TSTP Solution File: SYN460-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN460-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:55:35 EDT 2022
% Result : Unsatisfiable 2.72s 1.98s
% Output : Proof 2.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN460-1 : 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 : n008.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 04:02:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 2.72/1.98 % SZS status Unsatisfiable
% 2.72/1.98 % SZS output start Proof
% 2.72/1.98 tff(c3_1_type, type, (
% 2.72/1.98 c3_1: $i > $o)).
% 2.72/1.98 tff(a2252_type, type, (
% 2.72/1.98 a2252: $i)).
% 2.72/1.98 tff(a2190_type, type, (
% 2.72/1.98 a2190: $i)).
% 2.72/1.98 tff(c2_1_type, type, (
% 2.72/1.98 c2_1: $i > $o)).
% 2.72/1.98 tff(c1_1_type, type, (
% 2.72/1.98 c1_1: $i > $o)).
% 2.72/1.98 tff(c0_1_type, type, (
% 2.72/1.98 c0_1: $i > $o)).
% 2.72/1.98 tff(ndr1_0_type, type, (
% 2.72/1.98 ndr1_0: $o)).
% 2.72/1.98 tff(hskp3_type, type, (
% 2.72/1.98 hskp3: $o)).
% 2.72/1.98 tff(a2204_type, type, (
% 2.72/1.98 a2204: $i)).
% 2.72/1.98 tff(hskp40_type, type, (
% 2.72/1.98 hskp40: $o)).
% 2.72/1.98 tff(a2228_type, type, (
% 2.72/1.98 a2228: $i)).
% 2.72/1.98 tff(hskp48_type, type, (
% 2.72/1.98 hskp48: $o)).
% 2.72/1.98 tff(a2189_type, type, (
% 2.72/1.98 a2189: $i)).
% 2.72/1.98 tff(hskp34_type, type, (
% 2.72/1.98 hskp34: $o)).
% 2.72/1.98 tff(hskp46_type, type, (
% 2.72/1.98 hskp46: $o)).
% 2.72/1.98 tff(a2242_type, type, (
% 2.72/1.98 a2242: $i)).
% 2.72/1.98 tff(a2218_type, type, (
% 2.72/1.98 a2218: $i)).
% 2.72/1.98 tff(a2186_type, type, (
% 2.72/1.98 a2186: $i)).
% 2.72/1.98 tff(hskp32_type, type, (
% 2.72/1.98 hskp32: $o)).
% 2.72/1.98 tff(hskp18_type, type, (
% 2.72/1.98 hskp18: $o)).
% 2.72/1.98 tff(a2188_type, type, (
% 2.72/1.98 a2188: $i)).
% 2.72/1.98 tff(hskp33_type, type, (
% 2.72/1.98 hskp33: $o)).
% 2.72/1.98 tff(a2181_type, type, (
% 2.72/1.98 a2181: $i)).
% 2.72/1.98 tff(a2215_type, type, (
% 2.72/1.98 a2215: $i)).
% 2.72/1.98 tff(hskp44_type, type, (
% 2.72/1.98 hskp44: $o)).
% 2.72/1.98 tff(a2222_type, type, (
% 2.72/1.98 a2222: $i)).
% 2.72/1.98 tff(hskp53_type, type, (
% 2.72/1.98 hskp53: $o)).
% 2.72/1.98 tff(a2235_type, type, (
% 2.72/1.98 a2235: $i)).
% 2.72/1.98 tff(hskp0_type, type, (
% 2.72/1.98 hskp0: $o)).
% 2.72/1.98 tff(a2226_type, type, (
% 2.72/1.98 a2226: $i)).
% 2.72/1.98 tff(a2187_type, type, (
% 2.72/1.98 a2187: $i)).
% 2.72/1.98 tff(hskp58_type, type, (
% 2.72/1.98 hskp58: $o)).
% 2.72/1.98 tff(hskp21_type, type, (
% 2.72/1.98 hskp21: $o)).
% 2.72/1.98 tff(hskp55_type, type, (
% 2.72/1.98 hskp55: $o)).
% 2.72/1.98 tff(hskp54_type, type, (
% 2.72/1.98 hskp54: $o)).
% 2.72/1.98 tff(hskp2_type, type, (
% 2.72/1.98 hskp2: $o)).
% 2.72/1.98 tff(hskp47_type, type, (
% 2.72/1.98 hskp47: $o)).
% 2.72/1.98 tff(a2200_type, type, (
% 2.72/1.98 a2200: $i)).
% 2.72/1.98 tff(hskp38_type, type, (
% 2.72/1.98 hskp38: $o)).
% 2.72/1.98 tff(hskp37_type, type, (
% 2.72/1.98 hskp37: $o)).
% 2.72/1.98 tff(a2198_type, type, (
% 2.72/1.98 a2198: $i)).
% 2.72/1.98 tff(hskp7_type, type, (
% 2.72/1.98 hskp7: $o)).
% 2.72/1.98 tff(a2197_type, type, (
% 2.72/1.98 a2197: $i)).
% 2.72/1.98 tff(hskp6_type, type, (
% 2.72/1.98 hskp6: $o)).
% 2.72/1.98 tff(a2196_type, type, (
% 2.72/1.98 a2196: $i)).
% 2.72/1.98 tff(a2240_type, type, (
% 2.72/1.98 a2240: $i)).
% 2.72/1.98 tff(a2241_type, type, (
% 2.72/1.98 a2241: $i)).
% 2.72/1.98 tff(hskp26_type, type, (
% 2.72/1.98 hskp26: $o)).
% 2.72/1.98 tff(a2178_type, type, (
% 2.72/1.98 a2178: $i)).
% 2.72/1.98 tff(a2239_type, type, (
% 2.72/1.98 a2239: $i)).
% 2.72/1.98 tff(hskp17_type, type, (
% 2.72/1.98 hskp17: $o)).
% 2.72/1.98 tff(a2221_type, type, (
% 2.72/1.98 a2221: $i)).
% 2.72/1.98 tff(a2206_type, type, (
% 2.72/1.98 a2206: $i)).
% 2.72/1.98 tff(hskp10_type, type, (
% 2.72/1.98 hskp10: $o)).
% 2.72/1.98 tff(a2191_type, type, (
% 2.72/1.98 a2191: $i)).
% 2.72/1.98 tff(hskp4_type, type, (
% 2.72/1.98 hskp4: $o)).
% 2.72/1.98 tff(a2205_type, type, (
% 2.72/1.98 a2205: $i)).
% 2.72/1.98 tff(hskp41_type, type, (
% 2.72/1.98 hskp41: $o)).
% 2.72/1.98 tff(a2185_type, type, (
% 2.72/1.98 a2185: $i)).
% 2.72/1.98 tff(hskp31_type, type, (
% 2.72/1.98 hskp31: $o)).
% 2.72/1.98 tff(hskp56_type, type, (
% 2.72/1.98 hskp56: $o)).
% 2.72/1.98 tff(1,plain,
% 2.72/1.98 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 2.72/1.98 inference(bind,[status(th)],[])).
% 2.72/1.98 tff(2,plain,
% 2.72/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.72/1.98 inference(quant_intro,[status(thm)],[1])).
% 2.72/1.98 tff(3,plain,
% 2.72/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.72/1.98 inference(rewrite,[status(thm)],[])).
% 2.72/1.98 tff(4,plain,
% 2.72/1.98 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 2.72/1.98 inference(bind,[status(th)],[])).
% 2.72/1.98 tff(5,plain,
% 2.72/1.98 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.72/1.98 inference(quant_intro,[status(thm)],[4])).
% 2.72/1.98 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause290')).
% 2.72/1.98 tff(7,plain,
% 2.72/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[6, 5])).
% 2.72/1.98 tff(8,plain,
% 2.72/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.72/1.98 tff(9,plain,(
% 2.72/1.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.72/1.98 inference(skolemize,[status(sab)],[8])).
% 2.72/1.98 tff(10,plain,
% 2.72/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[9, 2])).
% 2.72/1.98 tff(11,plain,
% 2.72/1.98 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 2.72/1.98 inference(bind,[status(th)],[])).
% 2.72/1.98 tff(12,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.72/1.98 inference(quant_intro,[status(thm)],[11])).
% 2.72/1.98 tff(13,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.72/1.98 inference(rewrite,[status(thm)],[])).
% 2.72/1.98 tff(14,plain,
% 2.72/1.98 (^[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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 2.72/1.98 inference(bind,[status(th)],[])).
% 2.72/1.98 tff(15,plain,
% 2.72/1.98 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.72/1.98 inference(quant_intro,[status(thm)],[14])).
% 2.72/1.98 tff(16,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause273')).
% 2.72/1.98 tff(17,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[16, 15])).
% 2.72/1.98 tff(18,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[17, 13])).
% 2.72/1.98 tff(19,plain,(
% 2.72/1.98 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.72/1.98 inference(skolemize,[status(sab)],[18])).
% 2.72/1.98 tff(20,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[19, 12])).
% 2.72/1.98 tff(21,assumption,(c3_1(a2252)), introduced(assumption)).
% 2.72/1.98 tff(22,plain,
% 2.72/1.98 (^[V: $i, U: $i] : refl((hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 2.72/1.98 inference(bind,[status(th)],[])).
% 2.72/1.98 tff(23,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.72/1.98 inference(quant_intro,[status(thm)],[22])).
% 2.72/1.98 tff(24,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.72/1.98 inference(rewrite,[status(thm)],[])).
% 2.72/1.98 tff(25,plain,
% 2.72/1.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) | c2_1(V)) | hskp40) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp40))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp40) <=> (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) | c2_1(V)) | hskp40) <=> (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 2.72/1.98 inference(bind,[status(th)],[])).
% 2.72/1.98 tff(26,plain,
% 2.72/1.98 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) | c2_1(V)) | hskp40) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.72/1.98 inference(quant_intro,[status(thm)],[25])).
% 2.72/1.98 tff(27,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) | c2_1(V)) | hskp40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause282')).
% 2.72/1.98 tff(28,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[27, 26])).
% 2.72/1.98 tff(29,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[28, 24])).
% 2.72/1.98 tff(30,plain,(
% 2.72/1.98 ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.72/1.98 inference(skolemize,[status(sab)],[29])).
% 2.72/1.98 tff(31,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[30, 23])).
% 2.72/1.98 tff(32,plain,
% 2.72/1.98 (^[V: $i, U: $i] : refl((hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 2.72/1.98 inference(bind,[status(th)],[])).
% 2.72/1.98 tff(33,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.72/1.98 inference(quant_intro,[status(thm)],[32])).
% 2.72/1.98 tff(34,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.72/1.98 inference(rewrite,[status(thm)],[])).
% 2.72/1.98 tff(35,plain,
% 2.72/1.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp48) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp48))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp48) <=> (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp48) <=> (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 2.72/1.98 inference(bind,[status(th)],[])).
% 2.72/1.98 tff(36,plain,
% 2.72/1.98 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp48) <=> ![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.72/1.98 inference(quant_intro,[status(thm)],[35])).
% 2.72/1.98 tff(37,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause279')).
% 2.72/1.98 tff(38,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[37, 36])).
% 2.72/1.98 tff(39,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[38, 34])).
% 2.72/1.98 tff(40,plain,(
% 2.72/1.98 ![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.72/1.98 inference(skolemize,[status(sab)],[39])).
% 2.72/1.98 tff(41,plain,
% 2.72/1.98 (![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[40, 33])).
% 2.72/1.98 tff(42,plain,
% 2.72/1.98 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))))),
% 2.72/1.98 inference(bind,[status(th)],[])).
% 2.72/1.98 tff(43,plain,
% 2.72/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 2.72/1.98 inference(quant_intro,[status(thm)],[42])).
% 2.72/1.98 tff(44,plain,
% 2.72/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 2.72/1.98 inference(rewrite,[status(thm)],[])).
% 2.72/1.98 tff(45,plain,
% 2.72/1.98 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))))),
% 2.72/1.98 inference(bind,[status(th)],[])).
% 2.72/1.98 tff(46,plain,
% 2.72/1.98 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 2.72/1.98 inference(quant_intro,[status(thm)],[45])).
% 2.72/1.98 tff(47,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause292')).
% 2.72/1.98 tff(48,plain,
% 2.72/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[47, 46])).
% 2.72/1.98 tff(49,plain,
% 2.72/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[48, 44])).
% 2.72/1.98 tff(50,plain,(
% 2.72/1.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 2.72/1.98 inference(skolemize,[status(sab)],[49])).
% 2.72/1.98 tff(51,plain,
% 2.72/1.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 2.72/1.98 inference(modus_ponens,[status(thm)],[50, 43])).
% 2.72/1.98 tff(52,plain,
% 2.72/1.98 (^[U: $i] : refl((hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 2.72/1.98 inference(bind,[status(th)],[])).
% 2.72/1.98 tff(53,plain,
% 2.72/1.98 (![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.72/1.98 inference(quant_intro,[status(thm)],[52])).
% 2.72/1.98 tff(54,plain,
% 2.72/1.98 (![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.72/1.98 inference(rewrite,[status(thm)],[])).
% 2.72/1.98 tff(55,plain,
% 2.72/1.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) | hskp18) | c2_1(U)) <=> ((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite(((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U))) | c2_1(U)) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) | hskp18) | c2_1(U)) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 2.72/1.99 inference(bind,[status(th)],[])).
% 2.72/1.99 tff(56,plain,
% 2.72/1.99 (![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) | hskp18) | c2_1(U)) <=> ![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.72/1.99 inference(quant_intro,[status(thm)],[55])).
% 2.72/1.99 tff(57,axiom,(![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) | hskp18) | c2_1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause245')).
% 2.72/1.99 tff(58,plain,
% 2.72/1.99 (![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[57, 56])).
% 2.72/1.99 tff(59,plain,
% 2.72/1.99 (![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[58, 54])).
% 2.72/1.99 tff(60,plain,(
% 2.72/1.99 ![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.72/1.99 inference(skolemize,[status(sab)],[59])).
% 2.72/1.99 tff(61,plain,
% 2.72/1.99 (![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[60, 53])).
% 2.72/1.99 tff(62,plain,
% 2.72/1.99 (^[V: $i, U: $i] : refl((hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))))),
% 2.72/1.99 inference(bind,[status(th)],[])).
% 2.72/1.99 tff(63,plain,
% 2.72/1.99 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 2.72/1.99 inference(quant_intro,[status(thm)],[62])).
% 2.72/1.99 tff(64,plain,
% 2.72/1.99 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(65,plain,
% 2.72/1.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) | c0_1(U)) | hskp33) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) | hskp33))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) | hskp33) <=> (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) | c0_1(U)) | hskp33) <=> (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))))),
% 2.72/1.99 inference(bind,[status(th)],[])).
% 2.72/1.99 tff(66,plain,
% 2.72/1.99 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) | c0_1(U)) | hskp33) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 2.72/1.99 inference(quant_intro,[status(thm)],[65])).
% 2.72/1.99 tff(67,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) | c0_1(U)) | hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause284')).
% 2.72/1.99 tff(68,plain,
% 2.72/1.99 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[67, 66])).
% 2.72/1.99 tff(69,plain,
% 2.72/1.99 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[68, 64])).
% 2.72/1.99 tff(70,plain,(
% 2.72/1.99 ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 2.72/1.99 inference(skolemize,[status(sab)],[69])).
% 2.72/1.99 tff(71,plain,
% 2.72/1.99 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[70, 63])).
% 2.72/1.99 tff(72,assumption,(~hskp33), introduced(assumption)).
% 2.72/1.99 tff(73,assumption,(hskp32), introduced(assumption)).
% 2.72/1.99 tff(74,plain,
% 2.72/1.99 (((~hskp32) | c0_1(a2186)) <=> ((~hskp32) | c0_1(a2186))),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(75,axiom,((~hskp32) | c0_1(a2186)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 2.72/1.99 tff(76,plain,
% 2.72/1.99 ((~hskp32) | c0_1(a2186)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[75, 74])).
% 2.72/1.99 tff(77,plain,
% 2.72/1.99 ((~hskp32) | c0_1(a2186)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[76, 74])).
% 2.72/1.99 tff(78,plain,
% 2.72/1.99 ((~hskp32) | c0_1(a2186)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[77, 74])).
% 2.72/1.99 tff(79,plain,
% 2.72/1.99 ((~hskp32) | c0_1(a2186)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[78, 74])).
% 2.72/1.99 tff(80,plain,
% 2.72/1.99 ((~hskp32) | c0_1(a2186)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[79, 74])).
% 2.72/1.99 tff(81,plain,
% 2.72/1.99 ((~hskp32) | c0_1(a2186)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[80, 74])).
% 2.72/1.99 tff(82,plain,
% 2.72/1.99 ((~hskp32) | c0_1(a2186)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[81, 74])).
% 2.72/1.99 tff(83,plain,
% 2.72/1.99 ((~hskp32) | c0_1(a2186)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[82, 74])).
% 2.72/1.99 tff(84,plain,
% 2.72/1.99 (c0_1(a2186)),
% 2.72/1.99 inference(unit_resolution,[status(thm)],[83, 73])).
% 2.72/1.99 tff(85,plain,
% 2.72/1.99 (((~hskp32) | (~c3_1(a2186))) <=> ((~hskp32) | (~c3_1(a2186)))),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(86,plain,
% 2.72/1.99 (((~c3_1(a2186)) | (~hskp32)) <=> ((~hskp32) | (~c3_1(a2186)))),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(87,axiom,((~c3_1(a2186)) | (~hskp32)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 2.72/1.99 tff(88,plain,
% 2.72/1.99 ((~hskp32) | (~c3_1(a2186))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[87, 86])).
