 inference(quant_intro,[status(thm)],[2059])).
% 1.50/1.27 tff(2061,plain,
% 1.50/1.27 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2062,plain,
% 1.50/1.27 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.50/1.27 inference(bind,[status(th)],[])).
% 1.50/1.27 tff(2063,plain,
% 1.50/1.27 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.50/1.27 inference(quant_intro,[status(thm)],[2062])).
% 1.50/1.27 tff(2064,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 1.50/1.27 tff(2065,plain,
% 1.50/1.27 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2064, 2063])).
% 1.50/1.27 tff(2066,plain,
% 1.50/1.27 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2065, 2061])).
% 1.50/1.27 tff(2067,plain,(
% 1.50/1.27 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.50/1.27 inference(skolemize,[status(sab)],[2066])).
% 1.50/1.27 tff(2068,plain,
% 1.50/1.27 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2067, 2060])).
% 1.50/1.27 tff(2069,plain,
% 1.50/1.27 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp17 | c2_1(a249) | c1_1(a241) | c3_1(a241) | (~ndr1_0) | (~c2_1(a241)) | (~c3_1(a249)) | (~c0_1(a249)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp17 | c2_1(a249) | c1_1(a241) | c3_1(a241) | (~ndr1_0) | (~c2_1(a241)) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2070,plain,
% 1.50/1.27 ((hskp17 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a241) | c1_1(a241) | (~c2_1(a241))) <=> (hskp17 | c2_1(a249) | c1_1(a241) | c3_1(a241) | (~ndr1_0) | (~c2_1(a241)) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2071,plain,
% 1.50/1.27 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a241) | c1_1(a241) | (~c2_1(a241)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp17 | c2_1(a249) | c1_1(a241) | c3_1(a241) | (~ndr1_0) | (~c2_1(a241)) | (~c3_1(a249)) | (~c0_1(a249))))),
% 1.50/1.27 inference(monotonicity,[status(thm)],[2070])).
% 1.50/1.27 tff(2072,plain,
% 1.50/1.27 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a241) | c1_1(a241) | (~c2_1(a241)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp17 | c2_1(a249) | c1_1(a241) | c3_1(a241) | (~ndr1_0) | (~c2_1(a241)) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.27 inference(transitivity,[status(thm)],[2071, 2069])).
% 1.50/1.27 tff(2073,plain,
% 1.50/1.27 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a241) | c1_1(a241) | (~c2_1(a241)))),
% 1.50/1.27 inference(quant_inst,[status(thm)],[])).
% 1.50/1.27 tff(2074,plain,
% 1.50/1.27 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp17 | c2_1(a249) | c1_1(a241) | c3_1(a241) | (~ndr1_0) | (~c2_1(a241)) | (~c3_1(a249)) | (~c0_1(a249))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2073, 2072])).
% 1.50/1.27 tff(2075,plain,
% 1.50/1.27 (hskp17),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[2074, 128, 2008, 1997, 1986, 1476, 1475, 2068, 2058])).
% 1.50/1.27 tff(2076,plain,
% 1.50/1.27 (~c2_1(a232)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[795, 2075])).
% 1.50/1.27 tff(2077,plain,
% 1.50/1.27 (~c1_1(a232)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[801, 2075])).
% 1.50/1.27 tff(2078,plain,
% 1.50/1.27 (c3_1(a232)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[821, 2075])).
% 1.50/1.27 tff(2079,plain,
% 1.50/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a241) | c2_1(a238) | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a232)) | (~c3_1(a238)) | c0_1(a238))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a241) | c2_1(a238) | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a232)) | (~c3_1(a238)) | c0_1(a238))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2080,plain,
% 1.50/1.27 (((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a232) | (~c3_1(a232)) | c2_1(a232) | c2_1(a238) | c0_1(a238) | (~c3_1(a238))) <=> (c1_1(a241) | c2_1(a238) | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a232)) | (~c3_1(a238)) | c0_1(a238))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2081,plain,
% 1.50/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a232) | (~c3_1(a232)) | c2_1(a232) | c2_1(a238) | c0_1(a238) | (~c3_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a241) | c2_1(a238) | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a232)) | (~c3_1(a238)) | c0_1(a238)))),
% 1.50/1.27 inference(monotonicity,[status(thm)],[2080])).
% 1.50/1.27 tff(2082,plain,
% 1.50/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a232) | (~c3_1(a232)) | c2_1(a232) | c2_1(a238) | c0_1(a238) | (~c3_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a241) | c2_1(a238) | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a232)) | (~c3_1(a238)) | c0_1(a238))),
% 1.50/1.27 inference(transitivity,[status(thm)],[2081, 2079])).
% 1.50/1.27 tff(2083,plain,
% 1.50/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a232) | (~c3_1(a232)) | c2_1(a232) | c2_1(a238) | c0_1(a238) | (~c3_1(a238)))),
% 1.50/1.27 inference(quant_inst,[status(thm)],[])).
% 1.50/1.27 tff(2084,plain,
% 1.50/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a241) | c2_1(a238) | c1_1(a232) | c2_1(a232) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a232)) | (~c3_1(a238)) | c0_1(a238)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2083, 2082])).
% 1.50/1.27 tff(2085,plain,
% 1.50/1.27 (c0_1(a238)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[2084, 128, 1478, 1382, 2078, 1476, 1370, 2077, 2076, 886, 2058])).
% 1.50/1.27 tff(2086,plain,
% 1.50/1.27 (c0_1(a232)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[892, 128, 1478, 2078, 1476, 2077, 2076, 886, 2058])).
% 1.50/1.27 tff(2087,plain,
% 1.50/1.27 (hskp12),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[808, 128, 160, 2077, 2076, 725, 2086])).
% 1.50/1.27 tff(2088,plain,
% 1.50/1.27 (~c3_1(a217)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[974, 2087])).
% 1.50/1.27 tff(2089,plain,
% 1.50/1.27 (~c2_1(a217)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[980, 2087])).
% 1.50/1.27 tff(2090,plain,
% 1.50/1.27 (c0_1(a217)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[998, 2087])).
% 1.50/1.27 tff(2091,plain,
% 1.50/1.27 (hskp0),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[1015, 128, 211, 2090, 2089, 2088, 233])).
% 1.50/1.27 tff(2092,plain,
% 1.50/1.27 (~c1_1(a199)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[369, 2091])).
% 1.50/1.27 tff(2093,plain,
% 1.50/1.27 (~c0_1(a199)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[363, 2091])).
% 1.50/1.27 tff(2094,plain,
% 1.50/1.27 (c3_1(a199)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[403, 2091])).
% 1.50/1.27 tff(2095,plain,
% 1.50/1.27 (((~![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(a238) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))) <=> ((~![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(a238) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2096,plain,
% 1.50/1.27 (((~ndr1_0) | c2_1(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199))) <=> (c2_1(a238) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2097,plain,
% 1.50/1.27 (((~![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(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))) <=> ((~![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(a238) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238))))),
% 1.50/1.27 inference(monotonicity,[status(thm)],[2096])).
% 1.50/1.27 tff(2098,plain,
% 1.50/1.27 (((~![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(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))) <=> ((~![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(a238) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.50/1.27 inference(transitivity,[status(thm)],[2097, 2095])).
% 1.50/1.27 tff(2099,plain,
% 1.50/1.27 ((~![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(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))),
% 1.50/1.27 inference(quant_inst,[status(thm)],[])).
% 1.50/1.27 tff(2100,plain,
% 1.50/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a238) | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c3_1(a199)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238))),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2099, 2098])).
% 1.50/1.27 tff(2101,plain,
% 1.50/1.27 ($false),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[2100, 128, 1393, 1382, 2094, 1370, 2093, 2092, 682, 2085])).
% 1.50/1.27 tff(2102,plain,((~hskp19) | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.50/1.27 tff(2103,plain,
% 1.50/1.27 (~hskp19),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[2102, 160])).
% 1.50/1.27 tff(2104,plain,
% 1.50/1.27 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a256)) | (~c1_1(a256)) | c3_1(a256))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a256)) | (~c1_1(a256)) | c3_1(a256))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2105,plain,
% 1.50/1.27 ((hskp27 | hskp19 | (~ndr1_0) | c3_1(a256) | (~c2_1(a256)) | (~c1_1(a256))) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a256)) | (~c1_1(a256)) | c3_1(a256))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2106,plain,
% 1.50/1.27 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c3_1(a256) | (~c2_1(a256)) | (~c1_1(a256)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a256)) | (~c1_1(a256)) | c3_1(a256)))),
% 1.50/1.27 inference(monotonicity,[status(thm)],[2105])).
% 1.50/1.27 tff(2107,plain,
% 1.50/1.27 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c3_1(a256) | (~c2_1(a256)) | (~c1_1(a256)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a256)) | (~c1_1(a256)) | c3_1(a256))),
% 1.50/1.27 inference(transitivity,[status(thm)],[2106, 2104])).
% 1.50/1.27 tff(2108,plain,
% 1.50/1.27 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c3_1(a256) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.27 inference(quant_inst,[status(thm)],[])).
% 1.50/1.27 tff(2109,plain,
% 1.50/1.27 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a256)) | (~c1_1(a256)) | c3_1(a256)),
% 1.50/1.27 inference(modus_ponens,[status(thm)],[2108, 2107])).
% 1.50/1.27 tff(2110,plain,
% 1.50/1.27 (c3_1(a256)),
% 1.50/1.27 inference(unit_resolution,[status(thm)],[2109, 128, 160, 1, 2027, 2044, 2057])).
% 1.50/1.27 tff(2111,plain,
% 1.50/1.27 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.50/1.27 inference(bind,[status(th)],[])).
% 1.50/1.27 tff(2112,plain,
% 1.50/1.27 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.50/1.27 inference(quant_intro,[status(thm)],[2111])).
% 1.50/1.27 tff(2113,plain,
% 1.50/1.27 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.50/1.27 inference(rewrite,[status(thm)],[])).
% 1.50/1.27 tff(2114,plain,
% 1.50/1.27 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.50/1.28 inference(bind,[status(th)],[])).
% 1.50/1.28 tff(2115,plain,
% 1.50/1.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.50/1.28 inference(quant_intro,[status(thm)],[2114])).
% 1.50/1.28 tff(2116,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 1.50/1.28 tff(2117,plain,
% 1.50/1.28 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.50/1.28 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 1.50/1.28 tff(2118,plain,
% 1.50/1.28 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.50/1.28 inference(modus_ponens,[status(thm)],[2117, 2113])).
% 1.50/1.28 tff(2119,plain,(
% 1.50/1.28 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.50/1.28 inference(skolemize,[status(sab)],[2118])).
% 1.50/1.28 tff(2120,plain,
% 1.50/1.28 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.50/1.28 inference(modus_ponens,[status(thm)],[2119, 2112])).
% 1.50/1.28 tff(2121,assumption,(~hskp20), introduced(assumption)).
% 1.50/1.28 tff(2122,plain,
% 1.50/1.28 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c2_1(a249) | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c2_1(a249) | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2123,plain,
% 1.50/1.28 ((hskp20 | hskp19 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c0_1(a249))) <=> (hskp20 | hskp19 | c2_1(a249) | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2124,plain,
% 1.50/1.28 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c2_1(a249) | (~ndr1_0) | c1_1(a249) | (~c0_1(a249))))),
% 1.50/1.28 inference(monotonicity,[status(thm)],[2123])).
% 1.50/1.28 tff(2125,plain,
% 1.50/1.28 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c2_1(a249) | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)))),
% 1.50/1.28 inference(transitivity,[status(thm)],[2124, 2122])).
% 1.50/1.28 tff(2126,plain,
% 1.50/1.28 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)))),
% 1.50/1.28 inference(quant_inst,[status(thm)],[])).
% 1.50/1.28 tff(2127,plain,
% 1.50/1.28 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c2_1(a249) | (~ndr1_0) | c1_1(a249) | (~c0_1(a249))),
% 1.50/1.28 inference(modus_ponens,[status(thm)],[2126, 2125])).
% 1.50/1.28 tff(2128,plain,
% 1.50/1.28 (hskp20 | hskp19 | c1_1(a249)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2127, 128, 2008, 1986, 1341])).
% 1.50/1.28 tff(2129,plain,
% 1.50/1.28 (c1_1(a249)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2128, 1, 2121])).
% 1.50/1.28 tff(2130,plain,
% 1.50/1.28 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | (~c1_1(a249)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | (~c1_1(a249)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2131,plain,
% 1.50/1.28 ((hskp21 | (~ndr1_0) | c2_1(a249) | (~c3_1(a249)) | (~c1_1(a249))) <=> (hskp21 | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | (~c1_1(a249)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2132,plain,
% 1.50/1.28 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a249) | (~c3_1(a249)) | (~c1_1(a249)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | (~c1_1(a249))))),
% 1.50/1.28 inference(monotonicity,[status(thm)],[2131])).
% 1.50/1.28 tff(2133,plain,
% 1.50/1.28 (((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a249) | (~c3_1(a249)) | (~c1_1(a249)))) <=> ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | (~c1_1(a249)))),
% 1.50/1.28 inference(transitivity,[status(thm)],[2132, 2130])).
% 1.50/1.28 tff(2134,plain,
% 1.50/1.28 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | (~ndr1_0) | c2_1(a249) | (~c3_1(a249)) | (~c1_1(a249)))),
% 1.50/1.28 inference(quant_inst,[status(thm)],[])).
% 1.50/1.28 tff(2135,plain,
% 1.50/1.28 ((~![U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | (~c1_1(a249))),
% 1.50/1.28 inference(modus_ponens,[status(thm)],[2134, 2133])).
% 1.50/1.28 tff(2136,plain,
% 1.50/1.28 (hskp21 | (~c1_1(a249))),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2135, 128, 1997, 1986, 289])).
% 1.50/1.28 tff(2137,plain,
% 1.50/1.28 (hskp21),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2136, 2129])).
% 1.50/1.28 tff(2138,plain,
% 1.50/1.28 (~c3_1(a241)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[302, 2137])).
% 1.50/1.28 tff(2139,plain,
% 1.50/1.28 (~c1_1(a241)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[308, 2137])).
% 1.50/1.28 tff(2140,plain,
% 1.50/1.28 (c0_1(a241)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[330, 2137])).
% 1.50/1.28 tff(2141,plain,
% 1.50/1.28 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a256) | c1_1(a241) | c3_1(a241) | (~ndr1_0) | (~c0_1(a241)) | (~c1_1(a256)) | (~c3_1(a256)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a256) | c1_1(a241) | c3_1(a241) | (~ndr1_0) | (~c0_1(a241)) | (~c1_1(a256)) | (~c3_1(a256)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2142,plain,
% 1.50/1.28 ((hskp5 | (~ndr1_0) | c3_1(a241) | c1_1(a241) | (~c0_1(a241)) | c0_1(a256) | (~c3_1(a256)) | (~c1_1(a256))) <=> (hskp5 | c0_1(a256) | c1_1(a241) | c3_1(a241) | (~ndr1_0) | (~c0_1(a241)) | (~c1_1(a256)) | (~c3_1(a256)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2143,plain,
% 1.50/1.28 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a241) | c1_1(a241) | (~c0_1(a241)) | c0_1(a256) | (~c3_1(a256)) | (~c1_1(a256)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a256) | c1_1(a241) | c3_1(a241) | (~ndr1_0) | (~c0_1(a241)) | (~c1_1(a256)) | (~c3_1(a256))))),
% 1.50/1.28 inference(monotonicity,[status(thm)],[2142])).
% 1.50/1.28 tff(2144,plain,
% 1.50/1.28 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a241) | c1_1(a241) | (~c0_1(a241)) | c0_1(a256) | (~c3_1(a256)) | (~c1_1(a256)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a256) | c1_1(a241) | c3_1(a241) | (~ndr1_0) | (~c0_1(a241)) | (~c1_1(a256)) | (~c3_1(a256)))),
% 1.50/1.28 inference(transitivity,[status(thm)],[2143, 2141])).
% 1.50/1.28 tff(2145,plain,
% 1.50/1.28 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a241) | c1_1(a241) | (~c0_1(a241)) | c0_1(a256) | (~c3_1(a256)) | (~c1_1(a256)))),
% 1.50/1.28 inference(quant_inst,[status(thm)],[])).
% 1.50/1.28 tff(2146,plain,
% 1.50/1.28 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a256) | c1_1(a241) | c3_1(a241) | (~ndr1_0) | (~c0_1(a241)) | (~c1_1(a256)) | (~c3_1(a256))),
% 1.50/1.28 inference(modus_ponens,[status(thm)],[2145, 2144])).
% 1.50/1.28 tff(2147,plain,
% 1.50/1.28 ($false),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2146, 128, 1210, 2027, 2140, 2033, 2139, 2138, 2120, 2110])).
% 1.50/1.28 tff(2148,plain,(hskp19 | hskp5 | hskp27 | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.50/1.28 tff(2149,plain,
% 1.50/1.28 (hskp20),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2148, 1210, 160, 2103])).
% 1.50/1.28 tff(2150,plain,
% 1.50/1.28 (~c3_1(a239)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[1251, 2149])).
% 1.50/1.28 tff(2151,plain,
% 1.50/1.28 (c2_1(a239)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[1579, 2149])).
% 1.50/1.28 tff(2152,plain,
% 1.50/1.28 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | c3_1(a239) | (~ndr1_0) | (~c1_1(a239)) | (~c2_1(a239)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | c3_1(a239) | (~ndr1_0) | (~c1_1(a239)) | (~c2_1(a239)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2153,plain,
% 1.50/1.28 ((hskp27 | hskp19 | (~ndr1_0) | c3_1(a239) | (~c2_1(a239)) | (~c1_1(a239))) <=> (hskp27 | hskp19 | c3_1(a239) | (~ndr1_0) | (~c1_1(a239)) | (~c2_1(a239)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2154,plain,
% 1.50/1.28 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c3_1(a239) | (~c2_1(a239)) | (~c1_1(a239)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | c3_1(a239) | (~ndr1_0) | (~c1_1(a239)) | (~c2_1(a239))))),
% 1.50/1.28 inference(monotonicity,[status(thm)],[2153])).
% 1.50/1.28 tff(2155,plain,
% 1.50/1.28 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c3_1(a239) | (~c2_1(a239)) | (~c1_1(a239)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | c3_1(a239) | (~ndr1_0) | (~c1_1(a239)) | (~c2_1(a239)))),
% 1.50/1.28 inference(transitivity,[status(thm)],[2154, 2152])).
% 1.50/1.28 tff(2156,plain,
% 1.50/1.28 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c3_1(a239) | (~c2_1(a239)) | (~c1_1(a239)))),
% 1.50/1.28 inference(quant_inst,[status(thm)],[])).
% 1.50/1.28 tff(2157,plain,
% 1.50/1.28 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | c3_1(a239) | (~ndr1_0) | (~c1_1(a239)) | (~c2_1(a239))),
% 1.50/1.28 inference(modus_ponens,[status(thm)],[2156, 2155])).
% 1.50/1.28 tff(2158,plain,
% 1.50/1.28 (~c1_1(a239)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2157, 128, 160, 2103, 2151, 2150, 2057])).
% 1.50/1.28 tff(2159,plain,
% 1.50/1.28 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.50/1.28 inference(bind,[status(th)],[])).
% 1.50/1.28 tff(2160,plain,
% 1.50/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.50/1.28 inference(quant_intro,[status(thm)],[2159])).
% 1.50/1.28 tff(2161,plain,
% 1.50/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2162,plain,
% 1.50/1.28 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.50/1.28 inference(bind,[status(th)],[])).
% 1.50/1.28 tff(2163,plain,
% 1.50/1.28 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.50/1.28 inference(quant_intro,[status(thm)],[2162])).
% 1.50/1.28 tff(2164,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.50/1.28 tff(2165,plain,
% 1.50/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.50/1.28 inference(modus_ponens,[status(thm)],[2164, 2163])).
% 1.50/1.28 tff(2166,plain,
% 1.50/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.50/1.28 inference(modus_ponens,[status(thm)],[2165, 2161])).
% 1.50/1.28 tff(2167,plain,(
% 1.50/1.28 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.50/1.28 inference(skolemize,[status(sab)],[2166])).
% 1.50/1.28 tff(2168,plain,
% 1.50/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.50/1.28 inference(modus_ponens,[status(thm)],[2167, 2160])).
% 1.50/1.28 tff(2169,plain,
% 1.50/1.28 (~c0_1(a239)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[1257, 2149])).
% 1.50/1.28 tff(2170,plain,
% 1.50/1.28 (hskp4),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[1264, 128, 1210, 2169, 2150, 1209, 2158])).
% 1.50/1.28 tff(2171,plain,
% 1.50/1.28 (~c2_1(a204)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[386, 2170])).
% 1.50/1.28 tff(2172,plain,
% 1.50/1.28 (~c0_1(a204)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[392, 2170])).
% 1.50/1.28 tff(2173,plain,
% 1.50/1.28 (hskp25),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2015, 2103])).
% 1.50/1.28 tff(2174,plain,
% 1.50/1.28 (~c0_1(a256)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2032, 2173])).
% 1.50/1.28 tff(2175,plain,
% 1.50/1.28 (c2_1(a256)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2043, 2173])).
% 1.50/1.28 tff(2176,plain,
% 1.50/1.28 (c1_1(a256)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2026, 2173])).
% 1.50/1.28 tff(2177,plain,
% 1.50/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a256) | c3_1(a239) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | c1_1(a239) | (~c2_1(a239)) | (~c2_1(a256)) | (~c1_1(a256)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a256) | c3_1(a239) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | c1_1(a239) | (~c2_1(a239)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2178,plain,
% 1.50/1.28 (((~ndr1_0) | c3_1(a239) | c1_1(a239) | (~c2_1(a239)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c2_1(a204) | c0_1(a204) | (~c3_1(a204))) <=> (c0_1(a256) | c3_1(a239) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | c1_1(a239) | (~c2_1(a239)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2179,plain,
% 1.50/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a239) | c1_1(a239) | (~c2_1(a239)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c2_1(a204) | c0_1(a204) | (~c3_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a256) | c3_1(a239) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | c1_1(a239) | (~c2_1(a239)) | (~c2_1(a256)) | (~c1_1(a256))))),
% 1.50/1.28 inference(monotonicity,[status(thm)],[2178])).
% 1.50/1.28 tff(2180,plain,
% 1.50/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a239) | c1_1(a239) | (~c2_1(a239)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c2_1(a204) | c0_1(a204) | (~c3_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a256) | c3_1(a239) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | c1_1(a239) | (~c2_1(a239)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.28 inference(transitivity,[status(thm)],[2179, 2177])).
% 1.50/1.28 tff(2181,plain,
% 1.50/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a239) | c1_1(a239) | (~c2_1(a239)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c2_1(a204) | c0_1(a204) | (~c3_1(a204)))),
% 1.50/1.28 inference(quant_inst,[status(thm)],[])).
% 1.50/1.28 tff(2182,plain,
% 1.50/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a256) | c3_1(a239) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c3_1(a204)) | c1_1(a239) | (~c2_1(a239)) | (~c2_1(a256)) | (~c1_1(a256))),
% 1.50/1.28 inference(modus_ponens,[status(thm)],[2181, 2180])).
% 1.50/1.28 tff(2183,plain,
% 1.50/1.28 (~c3_1(a204)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2182, 128, 2176, 2175, 2151, 2174, 2150, 2172, 2171, 2168, 2158])).
% 1.50/1.28 tff(2184,plain,
% 1.50/1.28 (c1_1(a204)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[414, 2170])).
% 1.50/1.28 tff(2185,plain,
% 1.50/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a249) | c0_1(a239) | c0_1(a204) | (~ndr1_0) | c3_1(a204) | (~c1_1(a204)) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a249)) | (~c0_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a249) | c0_1(a239) | c0_1(a204) | (~ndr1_0) | c3_1(a204) | (~c1_1(a204)) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2186,plain,
% 1.50/1.28 (((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204)) | c1_1(a239) | c0_1(a239) | (~c2_1(a239))) <=> (c2_1(a249) | c0_1(a239) | c0_1(a204) | (~ndr1_0) | c3_1(a204) | (~c1_1(a204)) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2187,plain,
% 1.50/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204)) | c1_1(a239) | c0_1(a239) | (~c2_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a249) | c0_1(a239) | c0_1(a204) | (~ndr1_0) | c3_1(a204) | (~c1_1(a204)) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a249)) | (~c0_1(a249))))),
% 1.50/1.28 inference(monotonicity,[status(thm)],[2186])).
% 1.50/1.28 tff(2188,plain,
% 1.50/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204)) | c1_1(a239) | c0_1(a239) | (~c2_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a249) | c0_1(a239) | c0_1(a204) | (~ndr1_0) | c3_1(a204) | (~c1_1(a204)) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.28 inference(transitivity,[status(thm)],[2187, 2185])).
% 1.50/1.28 tff(2189,plain,
% 1.50/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204)) | c1_1(a239) | c0_1(a239) | (~c2_1(a239)))),
% 1.50/1.28 inference(quant_inst,[status(thm)],[])).
% 1.50/1.28 tff(2190,plain,
% 1.50/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a249) | c0_1(a239) | c0_1(a204) | (~ndr1_0) | c3_1(a204) | (~c1_1(a204)) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a249)) | (~c0_1(a249))),
% 1.50/1.28 inference(modus_ponens,[status(thm)],[2189, 2188])).
% 1.50/1.28 tff(2191,plain,
% 1.50/1.28 ($false),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2190, 128, 2008, 1997, 2151, 2184, 1986, 2169, 2172, 593, 2183, 2158])).
% 1.50/1.28 tff(2192,plain,(hskp5 | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.50/1.28 tff(2193,plain,
% 1.50/1.28 (hskp5),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2192, 160])).
% 1.50/1.28 tff(2194,plain,
% 1.50/1.28 (~c1_1(a205)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[58, 2193])).
% 1.50/1.28 tff(2195,plain,
% 1.50/1.28 (c3_1(a205)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[69, 2193])).
% 1.50/1.28 tff(2196,plain,
% 1.50/1.28 (c2_1(a205)),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[52, 2193])).
% 1.50/1.28 tff(2197,plain,
% 1.50/1.28 (((~![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(a249) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a249)) | (~c1_1(a249)) | (~c0_1(a249)))) <=> ((~![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(a249) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a249)) | (~c1_1(a249)) | (~c0_1(a249)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2198,plain,
% 1.50/1.28 (((~ndr1_0) | c2_1(a249) | (~c3_1(a249)) | (~c1_1(a249)) | c2_1(a249) | (~c1_1(a249)) | (~c0_1(a249)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205))) <=> (c2_1(a249) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a249)) | (~c1_1(a249)) | (~c0_1(a249)))),
% 1.50/1.28 inference(rewrite,[status(thm)],[])).
% 1.50/1.28 tff(2199,plain,
% 1.50/1.28 (((~![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(a249) | (~c3_1(a249)) | (~c1_1(a249)) | c2_1(a249) | (~c1_1(a249)) | (~c0_1(a249)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205)))) <=> ((~![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(a249) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a249)) | (~c1_1(a249)) | (~c0_1(a249))))),
% 1.50/1.28 inference(monotonicity,[status(thm)],[2198])).
% 1.50/1.28 tff(2200,plain,
% 1.50/1.28 (((~![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(a249) | (~c3_1(a249)) | (~c1_1(a249)) | c2_1(a249) | (~c1_1(a249)) | (~c0_1(a249)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205)))) <=> ((~![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(a249) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a249)) | (~c1_1(a249)) | (~c0_1(a249)))),
% 1.50/1.28 inference(transitivity,[status(thm)],[2199, 2197])).
% 1.50/1.28 tff(2201,plain,
% 1.50/1.28 ((~![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(a249) | (~c3_1(a249)) | (~c1_1(a249)) | c2_1(a249) | (~c1_1(a249)) | (~c0_1(a249)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205)))),
% 1.50/1.28 inference(quant_inst,[status(thm)],[])).
% 1.50/1.28 tff(2202,plain,
% 1.50/1.28 ((~![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(a249) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a249)) | (~c1_1(a249)) | (~c0_1(a249))),
% 1.50/1.28 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 1.50/1.28 tff(2203,plain,
% 1.50/1.28 (c0_1(a205) | (~c1_1(a249))),
% 1.50/1.28 inference(unit_resolution,[status(thm)],[2202, 128, 2008, 1997, 93, 1986, 92, 682])).