% 2.72/1.99 tff(89,plain,
% 2.72/1.99 ((~hskp32) | (~c3_1(a2186))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[88, 85])).
% 2.72/1.99 tff(90,plain,
% 2.72/1.99 (~c3_1(a2186)),
% 2.72/1.99 inference(unit_resolution,[status(thm)],[89, 73])).
% 2.72/1.99 tff(91,assumption,(hskp53), introduced(assumption)).
% 2.72/1.99 tff(92,plain,
% 2.72/1.99 (((~hskp53) | c0_1(a2235)) <=> ((~hskp53) | c0_1(a2235))),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(93,axiom,((~hskp53) | c0_1(a2235)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 2.72/1.99 tff(94,plain,
% 2.72/1.99 ((~hskp53) | c0_1(a2235)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[93, 92])).
% 2.72/1.99 tff(95,plain,
% 2.72/1.99 ((~hskp53) | c0_1(a2235)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[94, 92])).
% 2.72/1.99 tff(96,plain,
% 2.72/1.99 ((~hskp53) | c0_1(a2235)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[95, 92])).
% 2.72/1.99 tff(97,plain,
% 2.72/1.99 ((~hskp53) | c0_1(a2235)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[96, 92])).
% 2.72/1.99 tff(98,plain,
% 2.72/1.99 ((~hskp53) | c0_1(a2235)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[97, 92])).
% 2.72/1.99 tff(99,plain,
% 2.72/1.99 ((~hskp53) | c0_1(a2235)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[98, 92])).
% 2.72/1.99 tff(100,plain,
% 2.72/1.99 ((~hskp53) | c0_1(a2235)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[99, 92])).
% 2.72/1.99 tff(101,plain,
% 2.72/1.99 ((~hskp53) | c0_1(a2235)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[100, 92])).
% 2.72/1.99 tff(102,plain,
% 2.72/1.99 (c0_1(a2235)),
% 2.72/1.99 inference(unit_resolution,[status(thm)],[101, 91])).
% 2.72/1.99 tff(103,assumption,(~c2_1(a2181)), introduced(assumption)).
% 2.72/1.99 tff(104,assumption,(~c1_1(a2181)), introduced(assumption)).
% 2.72/1.99 tff(105,assumption,(~c0_1(a2181)), introduced(assumption)).
% 2.72/1.99 tff(106,assumption,(~hskp32), introduced(assumption)).
% 2.72/1.99 tff(107,assumption,(c3_1(a2181)), introduced(assumption)).
% 2.72/1.99 tff(108,plain,
% 2.72/1.99 (^[V: $i, U: $i] : refl((hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 2.72/1.99 inference(bind,[status(th)],[])).
% 2.72/1.99 tff(109,plain,
% 2.72/1.99 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.72/1.99 inference(quant_intro,[status(thm)],[108])).
% 2.72/1.99 tff(110,plain,
% 2.72/1.99 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(111,plain,
% 2.72/1.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp32) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp32))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp32) <=> (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp32) <=> (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 2.72/1.99 inference(bind,[status(th)],[])).
% 2.72/1.99 tff(112,plain,
% 2.72/1.99 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp32) <=> ![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.72/1.99 inference(quant_intro,[status(thm)],[111])).
% 2.72/1.99 tff(113,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp32)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause270')).
% 2.72/1.99 tff(114,plain,
% 2.72/1.99 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[113, 112])).
% 2.72/1.99 tff(115,plain,
% 2.72/1.99 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[114, 110])).
% 2.72/1.99 tff(116,plain,(
% 2.72/1.99 ![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.72/1.99 inference(skolemize,[status(sab)],[115])).
% 2.72/1.99 tff(117,plain,
% 2.72/1.99 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[116, 109])).
% 2.72/1.99 tff(118,plain,
% 2.72/1.99 (^[U: $i] : refl((hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 2.72/1.99 inference(bind,[status(th)],[])).
% 2.72/1.99 tff(119,plain,
% 2.72/1.99 (![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.72/1.99 inference(quant_intro,[status(thm)],[118])).
% 2.72/1.99 tff(120,plain,
% 2.72/1.99 (![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(121,plain,
% 2.72/1.99 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | hskp58) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U))) | hskp58))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U))) | hskp58) <=> (hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | hskp58) <=> (hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | hskp58) | c1_1(U)) <=> ((hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite(((hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U))) | c1_1(U)) <=> (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | hskp58) | c1_1(U)) <=> (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 2.72/1.99 inference(bind,[status(th)],[])).
% 2.72/1.99 tff(122,plain,
% 2.72/1.99 (![U: $i] : (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | hskp58) | c1_1(U)) <=> ![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.72/1.99 inference(quant_intro,[status(thm)],[121])).
% 2.72/1.99 tff(123,axiom,(![U: $i] : (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | hskp58) | c1_1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause246')).
% 2.72/1.99 tff(124,plain,
% 2.72/1.99 (![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[123, 122])).
% 2.72/1.99 tff(125,plain,
% 2.72/1.99 (![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[124, 120])).
% 2.72/1.99 tff(126,plain,(
% 2.72/1.99 ![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.72/1.99 inference(skolemize,[status(sab)],[125])).
% 2.72/1.99 tff(127,plain,
% 2.72/1.99 (![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[126, 119])).
% 2.72/1.99 tff(128,assumption,(~ndr1_0), introduced(assumption)).
% 2.72/1.99 tff(129,plain,
% 2.72/1.99 ((ndr1_0 | (~hskp21)) <=> (ndr1_0 | (~hskp21))),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(130,plain,
% 2.72/1.99 (((~hskp21) | ndr1_0) <=> (ndr1_0 | (~hskp21))),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(131,axiom,((~hskp21) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 2.72/1.99 tff(132,plain,
% 2.72/1.99 (ndr1_0 | (~hskp21)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[131, 130])).
% 2.72/1.99 tff(133,plain,
% 2.72/1.99 (ndr1_0 | (~hskp21)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[132, 129])).
% 2.72/1.99 tff(134,plain,
% 2.72/1.99 (~hskp21),
% 2.72/1.99 inference(unit_resolution,[status(thm)],[133, 128])).
% 2.72/1.99 tff(135,plain,
% 2.72/1.99 ((ndr1_0 | (~hskp55)) <=> (ndr1_0 | (~hskp55))),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(136,plain,
% 2.72/1.99 (((~hskp55) | ndr1_0) <=> (ndr1_0 | (~hskp55))),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(137,axiom,((~hskp55) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 2.72/1.99 tff(138,plain,
% 2.72/1.99 (ndr1_0 | (~hskp55)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[137, 136])).
% 2.72/1.99 tff(139,plain,
% 2.72/1.99 (ndr1_0 | (~hskp55)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[138, 135])).
% 2.72/1.99 tff(140,plain,
% 2.72/1.99 (~hskp55),
% 2.72/1.99 inference(unit_resolution,[status(thm)],[139, 128])).
% 2.72/1.99 tff(141,plain,
% 2.72/1.99 ((ndr1_0 | (~hskp54)) <=> (ndr1_0 | (~hskp54))),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(142,plain,
% 2.72/1.99 (((~hskp54) | ndr1_0) <=> (ndr1_0 | (~hskp54))),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(143,axiom,((~hskp54) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 2.72/1.99 tff(144,plain,
% 2.72/1.99 (ndr1_0 | (~hskp54)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[143, 142])).
% 2.72/1.99 tff(145,plain,
% 2.72/1.99 (ndr1_0 | (~hskp54)),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[144, 141])).
% 2.72/1.99 tff(146,plain,
% 2.72/1.99 (~hskp54),
% 2.72/1.99 inference(unit_resolution,[status(thm)],[145, 128])).
% 2.72/1.99 tff(147,plain,
% 2.72/1.99 ((hskp55 | hskp54 | hskp21) <=> (hskp55 | hskp54 | hskp21)),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(148,plain,
% 2.72/1.99 (((hskp21 | hskp54) | hskp55) <=> (hskp55 | hskp54 | hskp21)),
% 2.72/1.99 inference(rewrite,[status(thm)],[])).
% 2.72/1.99 tff(149,axiom,((hskp21 | hskp54) | hskp55), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 2.72/1.99 tff(150,plain,
% 2.72/1.99 (hskp55 | hskp54 | hskp21),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[149, 148])).
% 2.72/1.99 tff(151,plain,
% 2.72/1.99 (hskp55 | hskp54 | hskp21),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[150, 147])).
% 2.72/1.99 tff(152,plain,
% 2.72/1.99 (hskp55 | hskp54 | hskp21),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[151, 147])).
% 2.72/1.99 tff(153,plain,
% 2.72/1.99 (hskp55 | hskp54 | hskp21),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[152, 147])).
% 2.72/1.99 tff(154,plain,
% 2.72/1.99 (hskp55 | hskp54 | hskp21),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[153, 147])).
% 2.72/1.99 tff(155,plain,
% 2.72/1.99 (hskp55 | hskp54 | hskp21),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[154, 147])).
% 2.72/1.99 tff(156,plain,
% 2.72/1.99 (hskp55 | hskp54 | hskp21),
% 2.72/1.99 inference(modus_ponens,[status(thm)],[155, 147])).
% 2.72/1.99 tff(157,plain,
% 2.72/1.99 (hskp55 | hskp54 | hskp21),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[156, 147])).
% 2.81/1.99 tff(158,plain,
% 2.81/1.99 ($false),
% 2.81/1.99 inference(unit_resolution,[status(thm)],[157, 146, 140, 134])).
% 2.81/1.99 tff(159,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 2.81/1.99 tff(160,plain,
% 2.81/1.99 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.81/1.99 inference(rewrite,[status(thm)],[])).
% 2.81/1.99 tff(161,plain,
% 2.81/1.99 ((hskp58 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181))) <=> (hskp58 | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.81/1.99 inference(rewrite,[status(thm)],[])).
% 2.81/1.99 tff(162,plain,
% 2.81/1.99 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181))))),
% 2.81/1.99 inference(monotonicity,[status(thm)],[161])).
% 2.81/1.99 tff(163,plain,
% 2.81/1.99 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.81/1.99 inference(transitivity,[status(thm)],[162, 160])).
% 2.81/1.99 tff(164,plain,
% 2.81/1.99 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)))),
% 2.81/1.99 inference(quant_inst,[status(thm)],[])).
% 2.81/1.99 tff(165,plain,
% 2.81/1.99 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181))),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[164, 163])).
% 2.81/1.99 tff(166,plain,
% 2.81/1.99 (hskp58 | c1_1(a2181) | (~c3_1(a2181))),
% 2.81/1.99 inference(unit_resolution,[status(thm)],[165, 159, 103, 127])).
% 2.81/1.99 tff(167,plain,
% 2.81/1.99 (hskp58),
% 2.81/1.99 inference(unit_resolution,[status(thm)],[166, 107, 104])).
% 2.81/1.99 tff(168,plain,
% 2.81/1.99 (((~hskp58) | (~c1_1(a2252))) <=> ((~hskp58) | (~c1_1(a2252)))),
% 2.81/1.99 inference(rewrite,[status(thm)],[])).
% 2.81/1.99 tff(169,plain,
% 2.81/1.99 (((~c1_1(a2252)) | (~hskp58)) <=> ((~hskp58) | (~c1_1(a2252)))),
% 2.81/1.99 inference(rewrite,[status(thm)],[])).
% 2.81/1.99 tff(170,axiom,((~c1_1(a2252)) | (~hskp58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 2.81/1.99 tff(171,plain,
% 2.81/1.99 ((~hskp58) | (~c1_1(a2252))),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[170, 169])).
% 2.81/1.99 tff(172,plain,
% 2.81/1.99 ((~hskp58) | (~c1_1(a2252))),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[171, 168])).
% 2.81/1.99 tff(173,plain,
% 2.81/1.99 (~c1_1(a2252)),
% 2.81/1.99 inference(unit_resolution,[status(thm)],[172, 167])).
% 2.81/1.99 tff(174,plain,
% 2.81/1.99 (((~hskp58) | (~c2_1(a2252))) <=> ((~hskp58) | (~c2_1(a2252)))),
% 2.81/1.99 inference(rewrite,[status(thm)],[])).
% 2.81/1.99 tff(175,plain,
% 2.81/1.99 (((~c2_1(a2252)) | (~hskp58)) <=> ((~hskp58) | (~c2_1(a2252)))),
% 2.81/1.99 inference(rewrite,[status(thm)],[])).
% 2.81/1.99 tff(176,axiom,((~c2_1(a2252)) | (~hskp58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 2.81/1.99 tff(177,plain,
% 2.81/1.99 ((~hskp58) | (~c2_1(a2252))),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[176, 175])).
% 2.81/1.99 tff(178,plain,
% 2.81/1.99 ((~hskp58) | (~c2_1(a2252))),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[177, 174])).
% 2.81/1.99 tff(179,plain,
% 2.81/1.99 (~c2_1(a2252)),
% 2.81/1.99 inference(unit_resolution,[status(thm)],[178, 167])).
% 2.81/1.99 tff(180,plain,
% 2.81/1.99 (((~hskp58) | c0_1(a2252)) <=> ((~hskp58) | c0_1(a2252))),
% 2.81/1.99 inference(rewrite,[status(thm)],[])).
% 2.81/1.99 tff(181,axiom,((~hskp58) | c0_1(a2252)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 2.81/1.99 tff(182,plain,
% 2.81/1.99 ((~hskp58) | c0_1(a2252)),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[181, 180])).
% 2.81/1.99 tff(183,plain,
% 2.81/1.99 ((~hskp58) | c0_1(a2252)),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[182, 180])).
% 2.81/1.99 tff(184,plain,
% 2.81/1.99 ((~hskp58) | c0_1(a2252)),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[183, 180])).
% 2.81/1.99 tff(185,plain,
% 2.81/1.99 ((~hskp58) | c0_1(a2252)),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[184, 180])).
% 2.81/1.99 tff(186,plain,
% 2.81/1.99 ((~hskp58) | c0_1(a2252)),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[185, 180])).
% 2.81/1.99 tff(187,plain,
% 2.81/1.99 ((~hskp58) | c0_1(a2252)),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[186, 180])).
% 2.81/1.99 tff(188,plain,
% 2.81/1.99 ((~hskp58) | c0_1(a2252)),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[187, 180])).
% 2.81/1.99 tff(189,plain,
% 2.81/1.99 ((~hskp58) | c0_1(a2252)),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[188, 180])).
% 2.81/1.99 tff(190,plain,
% 2.81/1.99 (c0_1(a2252)),
% 2.81/1.99 inference(unit_resolution,[status(thm)],[189, 167])).
% 2.81/1.99 tff(191,plain,
% 2.81/1.99 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2252) | c1_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2252)))),
% 2.81/1.99 inference(rewrite,[status(thm)],[])).
% 2.81/1.99 tff(192,plain,
% 2.81/1.99 ((hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252))) <=> (hskp32 | c2_1(a2252) | c1_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2252)))),
% 2.81/1.99 inference(rewrite,[status(thm)],[])).
% 2.81/1.99 tff(193,plain,
% 2.81/1.99 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2252) | c1_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2252))))),
% 2.81/1.99 inference(monotonicity,[status(thm)],[192])).
% 2.81/1.99 tff(194,plain,
% 2.81/1.99 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2252)))),
% 2.81/1.99 inference(transitivity,[status(thm)],[193, 191])).
% 2.81/1.99 tff(195,plain,
% 2.81/1.99 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))),
% 2.81/1.99 inference(quant_inst,[status(thm)],[])).
% 2.81/1.99 tff(196,plain,
% 2.81/1.99 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2252))),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[195, 194])).
% 2.81/1.99 tff(197,plain,
% 2.81/1.99 ($false),
% 2.81/1.99 inference(unit_resolution,[status(thm)],[196, 159, 106, 190, 179, 173, 104, 103, 117, 107])).
% 2.81/1.99 tff(198,plain,((~c3_1(a2181)) | hskp32 | c1_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.81/1.99 tff(199,plain,
% 2.81/1.99 (~c3_1(a2181)),
% 2.81/1.99 inference(unit_resolution,[status(thm)],[198, 106, 104, 103])).
% 2.81/1.99 tff(200,plain,
% 2.81/1.99 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W)))),
% 2.81/1.99 inference(bind,[status(th)],[])).
% 2.81/1.99 tff(201,plain,
% 2.81/1.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 2.81/1.99 inference(quant_intro,[status(thm)],[200])).
% 2.81/1.99 tff(202,plain,
% 2.81/1.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 2.81/1.99 inference(rewrite,[status(thm)],[])).
% 2.81/1.99 tff(203,plain,
% 2.81/1.99 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c1_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c1_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))))),
% 2.81/1.99 inference(bind,[status(th)],[])).
% 2.81/1.99 tff(204,plain,
% 2.81/1.99 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 2.81/1.99 inference(quant_intro,[status(thm)],[203])).
% 2.81/1.99 tff(205,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause286')).
% 2.81/1.99 tff(206,plain,
% 2.81/1.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[205, 204])).
% 2.81/1.99 tff(207,plain,
% 2.81/1.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[206, 202])).
% 2.81/1.99 tff(208,plain,(
% 2.81/1.99 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 2.81/1.99 inference(skolemize,[status(sab)],[207])).
% 2.81/1.99 tff(209,plain,
% 2.81/1.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[208, 201])).
% 2.81/1.99 tff(210,plain,
% 2.81/1.99 (^[U: $i] : refl((hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) <=> (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)))),
% 2.81/1.99 inference(bind,[status(th)],[])).