% 1.50/1.29 tff(2204,plain,
% 1.50/1.29 (c0_1(a205)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2203, 2045])).
% 1.50/1.29 tff(2205,plain,
% 1.50/1.29 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c2_1(a249) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a249)) | (~c0_1(a249)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c2_1(a249) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a249)) | (~c0_1(a249)))),
% 1.50/1.29 inference(rewrite,[status(thm)],[])).
% 1.50/1.29 tff(2206,plain,
% 1.50/1.29 ((hskp3 | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c2_1(a249) | (~c1_1(a249)) | (~c0_1(a249))) <=> (hskp3 | c2_1(a249) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a249)) | (~c0_1(a249)))),
% 1.50/1.29 inference(rewrite,[status(thm)],[])).
% 1.50/1.29 tff(2207,plain,
% 1.50/1.29 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c2_1(a249) | (~c1_1(a249)) | (~c0_1(a249)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c2_1(a249) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a249)) | (~c0_1(a249))))),
% 1.50/1.29 inference(monotonicity,[status(thm)],[2206])).
% 1.50/1.29 tff(2208,plain,
% 1.50/1.29 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c2_1(a249) | (~c1_1(a249)) | (~c0_1(a249)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c2_1(a249) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a249)) | (~c0_1(a249)))),
% 1.50/1.29 inference(transitivity,[status(thm)],[2207, 2205])).
% 1.50/1.29 tff(2209,plain,
% 1.50/1.29 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c2_1(a249) | (~c1_1(a249)) | (~c0_1(a249)))),
% 1.50/1.29 inference(quant_inst,[status(thm)],[])).
% 1.50/1.29 tff(2210,plain,
% 1.50/1.29 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c2_1(a249) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a249)) | (~c0_1(a249))),
% 1.50/1.29 inference(modus_ponens,[status(thm)],[2209, 2208])).
% 1.50/1.29 tff(2211,plain,
% 1.50/1.29 (hskp3 | (~c0_1(a205)) | (~c1_1(a249))),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2210, 128, 2008, 1118, 93, 1986, 1429])).
% 1.50/1.29 tff(2212,plain,
% 1.50/1.29 (hskp3),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2211, 2204, 2045])).
% 1.50/1.29 tff(2213,plain,
% 1.50/1.29 (~c3_1(a203)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[619, 2212])).
% 1.50/1.29 tff(2214,plain,
% 1.50/1.29 (~c0_1(a203)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[625, 2212])).
% 1.50/1.29 tff(2215,plain,
% 1.50/1.29 (c1_1(a203)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[636, 2212])).
% 1.50/1.29 tff(2216,assumption,(c2_1(a256)), introduced(assumption)).
% 1.50/1.29 tff(2217,plain,
% 1.50/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a256) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c2_1(a256)) | (~c1_1(a256)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a256) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.29 inference(rewrite,[status(thm)],[])).
% 1.50/1.29 tff(2218,plain,
% 1.50/1.29 (((~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a203) | c3_1(a203) | (~c1_1(a203))) <=> (c0_1(a256) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.29 inference(rewrite,[status(thm)],[])).
% 1.50/1.29 tff(2219,plain,
% 1.50/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a203) | c3_1(a203) | (~c1_1(a203)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a256) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c2_1(a256)) | (~c1_1(a256))))),
% 1.50/1.29 inference(monotonicity,[status(thm)],[2218])).
% 1.50/1.29 tff(2220,plain,
% 1.50/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a203) | c3_1(a203) | (~c1_1(a203)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a256) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.29 inference(transitivity,[status(thm)],[2219, 2217])).
% 1.50/1.29 tff(2221,plain,
% 1.50/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a203) | c3_1(a203) | (~c1_1(a203)))),
% 1.50/1.29 inference(quant_inst,[status(thm)],[])).
% 1.50/1.29 tff(2222,plain,
% 1.50/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a256) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c2_1(a256)) | (~c1_1(a256))),
% 1.50/1.29 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 1.50/1.29 tff(2223,plain,
% 1.50/1.29 ($false),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2222, 128, 2047, 2216, 1118, 93, 2215, 2046, 2214, 2213, 1913, 2204])).
% 1.50/1.29 tff(2224,plain,((~c1_1(a249)) | (~c1_1(a256)) | (~c2_1(a256)) | (~c2_1(a205)) | (~c3_1(a205)) | c0_1(a256) | c1_1(a205)), inference(lemma,lemma(discharge,[]))).
% 1.50/1.29 tff(2225,plain,
% 1.50/1.29 (~c1_1(a249)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2224, 2176, 2175, 2196, 2195, 2174, 2194])).
% 1.50/1.29 tff(2226,plain,
% 1.50/1.29 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | c2_1(a249) | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp12 | c2_1(a249) | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)))),
% 1.50/1.29 inference(rewrite,[status(thm)],[])).
% 1.50/1.29 tff(2227,plain,
% 1.50/1.29 ((hskp27 | hskp12 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c0_1(a249))) <=> (hskp27 | hskp12 | c2_1(a249) | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)))),
% 1.50/1.29 inference(rewrite,[status(thm)],[])).
% 1.50/1.29 tff(2228,plain,
% 1.50/1.29 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | c2_1(a249) | (~ndr1_0) | c1_1(a249) | (~c0_1(a249))))),
% 1.50/1.29 inference(monotonicity,[status(thm)],[2227])).
% 1.50/1.29 tff(2229,plain,
% 1.50/1.29 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp12 | c2_1(a249) | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)))),
% 1.50/1.29 inference(transitivity,[status(thm)],[2228, 2226])).
% 1.50/1.29 tff(2230,plain,
% 1.50/1.29 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)))),
% 1.50/1.29 inference(quant_inst,[status(thm)],[])).
% 1.50/1.29 tff(2231,plain,
% 1.50/1.29 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp12 | c2_1(a249) | (~ndr1_0) | c1_1(a249) | (~c0_1(a249))),
% 1.50/1.29 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 1.50/1.29 tff(2232,plain,
% 1.50/1.29 (hskp27 | hskp12 | c1_1(a249)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2231, 128, 2008, 1986, 725])).
% 1.50/1.29 tff(2233,plain,
% 1.50/1.29 (hskp12),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2232, 2225, 160])).
% 1.50/1.29 tff(2234,plain,
% 1.50/1.29 (~c3_1(a217)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[974, 2233])).
% 1.50/1.29 tff(2235,plain,
% 1.50/1.29 (~c2_1(a217)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[980, 2233])).
% 1.50/1.29 tff(2236,plain,
% 1.50/1.29 (c1_1(a217)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[987, 128, 160, 2235, 2234, 188])).
% 1.50/1.29 tff(2237,plain,
% 1.50/1.29 (c0_1(a217)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[998, 2233])).
% 1.50/1.29 tff(2238,plain,
% 1.50/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a249) | c3_1(a217) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | (~c3_1(a205)) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a249) | (~c3_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a249) | c3_1(a217) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | (~c3_1(a205)) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a249) | (~c3_1(a249)))),
% 1.50/1.29 inference(rewrite,[status(thm)],[])).
% 1.50/1.29 tff(2239,plain,
% 1.50/1.29 (((~ndr1_0) | c3_1(a217) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a205) | (~c3_1(a205)) | (~c2_1(a205)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249))) <=> (c2_1(a249) | c3_1(a217) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | (~c3_1(a205)) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a249) | (~c3_1(a249)))),
% 1.50/1.29 inference(rewrite,[status(thm)],[])).
% 1.50/1.29 tff(2240,plain,
% 1.50/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a217) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a205) | (~c3_1(a205)) | (~c2_1(a205)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a249) | c3_1(a217) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | (~c3_1(a205)) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a249) | (~c3_1(a249))))),
% 1.50/1.29 inference(monotonicity,[status(thm)],[2239])).
% 1.50/1.29 tff(2241,plain,
% 1.50/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a217) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a205) | (~c3_1(a205)) | (~c2_1(a205)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a249) | c3_1(a217) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | (~c3_1(a205)) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a249) | (~c3_1(a249)))),
% 1.50/1.29 inference(transitivity,[status(thm)],[2240, 2238])).
% 1.50/1.29 tff(2242,plain,
% 1.50/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a217) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a205) | (~c3_1(a205)) | (~c2_1(a205)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))),
% 1.50/1.29 inference(quant_inst,[status(thm)],[])).
% 1.50/1.29 tff(2243,plain,
% 1.50/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a249) | c3_1(a217) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | (~c3_1(a205)) | (~c0_1(a217)) | (~c1_1(a217)) | c1_1(a249) | (~c3_1(a249))),
% 1.50/1.29 inference(modus_ponens,[status(thm)],[2242, 2241])).
% 1.50/1.29 tff(2244,plain,
% 1.50/1.29 ($false),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2243, 128, 1997, 2237, 2196, 2195, 1986, 2234, 2194, 1009, 2236, 2225])).
% 1.50/1.29 tff(2245,plain,(hskp27), inference(lemma,lemma(discharge,[]))).
% 1.50/1.29 tff(2246,plain,
% 1.50/1.29 (c2_1(a198)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[1087, 2245])).
% 1.50/1.29 tff(2247,plain,
% 1.50/1.29 (c1_1(a198)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[1098, 2245])).
% 1.50/1.29 tff(2248,plain,
% 1.50/1.29 (c0_1(a198)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[1109, 2245])).
% 1.50/1.29 tff(2249,plain,
% 1.50/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a256) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a249)) | (~c1_1(a249)) | (~c1_1(a256)) | (~c3_1(a256)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a256) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a249)) | (~c1_1(a249)) | (~c1_1(a256)) | (~c3_1(a256)))),
% 1.50/1.29 inference(rewrite,[status(thm)],[])).
% 1.50/1.29 tff(2250,plain,
% 1.50/1.29 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a249)) | c2_1(a249) | (~c1_1(a249)) | c0_1(a256) | (~c3_1(a256)) | (~c1_1(a256))) <=> (c0_1(a256) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a249)) | (~c1_1(a249)) | (~c1_1(a256)) | (~c3_1(a256)))),
% 1.50/1.29 inference(rewrite,[status(thm)],[])).
% 1.50/1.29 tff(2251,plain,
% 1.50/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a249)) | c2_1(a249) | (~c1_1(a249)) | c0_1(a256) | (~c3_1(a256)) | (~c1_1(a256)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a256) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a249)) | (~c1_1(a249)) | (~c1_1(a256)) | (~c3_1(a256))))),
% 1.50/1.29 inference(monotonicity,[status(thm)],[2250])).
% 1.50/1.29 tff(2252,plain,
% 1.50/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a249)) | c2_1(a249) | (~c1_1(a249)) | c0_1(a256) | (~c3_1(a256)) | (~c1_1(a256)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a256) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a249)) | (~c1_1(a249)) | (~c1_1(a256)) | (~c3_1(a256)))),
% 1.50/1.29 inference(transitivity,[status(thm)],[2251, 2249])).
% 1.50/1.29 tff(2253,plain,
% 1.50/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a249)) | c2_1(a249) | (~c1_1(a249)) | c0_1(a256) | (~c3_1(a256)) | (~c1_1(a256)))),
% 1.50/1.29 inference(quant_inst,[status(thm)],[])).
% 1.50/1.29 tff(2254,plain,
% 1.50/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a256) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a249)) | (~c1_1(a249)) | (~c1_1(a256)) | (~c3_1(a256))),
% 1.50/1.29 inference(modus_ponens,[status(thm)],[2253, 2252])).
% 1.50/1.29 tff(2255,plain,
% 1.50/1.29 ((~c1_1(a249)) | (~c3_1(a256))),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2254, 128, 2248, 2247, 2246, 2047, 1997, 2046, 1986, 80])).
% 1.50/1.29 tff(2256,plain,
% 1.50/1.29 (~c3_1(a256)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2255, 2045])).
% 1.50/1.29 tff(2257,plain,
% 1.50/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a256) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a249)) | (~c0_1(a249)) | (~c2_1(a256)) | c3_1(a256))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a256) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a249)) | (~c0_1(a249)) | (~c2_1(a256)) | c3_1(a256))),
% 1.50/1.29 inference(rewrite,[status(thm)],[])).
% 1.50/1.29 tff(2258,plain,
% 1.50/1.29 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a249) | (~c1_1(a249)) | (~c0_1(a249)) | c0_1(a256) | c3_1(a256) | (~c2_1(a256))) <=> (c0_1(a256) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a249)) | (~c0_1(a249)) | (~c2_1(a256)) | c3_1(a256))),
% 1.50/1.29 inference(rewrite,[status(thm)],[])).
% 1.50/1.29 tff(2259,plain,
% 1.50/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a249) | (~c1_1(a249)) | (~c0_1(a249)) | c0_1(a256) | c3_1(a256) | (~c2_1(a256)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a256) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a249)) | (~c0_1(a249)) | (~c2_1(a256)) | c3_1(a256)))),
% 1.50/1.29 inference(monotonicity,[status(thm)],[2258])).
% 1.50/1.29 tff(2260,plain,
% 1.50/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a249) | (~c1_1(a249)) | (~c0_1(a249)) | c0_1(a256) | c3_1(a256) | (~c2_1(a256)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a256) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a249)) | (~c0_1(a249)) | (~c2_1(a256)) | c3_1(a256))),
% 1.50/1.29 inference(transitivity,[status(thm)],[2259, 2257])).
% 1.50/1.29 tff(2261,plain,
% 1.50/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a249) | (~c1_1(a249)) | (~c0_1(a249)) | c0_1(a256) | c3_1(a256) | (~c2_1(a256)))),
% 1.50/1.29 inference(quant_inst,[status(thm)],[])).
% 1.50/1.29 tff(2262,plain,
% 1.50/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a256) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a249)) | (~c0_1(a249)) | (~c2_1(a256)) | c3_1(a256)),
% 1.50/1.29 inference(modus_ponens,[status(thm)],[2261, 2260])).
% 1.50/1.29 tff(2263,plain,
% 1.50/1.29 ((~c1_1(a249)) | c3_1(a256)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2262, 128, 2248, 2247, 2246, 2216, 2008, 2046, 1986, 22])).
% 1.50/1.29 tff(2264,plain,
% 1.50/1.29 ($false),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2263, 2256, 2045])).
% 1.50/1.29 tff(2265,plain,((~c1_1(a249)) | (~c2_1(a256)) | c0_1(a256) | (~c1_1(a256))), inference(lemma,lemma(discharge,[]))).
% 1.50/1.29 tff(2266,plain,
% 1.50/1.29 (~c1_1(a249)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2265, 2044, 2033, 2027])).
% 1.50/1.29 tff(2267,plain,
% 1.50/1.29 (hskp20),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[2128, 2266, 1])).
% 1.50/1.29 tff(2268,plain,
% 1.50/1.29 (~c3_1(a239)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[1251, 2267])).
% 1.50/1.29 tff(2269,plain,
% 1.50/1.29 (~c0_1(a239)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[1257, 2267])).
% 1.50/1.29 tff(2270,plain,
% 1.50/1.29 (c2_1(a239)),
% 1.50/1.29 inference(unit_resolution,[status(thm)],[1579, 2267])).
% 1.50/1.29 tff(2271,assumption,(~c1_1(a239)), introduced(assumption)).
% 1.50/1.29 tff(2272,assumption,(~c1_1(a249)), introduced(assumption)).
% 1.50/1.29 tff(2273,plain,
% 1.50/1.29 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.50/1.29 inference(bind,[status(th)],[])).
% 1.50/1.29 tff(2274,plain,
% 1.50/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.50/1.29 inference(quant_intro,[status(thm)],[2273])).
% 1.50/1.29 tff(2275,plain,
% 1.50/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.50/1.29 inference(rewrite,[status(thm)],[])).
% 1.50/1.29 tff(2276,plain,
% 1.50/1.29 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.50/1.29 inference(bind,[status(th)],[])).
% 1.50/1.29 tff(2277,plain,
% 1.50/1.29 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.50/1.29 inference(quant_intro,[status(thm)],[2276])).
% 1.50/1.29 tff(2278,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 1.50/1.29 tff(2279,plain,
% 1.50/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.50/1.29 inference(modus_ponens,[status(thm)],[2278, 2277])).
% 1.50/1.29 tff(2280,plain,
% 1.50/1.29 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.50/1.30 inference(modus_ponens,[status(thm)],[2279, 2275])).
% 1.50/1.30 tff(2281,plain,(
% 1.50/1.30 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.50/1.30 inference(skolemize,[status(sab)],[2280])).
% 1.50/1.30 tff(2282,plain,
% 1.50/1.30 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.50/1.30 inference(modus_ponens,[status(thm)],[2281, 2274])).
% 1.50/1.30 tff(2283,assumption,(~c3_1(a239)), introduced(assumption)).
% 1.50/1.30 tff(2284,assumption,(~c0_1(a239)), introduced(assumption)).
% 1.50/1.30 tff(2285,plain,
% 1.50/1.30 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c2_1(a249) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | c1_1(a239) | c1_1(a249) | (~c0_1(a249)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c2_1(a249) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | c1_1(a239) | c1_1(a249) | (~c0_1(a249)))),
% 1.50/1.30 inference(rewrite,[status(thm)],[])).
% 1.50/1.30 tff(2286,plain,
% 1.50/1.30 ((hskp3 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c3_1(a239) | c1_1(a239) | c0_1(a239)) <=> (hskp3 | c2_1(a249) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | c1_1(a239) | c1_1(a249) | (~c0_1(a249)))),
% 1.50/1.30 inference(rewrite,[status(thm)],[])).
% 1.50/1.30 tff(2287,plain,
% 1.50/1.30 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c3_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c2_1(a249) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | c1_1(a239) | c1_1(a249) | (~c0_1(a249))))),
% 1.50/1.30 inference(monotonicity,[status(thm)],[2286])).
% 1.50/1.30 tff(2288,plain,
% 1.50/1.30 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c3_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c2_1(a249) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | c1_1(a239) | c1_1(a249) | (~c0_1(a249)))),
% 1.50/1.30 inference(transitivity,[status(thm)],[2287, 2285])).
% 1.50/1.30 tff(2289,plain,
% 1.50/1.30 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c3_1(a239) | c1_1(a239) | c0_1(a239))),
% 1.50/1.30 inference(quant_inst,[status(thm)],[])).
% 1.50/1.30 tff(2290,plain,
% 1.50/1.30 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c2_1(a249) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | c1_1(a239) | c1_1(a249) | (~c0_1(a249))),
% 1.50/1.30 inference(modus_ponens,[status(thm)],[2289, 2288])).
% 1.50/1.30 tff(2291,plain,
% 1.50/1.30 (hskp3 | c1_1(a239)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2290, 128, 2008, 1986, 2284, 2283, 2282, 2272])).
% 1.50/1.30 tff(2292,plain,
% 1.50/1.30 (hskp3),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2291, 2271])).
% 1.50/1.30 tff(2293,plain,
% 1.50/1.30 (~c3_1(a203)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[619, 2292])).
% 1.50/1.30 tff(2294,plain,
% 1.50/1.30 (~c0_1(a203)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[625, 2292])).
% 1.50/1.30 tff(2295,plain,
% 1.50/1.30 (c1_1(a203)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[636, 2292])).
% 1.50/1.30 tff(2296,assumption,(c2_1(a239)), introduced(assumption)).
% 1.50/1.30 tff(2297,plain,
% 1.50/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a249) | c0_1(a239) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a249)) | (~c0_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a249) | c0_1(a239) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.30 inference(rewrite,[status(thm)],[])).
% 1.50/1.30 tff(2298,plain,
% 1.50/1.30 (((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)) | c1_1(a239) | c0_1(a239) | (~c2_1(a239))) <=> (c2_1(a249) | c0_1(a239) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.30 inference(rewrite,[status(thm)],[])).
% 1.50/1.30 tff(2299,plain,
% 1.50/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)) | c1_1(a239) | c0_1(a239) | (~c2_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a249) | c0_1(a239) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a249)) | (~c0_1(a249))))),
% 1.50/1.30 inference(monotonicity,[status(thm)],[2298])).
% 1.50/1.30 tff(2300,plain,
% 1.50/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)) | c1_1(a239) | c0_1(a239) | (~c2_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a249) | c0_1(a239) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.30 inference(transitivity,[status(thm)],[2299, 2297])).
% 1.50/1.30 tff(2301,plain,
% 1.50/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)) | c1_1(a239) | c0_1(a239) | (~c2_1(a239)))),
% 1.50/1.30 inference(quant_inst,[status(thm)],[])).
% 1.50/1.30 tff(2302,plain,
% 1.50/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a249) | c0_1(a239) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a203)) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a249)) | (~c0_1(a249))),
% 1.50/1.30 inference(modus_ponens,[status(thm)],[2301, 2300])).
% 1.50/1.30 tff(2303,plain,
% 1.50/1.30 ($false),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2302, 128, 2008, 1997, 2296, 2295, 1986, 2284, 2294, 2293, 593, 2271])).
% 1.50/1.30 tff(2304,plain,(c1_1(a239) | (~c2_1(a239)) | c0_1(a239) | c3_1(a239) | c1_1(a249)), inference(lemma,lemma(discharge,[]))).
% 1.50/1.30 tff(2305,plain,
% 1.50/1.30 (c1_1(a239)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2304, 2270, 2269, 2268, 2266])).
% 1.50/1.30 tff(2306,assumption,(hskp4), introduced(assumption)).
% 1.50/1.30 tff(2307,plain,
% 1.50/1.30 (~c2_1(a204)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[386, 2306])).
% 1.50/1.30 tff(2308,plain,
% 1.50/1.30 (~c0_1(a204)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[392, 2306])).
% 1.50/1.30 tff(2309,plain,
% 1.50/1.30 (c1_1(a204)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[414, 2306])).
% 1.50/1.30 tff(2310,plain,
% 1.50/1.30 ($false),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[1978, 128, 2248, 2247, 2246, 647, 646, 645, 80, 1597])).
% 1.50/1.30 tff(2311,plain,((~c3_1(a204)) | (~c1_1(a204)) | c0_1(a204) | c2_1(a204)), inference(lemma,lemma(discharge,[]))).
% 1.50/1.30 tff(2312,plain,
% 1.50/1.30 (~c3_1(a204)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2311, 2309, 2308, 2307])).
% 1.50/1.30 tff(2313,plain,
% 1.50/1.30 (hskp10),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[1808, 128, 2248, 2247, 2246, 2309, 2308, 1275, 2312])).
% 1.50/1.30 tff(2314,plain,
% 1.50/1.30 (~c3_1(a214)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[1300, 2313])).
% 1.50/1.30 tff(2315,plain,
% 1.50/1.30 (~c2_1(a214)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[1306, 2313])).
% 1.50/1.30 tff(2316,plain,
% 1.50/1.30 (~c0_1(a214)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[1817, 128, 2248, 2247, 2246, 2309, 2315, 2314, 2308, 2307, 1412])).
% 1.50/1.30 tff(2317,plain,
% 1.50/1.30 (c1_1(a214)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[1294, 2313])).
% 1.50/1.30 tff(2318,plain,
% 1.50/1.30 (~c3_1(a204)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2311, 647, 646, 645])).
% 1.50/1.30 tff(2319,plain,
% 1.50/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a256) | c0_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)) | (~c2_1(a256)) | (~c1_1(a256)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a256) | c0_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.30 inference(rewrite,[status(thm)],[])).
% 1.50/1.30 tff(2320,plain,
% 1.50/1.30 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a204) | c3_1(a204) | (~c1_1(a204))) <=> (c0_1(a256) | c0_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.30 inference(rewrite,[status(thm)],[])).
% 1.50/1.30 tff(2321,plain,
% 1.50/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a204) | c3_1(a204) | (~c1_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a256) | c0_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)) | (~c2_1(a256)) | (~c1_1(a256))))),
% 1.50/1.30 inference(monotonicity,[status(thm)],[2320])).
% 1.50/1.30 tff(2322,plain,
% 1.50/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a204) | c3_1(a204) | (~c1_1(a204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a256) | c0_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.30 inference(transitivity,[status(thm)],[2321, 2319])).
% 1.50/1.30 tff(2323,plain,
% 1.50/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a204) | c3_1(a204) | (~c1_1(a204)))),
% 1.50/1.30 inference(quant_inst,[status(thm)],[])).
% 1.50/1.30 tff(2324,plain,
% 1.50/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a256) | c0_1(a204) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)) | (~c2_1(a256)) | (~c1_1(a256))),
% 1.50/1.30 inference(modus_ponens,[status(thm)],[2323, 2322])).
% 1.50/1.30 tff(2325,plain,
% 1.50/1.30 ((~c3_1(a198)) | c3_1(a204)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2324, 128, 2248, 2246, 2047, 2216, 647, 2046, 646, 1913])).
% 1.50/1.30 tff(2326,plain,
% 1.50/1.30 (~c3_1(a198)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2325, 837])).
% 1.50/1.30 tff(2327,plain,
% 1.50/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a239) | c3_1(a239) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c3_1(a204) | (~c2_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a239) | c3_1(a239) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c3_1(a204) | (~c2_1(a239)))),
% 1.50/1.30 inference(rewrite,[status(thm)],[])).
% 1.50/1.30 tff(2328,plain,
% 1.50/1.30 (((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a239) | c0_1(a239) | (~c2_1(a239)) | c2_1(a204) | c0_1(a204) | c3_1(a204)) <=> (c0_1(a239) | c3_1(a239) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c3_1(a204) | (~c2_1(a239)))),
% 1.50/1.30 inference(rewrite,[status(thm)],[])).
% 1.50/1.30 tff(2329,plain,
% 1.50/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a239) | c0_1(a239) | (~c2_1(a239)) | c2_1(a204) | c0_1(a204) | c3_1(a204))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a239) | c3_1(a239) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c3_1(a204) | (~c2_1(a239))))),
% 1.50/1.30 inference(monotonicity,[status(thm)],[2328])).
% 1.50/1.30 tff(2330,plain,
% 1.50/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a239) | c0_1(a239) | (~c2_1(a239)) | c2_1(a204) | c0_1(a204) | c3_1(a204))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a239) | c3_1(a239) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c3_1(a204) | (~c2_1(a239)))),
% 1.50/1.30 inference(transitivity,[status(thm)],[2329, 2327])).
% 1.50/1.30 tff(2331,plain,
% 1.50/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a239) | c0_1(a239) | (~c2_1(a239)) | c2_1(a204) | c0_1(a204) | c3_1(a204))),
% 1.50/1.30 inference(quant_inst,[status(thm)],[])).
% 1.50/1.30 tff(2332,plain,
% 1.50/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a239) | c3_1(a239) | c0_1(a204) | c2_1(a204) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c3_1(a204) | (~c2_1(a239))),
% 1.50/1.30 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 1.50/1.30 tff(2333,plain,
% 1.50/1.30 ($false),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2332, 128, 2248, 2247, 2296, 2284, 2283, 646, 645, 665, 837, 2326])).
% 1.50/1.30 tff(2334,plain,(c3_1(a204) | (~c2_1(a239)) | c0_1(a239) | c3_1(a239) | c0_1(a204) | c2_1(a204) | (~c1_1(a256)) | (~c2_1(a256)) | (~c1_1(a204)) | c0_1(a256)), inference(lemma,lemma(discharge,[]))).
% 1.50/1.30 tff(2335,plain,
% 1.50/1.30 ($false),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2334, 2269, 2270, 2318, 2268, 646, 645, 2027, 2044, 647, 2033])).
% 1.50/1.30 tff(2336,plain,(hskp19 | c0_1(a204) | c2_1(a204) | (~c1_1(a204))), inference(lemma,lemma(discharge,[]))).
% 1.50/1.30 tff(2337,plain,
% 1.50/1.30 (hskp19),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2336, 2308, 2307, 2309])).
% 1.50/1.30 tff(2338,plain,
% 1.50/1.30 (c3_1(a198)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[1401, 2337, 2246, 2317, 2315, 2314, 2247])).
% 1.50/1.30 tff(2339,plain,
% 1.50/1.30 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a204) | (~ndr1_0) | (~c1_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a204) | (~ndr1_0) | (~c1_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)))),
% 1.50/1.30 inference(rewrite,[status(thm)],[])).