% 2.81/1.99 tff(211,plain,
% 2.81/1.99 (![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) <=> ![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 2.81/1.99 inference(quant_intro,[status(thm)],[210])).
% 2.81/1.99 tff(212,plain,
% 2.81/1.99 (![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) <=> ![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 2.81/1.99 inference(rewrite,[status(thm)],[])).
% 2.81/1.99 tff(213,plain,
% 2.81/1.99 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U))), ((((~ndr1_0) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U))), ((((~ndr1_0) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U)))), (((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U)) | c0_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))), (((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)))), ((((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) | hskp32) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) | hskp32))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) | hskp32) <=> (hskp32 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))), ((((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) | hskp32) <=> (hskp32 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)))), (((((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) | hskp32) | hskp2) <=> ((hskp32 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) | hskp2))), rewrite(((hskp32 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) | hskp2) <=> (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))), (((((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) | hskp32) | hskp2) <=> (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))))),
% 2.81/1.99 inference(bind,[status(th)],[])).
% 2.81/1.99 tff(214,plain,
% 2.81/1.99 (![U: $i] : ((((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) | hskp32) | hskp2) <=> ![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 2.81/1.99 inference(quant_intro,[status(thm)],[213])).
% 2.81/1.99 tff(215,axiom,(![U: $i] : ((((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) | hskp32) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause243')).
% 2.81/1.99 tff(216,plain,
% 2.81/1.99 (![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 2.81/1.99 inference(modus_ponens,[status(thm)],[215, 214])).
% 2.81/1.99 tff(217,plain,
% 2.81/2.00 (![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[216, 212])).
% 2.81/2.00 tff(218,plain,(
% 2.81/2.00 ![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 2.81/2.00 inference(skolemize,[status(sab)],[217])).
% 2.81/2.00 tff(219,plain,
% 2.81/2.00 (![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[218, 211])).
% 2.81/2.00 tff(220,plain,
% 2.81/2.00 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2181) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2181) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(221,plain,
% 2.81/2.00 ((hskp32 | hskp2 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | c0_1(a2181)) <=> (hskp32 | hskp2 | c0_1(a2181) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(222,plain,
% 2.81/2.00 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | c0_1(a2181))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2181) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181)))),
% 2.81/2.00 inference(monotonicity,[status(thm)],[221])).
% 2.81/2.00 tff(223,plain,
% 2.81/2.00 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | c0_1(a2181))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2181) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 2.81/2.00 inference(transitivity,[status(thm)],[222, 220])).
% 2.81/2.00 tff(224,plain,
% 2.81/2.00 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | c0_1(a2181))),
% 2.81/2.00 inference(quant_inst,[status(thm)],[])).
% 2.81/2.00 tff(225,plain,
% 2.81/2.00 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2181) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[224, 223])).
% 2.81/2.00 tff(226,plain,
% 2.81/2.00 (hskp32 | hskp2 | c0_1(a2181) | c3_1(a2181)),
% 2.81/2.00 inference(unit_resolution,[status(thm)],[225, 159, 104, 219])).
% 2.81/2.00 tff(227,plain,
% 2.81/2.00 (hskp2),
% 2.81/2.00 inference(unit_resolution,[status(thm)],[226, 199, 105, 106])).
% 2.81/2.00 tff(228,plain,
% 2.81/2.00 (((~hskp2) | (~c2_1(a2187))) <=> ((~hskp2) | (~c2_1(a2187)))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(229,plain,
% 2.81/2.00 (((~c2_1(a2187)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a2187)))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(230,axiom,((~c2_1(a2187)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause236')).
% 2.81/2.00 tff(231,plain,
% 2.81/2.00 ((~hskp2) | (~c2_1(a2187))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[230, 229])).
% 2.81/2.00 tff(232,plain,
% 2.81/2.00 ((~hskp2) | (~c2_1(a2187))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[231, 228])).
% 2.81/2.00 tff(233,plain,
% 2.81/2.00 (~c2_1(a2187)),
% 2.81/2.00 inference(unit_resolution,[status(thm)],[232, 227])).
% 2.81/2.00 tff(234,plain,
% 2.81/2.00 (((~hskp2) | c3_1(a2187)) <=> ((~hskp2) | c3_1(a2187))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(235,axiom,((~hskp2) | c3_1(a2187)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 2.81/2.00 tff(236,plain,
% 2.81/2.00 ((~hskp2) | c3_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[235, 234])).
% 2.81/2.00 tff(237,plain,
% 2.81/2.00 ((~hskp2) | c3_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[236, 234])).
% 2.81/2.00 tff(238,plain,
% 2.81/2.00 ((~hskp2) | c3_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[237, 234])).
% 2.81/2.00 tff(239,plain,
% 2.81/2.00 ((~hskp2) | c3_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[238, 234])).
% 2.81/2.00 tff(240,plain,
% 2.81/2.00 ((~hskp2) | c3_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[239, 234])).
% 2.81/2.00 tff(241,plain,
% 2.81/2.00 ((~hskp2) | c3_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[240, 234])).
% 2.81/2.00 tff(242,plain,
% 2.81/2.00 ((~hskp2) | c3_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[241, 234])).
% 2.81/2.00 tff(243,plain,
% 2.81/2.00 ((~hskp2) | c3_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[242, 234])).
% 2.81/2.00 tff(244,plain,
% 2.81/2.00 (c3_1(a2187)),
% 2.81/2.00 inference(unit_resolution,[status(thm)],[243, 227])).
% 2.81/2.00 tff(245,plain,
% 2.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2187) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | (~c0_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2187) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | (~c0_1(a2187)))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(246,plain,
% 2.81/2.00 (((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2181) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181) | c3_1(a2181) | c1_1(a2181)) <=> (c2_1(a2187) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | (~c0_1(a2187)))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(247,plain,
% 2.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2181) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181) | c3_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2187) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | (~c0_1(a2187))))),
% 2.81/2.00 inference(monotonicity,[status(thm)],[246])).
% 2.81/2.00 tff(248,plain,
% 2.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2181) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181) | c3_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2187) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | (~c0_1(a2187)))),
% 2.81/2.00 inference(transitivity,[status(thm)],[247, 245])).
% 2.81/2.00 tff(249,plain,
% 2.81/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2181) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181) | c3_1(a2181) | c1_1(a2181))),
% 2.81/2.00 inference(quant_inst,[status(thm)],[])).
% 2.81/2.00 tff(250,plain,
% 2.81/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2187) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | (~c0_1(a2187))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[249, 248])).
% 2.81/2.00 tff(251,plain,
% 2.81/2.00 (~c0_1(a2187)),
% 2.81/2.00 inference(unit_resolution,[status(thm)],[250, 159, 244, 233, 105, 104, 103, 209, 199])).
% 2.81/2.00 tff(252,plain,
% 2.81/2.00 (^[V: $i, U: $i] : refl((hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 2.81/2.00 inference(bind,[status(th)],[])).
% 2.81/2.00 tff(253,plain,
% 2.81/2.00 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.81/2.00 inference(quant_intro,[status(thm)],[252])).
% 2.81/2.00 tff(254,plain,
% 2.81/2.00 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(255,plain,
% 2.81/2.00 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) | c3_1(V)) | hskp33) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp33))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp33) <=> (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) | c3_1(V)) | hskp33) <=> (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 2.81/2.00 inference(bind,[status(th)],[])).
% 2.81/2.00 tff(256,plain,
% 2.81/2.00 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) | c3_1(V)) | hskp33) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.81/2.00 inference(quant_intro,[status(thm)],[255])).
% 2.81/2.00 tff(257,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) | c3_1(V)) | hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause269')).
% 2.81/2.00 tff(258,plain,
% 2.81/2.00 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[257, 256])).
% 2.81/2.00 tff(259,plain,
% 2.81/2.00 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[258, 254])).
% 2.81/2.00 tff(260,plain,(
% 2.81/2.00 ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.81/2.00 inference(skolemize,[status(sab)],[259])).
% 2.81/2.00 tff(261,plain,
% 2.81/2.00 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[260, 253])).
% 2.81/2.00 tff(262,plain,
% 2.81/2.00 (^[V: $i, U: $i] : refl((hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))),
% 2.81/2.00 inference(bind,[status(th)],[])).
% 2.81/2.00 tff(263,plain,
% 2.81/2.00 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.00 inference(quant_intro,[status(thm)],[262])).
% 2.81/2.00 tff(264,plain,
% 2.81/2.00 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(265,plain,
% 2.81/2.00 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp47) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | hskp47))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | hskp47) <=> (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp47) <=> (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))))),
% 2.81/2.00 inference(bind,[status(th)],[])).
% 2.81/2.00 tff(266,plain,
% 2.81/2.00 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp47) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.00 inference(quant_intro,[status(thm)],[265])).
% 2.81/2.00 tff(267,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause264')).
% 2.81/2.00 tff(268,plain,
% 2.81/2.00 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[267, 266])).
% 2.81/2.00 tff(269,plain,
% 2.81/2.00 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[268, 264])).
% 2.81/2.00 tff(270,plain,(
% 2.81/2.00 ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.00 inference(skolemize,[status(sab)],[269])).
% 2.81/2.00 tff(271,plain,
% 2.81/2.00 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[270, 263])).
% 2.81/2.00 tff(272,plain,
% 2.81/2.00 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c2_1(a2187) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | c0_1(a2187))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c2_1(a2187) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | c0_1(a2187))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(273,plain,
% 2.81/2.00 ((hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181)) <=> (hskp47 | c2_1(a2187) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | c0_1(a2187))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(274,plain,
% 2.81/2.00 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c2_1(a2187) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | c0_1(a2187)))),
% 2.81/2.00 inference(monotonicity,[status(thm)],[273])).
% 2.81/2.00 tff(275,plain,
% 2.81/2.00 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c2_1(a2187) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | c0_1(a2187))),
% 2.81/2.00 inference(transitivity,[status(thm)],[274, 272])).
% 2.81/2.00 tff(276,plain,
% 2.81/2.00 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))),
% 2.81/2.00 inference(quant_inst,[status(thm)],[])).
% 2.81/2.00 tff(277,plain,
% 2.81/2.00 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c2_1(a2187) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | c0_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[276, 275])).
% 2.81/2.00 tff(278,plain,
% 2.81/2.00 (hskp47),
% 2.81/2.00 inference(unit_resolution,[status(thm)],[277, 159, 244, 233, 104, 103, 271, 199, 251])).
% 2.81/2.00 tff(279,plain,
% 2.81/2.00 (((~hskp47) | (~c1_1(a2226))) <=> ((~hskp47) | (~c1_1(a2226)))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(280,plain,
% 2.81/2.00 (((~c1_1(a2226)) | (~hskp47)) <=> ((~hskp47) | (~c1_1(a2226)))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(281,axiom,((~c1_1(a2226)) | (~hskp47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 2.81/2.00 tff(282,plain,
% 2.81/2.00 ((~hskp47) | (~c1_1(a2226))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[281, 280])).
% 2.81/2.00 tff(283,plain,
% 2.81/2.00 ((~hskp47) | (~c1_1(a2226))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[282, 279])).
% 2.81/2.00 tff(284,plain,
% 2.81/2.00 (~c1_1(a2226)),
% 2.81/2.00 inference(unit_resolution,[status(thm)],[283, 278])).
% 2.81/2.00 tff(285,plain,
% 2.81/2.00 (((~hskp2) | c1_1(a2187)) <=> ((~hskp2) | c1_1(a2187))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(286,axiom,((~hskp2) | c1_1(a2187)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 2.81/2.00 tff(287,plain,
% 2.81/2.00 ((~hskp2) | c1_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[286, 285])).
% 2.81/2.00 tff(288,plain,
% 2.81/2.00 ((~hskp2) | c1_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[287, 285])).
% 2.81/2.00 tff(289,plain,
% 2.81/2.00 ((~hskp2) | c1_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[288, 285])).
% 2.81/2.00 tff(290,plain,
% 2.81/2.00 ((~hskp2) | c1_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[289, 285])).
% 2.81/2.00 tff(291,plain,
% 2.81/2.00 ((~hskp2) | c1_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[290, 285])).
% 2.81/2.00 tff(292,plain,
% 2.81/2.00 ((~hskp2) | c1_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[291, 285])).
% 2.81/2.00 tff(293,plain,
% 2.81/2.00 ((~hskp2) | c1_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[292, 285])).
% 2.81/2.00 tff(294,plain,
% 2.81/2.00 ((~hskp2) | c1_1(a2187)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[293, 285])).
% 2.81/2.00 tff(295,plain,
% 2.81/2.00 (c1_1(a2187)),
% 2.81/2.00 inference(unit_resolution,[status(thm)],[294, 227])).
% 2.81/2.00 tff(296,plain,
% 2.81/2.00 (((~hskp47) | c0_1(a2226)) <=> ((~hskp47) | c0_1(a2226))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(297,axiom,((~hskp47) | c0_1(a2226)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 2.81/2.00 tff(298,plain,
% 2.81/2.00 ((~hskp47) | c0_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[297, 296])).
% 2.81/2.00 tff(299,plain,
% 2.81/2.00 ((~hskp47) | c0_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[298, 296])).
% 2.81/2.00 tff(300,plain,
% 2.81/2.00 ((~hskp47) | c0_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[299, 296])).
% 2.81/2.00 tff(301,plain,
% 2.81/2.00 ((~hskp47) | c0_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[300, 296])).
% 2.81/2.00 tff(302,plain,
% 2.81/2.00 ((~hskp47) | c0_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[301, 296])).
% 2.81/2.00 tff(303,plain,
% 2.81/2.00 ((~hskp47) | c0_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[302, 296])).
% 2.81/2.00 tff(304,plain,
% 2.81/2.00 ((~hskp47) | c0_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[303, 296])).
% 2.81/2.00 tff(305,plain,
% 2.81/2.00 ((~hskp47) | c0_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[304, 296])).
% 2.81/2.00 tff(306,plain,
% 2.81/2.00 (c0_1(a2226)),
% 2.81/2.00 inference(unit_resolution,[status(thm)],[305, 278])).
% 2.81/2.00 tff(307,plain,
% 2.81/2.00 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c1_1(a2226) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | c0_1(a2187) | c3_1(a2226) | (~c0_1(a2226)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2226) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | c0_1(a2187) | c3_1(a2226) | (~c0_1(a2226)))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(308,plain,
% 2.81/2.00 ((hskp33 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c1_1(a2187)) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226))) <=> (hskp33 | c1_1(a2226) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | c0_1(a2187) | c3_1(a2226) | (~c0_1(a2226)))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(309,plain,
% 2.81/2.00 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c1_1(a2187)) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c1_1(a2226) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | c0_1(a2187) | c3_1(a2226) | (~c0_1(a2226))))),
% 2.81/2.00 inference(monotonicity,[status(thm)],[308])).
% 2.81/2.00 tff(310,plain,
% 2.81/2.00 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c1_1(a2187)) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2226) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | c0_1(a2187) | c3_1(a2226) | (~c0_1(a2226)))),
% 2.81/2.00 inference(transitivity,[status(thm)],[309, 307])).
% 2.81/2.00 tff(311,plain,
% 2.81/2.00 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c1_1(a2187)) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)))),
% 2.81/2.00 inference(quant_inst,[status(thm)],[])).
% 2.81/2.00 tff(312,plain,
% 2.81/2.00 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2226) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | c0_1(a2187) | c3_1(a2226) | (~c0_1(a2226))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[311, 310])).
% 2.81/2.00 tff(313,plain,
% 2.81/2.00 (c3_1(a2226)),
% 2.81/2.00 inference(unit_resolution,[status(thm)],[312, 159, 72, 306, 295, 284, 233, 261, 251])).
% 2.81/2.00 tff(314,plain,
% 2.81/2.00 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 2.81/2.00 inference(bind,[status(th)],[])).
% 2.81/2.00 tff(315,plain,
% 2.81/2.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_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)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 2.81/2.00 inference(quant_intro,[status(thm)],[314])).
% 2.81/2.00 tff(316,plain,
% 2.81/2.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_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)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(317,plain,
% 2.81/2.00 (^[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)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) <=> (((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))))), rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c2_1(W)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c2_1(W)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 2.81/2.00 inference(bind,[status(th)],[])).
% 2.81/2.00 tff(318,plain,
% 2.81/2.00 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c2_1(W)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 2.81/2.00 inference(quant_intro,[status(thm)],[317])).
% 2.81/2.00 tff(319,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c2_1(W)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause295')).
% 2.81/2.00 tff(320,plain,
% 2.81/2.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[319, 318])).
% 2.81/2.00 tff(321,plain,
% 2.81/2.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[320, 316])).
% 2.81/2.00 tff(322,plain,(
% 2.81/2.00 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 2.81/2.00 inference(skolemize,[status(sab)],[321])).
% 2.81/2.00 tff(323,plain,
% 2.81/2.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[322, 315])).
% 2.81/2.00 tff(324,plain,
% 2.81/2.00 (((~hskp47) | c2_1(a2226)) <=> ((~hskp47) | c2_1(a2226))),
% 2.81/2.00 inference(rewrite,[status(thm)],[])).
% 2.81/2.00 tff(325,axiom,((~hskp47) | c2_1(a2226)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 2.81/2.00 tff(326,plain,
% 2.81/2.00 ((~hskp47) | c2_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[325, 324])).
% 2.81/2.00 tff(327,plain,
% 2.81/2.00 ((~hskp47) | c2_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[326, 324])).
% 2.81/2.00 tff(328,plain,
% 2.81/2.00 ((~hskp47) | c2_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[327, 324])).
% 2.81/2.00 tff(329,plain,
% 2.81/2.00 ((~hskp47) | c2_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[328, 324])).
% 2.81/2.00 tff(330,plain,
% 2.81/2.00 ((~hskp47) | c2_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[329, 324])).
% 2.81/2.00 tff(331,plain,
% 2.81/2.00 ((~hskp47) | c2_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[330, 324])).
% 2.81/2.00 tff(332,plain,
% 2.81/2.00 ((~hskp47) | c2_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[331, 324])).
% 2.81/2.00 tff(333,plain,
% 2.81/2.00 ((~hskp47) | c2_1(a2226)),
% 2.81/2.00 inference(modus_ponens,[status(thm)],[332, 324])).
% 2.81/2.00 tff(334,plain,
% 2.81/2.00 (c2_1(a2226)),
% 2.81/2.00 inference(unit_resolution,[status(thm)],[333, 278])).
% 2.81/2.00 tff(335,plain,
% 2.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c3_1(a2226)) | (~c2_1(a2226)) | (~c0_1(a2226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c3_1(a2226)) | (~c2_1(a2226)) | (~c0_1(a2226)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(336,plain,
% 2.81/2.01 (((~ndr1_0) | (~c3_1(a2226)) | (~c0_1(a2226)) | (~c2_1(a2226)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187))) <=> (c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c3_1(a2226)) | (~c2_1(a2226)) | (~c0_1(a2226)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(337,plain,
% 2.81/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2226)) | (~c0_1(a2226)) | (~c2_1(a2226)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c3_1(a2226)) | (~c2_1(a2226)) | (~c0_1(a2226))))),
% 2.81/2.01 inference(monotonicity,[status(thm)],[336])).
% 2.81/2.01 tff(338,plain,
% 2.81/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2226)) | (~c0_1(a2226)) | (~c2_1(a2226)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c3_1(a2226)) | (~c2_1(a2226)) | (~c0_1(a2226)))),
% 2.81/2.01 inference(transitivity,[status(thm)],[337, 335])).
% 2.81/2.01 tff(339,plain,
% 2.81/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2226)) | (~c0_1(a2226)) | (~c2_1(a2226)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187)))),
% 2.81/2.01 inference(quant_inst,[status(thm)],[])).
% 2.81/2.01 tff(340,plain,
% 2.81/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c3_1(a2226)) | (~c2_1(a2226)) | (~c0_1(a2226))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[339, 338])).
% 2.81/2.01 tff(341,plain,
% 2.81/2.01 ($false),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[340, 159, 334, 306, 244, 295, 233, 323, 251, 313])).
% 2.81/2.01 tff(342,plain,(hskp32 | hskp33 | c1_1(a2181) | c2_1(a2181) | c0_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.01 tff(343,plain,
% 2.81/2.01 (hskp32),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[342, 105, 104, 103, 72])).
% 2.81/2.01 tff(344,plain,
% 2.81/2.01 (((~hskp32) | (~c2_1(a2186))) <=> ((~hskp32) | (~c2_1(a2186)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(345,plain,
% 2.81/2.01 (((~c2_1(a2186)) | (~hskp32)) <=> ((~hskp32) | (~c2_1(a2186)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(346,axiom,((~c2_1(a2186)) | (~hskp32)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 2.81/2.01 tff(347,plain,
% 2.81/2.01 ((~hskp32) | (~c2_1(a2186))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[346, 345])).
% 2.81/2.01 tff(348,plain,
% 2.81/2.01 ((~hskp32) | (~c2_1(a2186))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[347, 344])).
% 2.81/2.01 tff(349,plain,
% 2.81/2.01 (~c2_1(a2186)),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[348, 343])).
% 2.81/2.01 tff(350,plain,
% 2.81/2.01 (~c3_1(a2186)),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[89, 343])).
% 2.81/2.01 tff(351,plain,
% 2.81/2.01 (c0_1(a2186)),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[83, 343])).
% 2.81/2.01 tff(352,assumption,(~hskp34), introduced(assumption)).
% 2.81/2.01 tff(353,assumption,(c1_1(a2186)), introduced(assumption)).
% 2.81/2.01 tff(354,plain,
% 2.81/2.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 2.81/2.01 inference(bind,[status(th)],[])).
% 2.81/2.01 tff(355,plain,
% 2.81/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.81/2.01 inference(quant_intro,[status(thm)],[354])).
% 2.81/2.01 tff(356,plain,
% 2.81/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(357,plain,
% 2.81/2.01 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 2.81/2.01 inference(bind,[status(th)],[])).
% 2.81/2.01 tff(358,plain,
% 2.81/2.01 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.81/2.01 inference(quant_intro,[status(thm)],[357])).
% 2.81/2.01 tff(359,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause293')).
% 2.81/2.01 tff(360,plain,
% 2.81/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[359, 358])).
% 2.81/2.01 tff(361,plain,
% 2.81/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[360, 356])).
% 2.81/2.01 tff(362,plain,(
% 2.81/2.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.81/2.01 inference(skolemize,[status(sab)],[361])).
% 2.81/2.01 tff(363,plain,
% 2.81/2.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[362, 355])).
% 2.81/2.01 tff(364,plain,
% 2.81/2.01 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(365,plain,
% 2.81/2.01 ((hskp18 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186))) <=> (hskp18 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(366,plain,
% 2.81/2.01 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186))))),
% 2.81/2.01 inference(monotonicity,[status(thm)],[365])).
% 2.81/2.01 tff(367,plain,
% 2.81/2.01 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)))),
% 2.81/2.01 inference(transitivity,[status(thm)],[366, 364])).
% 2.81/2.01 tff(368,plain,
% 2.81/2.01 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)))),
% 2.81/2.01 inference(quant_inst,[status(thm)],[])).
% 2.81/2.01 tff(369,plain,
% 2.81/2.01 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[368, 367])).
% 2.81/2.01 tff(370,plain,
% 2.81/2.01 (hskp18 | (~c1_1(a2186))),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[369, 159, 350, 349, 61])).
% 2.81/2.01 tff(371,plain,
% 2.81/2.01 (hskp18),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[370, 353])).
% 2.81/2.01 tff(372,plain,
% 2.81/2.01 (((~hskp18) | (~c2_1(a2222))) <=> ((~hskp18) | (~c2_1(a2222)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(373,plain,
% 2.81/2.01 (((~c2_1(a2222)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a2222)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(374,axiom,((~c2_1(a2222)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 2.81/2.01 tff(375,plain,
% 2.81/2.01 ((~hskp18) | (~c2_1(a2222))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[374, 373])).
% 2.81/2.01 tff(376,plain,
% 2.81/2.01 ((~hskp18) | (~c2_1(a2222))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[375, 372])).
% 2.81/2.01 tff(377,plain,
% 2.81/2.01 (~c2_1(a2222)),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[376, 371])).
% 2.81/2.01 tff(378,plain,
% 2.81/2.01 (^[V: $i, U: $i] : refl((hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) <=> (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)))),
% 2.81/2.01 inference(bind,[status(th)],[])).
% 2.81/2.01 tff(379,plain,
% 2.81/2.01 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 2.81/2.01 inference(quant_intro,[status(thm)],[378])).
% 2.81/2.01 tff(380,plain,
% 2.81/2.01 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(381,plain,
% 2.81/2.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V))), (((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) | c3_1(U)) | hskp38) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) | hskp38))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) | hskp38) <=> (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) | c3_1(U)) | hskp38) <=> (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))))),
% 2.81/2.01 inference(bind,[status(th)],[])).
% 2.81/2.01 tff(382,plain,
% 2.81/2.01 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) | c3_1(U)) | hskp38) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 2.81/2.01 inference(quant_intro,[status(thm)],[381])).
% 2.81/2.01 tff(383,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) | c3_1(U)) | hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause266')).
% 2.81/2.01 tff(384,plain,
% 2.81/2.01 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[383, 382])).
% 2.81/2.01 tff(385,plain,
% 2.81/2.01 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[384, 380])).
% 2.81/2.01 tff(386,plain,(
% 2.81/2.01 ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 2.81/2.01 inference(skolemize,[status(sab)],[385])).
% 2.81/2.01 tff(387,plain,
% 2.81/2.01 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[386, 379])).
% 2.81/2.01 tff(388,plain,
% 2.81/2.01 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | c3_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2186)) | (~c0_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2186)) | (~c0_1(a2186)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(389,plain,
% 2.81/2.01 ((hskp38 | (~ndr1_0) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2186)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181)) <=> (hskp38 | c3_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2186)) | (~c0_1(a2186)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(390,plain,
% 2.81/2.01 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2186)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | c3_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2186)) | (~c0_1(a2186))))),
% 2.81/2.01 inference(monotonicity,[status(thm)],[389])).
% 2.81/2.01 tff(391,plain,
% 2.81/2.01 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2186)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2186)) | (~c0_1(a2186)))),
% 2.81/2.01 inference(transitivity,[status(thm)],[390, 388])).
% 2.81/2.01 tff(392,plain,
% 2.81/2.01 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2186)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181))),
% 2.81/2.01 inference(quant_inst,[status(thm)],[])).
% 2.81/2.01 tff(393,plain,
% 2.81/2.01 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2186)) | (~c0_1(a2186))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[392, 391])).
% 2.81/2.01 tff(394,plain,
% 2.81/2.01 (hskp38 | (~c1_1(a2186))),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[393, 159, 351, 350, 105, 104, 103, 387])).
% 2.81/2.01 tff(395,plain,
% 2.81/2.01 (hskp38),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[394, 353])).
% 2.81/2.01 tff(396,plain,
% 2.81/2.01 (((~hskp38) | (~c2_1(a2200))) <=> ((~hskp38) | (~c2_1(a2200)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(397,plain,
% 2.81/2.01 (((~c2_1(a2200)) | (~hskp38)) <=> ((~hskp38) | (~c2_1(a2200)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(398,axiom,((~c2_1(a2200)) | (~hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 2.81/2.01 tff(399,plain,
% 2.81/2.01 ((~hskp38) | (~c2_1(a2200))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[398, 397])).
% 2.81/2.01 tff(400,plain,
% 2.81/2.01 ((~hskp38) | (~c2_1(a2200))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[399, 396])).
% 2.81/2.01 tff(401,plain,
% 2.81/2.01 (~c2_1(a2200)),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[400, 395])).
% 2.81/2.01 tff(402,plain,
% 2.81/2.01 (((~hskp38) | (~c0_1(a2200))) <=> ((~hskp38) | (~c0_1(a2200)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(403,plain,
% 2.81/2.01 (((~c0_1(a2200)) | (~hskp38)) <=> ((~hskp38) | (~c0_1(a2200)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(404,axiom,((~c0_1(a2200)) | (~hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 2.81/2.01 tff(405,plain,
% 2.81/2.01 ((~hskp38) | (~c0_1(a2200))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[404, 403])).
% 2.81/2.01 tff(406,plain,
% 2.81/2.01 ((~hskp38) | (~c0_1(a2200))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[405, 402])).
% 2.81/2.01 tff(407,plain,
% 2.81/2.01 (~c0_1(a2200)),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[406, 395])).
% 2.81/2.01 tff(408,plain,
% 2.81/2.01 (((~hskp18) | c3_1(a2222)) <=> ((~hskp18) | c3_1(a2222))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(409,axiom,((~hskp18) | c3_1(a2222)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 2.81/2.01 tff(410,plain,
% 2.81/2.01 ((~hskp18) | c3_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[409, 408])).
% 2.81/2.01 tff(411,plain,
% 2.81/2.01 ((~hskp18) | c3_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[410, 408])).
% 2.81/2.01 tff(412,plain,
% 2.81/2.01 ((~hskp18) | c3_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[411, 408])).
% 2.81/2.01 tff(413,plain,
% 2.81/2.01 ((~hskp18) | c3_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[412, 408])).
% 2.81/2.01 tff(414,plain,
% 2.81/2.01 ((~hskp18) | c3_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[413, 408])).
% 2.81/2.01 tff(415,plain,
% 2.81/2.01 ((~hskp18) | c3_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[414, 408])).
% 2.81/2.01 tff(416,plain,
% 2.81/2.01 ((~hskp18) | c3_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[415, 408])).
% 2.81/2.01 tff(417,plain,
% 2.81/2.01 ((~hskp18) | c3_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[416, 408])).
% 2.81/2.01 tff(418,plain,
% 2.81/2.01 (c3_1(a2222)),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[417, 371])).
% 2.81/2.01 tff(419,plain,
% 2.81/2.01 (((~hskp38) | c1_1(a2200)) <=> ((~hskp38) | c1_1(a2200))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(420,axiom,((~hskp38) | c1_1(a2200)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 2.81/2.01 tff(421,plain,
% 2.81/2.01 ((~hskp38) | c1_1(a2200)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[420, 419])).
% 2.81/2.01 tff(422,plain,
% 2.81/2.01 ((~hskp38) | c1_1(a2200)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[421, 419])).
% 2.81/2.01 tff(423,plain,
% 2.81/2.01 ((~hskp38) | c1_1(a2200)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[422, 419])).
% 2.81/2.01 tff(424,plain,
% 2.81/2.01 ((~hskp38) | c1_1(a2200)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[423, 419])).
% 2.81/2.01 tff(425,plain,
% 2.81/2.01 ((~hskp38) | c1_1(a2200)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[424, 419])).
% 2.81/2.01 tff(426,plain,
% 2.81/2.01 ((~hskp38) | c1_1(a2200)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[425, 419])).
% 2.81/2.01 tff(427,plain,
% 2.81/2.01 ((~hskp38) | c1_1(a2200)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[426, 419])).
% 2.81/2.01 tff(428,plain,
% 2.81/2.01 ((~hskp38) | c1_1(a2200)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[427, 419])).
% 2.81/2.01 tff(429,plain,
% 2.81/2.01 (c1_1(a2200)),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[428, 395])).
% 2.81/2.01 tff(430,plain,
% 2.81/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2200) | c2_1(a2200) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c1_1(a2186)) | (~c0_1(a2186)) | (~c1_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2200) | c2_1(a2200) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c1_1(a2186)) | (~c0_1(a2186)) | (~c1_1(a2200)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(431,plain,
% 2.81/2.01 (((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200))) <=> (c0_1(a2200) | c2_1(a2200) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c1_1(a2186)) | (~c0_1(a2186)) | (~c1_1(a2200)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(432,plain,
% 2.81/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2200) | c2_1(a2200) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c1_1(a2186)) | (~c0_1(a2186)) | (~c1_1(a2200))))),
% 2.81/2.01 inference(monotonicity,[status(thm)],[431])).
% 2.81/2.01 tff(433,plain,
% 2.81/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2200) | c2_1(a2200) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c1_1(a2186)) | (~c0_1(a2186)) | (~c1_1(a2200)))),
% 2.81/2.01 inference(transitivity,[status(thm)],[432, 430])).
% 2.81/2.01 tff(434,plain,
% 2.81/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200)))),
% 2.81/2.01 inference(quant_inst,[status(thm)],[])).
% 2.81/2.01 tff(435,plain,
% 2.81/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2200) | c2_1(a2200) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c1_1(a2186)) | (~c0_1(a2186)) | (~c1_1(a2200))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[434, 433])).
% 2.81/2.01 tff(436,plain,
% 2.81/2.01 (~c1_1(a2222)),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[435, 159, 429, 351, 418, 407, 401, 349, 377, 363, 353])).
% 2.81/2.01 tff(437,plain,
% 2.81/2.01 (^[U: $i] : refl((hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.81/2.01 inference(bind,[status(th)],[])).
% 2.81/2.01 tff(438,plain,
% 2.81/2.01 (![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.81/2.01 inference(quant_intro,[status(thm)],[437])).
% 2.81/2.01 tff(439,plain,
% 2.81/2.01 (![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(440,plain,
% 2.81/2.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp46) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp46))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp46) <=> (hskp46 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp46) <=> (hskp46 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp46) | hskp34) <=> ((hskp46 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp34))), rewrite(((hskp46 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp34) <=> (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp46) | hskp34) <=> (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.81/2.01 inference(bind,[status(th)],[])).
% 2.81/2.01 tff(441,plain,
% 2.81/2.01 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp46) | hskp34) <=> ![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.81/2.01 inference(quant_intro,[status(thm)],[440])).
% 2.81/2.01 tff(442,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp46) | hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause259')).
% 2.81/2.01 tff(443,plain,
% 2.81/2.01 (![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[442, 441])).
% 2.81/2.01 tff(444,plain,
% 2.81/2.01 (![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[443, 439])).
% 2.81/2.01 tff(445,plain,(
% 2.81/2.01 ![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.81/2.01 inference(skolemize,[status(sab)],[444])).
% 2.81/2.01 tff(446,plain,
% 2.81/2.01 (![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[445, 438])).
% 2.81/2.01 tff(447,plain,
% 2.81/2.01 (((~hskp18) | c0_1(a2222)) <=> ((~hskp18) | c0_1(a2222))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(448,axiom,((~hskp18) | c0_1(a2222)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 2.81/2.01 tff(449,plain,
% 2.81/2.01 ((~hskp18) | c0_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[448, 447])).
% 2.81/2.01 tff(450,plain,
% 2.81/2.01 ((~hskp18) | c0_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[449, 447])).
% 2.81/2.01 tff(451,plain,
% 2.81/2.01 ((~hskp18) | c0_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[450, 447])).
% 2.81/2.01 tff(452,plain,
% 2.81/2.01 ((~hskp18) | c0_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[451, 447])).