% 1.50/1.30 tff(2340,plain,
% 1.50/1.30 ((hskp12 | (~ndr1_0) | (~c2_1(a198)) | (~c3_1(a198)) | (~c1_1(a198)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204))) <=> (hskp12 | c0_1(a204) | (~ndr1_0) | (~c1_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)))),
% 1.50/1.30 inference(rewrite,[status(thm)],[])).
% 1.50/1.30 tff(2341,plain,
% 1.50/1.30 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a198)) | (~c3_1(a198)) | (~c1_1(a198)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a204) | (~ndr1_0) | (~c1_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204))))),
% 1.50/1.30 inference(monotonicity,[status(thm)],[2340])).
% 1.50/1.30 tff(2342,plain,
% 1.50/1.30 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a198)) | (~c3_1(a198)) | (~c1_1(a198)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a204) | (~ndr1_0) | (~c1_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204)))),
% 1.50/1.30 inference(transitivity,[status(thm)],[2341, 2339])).
% 1.50/1.30 tff(2343,plain,
% 1.50/1.30 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a198)) | (~c3_1(a198)) | (~c1_1(a198)) | c3_1(a204) | c0_1(a204) | (~c1_1(a204)))),
% 1.50/1.30 inference(quant_inst,[status(thm)],[])).
% 1.50/1.30 tff(2344,plain,
% 1.50/1.30 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a204) | (~ndr1_0) | (~c1_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | c3_1(a204) | (~c1_1(a204))),
% 1.50/1.30 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 1.50/1.30 tff(2345,plain,
% 1.50/1.30 (hskp12 | (~c3_1(a198))),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2344, 128, 2247, 2246, 2309, 2308, 949, 2312])).
% 1.50/1.30 tff(2346,plain,
% 1.50/1.30 (hskp12),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2345, 2338])).
% 1.50/1.30 tff(2347,plain,
% 1.50/1.30 (~c3_1(a217)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[974, 2346])).
% 1.50/1.30 tff(2348,plain,
% 1.50/1.30 (~c2_1(a217)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[980, 2346])).
% 1.50/1.30 tff(2349,plain,
% 1.50/1.30 (c0_1(a217)),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[998, 2346])).
% 1.50/1.30 tff(2350,plain,
% 1.50/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a217) | c3_1(a217) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a217) | c3_1(a217) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a217)))),
% 1.50/1.30 inference(rewrite,[status(thm)],[])).
% 1.50/1.30 tff(2351,plain,
% 1.50/1.30 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a217) | c2_1(a217) | (~c0_1(a217)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214))) <=> (c2_1(a217) | c3_1(a217) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a217)))),
% 1.50/1.30 inference(rewrite,[status(thm)],[])).
% 1.50/1.30 tff(2352,plain,
% 1.50/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a217) | c2_1(a217) | (~c0_1(a217)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a217) | c3_1(a217) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a217))))),
% 1.50/1.30 inference(monotonicity,[status(thm)],[2351])).
% 1.50/1.30 tff(2353,plain,
% 1.50/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a217) | c2_1(a217) | (~c0_1(a217)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a217) | c3_1(a217) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a217)))),
% 1.50/1.30 inference(transitivity,[status(thm)],[2352, 2350])).
% 1.50/1.30 tff(2354,plain,
% 1.50/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a217) | c2_1(a217) | (~c0_1(a217)) | c2_1(a214) | c0_1(a214) | (~c1_1(a214)))),
% 1.50/1.30 inference(quant_inst,[status(thm)],[])).
% 1.50/1.30 tff(2355,plain,
% 1.50/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a217) | c3_1(a217) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | c0_1(a214) | (~c1_1(a214)) | (~c0_1(a217))),
% 1.50/1.30 inference(modus_ponens,[status(thm)],[2354, 2353])).
% 1.50/1.30 tff(2356,plain,
% 1.50/1.30 ($false),
% 1.50/1.30 inference(unit_resolution,[status(thm)],[2355, 128, 2248, 2247, 2246, 2349, 2317, 2348, 2347, 2315, 1412, 2316])).
% 1.50/1.30 tff(2357,plain,(~hskp4), inference(lemma,lemma(discharge,[]))).
% 1.50/1.30 tff(2358,plain,
% 1.50/1.30 (^[U: $i] : refl((hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.50/1.30 inference(bind,[status(th)],[])).
% 1.50/1.30 tff(2359,plain,
% 1.50/1.30 (![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.50/1.30 inference(quant_intro,[status(thm)],[2358])).
% 1.50/1.30 tff(2360,plain,
% 1.50/1.30 (![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.50/1.30 inference(rewrite,[status(thm)],[])).
% 1.50/1.30 tff(2361,plain,
% 1.50/1.30 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp15) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp15))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp15) <=> (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.50/1.30 inference(bind,[status(th)],[])).
% 1.50/1.30 tff(2362,plain,
% 1.50/1.30 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp15) <=> ![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.50/1.30 inference(quant_intro,[status(thm)],[2361])).
% 1.50/1.30 tff(2363,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.50/1.30 tff(2364,plain,
% 1.50/1.30 (![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.50/1.30 inference(modus_ponens,[status(thm)],[2363, 2362])).
% 1.50/1.30 tff(2365,plain,
% 1.50/1.30 (![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.50/1.30 inference(modus_ponens,[status(thm)],[2364, 2360])).
% 1.50/1.30 tff(2366,plain,(
% 1.50/1.30 ![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.50/1.30 inference(skolemize,[status(sab)],[2365])).
% 1.50/1.30 tff(2367,plain,
% 1.50/1.30 (![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2366, 2359])).
% 1.50/1.31 tff(2368,plain,
% 1.50/1.31 (c1_1(a239)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[1264, 128, 1210, 23, 2269, 2268, 1209])).
% 1.50/1.31 tff(2369,plain,
% 1.50/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a256) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a239)) | (~c2_1(a256)) | (~c1_1(a256)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a256) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a239)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2370,plain,
% 1.50/1.31 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a239) | c3_1(a239) | (~c1_1(a239))) <=> (c0_1(a256) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a239)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2371,plain,
% 1.50/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a239) | c3_1(a239) | (~c1_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a256) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a239)) | (~c2_1(a256)) | (~c1_1(a256))))),
% 1.50/1.31 inference(monotonicity,[status(thm)],[2370])).
% 1.50/1.31 tff(2372,plain,
% 1.50/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a239) | c3_1(a239) | (~c1_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a256) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a239)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.31 inference(transitivity,[status(thm)],[2371, 2369])).
% 1.50/1.31 tff(2373,plain,
% 1.50/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c3_1(a198)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a239) | c3_1(a239) | (~c1_1(a239)))),
% 1.50/1.31 inference(quant_inst,[status(thm)],[])).
% 1.50/1.31 tff(2374,plain,
% 1.50/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a256) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c0_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a239)) | (~c2_1(a256)) | (~c1_1(a256))),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2373, 2372])).
% 1.50/1.31 tff(2375,plain,
% 1.50/1.31 ((~c3_1(a198)) | (~c1_1(a239))),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2374, 128, 2248, 2246, 2027, 2044, 2033, 2269, 2268, 1913])).
% 1.50/1.31 tff(2376,plain,
% 1.50/1.31 (~c3_1(a198)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2375, 2368])).
% 1.50/1.31 tff(2377,plain,
% 1.50/1.31 (hskp10),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[1281, 128, 2248, 2247, 2246, 2269, 2268, 1275, 2368])).
% 1.50/1.31 tff(2378,plain,
% 1.50/1.31 (~c3_1(a214)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[1300, 2377])).
% 1.50/1.31 tff(2379,plain,
% 1.50/1.31 (~c2_1(a214)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[1306, 2377])).
% 1.50/1.31 tff(2380,plain,
% 1.50/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a239) | c3_1(a239) | c2_1(a214) | c3_1(a214) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c0_1(a214) | (~c2_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a239) | c3_1(a239) | c2_1(a214) | c3_1(a214) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c0_1(a214) | (~c2_1(a239)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2381,plain,
% 1.50/1.31 (((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a239) | c0_1(a239) | (~c2_1(a239)) | c2_1(a214) | c0_1(a214) | c3_1(a214)) <=> (c0_1(a239) | c3_1(a239) | c2_1(a214) | c3_1(a214) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c0_1(a214) | (~c2_1(a239)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2382,plain,
% 1.50/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a239) | c0_1(a239) | (~c2_1(a239)) | c2_1(a214) | c0_1(a214) | c3_1(a214))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a239) | c3_1(a239) | c2_1(a214) | c3_1(a214) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c0_1(a214) | (~c2_1(a239))))),
% 1.50/1.31 inference(monotonicity,[status(thm)],[2381])).
% 1.50/1.31 tff(2383,plain,
% 1.50/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a239) | c0_1(a239) | (~c2_1(a239)) | c2_1(a214) | c0_1(a214) | c3_1(a214))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a239) | c3_1(a239) | c2_1(a214) | c3_1(a214) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c0_1(a214) | (~c2_1(a239)))),
% 1.50/1.31 inference(transitivity,[status(thm)],[2382, 2380])).
% 1.50/1.31 tff(2384,plain,
% 1.50/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a198) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a239) | c0_1(a239) | (~c2_1(a239)) | c2_1(a214) | c0_1(a214) | c3_1(a214))),
% 1.50/1.31 inference(quant_inst,[status(thm)],[])).
% 1.50/1.31 tff(2385,plain,
% 1.50/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a239) | c3_1(a239) | c2_1(a214) | c3_1(a214) | (~ndr1_0) | (~c0_1(a198)) | c3_1(a198) | (~c1_1(a198)) | c0_1(a214) | (~c2_1(a239))),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 1.50/1.31 tff(2386,plain,
% 1.50/1.31 (c0_1(a214)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2385, 128, 2248, 2247, 2270, 2269, 2268, 2379, 2378, 665, 2376])).
% 1.50/1.31 tff(2387,plain,
% 1.50/1.31 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp21 | c2_1(a249) | c3_1(a239) | (~ndr1_0) | (~c1_1(a239)) | (~c2_1(a239)) | c1_1(a249) | (~c3_1(a249)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | hskp21 | c2_1(a249) | c3_1(a239) | (~ndr1_0) | (~c1_1(a239)) | (~c2_1(a239)) | c1_1(a249) | (~c3_1(a249)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2388,plain,
% 1.50/1.31 ((hskp21 | (~ndr1_0) | c3_1(a239) | (~c2_1(a239)) | (~c1_1(a239)) | c1_1(a249) | (~c3_1(a249)) | c2_1(a249)) <=> (hskp21 | c2_1(a249) | c3_1(a239) | (~ndr1_0) | (~c1_1(a239)) | (~c2_1(a239)) | c1_1(a249) | (~c3_1(a249)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2389,plain,
% 1.50/1.31 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a239) | (~c2_1(a239)) | (~c1_1(a239)) | c1_1(a249) | (~c3_1(a249)) | c2_1(a249))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp21 | c2_1(a249) | c3_1(a239) | (~ndr1_0) | (~c1_1(a239)) | (~c2_1(a239)) | c1_1(a249) | (~c3_1(a249))))),
% 1.50/1.31 inference(monotonicity,[status(thm)],[2388])).
% 1.50/1.31 tff(2390,plain,
% 1.50/1.31 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a239) | (~c2_1(a239)) | (~c1_1(a239)) | c1_1(a249) | (~c3_1(a249)) | c2_1(a249))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | hskp21 | c2_1(a249) | c3_1(a239) | (~ndr1_0) | (~c1_1(a239)) | (~c2_1(a239)) | c1_1(a249) | (~c3_1(a249)))),
% 1.50/1.31 inference(transitivity,[status(thm)],[2389, 2387])).
% 1.50/1.31 tff(2391,plain,
% 1.50/1.31 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a239) | (~c2_1(a239)) | (~c1_1(a239)) | c1_1(a249) | (~c3_1(a249)) | c2_1(a249))),
% 1.50/1.31 inference(quant_inst,[status(thm)],[])).
% 1.50/1.31 tff(2392,plain,
% 1.50/1.31 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V))) | hskp21 | c2_1(a249) | c3_1(a239) | (~ndr1_0) | (~c1_1(a239)) | (~c2_1(a239)) | c1_1(a249) | (~c3_1(a249))),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2391, 2390])).
% 1.50/1.31 tff(2393,plain,
% 1.50/1.31 (hskp21 | (~c1_1(a239))),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2392, 128, 1997, 2270, 1986, 2268, 1877, 2266])).
% 1.50/1.31 tff(2394,plain,
% 1.50/1.31 (hskp21),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2393, 2368])).
% 1.50/1.31 tff(2395,plain,
% 1.50/1.31 (~c3_1(a241)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[302, 2394])).
% 1.50/1.31 tff(2396,plain,
% 1.50/1.31 (~c1_1(a241)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[308, 2394])).
% 1.50/1.31 tff(2397,plain,
% 1.50/1.31 (c0_1(a241)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[330, 2394])).
% 1.50/1.31 tff(2398,plain,
% 1.50/1.31 (~c3_1(a256)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2146, 128, 1210, 2027, 2397, 2033, 2396, 2395, 2120])).
% 1.50/1.31 tff(2399,plain,
% 1.50/1.31 (c1_1(a214)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[1294, 2377])).
% 1.50/1.31 tff(2400,plain,
% 1.50/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a256) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a214)) | (~c1_1(a214)) | (~c2_1(a256)) | c3_1(a256))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a256) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a214)) | (~c1_1(a214)) | (~c2_1(a256)) | c3_1(a256))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2401,plain,
% 1.50/1.31 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a214) | (~c1_1(a214)) | (~c0_1(a214)) | c0_1(a256) | c3_1(a256) | (~c2_1(a256))) <=> (c0_1(a256) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a214)) | (~c1_1(a214)) | (~c2_1(a256)) | c3_1(a256))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2402,plain,
% 1.50/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a214) | (~c1_1(a214)) | (~c0_1(a214)) | c0_1(a256) | c3_1(a256) | (~c2_1(a256)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a256) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a214)) | (~c1_1(a214)) | (~c2_1(a256)) | c3_1(a256)))),
% 1.50/1.31 inference(monotonicity,[status(thm)],[2401])).
% 1.50/1.31 tff(2403,plain,
% 1.50/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a214) | (~c1_1(a214)) | (~c0_1(a214)) | c0_1(a256) | c3_1(a256) | (~c2_1(a256)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a256) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a214)) | (~c1_1(a214)) | (~c2_1(a256)) | c3_1(a256))),
% 1.50/1.31 inference(transitivity,[status(thm)],[2402, 2400])).