% 2.81/2.01 tff(453,plain,
% 2.81/2.01 ((~hskp18) | c0_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[452, 447])).
% 2.81/2.01 tff(454,plain,
% 2.81/2.01 ((~hskp18) | c0_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[453, 447])).
% 2.81/2.01 tff(455,plain,
% 2.81/2.01 ((~hskp18) | c0_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[454, 447])).
% 2.81/2.01 tff(456,plain,
% 2.81/2.01 ((~hskp18) | c0_1(a2222)),
% 2.81/2.01 inference(modus_ponens,[status(thm)],[455, 447])).
% 2.81/2.01 tff(457,plain,
% 2.81/2.01 (c0_1(a2222)),
% 2.81/2.01 inference(unit_resolution,[status(thm)],[456, 371])).
% 2.81/2.01 tff(458,plain,
% 2.81/2.01 (((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp46 | hskp34 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.81/2.01 inference(rewrite,[status(thm)],[])).
% 2.81/2.01 tff(459,plain,
% 2.81/2.01 ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.81/2.01 inference(quant_inst,[status(thm)],[])).
% 2.81/2.01 tff(460,plain,
% 2.81/2.01 ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp46 | hskp34 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[459, 458])).
% 2.81/2.02 tff(461,plain,
% 2.81/2.02 (hskp46 | c1_1(a2222)),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[460, 159, 352, 457, 418, 446])).
% 2.81/2.02 tff(462,plain,
% 2.81/2.02 (hskp46),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[461, 436])).
% 2.81/2.02 tff(463,plain,
% 2.81/2.02 (((~hskp46) | c2_1(a2218)) <=> ((~hskp46) | c2_1(a2218))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(464,axiom,((~hskp46) | c2_1(a2218)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 2.81/2.02 tff(465,plain,
% 2.81/2.02 ((~hskp46) | c2_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[464, 463])).
% 2.81/2.02 tff(466,plain,
% 2.81/2.02 ((~hskp46) | c2_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[465, 463])).
% 2.81/2.02 tff(467,plain,
% 2.81/2.02 ((~hskp46) | c2_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[466, 463])).
% 2.81/2.02 tff(468,plain,
% 2.81/2.02 ((~hskp46) | c2_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[467, 463])).
% 2.81/2.02 tff(469,plain,
% 2.81/2.02 ((~hskp46) | c2_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[468, 463])).
% 2.81/2.02 tff(470,plain,
% 2.81/2.02 ((~hskp46) | c2_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[469, 463])).
% 2.81/2.02 tff(471,plain,
% 2.81/2.02 ((~hskp46) | c2_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[470, 463])).
% 2.81/2.02 tff(472,plain,
% 2.81/2.02 ((~hskp46) | c2_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[471, 463])).
% 2.81/2.02 tff(473,plain,
% 2.81/2.02 (c2_1(a2218)),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[472, 462])).
% 2.81/2.02 tff(474,plain,
% 2.81/2.02 (((~hskp46) | c0_1(a2218)) <=> ((~hskp46) | c0_1(a2218))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(475,axiom,((~hskp46) | c0_1(a2218)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 2.81/2.02 tff(476,plain,
% 2.81/2.02 ((~hskp46) | c0_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[475, 474])).
% 2.81/2.02 tff(477,plain,
% 2.81/2.02 ((~hskp46) | c0_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[476, 474])).
% 2.81/2.02 tff(478,plain,
% 2.81/2.02 ((~hskp46) | c0_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[477, 474])).
% 2.81/2.02 tff(479,plain,
% 2.81/2.02 ((~hskp46) | c0_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[478, 474])).
% 2.81/2.02 tff(480,plain,
% 2.81/2.02 ((~hskp46) | c0_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[479, 474])).
% 2.81/2.02 tff(481,plain,
% 2.81/2.02 ((~hskp46) | c0_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[480, 474])).
% 2.81/2.02 tff(482,plain,
% 2.81/2.02 ((~hskp46) | c0_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[481, 474])).
% 2.81/2.02 tff(483,plain,
% 2.81/2.02 ((~hskp46) | c0_1(a2218)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[482, 474])).
% 2.81/2.02 tff(484,plain,
% 2.81/2.02 (c0_1(a2218)),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[483, 462])).
% 2.81/2.02 tff(485,plain,
% 2.81/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(486,plain,
% 2.81/2.02 (((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2222) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218))) <=> (c3_1(a2186) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(487,plain,
% 2.81/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2222) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218))))),
% 2.81/2.02 inference(monotonicity,[status(thm)],[486])).
% 2.81/2.02 tff(488,plain,
% 2.81/2.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2222) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 2.81/2.02 inference(transitivity,[status(thm)],[487, 485])).
% 2.81/2.02 tff(489,plain,
% 2.81/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2222) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))),
% 2.81/2.02 inference(quant_inst,[status(thm)],[])).
% 2.81/2.02 tff(490,plain,
% 2.81/2.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[489, 488])).
% 2.81/2.02 tff(491,plain,
% 2.81/2.02 (~c1_1(a2218)),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[490, 159, 484, 473, 351, 418, 350, 349, 377, 51, 436])).
% 2.81/2.02 tff(492,plain,
% 2.81/2.02 (^[U: $i] : refl((hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 2.81/2.02 inference(bind,[status(th)],[])).
% 2.81/2.02 tff(493,plain,
% 2.81/2.02 (![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.02 inference(quant_intro,[status(thm)],[492])).
% 2.81/2.02 tff(494,plain,
% 2.81/2.02 (![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(495,plain,
% 2.81/2.02 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp33) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp33))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp33) <=> (hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp33) <=> (hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp33) | hskp34) <=> ((hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp34))), rewrite(((hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp34) <=> (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp33) | hskp34) <=> (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 2.81/2.02 inference(bind,[status(th)],[])).
% 2.81/2.02 tff(496,plain,
% 2.81/2.02 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp33) | hskp34) <=> ![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.02 inference(quant_intro,[status(thm)],[495])).
% 2.81/2.02 tff(497,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp33) | hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause257')).
% 2.81/2.02 tff(498,plain,
% 2.81/2.02 (![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[497, 496])).
% 2.81/2.02 tff(499,plain,
% 2.81/2.02 (![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[498, 494])).
% 2.81/2.02 tff(500,plain,(
% 2.81/2.02 ![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.02 inference(skolemize,[status(sab)],[499])).
% 2.81/2.02 tff(501,plain,
% 2.81/2.02 (![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[500, 493])).
% 2.81/2.02 tff(502,plain,
% 2.81/2.02 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(503,plain,
% 2.81/2.02 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 2.81/2.02 inference(quant_inst,[status(thm)],[])).
% 2.81/2.02 tff(504,plain,
% 2.81/2.02 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[503, 502])).
% 2.81/2.02 tff(505,plain,
% 2.81/2.02 ($false),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[504, 159, 352, 72, 484, 473, 501, 491])).
% 2.81/2.02 tff(506,plain,((~c1_1(a2186)) | hskp34 | hskp33 | c0_1(a2181) | c1_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.02 tff(507,plain,
% 2.81/2.02 (~c1_1(a2186)),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[506, 352, 72, 105, 104, 103])).
% 2.81/2.02 tff(508,assumption,(~c1_1(a2186)), introduced(assumption)).
% 2.81/2.02 tff(509,plain,
% 2.81/2.02 (^[V: $i, U: $i] : refl((hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))),
% 2.81/2.02 inference(bind,[status(th)],[])).
% 2.81/2.02 tff(510,plain,
% 2.81/2.02 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.02 inference(quant_intro,[status(thm)],[509])).
% 2.81/2.02 tff(511,plain,
% 2.81/2.02 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(512,plain,
% 2.81/2.02 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(V))), (((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | c3_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | c3_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(V) | c2_1(V))), (((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | c3_1(V) | c2_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | c3_1(V) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) | c1_1(U)) | hskp53) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | hskp53))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | hskp53) <=> (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), (((((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) | c1_1(U)) | hskp53) <=> (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))))),
% 2.81/2.02 inference(bind,[status(th)],[])).
% 2.81/2.02 tff(513,plain,
% 2.81/2.02 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) | c1_1(U)) | hskp53) <=> ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.02 inference(quant_intro,[status(thm)],[512])).
% 2.81/2.02 tff(514,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) | c1_1(U)) | hskp53)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause265')).
% 2.81/2.02 tff(515,plain,
% 2.81/2.02 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[514, 513])).
% 2.81/2.02 tff(516,plain,
% 2.81/2.02 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[515, 511])).
% 2.81/2.02 tff(517,plain,(
% 2.81/2.02 ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.02 inference(skolemize,[status(sab)],[516])).
% 2.81/2.02 tff(518,plain,
% 2.81/2.02 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[517, 510])).
% 2.81/2.02 tff(519,assumption,(~c2_1(a2186)), introduced(assumption)).
% 2.81/2.02 tff(520,assumption,(~c3_1(a2186)), introduced(assumption)).
% 2.81/2.02 tff(521,assumption,(c0_1(a2186)), introduced(assumption)).
% 2.81/2.02 tff(522,assumption,(~hskp53), introduced(assumption)).
% 2.81/2.02 tff(523,plain,
% 2.81/2.02 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(524,plain,
% 2.81/2.02 ((hskp53 | (~ndr1_0) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2186) | c3_1(a2186) | c2_1(a2186)) <=> (hskp53 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(525,plain,
% 2.81/2.02 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2186) | c3_1(a2186) | c2_1(a2186))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186))))),
% 2.81/2.02 inference(monotonicity,[status(thm)],[524])).
% 2.81/2.02 tff(526,plain,
% 2.81/2.02 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2186) | c3_1(a2186) | c2_1(a2186))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)))),
% 2.81/2.02 inference(transitivity,[status(thm)],[525, 523])).
% 2.81/2.02 tff(527,plain,
% 2.81/2.02 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2186) | c3_1(a2186) | c2_1(a2186))),
% 2.81/2.02 inference(quant_inst,[status(thm)],[])).
% 2.81/2.02 tff(528,plain,
% 2.81/2.02 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[527, 526])).
% 2.81/2.02 tff(529,plain,
% 2.81/2.02 ($false),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[528, 159, 522, 521, 520, 519, 518, 508])).
% 2.81/2.02 tff(530,plain,(c1_1(a2186) | hskp53 | (~c0_1(a2186)) | c3_1(a2186) | c2_1(a2186)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.02 tff(531,plain,
% 2.81/2.02 (hskp53),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[530, 507, 351, 350, 349])).
% 2.81/2.02 tff(532,plain,
% 2.81/2.02 (c0_1(a2235)),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[101, 531])).
% 2.81/2.02 tff(533,assumption,(~hskp37), introduced(assumption)).
% 2.81/2.02 tff(534,plain,
% 2.81/2.02 (^[U: $i] : refl((hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 2.81/2.02 inference(bind,[status(th)],[])).
% 2.81/2.02 tff(535,plain,
% 2.81/2.02 (![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.81/2.02 inference(quant_intro,[status(thm)],[534])).
% 2.81/2.02 tff(536,plain,
% 2.81/2.02 (![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(537,plain,
% 2.81/2.02 (^[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) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp37) <=> ((hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp37))), rewrite(((hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp37) <=> (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp37) <=> (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 2.81/2.02 inference(bind,[status(th)],[])).
% 2.81/2.02 tff(538,plain,
% 2.81/2.02 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp37) <=> ![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.81/2.02 inference(quant_intro,[status(thm)],[537])).
% 2.81/2.02 tff(539,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause247')).
% 2.81/2.02 tff(540,plain,
% 2.81/2.02 (![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[539, 538])).
% 2.81/2.02 tff(541,plain,
% 2.81/2.02 (![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[540, 536])).
% 2.81/2.02 tff(542,plain,(
% 2.81/2.02 ![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.81/2.02 inference(skolemize,[status(sab)],[541])).
% 2.81/2.02 tff(543,plain,
% 2.81/2.02 (![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[542, 535])).
% 2.81/2.02 tff(544,plain,
% 2.81/2.02 (((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp37 | hskp7 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)))) <=> ((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp37 | hskp7 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(545,plain,
% 2.81/2.02 ((hskp37 | hskp7 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186))) <=> (hskp37 | hskp7 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(546,plain,
% 2.81/2.02 (((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp37 | hskp7 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp37 | hskp7 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186))))),
% 2.81/2.02 inference(monotonicity,[status(thm)],[545])).
% 2.81/2.02 tff(547,plain,
% 2.81/2.02 (((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp37 | hskp7 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp37 | hskp7 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)))),
% 2.81/2.02 inference(transitivity,[status(thm)],[546, 544])).
% 2.81/2.02 tff(548,plain,
% 2.81/2.02 ((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp37 | hskp7 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))),
% 2.81/2.02 inference(quant_inst,[status(thm)],[])).
% 2.81/2.02 tff(549,plain,
% 2.81/2.02 ((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp37 | hskp7 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[548, 547])).
% 2.81/2.02 tff(550,plain,
% 2.81/2.02 (hskp37 | hskp7),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[549, 159, 351, 350, 349, 543])).
% 2.81/2.02 tff(551,plain,
% 2.81/2.02 (hskp7),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[550, 533])).
% 2.81/2.02 tff(552,plain,
% 2.81/2.02 (((~hskp7) | c0_1(a2198)) <=> ((~hskp7) | c0_1(a2198))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(553,axiom,((~hskp7) | c0_1(a2198)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 2.81/2.02 tff(554,plain,
% 2.81/2.02 ((~hskp7) | c0_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[553, 552])).
% 2.81/2.02 tff(555,plain,
% 2.81/2.02 ((~hskp7) | c0_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[554, 552])).
% 2.81/2.02 tff(556,plain,
% 2.81/2.02 ((~hskp7) | c0_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[555, 552])).
% 2.81/2.02 tff(557,plain,
% 2.81/2.02 ((~hskp7) | c0_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[556, 552])).
% 2.81/2.02 tff(558,plain,
% 2.81/2.02 ((~hskp7) | c0_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[557, 552])).
% 2.81/2.02 tff(559,plain,
% 2.81/2.02 ((~hskp7) | c0_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[558, 552])).
% 2.81/2.02 tff(560,plain,
% 2.81/2.02 ((~hskp7) | c0_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[559, 552])).
% 2.81/2.02 tff(561,plain,
% 2.81/2.02 ((~hskp7) | c0_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[560, 552])).
% 2.81/2.02 tff(562,plain,
% 2.81/2.02 (c0_1(a2198)),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[561, 551])).
% 2.81/2.02 tff(563,plain,
% 2.81/2.02 (((~hskp7) | c2_1(a2198)) <=> ((~hskp7) | c2_1(a2198))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(564,axiom,((~hskp7) | c2_1(a2198)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 2.81/2.02 tff(565,plain,
% 2.81/2.02 ((~hskp7) | c2_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[564, 563])).
% 2.81/2.02 tff(566,plain,
% 2.81/2.02 ((~hskp7) | c2_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[565, 563])).
% 2.81/2.02 tff(567,plain,
% 2.81/2.02 ((~hskp7) | c2_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[566, 563])).
% 2.81/2.02 tff(568,plain,
% 2.81/2.02 ((~hskp7) | c2_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[567, 563])).
% 2.81/2.02 tff(569,plain,
% 2.81/2.02 ((~hskp7) | c2_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[568, 563])).
% 2.81/2.02 tff(570,plain,
% 2.81/2.02 ((~hskp7) | c2_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[569, 563])).
% 2.81/2.02 tff(571,plain,
% 2.81/2.02 ((~hskp7) | c2_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[570, 563])).
% 2.81/2.02 tff(572,plain,
% 2.81/2.02 ((~hskp7) | c2_1(a2198)),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[571, 563])).
% 2.81/2.02 tff(573,plain,
% 2.81/2.02 (c2_1(a2198)),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[572, 551])).
% 2.81/2.02 tff(574,plain,
% 2.81/2.02 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | c1_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(575,plain,
% 2.81/2.02 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)))),
% 2.81/2.02 inference(quant_inst,[status(thm)],[])).
% 2.81/2.02 tff(576,plain,
% 2.81/2.02 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | c1_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[575, 574])).
% 2.81/2.02 tff(577,plain,
% 2.81/2.02 (c1_1(a2198)),
% 2.81/2.02 inference(unit_resolution,[status(thm)],[576, 159, 352, 72, 573, 562, 501])).
% 2.81/2.02 tff(578,plain,
% 2.81/2.02 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W)))),
% 2.81/2.02 inference(bind,[status(th)],[])).
% 2.81/2.02 tff(579,plain,
% 2.81/2.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 2.81/2.02 inference(quant_intro,[status(thm)],[578])).
% 2.81/2.02 tff(580,plain,
% 2.81/2.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 2.81/2.02 inference(rewrite,[status(thm)],[])).
% 2.81/2.02 tff(581,plain,
% 2.81/2.02 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))))),
% 2.81/2.02 inference(bind,[status(th)],[])).
% 2.81/2.02 tff(582,plain,
% 2.81/2.02 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 2.81/2.02 inference(quant_intro,[status(thm)],[581])).
% 2.81/2.02 tff(583,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause287')).
% 2.81/2.02 tff(584,plain,
% 2.81/2.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[583, 582])).
% 2.81/2.02 tff(585,plain,
% 2.81/2.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 2.81/2.02 inference(modus_ponens,[status(thm)],[584, 580])).
% 2.81/2.02 tff(586,plain,(
% 2.81/2.02 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 2.81/2.03 inference(skolemize,[status(sab)],[585])).
% 2.81/2.03 tff(587,plain,
% 2.81/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[586, 579])).