% 1.50/1.31 tff(2404,plain,
% 1.50/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a214) | (~c1_1(a214)) | (~c0_1(a214)) | c0_1(a256) | c3_1(a256) | (~c2_1(a256)))),
% 1.50/1.31 inference(quant_inst,[status(thm)],[])).
% 1.50/1.31 tff(2405,plain,
% 1.50/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a256) | c2_1(a214) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a214)) | (~c1_1(a214)) | (~c2_1(a256)) | c3_1(a256)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2404, 2403])).
% 1.50/1.31 tff(2406,plain,
% 1.50/1.31 ($false),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2405, 128, 2248, 2247, 2246, 2044, 2399, 2033, 2379, 22, 2398, 2386])).
% 1.50/1.31 tff(2407,plain,(hskp19 | hskp5 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.50/1.31 tff(2408,plain,
% 1.50/1.31 (hskp19),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2407, 23, 1210])).
% 1.50/1.31 tff(2409,plain,
% 1.50/1.31 (~c2_1(a238)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[1369, 2408])).
% 1.50/1.31 tff(2410,plain,
% 1.50/1.31 (c3_1(a238)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[1381, 2408])).
% 1.50/1.31 tff(2411,plain,
% 1.50/1.31 (c1_1(a238)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[1392, 2408])).
% 1.50/1.31 tff(2412,plain,
% 1.50/1.31 (((~![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp6 | hskp15 | c2_1(a238) | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp6 | hskp15 | c2_1(a238) | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2413,plain,
% 1.50/1.31 ((hskp6 | hskp15 | (~ndr1_0) | c2_1(a238) | (~c3_1(a238)) | (~c1_1(a238))) <=> (hskp6 | hskp15 | c2_1(a238) | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2414,plain,
% 1.50/1.31 (((~![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp6 | hskp15 | (~ndr1_0) | c2_1(a238) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp6 | hskp15 | c2_1(a238) | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238))))),
% 1.50/1.31 inference(monotonicity,[status(thm)],[2413])).
% 1.50/1.31 tff(2415,plain,
% 1.50/1.31 (((~![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp6 | hskp15 | (~ndr1_0) | c2_1(a238) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp6 | hskp15 | c2_1(a238) | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.50/1.31 inference(transitivity,[status(thm)],[2414, 2412])).
% 1.50/1.31 tff(2416,plain,
% 1.50/1.31 ((~![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp6 | hskp15 | (~ndr1_0) | c2_1(a238) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.50/1.31 inference(quant_inst,[status(thm)],[])).
% 1.50/1.31 tff(2417,plain,
% 1.50/1.31 ((~![U: $i] : (hskp6 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp6 | hskp15 | c2_1(a238) | (~ndr1_0) | (~c3_1(a238)) | (~c1_1(a238))),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2416, 2415])).
% 1.50/1.31 tff(2418,plain,
% 1.50/1.31 (hskp6 | hskp15),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2417, 128, 2411, 2410, 2409, 2367])).
% 1.50/1.31 tff(2419,plain,
% 1.50/1.31 (hskp15),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2418, 1129])).
% 1.50/1.31 tff(2420,plain,
% 1.50/1.31 (((~hskp15) | (~c1_1(a228))) <=> ((~hskp15) | (~c1_1(a228)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2421,plain,
% 1.50/1.31 (((~c1_1(a228)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a228)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2422,axiom,((~c1_1(a228)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.50/1.31 tff(2423,plain,
% 1.50/1.31 ((~hskp15) | (~c1_1(a228))),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 1.50/1.31 tff(2424,plain,
% 1.50/1.31 ((~hskp15) | (~c1_1(a228))),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2423, 2420])).
% 1.50/1.31 tff(2425,plain,
% 1.50/1.31 (~c1_1(a228)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2424, 2419])).
% 1.50/1.31 tff(2426,plain,
% 1.50/1.31 (((~hskp15) | c2_1(a228)) <=> ((~hskp15) | c2_1(a228))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2427,axiom,((~hskp15) | c2_1(a228)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.50/1.31 tff(2428,plain,
% 1.50/1.31 ((~hskp15) | c2_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2427, 2426])).
% 1.50/1.31 tff(2429,plain,
% 1.50/1.31 ((~hskp15) | c2_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2428, 2426])).
% 1.50/1.31 tff(2430,plain,
% 1.50/1.31 ((~hskp15) | c2_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2429, 2426])).
% 1.50/1.31 tff(2431,plain,
% 1.50/1.31 ((~hskp15) | c2_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2430, 2426])).
% 1.50/1.31 tff(2432,plain,
% 1.50/1.31 ((~hskp15) | c2_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2431, 2426])).
% 1.50/1.31 tff(2433,plain,
% 1.50/1.31 ((~hskp15) | c2_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2432, 2426])).
% 1.50/1.31 tff(2434,plain,
% 1.50/1.31 ((~hskp15) | c2_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2433, 2426])).
% 1.50/1.31 tff(2435,plain,
% 1.50/1.31 ((~hskp15) | c2_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2434, 2426])).
% 1.50/1.31 tff(2436,plain,
% 1.50/1.31 (c2_1(a228)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2435, 2419])).
% 1.50/1.31 tff(2437,plain,
% 1.50/1.31 (((~hskp15) | c0_1(a228)) <=> ((~hskp15) | c0_1(a228))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2438,axiom,((~hskp15) | c0_1(a228)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.50/1.31 tff(2439,plain,
% 1.50/1.31 ((~hskp15) | c0_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2438, 2437])).
% 1.50/1.31 tff(2440,plain,
% 1.50/1.31 ((~hskp15) | c0_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2439, 2437])).
% 1.50/1.31 tff(2441,plain,
% 1.50/1.31 ((~hskp15) | c0_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2440, 2437])).
% 1.50/1.31 tff(2442,plain,
% 1.50/1.31 ((~hskp15) | c0_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2441, 2437])).
% 1.50/1.31 tff(2443,plain,
% 1.50/1.31 ((~hskp15) | c0_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2442, 2437])).
% 1.50/1.31 tff(2444,plain,
% 1.50/1.31 ((~hskp15) | c0_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2443, 2437])).
% 1.50/1.31 tff(2445,plain,
% 1.50/1.31 ((~hskp15) | c0_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2444, 2437])).
% 1.50/1.31 tff(2446,plain,
% 1.50/1.31 ((~hskp15) | c0_1(a228)),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2445, 2437])).
% 1.50/1.31 tff(2447,plain,
% 1.50/1.31 (c0_1(a228)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2446, 2419])).
% 1.50/1.31 tff(2448,plain,
% 1.50/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a228) | c0_1(a213) | c1_1(a213) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c2_1(a228)) | (~c0_1(a228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a228) | c0_1(a213) | c1_1(a213) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c2_1(a228)) | (~c0_1(a228)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2449,plain,
% 1.50/1.31 (((~ndr1_0) | c1_1(a228) | (~c2_1(a228)) | (~c0_1(a228)) | c1_1(a213) | (~c3_1(a213)) | c2_1(a213) | c2_1(a213) | c0_1(a213) | (~c3_1(a213))) <=> (c1_1(a228) | c0_1(a213) | c1_1(a213) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c2_1(a228)) | (~c0_1(a228)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2450,plain,
% 1.50/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a228) | (~c2_1(a228)) | (~c0_1(a228)) | c1_1(a213) | (~c3_1(a213)) | c2_1(a213) | c2_1(a213) | c0_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a228) | c0_1(a213) | c1_1(a213) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c2_1(a228)) | (~c0_1(a228))))),
% 1.50/1.31 inference(monotonicity,[status(thm)],[2449])).
% 1.50/1.31 tff(2451,plain,
% 1.50/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a228) | (~c2_1(a228)) | (~c0_1(a228)) | c1_1(a213) | (~c3_1(a213)) | c2_1(a213) | c2_1(a213) | c0_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a228) | c0_1(a213) | c1_1(a213) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c2_1(a228)) | (~c0_1(a228)))),
% 1.50/1.31 inference(transitivity,[status(thm)],[2450, 2448])).
% 1.50/1.31 tff(2452,plain,
% 1.50/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a228) | (~c2_1(a228)) | (~c0_1(a228)) | c1_1(a213) | (~c3_1(a213)) | c2_1(a213) | c2_1(a213) | c0_1(a213) | (~c3_1(a213)))),
% 1.50/1.31 inference(quant_inst,[status(thm)],[])).
% 1.50/1.31 tff(2453,plain,
% 1.50/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a228) | c0_1(a213) | c1_1(a213) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c2_1(a228)) | (~c0_1(a228))),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2452, 2451])).
% 1.50/1.31 tff(2454,plain,
% 1.50/1.31 (~c3_1(a213)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2453, 128, 2447, 2436, 2425, 1157, 1151, 1150, 886])).
% 1.50/1.31 tff(2455,plain,
% 1.50/1.31 ($false),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[1216, 128, 1210, 23, 1157, 1151, 1209, 2454])).
% 1.50/1.31 tff(2456,plain,(hskp6 | hskp5 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.50/1.31 tff(2457,plain,
% 1.50/1.31 (hskp6),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2456, 23, 1210])).
% 1.50/1.31 tff(2458,plain,
% 1.50/1.31 (~c2_1(a208)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[177, 2457])).
% 1.50/1.31 tff(2459,plain,
% 1.50/1.31 (c1_1(a208)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[221, 2457])).
% 1.50/1.31 tff(2460,plain,
% 1.50/1.31 (c0_1(a208)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[171, 2457])).
% 1.50/1.31 tff(2461,plain,
% 1.50/1.31 (((~![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(a238) | c0_1(a213) | c1_1(a213) | c2_1(a208) | (~ndr1_0) | (~c1_1(a208)) | (~c0_1(a208)) | (~c3_1(a213)) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![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(a238) | c0_1(a213) | c1_1(a213) | c2_1(a208) | (~ndr1_0) | (~c1_1(a208)) | (~c0_1(a208)) | (~c3_1(a213)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2462,plain,
% 1.50/1.31 (((~ndr1_0) | c2_1(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213))) <=> (c2_1(a238) | c0_1(a213) | c1_1(a213) | c2_1(a208) | (~ndr1_0) | (~c1_1(a208)) | (~c0_1(a208)) | (~c3_1(a213)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2463,plain,
% 1.50/1.31 (((~![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(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213)))) <=> ((~![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(a238) | c0_1(a213) | c1_1(a213) | c2_1(a208) | (~ndr1_0) | (~c1_1(a208)) | (~c0_1(a208)) | (~c3_1(a213)) | (~c3_1(a238)) | (~c1_1(a238))))),
% 1.50/1.31 inference(monotonicity,[status(thm)],[2462])).
% 1.50/1.31 tff(2464,plain,
% 1.50/1.31 (((~![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(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213)))) <=> ((~![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(a238) | c0_1(a213) | c1_1(a213) | c2_1(a208) | (~ndr1_0) | (~c1_1(a208)) | (~c0_1(a208)) | (~c3_1(a213)) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.50/1.31 inference(transitivity,[status(thm)],[2463, 2461])).
% 1.50/1.31 tff(2465,plain,
% 1.50/1.31 ((~![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(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a208) | (~c1_1(a208)) | (~c0_1(a208)) | c1_1(a213) | c0_1(a213) | (~c3_1(a213)))),
% 1.50/1.31 inference(quant_inst,[status(thm)],[])).
% 1.50/1.31 tff(2466,plain,
% 1.50/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a238) | c0_1(a213) | c1_1(a213) | c2_1(a208) | (~ndr1_0) | (~c1_1(a208)) | (~c0_1(a208)) | (~c3_1(a213)) | (~c3_1(a238)) | (~c1_1(a238))),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2465, 2464])).
% 1.50/1.31 tff(2467,plain,
% 1.50/1.31 (c0_1(a213) | (~c3_1(a213))),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2466, 128, 2411, 2410, 2460, 2459, 2409, 714, 2458, 682])).
% 1.50/1.31 tff(2468,plain,
% 1.50/1.31 (~c3_1(a213)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2467, 1317])).
% 1.50/1.31 tff(2469,plain,
% 1.50/1.31 (c0_1(a213) | c3_1(a213)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[1216, 128, 1210, 23, 714, 1209])).
% 1.50/1.31 tff(2470,plain,
% 1.50/1.31 ($false),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2469, 2468, 1317])).
% 1.50/1.31 tff(2471,plain,(c0_1(a213) | hskp5 | hskp4 | c1_1(a213)), inference(lemma,lemma(discharge,[]))).
% 1.50/1.31 tff(2472,plain,
% 1.50/1.31 ($false),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2471, 1924, 1929, 23, 1210])).
% 1.50/1.31 tff(2473,plain,((~hskp9) | hskp4 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.50/1.31 tff(2474,plain,
% 1.50/1.31 (~hskp9),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2473, 23, 1210])).
% 1.50/1.31 tff(2475,assumption,(~c2_1(a238)), introduced(assumption)).
% 1.50/1.31 tff(2476,plain,
% 1.50/1.31 (~c0_1(a238)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[1517, 1231, 1733])).
% 1.50/1.31 tff(2477,plain,
% 1.50/1.31 (((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp10 | (~ndr1_0) | (~c3_1(a249)) | (~c1_1(a249)) | (~c0_1(a249)))) <=> ((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp10 | (~ndr1_0) | (~c3_1(a249)) | (~c1_1(a249)) | (~c0_1(a249)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2478,plain,
% 1.50/1.31 ((hskp9 | hskp10 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249))) <=> (hskp9 | hskp10 | (~ndr1_0) | (~c3_1(a249)) | (~c1_1(a249)) | (~c0_1(a249)))),
% 1.50/1.31 inference(rewrite,[status(thm)],[])).
% 1.50/1.31 tff(2479,plain,
% 1.50/1.31 (((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))) <=> ((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp10 | (~ndr1_0) | (~c3_1(a249)) | (~c1_1(a249)) | (~c0_1(a249))))),
% 1.50/1.31 inference(monotonicity,[status(thm)],[2478])).
% 1.50/1.31 tff(2480,plain,
% 1.50/1.31 (((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))) <=> ((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp10 | (~ndr1_0) | (~c3_1(a249)) | (~c1_1(a249)) | (~c0_1(a249)))),
% 1.50/1.31 inference(transitivity,[status(thm)],[2479, 2477])).
% 1.50/1.31 tff(2481,plain,
% 1.50/1.31 ((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))),
% 1.50/1.31 inference(quant_inst,[status(thm)],[])).
% 1.50/1.31 tff(2482,plain,
% 1.50/1.31 ((~![U: $i] : (hskp9 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp10 | (~ndr1_0) | (~c3_1(a249)) | (~c1_1(a249)) | (~c0_1(a249))),
% 1.50/1.31 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 1.50/1.31 tff(2483,plain,
% 1.50/1.31 (hskp9 | hskp10 | (~c1_1(a249))),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2482, 128, 2008, 1997, 1508])).
% 1.50/1.31 tff(2484,plain,
% 1.50/1.31 (~c1_1(a249)),
% 1.50/1.31 inference(unit_resolution,[status(thm)],[2483, 1231, 1733])).
% 1.50/1.32 tff(2485,assumption,(~c0_1(a238)), introduced(assumption)).
% 1.50/1.32 tff(2486,plain,
% 1.50/1.32 (hskp21),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[1473, 128, 1510, 1509, 2475, 289])).
% 1.50/1.32 tff(2487,plain,
% 1.50/1.32 (~c3_1(a241)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[302, 2486])).
% 1.50/1.32 tff(2488,plain,
% 1.50/1.32 (c0_1(a241)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[330, 2486])).
% 1.50/1.32 tff(2489,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a241) | c2_1(a238) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a241)) | c2_1(a241) | (~c1_1(a238)) | c0_1(a238))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a241) | c2_1(a238) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a241)) | c2_1(a241) | (~c1_1(a238)) | c0_1(a238))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2490,plain,
% 1.50/1.32 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a241) | c2_1(a241) | (~c0_1(a241)) | c2_1(a238) | c0_1(a238) | (~c1_1(a238))) <=> (c3_1(a241) | c2_1(a238) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a241)) | c2_1(a241) | (~c1_1(a238)) | c0_1(a238))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2491,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a241) | c2_1(a241) | (~c0_1(a241)) | c2_1(a238) | c0_1(a238) | (~c1_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a241) | c2_1(a238) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a241)) | c2_1(a241) | (~c1_1(a238)) | c0_1(a238)))),
% 1.50/1.32 inference(monotonicity,[status(thm)],[2490])).
% 1.50/1.32 tff(2492,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a241) | c2_1(a241) | (~c0_1(a241)) | c2_1(a238) | c0_1(a238) | (~c1_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a241) | c2_1(a238) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a241)) | c2_1(a241) | (~c1_1(a238)) | c0_1(a238))),
% 1.50/1.32 inference(transitivity,[status(thm)],[2491, 2489])).
% 1.50/1.32 tff(2493,plain,
% 1.50/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a241) | c2_1(a241) | (~c0_1(a241)) | c2_1(a238) | c0_1(a238) | (~c1_1(a238)))),
% 1.50/1.32 inference(quant_inst,[status(thm)],[])).
% 1.50/1.32 tff(2494,plain,
% 1.50/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a241) | c2_1(a238) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c0_1(a241)) | c2_1(a241) | (~c1_1(a238)) | c0_1(a238)),
% 1.50/1.32 inference(modus_ponens,[status(thm)],[2493, 2492])).
% 1.50/1.32 tff(2495,plain,
% 1.50/1.32 (c2_1(a241) | c0_1(a238)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2494, 128, 2248, 2247, 2246, 2488, 1510, 2487, 2475, 1412])).
% 1.50/1.32 tff(2496,plain,
% 1.50/1.32 (c2_1(a241)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2495, 2485])).
% 1.50/1.32 tff(2497,plain,
% 1.50/1.32 (~c1_1(a241)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[308, 2486])).
% 1.50/1.32 tff(2498,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a249) | c1_1(a241) | c2_1(a238) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a238)) | c0_1(a238) | c1_1(a249) | (~c3_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a249) | c1_1(a241) | c2_1(a238) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a238)) | c0_1(a238) | c1_1(a249) | (~c3_1(a249)))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2499,plain,
% 1.50/1.32 (((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a249) | (~c3_1(a249)) | c2_1(a249) | c2_1(a238) | c0_1(a238) | (~c3_1(a238))) <=> (c2_1(a249) | c1_1(a241) | c2_1(a238) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a238)) | c0_1(a238) | c1_1(a249) | (~c3_1(a249)))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2500,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a249) | (~c3_1(a249)) | c2_1(a249) | c2_1(a238) | c0_1(a238) | (~c3_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a249) | c1_1(a241) | c2_1(a238) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a238)) | c0_1(a238) | c1_1(a249) | (~c3_1(a249))))),
% 1.50/1.32 inference(monotonicity,[status(thm)],[2499])).
% 1.50/1.32 tff(2501,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a249) | (~c3_1(a249)) | c2_1(a249) | c2_1(a238) | c0_1(a238) | (~c3_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a249) | c1_1(a241) | c2_1(a238) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a238)) | c0_1(a238) | c1_1(a249) | (~c3_1(a249)))),
% 1.50/1.32 inference(transitivity,[status(thm)],[2500, 2498])).
% 1.50/1.32 tff(2502,plain,
% 1.50/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c0_1(a241)) | c1_1(a249) | (~c3_1(a249)) | c2_1(a249) | c2_1(a238) | c0_1(a238) | (~c3_1(a238)))),
% 1.50/1.32 inference(quant_inst,[status(thm)],[])).
% 1.50/1.32 tff(2503,plain,
% 1.50/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | c2_1(V) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a249) | c1_1(a241) | c2_1(a238) | (~ndr1_0) | (~c0_1(a241)) | (~c2_1(a241)) | (~c3_1(a238)) | c0_1(a238) | c1_1(a249) | (~c3_1(a249))),
% 1.50/1.32 inference(modus_ponens,[status(thm)],[2502, 2501])).
% 1.50/1.32 tff(2504,plain,
% 1.50/1.32 ((~c2_1(a241)) | c0_1(a238)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2503, 128, 1997, 2488, 1509, 1986, 2497, 2475, 886, 2272])).
% 1.50/1.32 tff(2505,plain,
% 1.50/1.32 ($false),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2504, 2496, 2485])).
% 1.50/1.32 tff(2506,plain,(c0_1(a238) | (~c3_1(a238)) | c2_1(a238) | c1_1(a249) | (~c1_1(a238))), inference(lemma,lemma(discharge,[]))).
% 1.50/1.32 tff(2507,plain,
% 1.50/1.32 ($false),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2506, 2484, 2476, 2475, 1509, 1510])).
% 1.50/1.32 tff(2508,plain,(hskp10 | c2_1(a238) | (~c3_1(a238)) | (~c1_1(a238)) | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.50/1.32 tff(2509,plain,
% 1.50/1.32 (hskp10),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2508, 2409, 2410, 2411, 2474])).
% 1.50/1.32 tff(2510,plain,
% 1.50/1.32 (~c3_1(a214)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[1300, 2509])).
% 1.50/1.32 tff(2511,plain,
% 1.50/1.32 (~c2_1(a214)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[1306, 2509])).
% 1.50/1.32 tff(2512,plain,
% 1.50/1.32 (c1_1(a214)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[1294, 2509])).
% 1.50/1.32 tff(2513,plain,
% 1.50/1.32 (c3_1(a198)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[1401, 2512, 2246, 2408, 2511, 2510, 2247])).
% 1.50/1.32 tff(2514,plain,
% 1.50/1.32 (hskp3 | (~c3_1(a198))),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[1544, 128, 2248, 2246, 2460, 2459, 2458, 1429])).
% 1.50/1.32 tff(2515,plain,
% 1.50/1.32 (hskp3),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2514, 2513])).
% 1.50/1.32 tff(2516,plain,
% 1.50/1.32 (~c3_1(a203)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[619, 2515])).
% 1.50/1.32 tff(2517,plain,
% 1.50/1.32 (c1_1(a203)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[636, 2515])).
% 1.50/1.32 tff(2518,plain,
% 1.50/1.32 (~c2_1(a203)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[1554, 128, 2411, 2410, 2512, 2517, 2409, 2511, 2510, 2516, 1361])).
% 1.50/1.32 tff(2519,plain,
% 1.50/1.32 (~c0_1(a203)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[625, 2515])).
% 1.50/1.32 tff(2520,plain,
% 1.50/1.32 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2521,plain,
% 1.50/1.32 ((hskp12 | (~ndr1_0) | (~c2_1(a198)) | (~c3_1(a198)) | (~c1_1(a198)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203))) <=> (hskp12 | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2522,plain,
% 1.50/1.32 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a198)) | (~c3_1(a198)) | (~c1_1(a198)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a203))))),
% 1.50/1.32 inference(monotonicity,[status(thm)],[2521])).
% 1.50/1.32 tff(2523,plain,
% 1.50/1.32 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a198)) | (~c3_1(a198)) | (~c1_1(a198)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)))),
% 1.50/1.32 inference(transitivity,[status(thm)],[2522, 2520])).
% 1.50/1.32 tff(2524,plain,
% 1.50/1.32 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a198)) | (~c3_1(a198)) | (~c1_1(a198)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)))),
% 1.50/1.32 inference(quant_inst,[status(thm)],[])).
% 1.50/1.32 tff(2525,plain,
% 1.50/1.32 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c1_1(a198)) | (~c3_1(a198)) | (~c2_1(a198)) | (~c1_1(a203))),
% 1.50/1.32 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 1.50/1.32 tff(2526,plain,
% 1.50/1.32 (hskp12),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2525, 128, 2247, 2246, 2517, 2519, 2516, 949, 2513])).
% 1.50/1.32 tff(2527,plain,
% 1.50/1.32 (~c3_1(a217)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[974, 2526])).
% 1.50/1.32 tff(2528,plain,
% 1.50/1.32 (~c2_1(a217)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[980, 2526])).
% 1.50/1.32 tff(2529,plain,
% 1.50/1.32 (c0_1(a217)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[998, 2526])).
% 1.50/1.32 tff(2530,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a217) | c3_1(a217) | c0_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)) | c2_1(a203) | (~c0_1(a217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a217) | c3_1(a217) | c0_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)) | c2_1(a203) | (~c0_1(a217)))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2531,plain,
% 1.50/1.32 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a217) | c2_1(a217) | (~c0_1(a217)) | c2_1(a203) | c0_1(a203) | (~c1_1(a203))) <=> (c2_1(a217) | c3_1(a217) | c0_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)) | c2_1(a203) | (~c0_1(a217)))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2532,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a217) | c2_1(a217) | (~c0_1(a217)) | c2_1(a203) | c0_1(a203) | (~c1_1(a203)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a217) | c3_1(a217) | c0_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)) | c2_1(a203) | (~c0_1(a217))))),
% 1.50/1.32 inference(monotonicity,[status(thm)],[2531])).
% 1.50/1.32 tff(2533,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a217) | c2_1(a217) | (~c0_1(a217)) | c2_1(a203) | c0_1(a203) | (~c1_1(a203)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a217) | c3_1(a217) | c0_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)) | c2_1(a203) | (~c0_1(a217)))),
% 1.50/1.32 inference(transitivity,[status(thm)],[2532, 2530])).
% 1.50/1.32 tff(2534,plain,
% 1.50/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a217) | c2_1(a217) | (~c0_1(a217)) | c2_1(a203) | c0_1(a203) | (~c1_1(a203)))),
% 1.50/1.32 inference(quant_inst,[status(thm)],[])).
% 1.50/1.32 tff(2535,plain,
% 1.50/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a217) | c3_1(a217) | c0_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)) | c2_1(a203) | (~c0_1(a217))),
% 1.50/1.32 inference(modus_ponens,[status(thm)],[2534, 2533])).
% 1.50/1.32 tff(2536,plain,
% 1.50/1.32 ($false),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2535, 128, 2248, 2247, 2246, 2529, 2517, 2528, 2527, 2519, 1412, 2518])).
% 1.50/1.32 tff(2537,plain,(hskp4 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.50/1.32 tff(2538,plain,
% 1.50/1.32 (hskp5),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2537, 2357])).
% 1.50/1.32 tff(2539,plain,
% 1.50/1.32 (c3_1(a205)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[69, 2538])).
% 1.50/1.32 tff(2540,plain,
% 1.50/1.32 (c2_1(a205)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[52, 2538])).
% 1.50/1.32 tff(2541,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a256) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a239)) | (~c2_1(a256)) | (~c1_1(a256)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a256) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a239)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2542,plain,
% 1.50/1.32 (((~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a239) | c3_1(a239) | (~c1_1(a239))) <=> (c0_1(a256) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a239)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2543,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a239) | c3_1(a239) | (~c1_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a256) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a239)) | (~c2_1(a256)) | (~c1_1(a256))))),
% 1.50/1.32 inference(monotonicity,[status(thm)],[2542])).
% 1.50/1.32 tff(2544,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a239) | c3_1(a239) | (~c1_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a256) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a239)) | (~c2_1(a256)) | (~c1_1(a256)))),
% 1.50/1.32 inference(transitivity,[status(thm)],[2543, 2541])).
% 1.50/1.32 tff(2545,plain,
% 1.50/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c0_1(a256) | (~c2_1(a256)) | (~c1_1(a256)) | c0_1(a239) | c3_1(a239) | (~c1_1(a239)))),
% 1.50/1.32 inference(quant_inst,[status(thm)],[])).
% 1.50/1.32 tff(2546,plain,
% 1.50/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a256) | c0_1(a239) | c3_1(a239) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a239)) | (~c2_1(a256)) | (~c1_1(a256))),
% 1.50/1.32 inference(modus_ponens,[status(thm)],[2545, 2544])).
% 1.50/1.32 tff(2547,plain,
% 1.50/1.32 ((~c0_1(a205)) | (~c1_1(a239))),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2546, 128, 2027, 2044, 2540, 2539, 2033, 2269, 2268, 1913])).
% 1.50/1.32 tff(2548,plain,
% 1.50/1.32 (~c0_1(a205)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2547, 2305])).
% 1.50/1.32 tff(2549,plain,
% 1.50/1.32 (~c1_1(a205)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[58, 2538])).