% 2.81/2.03 tff(588,plain,
% 2.81/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2186)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(589,plain,
% 2.81/2.03 (((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2198)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181)) <=> (c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2186)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(590,plain,
% 2.81/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2198)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2186))))),
% 2.81/2.03 inference(monotonicity,[status(thm)],[589])).
% 2.81/2.03 tff(591,plain,
% 2.81/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2198)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2186)))),
% 2.81/2.03 inference(transitivity,[status(thm)],[590, 588])).
% 2.81/2.03 tff(592,plain,
% 2.81/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2198)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))),
% 2.81/2.03 inference(quant_inst,[status(thm)],[])).
% 2.81/2.03 tff(593,plain,
% 2.81/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2186))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[592, 591])).
% 2.81/2.03 tff(594,plain,
% 2.81/2.03 (~c1_1(a2186)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[593, 159, 573, 562, 350, 349, 105, 104, 103, 587, 577])).
% 2.81/2.03 tff(595,plain,
% 2.81/2.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))))),
% 2.81/2.03 inference(bind,[status(th)],[])).
% 2.81/2.03 tff(596,plain,
% 2.81/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 2.81/2.03 inference(quant_intro,[status(thm)],[595])).
% 2.81/2.03 tff(597,plain,
% 2.81/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(598,plain,
% 2.81/2.03 (^[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) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))))),
% 2.81/2.03 inference(bind,[status(th)],[])).
% 2.81/2.03 tff(599,plain,
% 2.81/2.03 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 2.81/2.03 inference(quant_intro,[status(thm)],[598])).
% 2.81/2.03 tff(600,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause291')).
% 2.81/2.03 tff(601,plain,
% 2.81/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[600, 599])).
% 2.81/2.03 tff(602,plain,
% 2.81/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[601, 597])).
% 2.81/2.03 tff(603,plain,(
% 2.81/2.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 2.81/2.03 inference(skolemize,[status(sab)],[602])).
% 2.81/2.03 tff(604,plain,
% 2.81/2.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[603, 596])).
% 2.81/2.03 tff(605,plain,
% 2.81/2.03 ((hskp37 | hskp34 | hskp6) <=> (hskp37 | hskp34 | hskp6)),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(606,plain,
% 2.81/2.03 (((hskp34 | hskp37) | hskp6) <=> (hskp37 | hskp34 | hskp6)),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(607,axiom,((hskp34 | hskp37) | hskp6), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 2.81/2.03 tff(608,plain,
% 2.81/2.03 (hskp37 | hskp34 | hskp6),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[607, 606])).
% 2.81/2.03 tff(609,plain,
% 2.81/2.03 (hskp37 | hskp34 | hskp6),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[608, 605])).
% 2.81/2.03 tff(610,plain,
% 2.81/2.03 (hskp37 | hskp34 | hskp6),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[609, 605])).
% 2.81/2.03 tff(611,plain,
% 2.81/2.03 (hskp37 | hskp34 | hskp6),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[610, 605])).
% 2.81/2.03 tff(612,plain,
% 2.81/2.03 (hskp37 | hskp34 | hskp6),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[611, 605])).
% 2.81/2.03 tff(613,plain,
% 2.81/2.03 (hskp37 | hskp34 | hskp6),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[612, 605])).
% 2.81/2.03 tff(614,plain,
% 2.81/2.03 (hskp37 | hskp34 | hskp6),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[613, 605])).
% 2.81/2.03 tff(615,plain,
% 2.81/2.03 (hskp37 | hskp34 | hskp6),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[614, 605])).
% 2.81/2.03 tff(616,plain,
% 2.81/2.03 (hskp6),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[615, 533, 352])).
% 2.81/2.03 tff(617,plain,
% 2.81/2.03 (((~hskp6) | (~c1_1(a2197))) <=> ((~hskp6) | (~c1_1(a2197)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(618,plain,
% 2.81/2.03 (((~c1_1(a2197)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a2197)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(619,axiom,((~c1_1(a2197)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause229')).
% 2.81/2.03 tff(620,plain,
% 2.81/2.03 ((~hskp6) | (~c1_1(a2197))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[619, 618])).
% 2.81/2.03 tff(621,plain,
% 2.81/2.03 ((~hskp6) | (~c1_1(a2197))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[620, 617])).
% 2.81/2.03 tff(622,plain,
% 2.81/2.03 (~c1_1(a2197)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[621, 616])).
% 2.81/2.03 tff(623,plain,
% 2.81/2.03 (((~hskp6) | (~c0_1(a2197))) <=> ((~hskp6) | (~c0_1(a2197)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(624,plain,
% 2.81/2.03 (((~c0_1(a2197)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a2197)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(625,axiom,((~c0_1(a2197)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause227')).
% 2.81/2.03 tff(626,plain,
% 2.81/2.03 ((~hskp6) | (~c0_1(a2197))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[625, 624])).
% 2.81/2.03 tff(627,plain,
% 2.81/2.03 ((~hskp6) | (~c0_1(a2197))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[626, 623])).
% 2.81/2.03 tff(628,plain,
% 2.81/2.03 (~c0_1(a2197)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[627, 616])).
% 2.81/2.03 tff(629,plain,
% 2.81/2.03 (((~hskp7) | (~c3_1(a2198))) <=> ((~hskp7) | (~c3_1(a2198)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(630,plain,
% 2.81/2.03 (((~c3_1(a2198)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a2198)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(631,axiom,((~c3_1(a2198)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause226')).
% 2.81/2.03 tff(632,plain,
% 2.81/2.03 ((~hskp7) | (~c3_1(a2198))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[631, 630])).
% 2.81/2.03 tff(633,plain,
% 2.81/2.03 ((~hskp7) | (~c3_1(a2198))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[632, 629])).
% 2.81/2.03 tff(634,plain,
% 2.81/2.03 (~c3_1(a2198)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[633, 551])).
% 2.81/2.03 tff(635,plain,
% 2.81/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2186) | c2_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c0_1(a2186)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(636,plain,
% 2.81/2.03 (((~ndr1_0) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186))) <=> (c3_1(a2186) | c2_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c0_1(a2186)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(637,plain,
% 2.81/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c0_1(a2186))))),
% 2.81/2.03 inference(monotonicity,[status(thm)],[636])).
% 2.81/2.03 tff(638,plain,
% 2.81/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2186) | c2_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c0_1(a2186)))),
% 2.81/2.03 inference(transitivity,[status(thm)],[637, 635])).
% 2.81/2.03 tff(639,plain,
% 2.81/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))),
% 2.81/2.03 inference(quant_inst,[status(thm)],[])).
% 2.81/2.03 tff(640,plain,
% 2.81/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2186) | c2_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c0_1(a2186))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[639, 638])).
% 2.81/2.03 tff(641,plain,
% 2.81/2.03 (~c2_1(a2197)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[640, 159, 351, 573, 562, 350, 349, 634, 628, 622, 604])).
% 2.81/2.03 tff(642,plain,
% 2.81/2.03 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c1_1(a2198)) | (~c0_1(a2198)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c1_1(a2198)) | (~c0_1(a2198)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(643,plain,
% 2.81/2.03 ((hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2197) | c1_1(a2197) | c2_1(a2197)) <=> (hskp38 | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c1_1(a2198)) | (~c0_1(a2198)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(644,plain,
% 2.81/2.03 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2197) | c1_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c1_1(a2198)) | (~c0_1(a2198))))),
% 2.81/2.03 inference(monotonicity,[status(thm)],[643])).
% 2.81/2.03 tff(645,plain,
% 2.81/2.03 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2197) | c1_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c1_1(a2198)) | (~c0_1(a2198)))),
% 2.81/2.03 inference(transitivity,[status(thm)],[644, 642])).
% 2.81/2.03 tff(646,plain,
% 2.81/2.03 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2197) | c1_1(a2197) | c2_1(a2197))),
% 2.81/2.03 inference(quant_inst,[status(thm)],[])).
% 2.81/2.03 tff(647,plain,
% 2.81/2.03 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c1_1(a2198)) | (~c0_1(a2198))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[646, 645])).
% 2.81/2.03 tff(648,plain,
% 2.81/2.03 (hskp38),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[647, 159, 562, 634, 628, 622, 387, 577, 641])).
% 2.81/2.03 tff(649,plain,
% 2.81/2.03 (~c2_1(a2200)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[400, 648])).
% 2.81/2.03 tff(650,plain,
% 2.81/2.03 (~c0_1(a2200)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[406, 648])).
% 2.81/2.03 tff(651,plain,
% 2.81/2.03 (c1_1(a2200)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[428, 648])).
% 2.81/2.03 tff(652,plain,
% 2.81/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c0_1(a2200) | c2_1(a2200) | c3_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c0_1(a2200) | c2_1(a2200) | c3_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2200)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(653,plain,
% 2.81/2.03 ((hskp33 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c1_1(a2200)) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186))) <=> (hskp33 | c0_1(a2200) | c2_1(a2200) | c3_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2200)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(654,plain,
% 2.81/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c1_1(a2200)) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c0_1(a2200) | c2_1(a2200) | c3_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2200))))),
% 2.81/2.03 inference(monotonicity,[status(thm)],[653])).
% 2.81/2.03 tff(655,plain,
% 2.81/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c1_1(a2200)) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c0_1(a2200) | c2_1(a2200) | c3_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2200)))),
% 2.81/2.03 inference(transitivity,[status(thm)],[654, 652])).
% 2.81/2.03 tff(656,plain,
% 2.81/2.03 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c1_1(a2200)) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))),
% 2.81/2.03 inference(quant_inst,[status(thm)],[])).
% 2.81/2.03 tff(657,plain,
% 2.81/2.03 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c0_1(a2200) | c2_1(a2200) | c3_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2200))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[656, 655])).
% 2.81/2.03 tff(658,plain,
% 2.81/2.03 ($false),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[657, 159, 72, 651, 351, 650, 649, 350, 261, 594])).
% 2.81/2.03 tff(659,plain,(hskp37 | hskp33 | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | hskp34), inference(lemma,lemma(discharge,[]))).
% 2.81/2.03 tff(660,plain,
% 2.81/2.03 (hskp37),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[659, 352, 105, 104, 103, 72])).
% 2.81/2.03 tff(661,plain,
% 2.81/2.03 (((~hskp53) | c2_1(a2235)) <=> ((~hskp53) | c2_1(a2235))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(662,axiom,((~hskp53) | c2_1(a2235)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 2.81/2.03 tff(663,plain,
% 2.81/2.03 ((~hskp53) | c2_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[662, 661])).
% 2.81/2.03 tff(664,plain,
% 2.81/2.03 ((~hskp53) | c2_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[663, 661])).
% 2.81/2.03 tff(665,plain,
% 2.81/2.03 ((~hskp53) | c2_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[664, 661])).
% 2.81/2.03 tff(666,plain,
% 2.81/2.03 ((~hskp53) | c2_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[665, 661])).
% 2.81/2.03 tff(667,plain,
% 2.81/2.03 ((~hskp53) | c2_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[666, 661])).
% 2.81/2.03 tff(668,plain,
% 2.81/2.03 ((~hskp53) | c2_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[667, 661])).
% 2.81/2.03 tff(669,plain,
% 2.81/2.03 ((~hskp53) | c2_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[668, 661])).
% 2.81/2.03 tff(670,plain,
% 2.81/2.03 ((~hskp53) | c2_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[669, 661])).
% 2.81/2.03 tff(671,plain,
% 2.81/2.03 (c2_1(a2235)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[670, 531])).
% 2.81/2.03 tff(672,plain,
% 2.81/2.03 (((~hskp53) | c3_1(a2235)) <=> ((~hskp53) | c3_1(a2235))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(673,axiom,((~hskp53) | c3_1(a2235)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 2.81/2.03 tff(674,plain,
% 2.81/2.03 ((~hskp53) | c3_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[673, 672])).
% 2.81/2.03 tff(675,plain,
% 2.81/2.03 ((~hskp53) | c3_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[674, 672])).
% 2.81/2.03 tff(676,plain,
% 2.81/2.03 ((~hskp53) | c3_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[675, 672])).
% 2.81/2.03 tff(677,plain,
% 2.81/2.03 ((~hskp53) | c3_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[676, 672])).
% 2.81/2.03 tff(678,plain,
% 2.81/2.03 ((~hskp53) | c3_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[677, 672])).
% 2.81/2.03 tff(679,plain,
% 2.81/2.03 ((~hskp53) | c3_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[678, 672])).
% 2.81/2.03 tff(680,plain,
% 2.81/2.03 ((~hskp53) | c3_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[679, 672])).
% 2.81/2.03 tff(681,plain,
% 2.81/2.03 ((~hskp53) | c3_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[680, 672])).
% 2.81/2.03 tff(682,plain,
% 2.81/2.03 (c3_1(a2235)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[681, 531])).
% 2.81/2.03 tff(683,assumption,(hskp37), introduced(assumption)).
% 2.81/2.03 tff(684,plain,
% 2.81/2.03 (((~hskp37) | (~c0_1(a2196))) <=> ((~hskp37) | (~c0_1(a2196)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(685,plain,
% 2.81/2.03 (((~c0_1(a2196)) | (~hskp37)) <=> ((~hskp37) | (~c0_1(a2196)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(686,axiom,((~c0_1(a2196)) | (~hskp37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 2.81/2.03 tff(687,plain,
% 2.81/2.03 ((~hskp37) | (~c0_1(a2196))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[686, 685])).
% 2.81/2.03 tff(688,plain,
% 2.81/2.03 ((~hskp37) | (~c0_1(a2196))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[687, 684])).
% 2.81/2.03 tff(689,plain,
% 2.81/2.03 (~c0_1(a2196)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[688, 683])).
% 2.81/2.03 tff(690,plain,
% 2.81/2.03 (((~hskp37) | c2_1(a2196)) <=> ((~hskp37) | c2_1(a2196))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(691,axiom,((~hskp37) | c2_1(a2196)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 2.81/2.03 tff(692,plain,
% 2.81/2.03 ((~hskp37) | c2_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[691, 690])).
% 2.81/2.03 tff(693,plain,
% 2.81/2.03 ((~hskp37) | c2_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[692, 690])).
% 2.81/2.03 tff(694,plain,
% 2.81/2.03 ((~hskp37) | c2_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[693, 690])).
% 2.81/2.03 tff(695,plain,
% 2.81/2.03 ((~hskp37) | c2_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[694, 690])).
% 2.81/2.03 tff(696,plain,
% 2.81/2.03 ((~hskp37) | c2_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[695, 690])).
% 2.81/2.03 tff(697,plain,
% 2.81/2.03 ((~hskp37) | c2_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[696, 690])).
% 2.81/2.03 tff(698,plain,
% 2.81/2.03 ((~hskp37) | c2_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[697, 690])).
% 2.81/2.03 tff(699,plain,
% 2.81/2.03 ((~hskp37) | c2_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[698, 690])).
% 2.81/2.03 tff(700,plain,
% 2.81/2.03 (c2_1(a2196)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[699, 683])).
% 2.81/2.03 tff(701,plain,
% 2.81/2.03 (((~hskp37) | c1_1(a2196)) <=> ((~hskp37) | c1_1(a2196))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(702,axiom,((~hskp37) | c1_1(a2196)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 2.81/2.03 tff(703,plain,
% 2.81/2.03 ((~hskp37) | c1_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[702, 701])).
% 2.81/2.03 tff(704,plain,
% 2.81/2.03 ((~hskp37) | c1_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[703, 701])).
% 2.81/2.03 tff(705,plain,
% 2.81/2.03 ((~hskp37) | c1_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[704, 701])).
% 2.81/2.03 tff(706,plain,
% 2.81/2.03 ((~hskp37) | c1_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[705, 701])).
% 2.81/2.03 tff(707,plain,
% 2.81/2.03 ((~hskp37) | c1_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[706, 701])).
% 2.81/2.03 tff(708,plain,
% 2.81/2.03 ((~hskp37) | c1_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[707, 701])).
% 2.81/2.03 tff(709,plain,
% 2.81/2.03 ((~hskp37) | c1_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[708, 701])).
% 2.81/2.03 tff(710,plain,
% 2.81/2.03 ((~hskp37) | c1_1(a2196)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[709, 701])).
% 2.81/2.03 tff(711,plain,
% 2.81/2.03 (c1_1(a2196)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[710, 683])).
% 2.81/2.03 tff(712,assumption,(c3_1(a2235)), introduced(assumption)).
% 2.81/2.03 tff(713,assumption,(c2_1(a2235)), introduced(assumption)).
% 2.81/2.03 tff(714,plain,
% 2.81/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2196) | (~ndr1_0) | (~c2_1(a2196)) | (~c1_1(a2196)) | (~c2_1(a2235)) | (~c1_1(a2235)) | (~c3_1(a2235)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2196) | (~ndr1_0) | (~c2_1(a2196)) | (~c1_1(a2196)) | (~c2_1(a2235)) | (~c1_1(a2235)) | (~c3_1(a2235)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(715,plain,
% 2.81/2.03 ((hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235))) <=> (hskp33 | c0_1(a2196) | (~ndr1_0) | (~c2_1(a2196)) | (~c1_1(a2196)) | (~c2_1(a2235)) | (~c1_1(a2235)) | (~c3_1(a2235)))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(716,plain,
% 2.81/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2196) | (~ndr1_0) | (~c2_1(a2196)) | (~c1_1(a2196)) | (~c2_1(a2235)) | (~c1_1(a2235)) | (~c3_1(a2235))))),
% 2.81/2.03 inference(monotonicity,[status(thm)],[715])).