% 1.50/1.32 tff(2550,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a249) | c0_1(a239) | c3_1(a239) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c1_1(a239)) | (~c3_1(a249)) | (~c0_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a249) | c0_1(a239) | c3_1(a239) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c1_1(a239)) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2551,plain,
% 1.50/1.32 (((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205))) <=> (c2_1(a249) | c0_1(a239) | c3_1(a239) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c1_1(a239)) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2552,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a249) | c0_1(a239) | c3_1(a239) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c1_1(a239)) | (~c3_1(a249)) | (~c0_1(a249))))),
% 1.50/1.32 inference(monotonicity,[status(thm)],[2551])).
% 1.50/1.32 tff(2553,plain,
% 1.50/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a249) | c0_1(a239) | c3_1(a239) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c1_1(a239)) | (~c3_1(a249)) | (~c0_1(a249)))),
% 1.50/1.32 inference(transitivity,[status(thm)],[2552, 2550])).
% 1.50/1.32 tff(2554,plain,
% 1.50/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c3_1(a239) | c0_1(a239) | (~c1_1(a239)) | c1_1(a205) | c0_1(a205) | (~c2_1(a205)))),
% 1.50/1.32 inference(quant_inst,[status(thm)],[])).
% 1.50/1.32 tff(2555,plain,
% 1.50/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a249) | c0_1(a239) | c3_1(a239) | c1_1(a205) | (~ndr1_0) | (~c2_1(a205)) | c0_1(a205) | (~c1_1(a239)) | (~c3_1(a249)) | (~c0_1(a249))),
% 1.50/1.32 inference(modus_ponens,[status(thm)],[2554, 2553])).
% 1.50/1.32 tff(2556,plain,
% 1.50/1.32 (c0_1(a205) | (~c1_1(a239))),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2555, 128, 2008, 1997, 2540, 1986, 2269, 2268, 2549, 593])).
% 1.50/1.32 tff(2557,plain,
% 1.50/1.32 ($false),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[2556, 2548, 2305])).
% 1.50/1.32 tff(2558,plain,(hskp19), inference(lemma,lemma(discharge,[]))).
% 1.50/1.32 tff(2559,plain,
% 1.50/1.32 (c1_1(a238)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[1392, 2558])).
% 1.50/1.32 tff(2560,plain,
% 1.50/1.32 (~c2_1(a238)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[1369, 2558])).
% 1.50/1.32 tff(2561,plain,
% 1.50/1.32 (c3_1(a238)),
% 1.50/1.32 inference(unit_resolution,[status(thm)],[1381, 2558])).
% 1.50/1.32 tff(2562,plain,
% 1.50/1.32 (((~![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(a238) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))) <=> ((~![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(a238) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2563,plain,
% 1.50/1.32 (((~ndr1_0) | c2_1(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205))) <=> (c2_1(a238) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.50/1.32 inference(rewrite,[status(thm)],[])).
% 1.50/1.32 tff(2564,plain,
% 1.50/1.32 (((~![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(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205)))) <=> ((~![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(a238) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238))))),
% 1.50/1.32 inference(monotonicity,[status(thm)],[2563])).
% 1.50/1.32 tff(2565,plain,
% 1.50/1.32 (((~![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(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205)))) <=> ((~![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(a238) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.50/1.32 inference(transitivity,[status(thm)],[2564, 2562])).
% 1.50/1.32 tff(2566,plain,
% 1.50/1.32 ((~![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(a238) | (~c3_1(a238)) | (~c1_1(a238)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c1_1(a205) | c0_1(a205) | (~c3_1(a205)))),
% 1.50/1.33 inference(quant_inst,[status(thm)],[])).
% 1.50/1.33 tff(2567,plain,
% 1.50/1.33 ((~![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(a238) | c1_1(a205) | (~ndr1_0) | c0_1(a205) | (~c3_1(a205)) | (~c3_1(a238)) | (~c1_1(a238)) | (~c0_1(a238))),
% 1.50/1.33 inference(modus_ponens,[status(thm)],[2566, 2565])).
% 1.50/1.33 tff(2568,plain,
% 1.50/1.33 (c0_1(a205) | (~c0_1(a238))),
% 1.50/1.33 inference(unit_resolution,[status(thm)],[2567, 128, 2559, 2561, 2539, 2560, 2549, 682])).
% 1.50/1.33 tff(2569,plain,
% 1.50/1.33 (c0_1(a205)),
% 1.50/1.33 inference(unit_resolution,[status(thm)],[2568, 1498])).
% 1.50/1.33 tff(2570,plain,
% 1.50/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c2_1(a238) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a238)) | (~c0_1(a238)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c2_1(a238) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.50/1.33 inference(rewrite,[status(thm)],[])).
% 1.50/1.33 tff(2571,plain,
% 1.50/1.33 ((hskp3 | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238))) <=> (hskp3 | c2_1(a238) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.50/1.33 inference(rewrite,[status(thm)],[])).
% 1.50/1.33 tff(2572,plain,
% 1.50/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c2_1(a238) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a238)) | (~c0_1(a238))))),
% 1.50/1.33 inference(monotonicity,[status(thm)],[2571])).
% 1.50/1.33 tff(2573,plain,
% 1.50/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c2_1(a238) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.50/1.33 inference(transitivity,[status(thm)],[2572, 2570])).
% 1.50/1.33 tff(2574,plain,
% 1.50/1.33 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.50/1.33 inference(quant_inst,[status(thm)],[])).
% 1.50/1.33 tff(2575,plain,
% 1.50/1.33 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c2_1(a238) | (~ndr1_0) | (~c2_1(a205)) | (~c0_1(a205)) | (~c3_1(a205)) | (~c1_1(a238)) | (~c0_1(a238))),
% 1.50/1.33 inference(modus_ponens,[status(thm)],[2574, 2573])).
% 1.50/1.33 tff(2576,plain,
% 1.50/1.33 (hskp3 | (~c0_1(a205)) | (~c0_1(a238))),
% 1.50/1.33 inference(unit_resolution,[status(thm)],[2575, 128, 2559, 2540, 2539, 2560, 1429])).
% 1.50/1.33 tff(2577,plain,
% 1.50/1.33 (hskp3),
% 1.50/1.33 inference(unit_resolution,[status(thm)],[2576, 2569, 1498])).
% 1.50/1.33 tff(2578,plain,
% 1.50/1.33 (~c3_1(a203)),
% 1.50/1.33 inference(unit_resolution,[status(thm)],[619, 2577])).
% 1.50/1.33 tff(2579,plain,
% 1.50/1.33 (~c0_1(a203)),
% 1.50/1.33 inference(unit_resolution,[status(thm)],[625, 2577])).
% 1.50/1.33 tff(2580,plain,
% 1.50/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a238) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c2_1(a203)) | (~c1_1(a238)) | (~c0_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a238) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c2_1(a203)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.50/1.33 inference(rewrite,[status(thm)],[])).
% 1.50/1.33 tff(2581,plain,
% 1.50/1.33 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a203) | c3_1(a203) | (~c2_1(a203))) <=> (c2_1(a238) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c2_1(a203)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.50/1.33 inference(rewrite,[status(thm)],[])).
% 1.50/1.33 tff(2582,plain,
% 1.50/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a203) | c3_1(a203) | (~c2_1(a203)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a238) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c2_1(a203)) | (~c1_1(a238)) | (~c0_1(a238))))),
% 1.60/1.33 inference(monotonicity,[status(thm)],[2581])).
% 1.60/1.33 tff(2583,plain,
% 1.60/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a203) | c3_1(a203) | (~c2_1(a203)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a238) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c2_1(a203)) | (~c1_1(a238)) | (~c0_1(a238)))),
% 1.60/1.33 inference(transitivity,[status(thm)],[2582, 2580])).
% 1.60/1.33 tff(2584,plain,
% 1.60/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c2_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a203) | c3_1(a203) | (~c2_1(a203)))),
% 1.60/1.33 inference(quant_inst,[status(thm)],[])).
% 1.60/1.33 tff(2585,plain,
% 1.60/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a238) | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c2_1(a203)) | (~c1_1(a238)) | (~c0_1(a238))),
% 1.60/1.33 inference(modus_ponens,[status(thm)],[2584, 2583])).
% 1.60/1.33 tff(2586,plain,
% 1.60/1.33 (~c2_1(a203)),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[2585, 128, 2248, 2247, 2246, 2559, 2560, 2579, 2578, 22, 1498])).
% 1.60/1.33 tff(2587,plain,
% 1.60/1.33 (c1_1(a203)),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[636, 2577])).
% 1.60/1.33 tff(2588,plain,
% 1.60/1.33 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)))),
% 1.60/1.33 inference(rewrite,[status(thm)],[])).
% 1.60/1.33 tff(2589,plain,
% 1.60/1.33 ((hskp10 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203))) <=> (hskp10 | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)))),
% 1.60/1.33 inference(rewrite,[status(thm)],[])).
% 1.60/1.33 tff(2590,plain,
% 1.60/1.33 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203))))),
% 1.60/1.33 inference(monotonicity,[status(thm)],[2589])).
% 1.60/1.33 tff(2591,plain,
% 1.60/1.33 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203)))),
% 1.60/1.33 inference(transitivity,[status(thm)],[2590, 2588])).
% 1.60/1.33 tff(2592,plain,
% 1.60/1.33 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | c3_1(a203) | c0_1(a203) | (~c1_1(a203)))),
% 1.60/1.33 inference(quant_inst,[status(thm)],[])).
% 1.60/1.33 tff(2593,plain,
% 1.60/1.33 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a203) | c3_1(a203) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c1_1(a203))),
% 1.60/1.33 inference(modus_ponens,[status(thm)],[2592, 2591])).
% 1.60/1.33 tff(2594,plain,
% 1.60/1.33 (hskp10),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[2593, 128, 2248, 2247, 2246, 2587, 2579, 2578, 1275])).
% 1.60/1.33 tff(2595,plain,
% 1.60/1.33 (~c3_1(a214)),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[1300, 2594])).
% 1.60/1.33 tff(2596,plain,
% 1.60/1.33 (~c2_1(a214)),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[1306, 2594])).
% 1.60/1.33 tff(2597,plain,
% 1.60/1.33 (c1_1(a214)),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[1294, 2594])).
% 1.60/1.33 tff(2598,plain,
% 1.60/1.33 (c3_1(a198)),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[1401, 2597, 2246, 2558, 2596, 2595, 2247])).
% 1.60/1.33 tff(2599,plain,
% 1.60/1.33 (hskp12 | (~c3_1(a198))),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[2525, 128, 2247, 2246, 2587, 2579, 2578, 949])).
% 1.60/1.33 tff(2600,plain,
% 1.60/1.33 (hskp12),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[2599, 2598])).
% 1.60/1.33 tff(2601,plain,
% 1.60/1.33 (~c3_1(a217)),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[974, 2600])).
% 1.60/1.33 tff(2602,plain,
% 1.60/1.33 (~c2_1(a217)),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[980, 2600])).
% 1.60/1.33 tff(2603,plain,
% 1.60/1.33 (c0_1(a217)),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[998, 2600])).
% 1.60/1.33 tff(2604,plain,
% 1.60/1.33 ($false),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[2535, 128, 2248, 2247, 2246, 2603, 2587, 2602, 2601, 2579, 1412, 2586])).
% 1.60/1.33 tff(2605,plain,(~c0_1(a238)), inference(lemma,lemma(discharge,[]))).
% 1.60/1.33 tff(2606,plain,
% 1.60/1.33 (c1_1(a249)),
% 1.60/1.33 inference(unit_resolution,[status(thm)],[2506, 2605, 2561, 2560, 2559])).
% 1.60/1.33 tff(2607,plain,
% 1.60/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a238)) | (~c1_1(a238)) | c0_1(a238) | (~c3_1(a249)) | (~c1_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a238)) | (~c1_1(a238)) | c0_1(a238) | (~c3_1(a249)) | (~c1_1(a249)))),
% 1.60/1.33 inference(rewrite,[status(thm)],[])).
% 1.60/1.33 tff(2608,plain,
% 1.60/1.33 (((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a249)) | c2_1(a249) | (~c1_1(a249)) | c0_1(a238) | (~c3_1(a238)) | (~c1_1(a238))) <=> (c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a238)) | (~c1_1(a238)) | c0_1(a238) | (~c3_1(a249)) | (~c1_1(a249)))),
% 1.60/1.33 inference(rewrite,[status(thm)],[])).
% 1.60/1.33 tff(2609,plain,
% 1.60/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a249)) | c2_1(a249) | (~c1_1(a249)) | c0_1(a238) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a238)) | (~c1_1(a238)) | c0_1(a238) | (~c3_1(a249)) | (~c1_1(a249))))),
% 1.60/1.34 inference(monotonicity,[status(thm)],[2608])).
% 1.60/1.34 tff(2610,plain,
% 1.60/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a249)) | c2_1(a249) | (~c1_1(a249)) | c0_1(a238) | (~c3_1(a238)) | (~c1_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a238)) | (~c1_1(a238)) | c0_1(a238) | (~c3_1(a249)) | (~c1_1(a249)))),
% 1.60/1.34 inference(transitivity,[status(thm)],[2609, 2607])).
% 1.60/1.34 tff(2611,plain,
% 1.60/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a198)) | (~c0_1(a198)) | (~c1_1(a198)) | (~c3_1(a249)) | c2_1(a249) | (~c1_1(a249)) | c0_1(a238) | (~c3_1(a238)) | (~c1_1(a238)))),
% 1.60/1.34 inference(quant_inst,[status(thm)],[])).
% 1.60/1.34 tff(2612,plain,
% 1.60/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a249) | (~ndr1_0) | (~c0_1(a198)) | (~c1_1(a198)) | (~c2_1(a198)) | (~c3_1(a238)) | (~c1_1(a238)) | c0_1(a238) | (~c3_1(a249)) | (~c1_1(a249))),
% 1.60/1.34 inference(modus_ponens,[status(thm)],[2611, 2610])).
% 1.60/1.34 tff(2613,plain,
% 1.60/1.34 ($false),
% 1.60/1.34 inference(unit_resolution,[status(thm)],[2612, 128, 2248, 2247, 2246, 1997, 2559, 2561, 1986, 80, 2605, 2606])).
% 1.60/1.34 % SZS output end Proof
%------------------------------------------------------------------------------