% 2.81/2.03 tff(717,plain,
% 2.81/2.03 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2196) | (~ndr1_0) | (~c2_1(a2196)) | (~c1_1(a2196)) | (~c2_1(a2235)) | (~c1_1(a2235)) | (~c3_1(a2235)))),
% 2.81/2.03 inference(transitivity,[status(thm)],[716, 714])).
% 2.81/2.03 tff(718,plain,
% 2.81/2.03 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))),
% 2.81/2.03 inference(quant_inst,[status(thm)],[])).
% 2.81/2.03 tff(719,plain,
% 2.81/2.03 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2196) | (~ndr1_0) | (~c2_1(a2196)) | (~c1_1(a2196)) | (~c2_1(a2235)) | (~c1_1(a2235)) | (~c3_1(a2235))),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[718, 717])).
% 2.81/2.03 tff(720,plain,
% 2.81/2.03 (~c1_1(a2235)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[719, 159, 72, 713, 712, 711, 700, 689, 71])).
% 2.81/2.03 tff(721,assumption,(c0_1(a2235)), introduced(assumption)).
% 2.81/2.03 tff(722,plain,
% 2.81/2.03 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | c1_1(a2235))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | c1_1(a2235))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(723,plain,
% 2.81/2.03 ((hskp34 | hskp33 | (~ndr1_0) | c1_1(a2235) | (~c0_1(a2235)) | (~c2_1(a2235))) <=> (hskp34 | hskp33 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | c1_1(a2235))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(724,plain,
% 2.81/2.03 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2235) | (~c0_1(a2235)) | (~c2_1(a2235)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | c1_1(a2235)))),
% 2.81/2.03 inference(monotonicity,[status(thm)],[723])).
% 2.81/2.03 tff(725,plain,
% 2.81/2.03 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2235) | (~c0_1(a2235)) | (~c2_1(a2235)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | c1_1(a2235))),
% 2.81/2.03 inference(transitivity,[status(thm)],[724, 722])).
% 2.81/2.03 tff(726,plain,
% 2.81/2.03 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2235) | (~c0_1(a2235)) | (~c2_1(a2235)))),
% 2.81/2.03 inference(quant_inst,[status(thm)],[])).
% 2.81/2.03 tff(727,plain,
% 2.81/2.03 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | c1_1(a2235)),
% 2.81/2.03 inference(modus_ponens,[status(thm)],[726, 725])).
% 2.81/2.03 tff(728,plain,
% 2.81/2.03 (hskp34 | hskp33 | c1_1(a2235)),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[727, 159, 721, 713, 501])).
% 2.81/2.03 tff(729,plain,
% 2.81/2.03 (hskp34),
% 2.81/2.03 inference(unit_resolution,[status(thm)],[728, 720, 72])).
% 2.81/2.03 tff(730,plain,
% 2.81/2.03 (((~hskp34) | c3_1(a2189)) <=> ((~hskp34) | c3_1(a2189))),
% 2.81/2.03 inference(rewrite,[status(thm)],[])).
% 2.81/2.03 tff(731,axiom,((~hskp34) | c3_1(a2189)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 2.81/2.04 tff(732,plain,
% 2.81/2.04 ((~hskp34) | c3_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[731, 730])).
% 2.81/2.04 tff(733,plain,
% 2.81/2.04 ((~hskp34) | c3_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[732, 730])).
% 2.81/2.04 tff(734,plain,
% 2.81/2.04 ((~hskp34) | c3_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[733, 730])).
% 2.81/2.04 tff(735,plain,
% 2.81/2.04 ((~hskp34) | c3_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[734, 730])).
% 2.81/2.04 tff(736,plain,
% 2.81/2.04 ((~hskp34) | c3_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[735, 730])).
% 2.81/2.04 tff(737,plain,
% 2.81/2.04 ((~hskp34) | c3_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[736, 730])).
% 2.81/2.04 tff(738,plain,
% 2.81/2.04 ((~hskp34) | c3_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[737, 730])).
% 2.81/2.04 tff(739,plain,
% 2.81/2.04 ((~hskp34) | c3_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[738, 730])).
% 2.81/2.04 tff(740,plain,
% 2.81/2.04 (c3_1(a2189)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[739, 729])).
% 2.81/2.04 tff(741,plain,
% 2.81/2.04 (((~hskp34) | c1_1(a2189)) <=> ((~hskp34) | c1_1(a2189))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(742,axiom,((~hskp34) | c1_1(a2189)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 2.81/2.04 tff(743,plain,
% 2.81/2.04 ((~hskp34) | c1_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[742, 741])).
% 2.81/2.04 tff(744,plain,
% 2.81/2.04 ((~hskp34) | c1_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[743, 741])).
% 2.81/2.04 tff(745,plain,
% 2.81/2.04 ((~hskp34) | c1_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[744, 741])).
% 2.81/2.04 tff(746,plain,
% 2.81/2.04 ((~hskp34) | c1_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[745, 741])).
% 2.81/2.04 tff(747,plain,
% 2.81/2.04 ((~hskp34) | c1_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[746, 741])).
% 2.81/2.04 tff(748,plain,
% 2.81/2.04 ((~hskp34) | c1_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[747, 741])).
% 2.81/2.04 tff(749,plain,
% 2.81/2.04 ((~hskp34) | c1_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[748, 741])).
% 2.81/2.04 tff(750,plain,
% 2.81/2.04 ((~hskp34) | c1_1(a2189)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[749, 741])).
% 2.81/2.04 tff(751,plain,
% 2.81/2.04 (c1_1(a2189)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[750, 729])).
% 2.81/2.04 tff(752,plain,
% 2.81/2.04 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2196) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2196)) | (~c1_1(a2196)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2196) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2196)) | (~c1_1(a2196)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(753,plain,
% 2.81/2.04 ((hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189))) <=> (hskp33 | c0_1(a2196) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2196)) | (~c1_1(a2196)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(754,plain,
% 2.81/2.04 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2196) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2196)) | (~c1_1(a2196))))),
% 2.81/2.04 inference(monotonicity,[status(thm)],[753])).
% 2.81/2.04 tff(755,plain,
% 2.81/2.04 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2196) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2196)) | (~c1_1(a2196)))),
% 2.81/2.04 inference(transitivity,[status(thm)],[754, 752])).
% 2.81/2.04 tff(756,plain,
% 2.81/2.04 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))),
% 2.81/2.04 inference(quant_inst,[status(thm)],[])).
% 2.81/2.04 tff(757,plain,
% 2.81/2.04 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2196) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2196)) | (~c1_1(a2196))),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[756, 755])).
% 2.81/2.04 tff(758,plain,
% 2.81/2.04 (~c2_1(a2189)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[757, 159, 72, 711, 700, 751, 740, 689, 71])).
% 2.81/2.04 tff(759,plain,
% 2.81/2.04 (((~hskp34) | (~c0_1(a2189))) <=> ((~hskp34) | (~c0_1(a2189)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(760,plain,
% 2.81/2.04 (((~c0_1(a2189)) | (~hskp34)) <=> ((~hskp34) | (~c0_1(a2189)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(761,axiom,((~c0_1(a2189)) | (~hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 2.81/2.04 tff(762,plain,
% 2.81/2.04 ((~hskp34) | (~c0_1(a2189))),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[761, 760])).
% 2.81/2.04 tff(763,plain,
% 2.81/2.04 ((~hskp34) | (~c0_1(a2189))),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[762, 759])).
% 2.81/2.04 tff(764,plain,
% 2.81/2.04 (~c0_1(a2189)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[763, 729])).
% 2.81/2.04 tff(765,plain,
% 2.81/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(766,plain,
% 2.81/2.04 (((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189))) <=> (c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(767,plain,
% 2.81/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235))))),
% 2.81/2.04 inference(monotonicity,[status(thm)],[766])).
% 2.81/2.04 tff(768,plain,
% 2.81/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))),
% 2.81/2.04 inference(transitivity,[status(thm)],[767, 765])).
% 2.81/2.04 tff(769,plain,
% 2.81/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))),
% 2.81/2.04 inference(quant_inst,[status(thm)],[])).
% 2.81/2.04 tff(770,plain,
% 2.81/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235))),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[769, 768])).
% 2.81/2.04 tff(771,plain,
% 2.81/2.04 ($false),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[770, 159, 721, 713, 712, 751, 740, 764, 323, 758])).
% 2.81/2.04 tff(772,plain,((~hskp37) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)) | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.81/2.04 tff(773,plain,
% 2.81/2.04 ($false),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[772, 682, 671, 72, 660, 532])).
% 2.81/2.04 tff(774,plain,(hskp34 | hskp33 | c0_1(a2181) | c1_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.04 tff(775,plain,
% 2.81/2.04 (hskp34),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[774, 105, 72, 104, 103])).
% 2.81/2.04 tff(776,plain,
% 2.81/2.04 (~c0_1(a2189)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[763, 775])).
% 2.81/2.04 tff(777,plain,
% 2.81/2.04 (c3_1(a2189)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[739, 775])).
% 2.81/2.04 tff(778,plain,
% 2.81/2.04 (c1_1(a2189)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[750, 775])).
% 2.81/2.04 tff(779,plain,
% 2.81/2.04 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(780,plain,
% 2.81/2.04 ((hskp33 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189))) <=> (hskp33 | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(781,plain,
% 2.81/2.04 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189))))),
% 2.81/2.04 inference(monotonicity,[status(thm)],[780])).
% 2.81/2.04 tff(782,plain,
% 2.81/2.04 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)))),
% 2.81/2.04 inference(transitivity,[status(thm)],[781, 779])).
% 2.81/2.04 tff(783,plain,
% 2.81/2.04 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))),
% 2.81/2.04 inference(quant_inst,[status(thm)],[])).
% 2.81/2.04 tff(784,plain,
% 2.81/2.04 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189))),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[783, 782])).
% 2.81/2.04 tff(785,plain,
% 2.81/2.04 (~c2_1(a2189)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[784, 159, 72, 778, 777, 776, 71])).
% 2.81/2.04 tff(786,plain,
% 2.81/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2189) | c2_1(a2186) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2186)) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | c2_1(a2186) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2186)) | (~c0_1(a2186)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(787,plain,
% 2.81/2.04 (((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189))) <=> (c0_1(a2189) | c2_1(a2186) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2186)) | (~c0_1(a2186)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(788,plain,
% 2.81/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2189) | c2_1(a2186) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2186)) | (~c0_1(a2186))))),
% 2.81/2.04 inference(monotonicity,[status(thm)],[787])).
% 2.81/2.04 tff(789,plain,
% 2.81/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | c2_1(a2186) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2186)) | (~c0_1(a2186)))),
% 2.81/2.04 inference(transitivity,[status(thm)],[788, 786])).
% 2.81/2.04 tff(790,plain,
% 2.81/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))),
% 2.81/2.04 inference(quant_inst,[status(thm)],[])).
% 2.81/2.04 tff(791,plain,
% 2.81/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | c2_1(a2186) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2186)) | (~c0_1(a2186))),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[790, 789])).
% 2.81/2.04 tff(792,plain,
% 2.81/2.04 (~c1_1(a2186)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[791, 159, 778, 777, 351, 776, 349, 363, 785])).
% 2.81/2.04 tff(793,plain,
% 2.81/2.04 (hskp53),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[530, 792, 351, 350, 349])).
% 2.81/2.04 tff(794,plain,
% 2.81/2.04 (c0_1(a2235)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[101, 793])).
% 2.81/2.04 tff(795,plain,
% 2.81/2.04 (c2_1(a2235)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[670, 793])).
% 2.81/2.04 tff(796,plain,
% 2.81/2.04 (c3_1(a2235)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[681, 793])).
% 2.81/2.04 tff(797,assumption,(hskp34), introduced(assumption)).
% 2.81/2.04 tff(798,plain,
% 2.81/2.04 (~c0_1(a2189)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[763, 797])).
% 2.81/2.04 tff(799,plain,
% 2.81/2.04 (c3_1(a2189)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[739, 797])).
% 2.81/2.04 tff(800,plain,
% 2.81/2.04 (c1_1(a2189)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[750, 797])).
% 2.81/2.04 tff(801,plain,
% 2.81/2.04 (~c2_1(a2189)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[784, 159, 72, 800, 799, 798, 71])).
% 2.81/2.04 tff(802,plain,
% 2.81/2.04 ($false),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[770, 159, 721, 713, 712, 800, 799, 798, 323, 801])).
% 2.81/2.04 tff(803,plain,((~hskp34) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)) | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.81/2.04 tff(804,plain,
% 2.81/2.04 ($false),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[803, 796, 795, 72, 775, 794])).
% 2.81/2.04 tff(805,plain,(c0_1(a2181) | hskp33 | c1_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.04 tff(806,plain,
% 2.81/2.04 (c0_1(a2181)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[805, 104, 72, 103])).
% 2.81/2.04 tff(807,plain,
% 2.81/2.04 (((~hskp0) | (~c0_1(a2181))) <=> ((~hskp0) | (~c0_1(a2181)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(808,plain,
% 2.81/2.04 (((~c0_1(a2181)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a2181)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(809,axiom,((~c0_1(a2181)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause239')).
% 2.81/2.04 tff(810,plain,
% 2.81/2.04 ((~hskp0) | (~c0_1(a2181))),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[809, 808])).
% 2.81/2.04 tff(811,plain,
% 2.81/2.04 ((~hskp0) | (~c0_1(a2181))),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[810, 807])).
% 2.81/2.04 tff(812,plain,
% 2.81/2.04 (~hskp0),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[811, 806])).
% 2.81/2.04 tff(813,plain,
% 2.81/2.04 (c2_1(a2235)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[670, 91])).
% 2.81/2.04 tff(814,plain,
% 2.81/2.04 (c1_1(a2235)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[727, 159, 352, 72, 102, 813, 501])).
% 2.81/2.04 tff(815,plain,
% 2.81/2.04 (^[U: $i] : refl((hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))),
% 2.81/2.04 inference(bind,[status(th)],[])).
% 2.81/2.04 tff(816,plain,
% 2.81/2.04 (![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.04 inference(quant_intro,[status(thm)],[815])).
% 2.81/2.04 tff(817,plain,
% 2.81/2.04 (![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(818,plain,
% 2.81/2.04 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~c0_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> (((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))))), rewrite((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp0))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))))),
% 2.81/2.04 inference(bind,[status(th)],[])).
% 2.81/2.04 tff(819,plain,
% 2.81/2.04 (![U: $i] : (((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> ![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.04 inference(quant_intro,[status(thm)],[818])).
% 2.81/2.04 tff(820,axiom,(![U: $i] : (((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause256')).
% 2.81/2.04 tff(821,plain,
% 2.81/2.04 (![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[820, 819])).
% 2.81/2.04 tff(822,plain,
% 2.81/2.04 (![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[821, 817])).
% 2.81/2.04 tff(823,plain,(
% 2.81/2.04 ![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.04 inference(skolemize,[status(sab)],[822])).
% 2.81/2.04 tff(824,plain,
% 2.81/2.04 (![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[823, 816])).
% 2.81/2.04 tff(825,assumption,(~hskp0), introduced(assumption)).
% 2.81/2.04 tff(826,plain,
% 2.81/2.04 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(827,plain,
% 2.81/2.04 ((hskp0 | (~ndr1_0) | (~c1_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235))) <=> (hskp0 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(828,plain,
% 2.81/2.04 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235))))),
% 2.81/2.04 inference(monotonicity,[status(thm)],[827])).
% 2.81/2.04 tff(829,plain,
% 2.81/2.04 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))),
% 2.81/2.04 inference(transitivity,[status(thm)],[828, 826])).
% 2.81/2.04 tff(830,plain,
% 2.81/2.04 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)))),
% 2.81/2.04 inference(quant_inst,[status(thm)],[])).
% 2.81/2.04 tff(831,plain,
% 2.81/2.04 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235))),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[830, 829])).
% 2.81/2.04 tff(832,plain,
% 2.81/2.04 ($false),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[831, 159, 825, 102, 813, 824, 814])).
% 2.81/2.04 tff(833,plain,((~hskp53) | hskp0 | hskp34 | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.81/2.04 tff(834,plain,
% 2.81/2.04 (~hskp53),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[833, 352, 812, 72])).
% 2.81/2.04 tff(835,plain,
% 2.81/2.04 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(836,plain,
% 2.81/2.04 ((hskp53 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181)) <=> (hskp53 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(837,plain,
% 2.81/2.04 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181)))),
% 2.81/2.04 inference(monotonicity,[status(thm)],[836])).
% 2.81/2.04 tff(838,plain,
% 2.81/2.04 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 2.81/2.04 inference(transitivity,[status(thm)],[837, 835])).
% 2.81/2.04 tff(839,plain,
% 2.81/2.04 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))),
% 2.81/2.04 inference(quant_inst,[status(thm)],[])).
% 2.81/2.04 tff(840,plain,
% 2.81/2.04 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181)),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[839, 838])).
% 2.81/2.04 tff(841,plain,
% 2.81/2.04 (hskp53 | (~c0_1(a2181)) | c3_1(a2181)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[840, 159, 104, 103, 518])).
% 2.81/2.04 tff(842,plain,
% 2.81/2.04 (c3_1(a2181)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[841, 834, 806])).
% 2.81/2.04 tff(843,plain,
% 2.81/2.04 (hskp32),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[198, 842, 104, 103])).
% 2.81/2.04 tff(844,plain,
% 2.81/2.04 (~c2_1(a2186)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[348, 843])).
% 2.81/2.04 tff(845,plain,
% 2.81/2.04 (c0_1(a2186)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[83, 843])).
% 2.81/2.04 tff(846,plain,
% 2.81/2.04 (((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))) <=> ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp46 | hskp34 | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(847,plain,
% 2.81/2.04 ((hskp46 | hskp34 | (~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181))) <=> (hskp46 | hskp34 | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(848,plain,
% 2.81/2.04 (((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)))) <=> ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | (~c3_1(a2181))))),
% 2.81/2.04 inference(monotonicity,[status(thm)],[847])).
% 2.81/2.04 tff(849,plain,
% 2.81/2.04 (((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)))) <=> ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp46 | hskp34 | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.81/2.04 inference(transitivity,[status(thm)],[848, 846])).
% 2.81/2.04 tff(850,plain,
% 2.81/2.04 ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)))),
% 2.81/2.04 inference(quant_inst,[status(thm)],[])).
% 2.81/2.04 tff(851,plain,
% 2.81/2.04 ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp46 | hskp34 | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | (~c3_1(a2181))),
% 2.81/2.04 inference(modus_ponens,[status(thm)],[850, 849])).
% 2.81/2.04 tff(852,plain,
% 2.81/2.04 (hskp46 | hskp34 | (~c0_1(a2181)) | (~c3_1(a2181))),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[851, 159, 104, 446])).
% 2.81/2.04 tff(853,plain,
% 2.81/2.04 (hskp46),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[852, 842, 806, 352])).
% 2.81/2.04 tff(854,plain,
% 2.81/2.04 (c2_1(a2218)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[472, 853])).
% 2.81/2.04 tff(855,plain,
% 2.81/2.04 (c0_1(a2218)),
% 2.81/2.04 inference(unit_resolution,[status(thm)],[483, 853])).
% 2.81/2.04 tff(856,plain,
% 2.81/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(857,plain,
% 2.81/2.04 (((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218))) <=> (c3_1(a2186) | c2_1(a2186) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 2.81/2.04 inference(rewrite,[status(thm)],[])).
% 2.81/2.04 tff(858,plain,
% 2.81/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218))))),
% 2.81/2.05 inference(monotonicity,[status(thm)],[857])).
% 2.81/2.05 tff(859,plain,
% 2.81/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 2.81/2.05 inference(transitivity,[status(thm)],[858, 856])).
% 2.81/2.05 tff(860,plain,
% 2.81/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))),
% 2.81/2.05 inference(quant_inst,[status(thm)],[])).
% 2.81/2.05 tff(861,plain,
% 2.81/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218))),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[860, 859])).
% 2.81/2.05 tff(862,plain,
% 2.81/2.05 (~c1_1(a2218)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[861, 159, 855, 854, 845, 520, 844, 104, 103, 51, 842])).
% 2.81/2.05 tff(863,plain,
% 2.81/2.05 ($false),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[504, 159, 352, 72, 855, 854, 501, 862])).
% 2.81/2.05 tff(864,plain,(hskp34 | hskp33 | c3_1(a2186) | c1_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.05 tff(865,plain,
% 2.81/2.05 (hskp34),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[864, 520, 72, 104, 103])).
% 2.81/2.05 tff(866,plain,
% 2.81/2.05 (~c0_1(a2189)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[763, 865])).
% 2.81/2.05 tff(867,plain,
% 2.81/2.05 (c3_1(a2189)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[739, 865])).
% 2.81/2.05 tff(868,plain,
% 2.81/2.05 (c1_1(a2189)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[750, 865])).
% 2.81/2.05 tff(869,plain,
% 2.81/2.05 (~c2_1(a2189)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[784, 159, 72, 868, 867, 866, 71])).
% 2.81/2.05 tff(870,plain,
% 2.81/2.05 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c0_1(a2189) | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c0_1(a2189) | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181) | c2_1(a2189) | (~c1_1(a2189)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(871,plain,
% 2.81/2.05 ((hskp33 | (~ndr1_0) | c2_1(a2189) | c0_1(a2189) | (~c1_1(a2189)) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181))) <=> (hskp33 | c0_1(a2189) | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181) | c2_1(a2189) | (~c1_1(a2189)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(872,plain,
% 2.81/2.05 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2189) | c0_1(a2189) | (~c1_1(a2189)) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c0_1(a2189) | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181) | c2_1(a2189) | (~c1_1(a2189))))),
% 2.81/2.05 inference(monotonicity,[status(thm)],[871])).
% 2.81/2.05 tff(873,plain,
% 2.81/2.05 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2189) | c0_1(a2189) | (~c1_1(a2189)) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c0_1(a2189) | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181) | c2_1(a2189) | (~c1_1(a2189)))),
% 2.81/2.05 inference(transitivity,[status(thm)],[872, 870])).
% 2.81/2.05 tff(874,plain,
% 2.81/2.05 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2189) | c0_1(a2189) | (~c1_1(a2189)) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)))),
% 2.81/2.05 inference(quant_inst,[status(thm)],[])).
% 2.81/2.05 tff(875,plain,
% 2.81/2.05 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c0_1(a2189) | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181) | c2_1(a2189) | (~c1_1(a2189))),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[874, 873])).
% 2.81/2.05 tff(876,plain,
% 2.81/2.05 (c3_1(a2181)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[875, 159, 72, 868, 866, 806, 104, 261, 869])).
% 2.81/2.05 tff(877,plain,
% 2.81/2.05 (hskp32),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[198, 876, 104, 103])).
% 2.81/2.05 tff(878,plain,
% 2.81/2.05 (~c2_1(a2186)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[348, 877])).
% 2.81/2.05 tff(879,plain,
% 2.81/2.05 (c0_1(a2186)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[83, 877])).
% 2.81/2.05 tff(880,plain,
% 2.81/2.05 (~c1_1(a2186)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[791, 159, 868, 867, 879, 866, 878, 363, 869])).
% 2.81/2.05 tff(881,plain,
% 2.81/2.05 (hskp53),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[530, 880, 879, 520, 878])).
% 2.81/2.05 tff(882,plain,
% 2.81/2.05 (c0_1(a2235)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[101, 881])).
% 2.81/2.05 tff(883,plain,
% 2.81/2.05 (c2_1(a2235)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[670, 881])).
% 2.81/2.05 tff(884,plain,
% 2.81/2.05 (c3_1(a2235)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[681, 881])).
% 2.81/2.05 tff(885,plain,
% 2.81/2.05 ($false),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[803, 884, 883, 72, 865, 882])).
% 2.81/2.05 tff(886,plain,(c3_1(a2186) | hskp33 | c1_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.05 tff(887,plain,
% 2.81/2.05 (c3_1(a2186)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[886, 104, 72, 103])).
% 2.81/2.05 tff(888,plain,
% 2.81/2.05 (~hskp32),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[89, 887])).
% 2.81/2.05 tff(889,plain,
% 2.81/2.05 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(890,plain,
% 2.81/2.05 ((hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~c0_1(a2181))) <=> (hskp32 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(891,plain,
% 2.81/2.05 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~c0_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181))))),
% 2.81/2.05 inference(monotonicity,[status(thm)],[890])).
% 2.81/2.05 tff(892,plain,
% 2.81/2.05 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~c0_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.81/2.05 inference(transitivity,[status(thm)],[891, 889])).
% 2.81/2.05 tff(893,plain,
% 2.81/2.05 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~c0_1(a2181)))),
% 2.81/2.05 inference(quant_inst,[status(thm)],[])).
% 2.81/2.05 tff(894,plain,
% 2.81/2.05 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181))),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[893, 892])).
% 2.81/2.05 tff(895,plain,
% 2.81/2.05 (hskp32 | (~c0_1(a2181)) | (~c3_1(a2181))),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[894, 159, 104, 103, 117])).
% 2.81/2.05 tff(896,plain,
% 2.81/2.05 (~c3_1(a2181)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[895, 888, 806])).
% 2.81/2.05 tff(897,plain,
% 2.81/2.05 (hskp53),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[841, 896, 806])).
% 2.81/2.05 tff(898,plain,
% 2.81/2.05 (c0_1(a2235)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[101, 897])).
% 2.81/2.05 tff(899,plain,
% 2.81/2.05 (hskp34),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[833, 897, 812, 72])).
% 2.81/2.05 tff(900,plain,
% 2.81/2.05 (c2_1(a2235)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[670, 897])).
% 2.81/2.05 tff(901,plain,
% 2.81/2.05 (c3_1(a2235)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[681, 897])).
% 2.81/2.05 tff(902,plain,
% 2.81/2.05 ($false),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[803, 901, 900, 72, 899, 898])).
% 2.81/2.05 tff(903,plain,(c1_1(a2181) | hskp33 | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.05 tff(904,plain,
% 2.81/2.05 (c1_1(a2181)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[903, 103, 72])).
% 2.81/2.05 tff(905,assumption,(hskp55), introduced(assumption)).
% 2.81/2.05 tff(906,plain,
% 2.81/2.05 (((~hskp55) | c2_1(a2241)) <=> ((~hskp55) | c2_1(a2241))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(907,axiom,((~hskp55) | c2_1(a2241)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 2.81/2.05 tff(908,plain,
% 2.81/2.05 ((~hskp55) | c2_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[907, 906])).
% 2.81/2.05 tff(909,plain,
% 2.81/2.05 ((~hskp55) | c2_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[908, 906])).
% 2.81/2.05 tff(910,plain,
% 2.81/2.05 ((~hskp55) | c2_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[909, 906])).
% 2.81/2.05 tff(911,plain,
% 2.81/2.05 ((~hskp55) | c2_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[910, 906])).
% 2.81/2.05 tff(912,plain,
% 2.81/2.05 ((~hskp55) | c2_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[911, 906])).
% 2.81/2.05 tff(913,plain,
% 2.81/2.05 ((~hskp55) | c2_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[912, 906])).
% 2.81/2.05 tff(914,plain,
% 2.81/2.05 ((~hskp55) | c2_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[913, 906])).
% 2.81/2.05 tff(915,plain,
% 2.81/2.05 ((~hskp55) | c2_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[914, 906])).
% 2.81/2.05 tff(916,plain,
% 2.81/2.05 (c2_1(a2241)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[915, 905])).
% 2.81/2.05 tff(917,plain,
% 2.81/2.05 (((~hskp55) | c0_1(a2241)) <=> ((~hskp55) | c0_1(a2241))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(918,axiom,((~hskp55) | c0_1(a2241)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 2.81/2.05 tff(919,plain,
% 2.81/2.05 ((~hskp55) | c0_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[918, 917])).
% 2.81/2.05 tff(920,plain,
% 2.81/2.05 ((~hskp55) | c0_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[919, 917])).
% 2.81/2.05 tff(921,plain,
% 2.81/2.05 ((~hskp55) | c0_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[920, 917])).
% 2.81/2.05 tff(922,plain,
% 2.81/2.05 ((~hskp55) | c0_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[921, 917])).
% 2.81/2.05 tff(923,plain,
% 2.81/2.05 ((~hskp55) | c0_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[922, 917])).
% 2.81/2.05 tff(924,plain,
% 2.81/2.05 ((~hskp55) | c0_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[923, 917])).
% 2.81/2.05 tff(925,plain,
% 2.81/2.05 ((~hskp55) | c0_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[924, 917])).
% 2.81/2.05 tff(926,plain,
% 2.81/2.05 ((~hskp55) | c0_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[925, 917])).
% 2.81/2.05 tff(927,plain,
% 2.81/2.05 (c0_1(a2241)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[926, 905])).
% 2.81/2.05 tff(928,plain,
% 2.81/2.05 (((~hskp55) | c1_1(a2241)) <=> ((~hskp55) | c1_1(a2241))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(929,axiom,((~hskp55) | c1_1(a2241)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 2.81/2.05 tff(930,plain,
% 2.81/2.05 ((~hskp55) | c1_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[929, 928])).
% 2.81/2.05 tff(931,plain,
% 2.81/2.05 ((~hskp55) | c1_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[930, 928])).
% 2.81/2.05 tff(932,plain,
% 2.81/2.05 ((~hskp55) | c1_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[931, 928])).
% 2.81/2.05 tff(933,plain,
% 2.81/2.05 ((~hskp55) | c1_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[932, 928])).
% 2.81/2.05 tff(934,plain,
% 2.81/2.05 ((~hskp55) | c1_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[933, 928])).
% 2.81/2.05 tff(935,plain,
% 2.81/2.05 ((~hskp55) | c1_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[934, 928])).
% 2.81/2.05 tff(936,plain,
% 2.81/2.05 ((~hskp55) | c1_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[935, 928])).
% 2.81/2.05 tff(937,plain,
% 2.81/2.05 ((~hskp55) | c1_1(a2241)),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[936, 928])).
% 2.81/2.05 tff(938,plain,
% 2.81/2.05 (c1_1(a2241)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[937, 905])).
% 2.81/2.05 tff(939,plain,
% 2.81/2.05 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(940,plain,
% 2.81/2.05 ((hskp0 | (~ndr1_0) | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241))) <=> (hskp0 | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(941,plain,
% 2.81/2.05 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241))))),
% 2.81/2.05 inference(monotonicity,[status(thm)],[940])).
% 2.81/2.05 tff(942,plain,
% 2.81/2.05 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)))),
% 2.81/2.05 inference(transitivity,[status(thm)],[941, 939])).
% 2.81/2.05 tff(943,plain,
% 2.81/2.05 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241)))),
% 2.81/2.05 inference(quant_inst,[status(thm)],[])).
% 2.81/2.05 tff(944,plain,
% 2.81/2.05 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241))),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[943, 942])).
% 2.81/2.05 tff(945,plain,
% 2.81/2.05 (hskp0),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[944, 159, 938, 927, 916, 824])).
% 2.81/2.05 tff(946,plain,
% 2.81/2.05 (((~hskp0) | (~c2_1(a2181))) <=> ((~hskp0) | (~c2_1(a2181)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(947,plain,
% 2.81/2.05 (((~c2_1(a2181)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a2181)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(948,axiom,((~c2_1(a2181)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause241')).
% 2.81/2.05 tff(949,plain,
% 2.81/2.05 ((~hskp0) | (~c2_1(a2181))),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[948, 947])).
% 2.81/2.05 tff(950,plain,
% 2.81/2.05 ((~hskp0) | (~c2_1(a2181))),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[949, 946])).
% 2.81/2.05 tff(951,plain,
% 2.81/2.05 (~c2_1(a2181)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[950, 945])).
% 2.81/2.05 tff(952,plain,
% 2.81/2.05 (((~hskp0) | (~c1_1(a2181))) <=> ((~hskp0) | (~c1_1(a2181)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(953,plain,
% 2.81/2.05 (((~c1_1(a2181)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a2181)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(954,axiom,((~c1_1(a2181)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause240')).
% 2.81/2.05 tff(955,plain,
% 2.81/2.05 ((~hskp0) | (~c1_1(a2181))),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[954, 953])).
% 2.81/2.05 tff(956,plain,
% 2.81/2.05 ((~hskp0) | (~c1_1(a2181))),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[955, 952])).
% 2.81/2.05 tff(957,plain,
% 2.81/2.05 (~c1_1(a2181)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[956, 945])).
% 2.81/2.05 tff(958,plain,
% 2.81/2.05 (~c0_1(a2181)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[811, 945])).
% 2.81/2.05 tff(959,assumption,(c1_1(a2241)), introduced(assumption)).
% 2.81/2.05 tff(960,assumption,(c2_1(a2241)), introduced(assumption)).
% 2.81/2.05 tff(961,assumption,(c0_1(a2241)), introduced(assumption)).
% 2.81/2.05 tff(962,plain,
% 2.81/2.05 (hskp0),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[944, 159, 959, 961, 960, 824])).
% 2.81/2.05 tff(963,plain,
% 2.81/2.05 (~c2_1(a2181)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[950, 962])).
% 2.81/2.05 tff(964,plain,
% 2.81/2.05 (~c1_1(a2181)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[956, 962])).
% 2.81/2.05 tff(965,plain,
% 2.81/2.05 (~c0_1(a2181)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[811, 962])).
% 2.81/2.05 tff(966,plain,
% 2.81/2.05 (~c2_1(a2186)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[348, 73])).
% 2.81/2.05 tff(967,plain,
% 2.81/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2186)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(968,plain,
% 2.81/2.05 (((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181)) <=> (c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2186)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(969,plain,
% 2.81/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2186))))),
% 2.81/2.05 inference(monotonicity,[status(thm)],[968])).
% 2.81/2.05 tff(970,plain,
% 2.81/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2186)))),
% 2.81/2.05 inference(transitivity,[status(thm)],[969, 967])).
% 2.81/2.05 tff(971,plain,
% 2.81/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))),
% 2.81/2.05 inference(quant_inst,[status(thm)],[])).
% 2.81/2.05 tff(972,plain,
% 2.81/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2186))),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[971, 970])).
% 2.81/2.05 tff(973,plain,
% 2.81/2.05 (~c1_1(a2186)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[972, 159, 959, 961, 960, 90, 966, 965, 964, 963, 587])).
% 2.81/2.05 tff(974,plain,
% 2.81/2.05 ($false),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[528, 159, 522, 84, 90, 966, 518, 973])).
% 2.81/2.05 tff(975,plain,((~hskp32) | hskp53 | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.05 tff(976,plain,
% 2.81/2.05 (~hskp32),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[975, 522, 959, 961, 960])).
% 2.81/2.05 tff(977,plain,
% 2.81/2.05 (hskp58 | (~c3_1(a2181))),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[165, 159, 964, 963, 127])).
% 2.81/2.05 tff(978,plain,
% 2.81/2.05 (hskp58),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[977, 107])).
% 2.81/2.05 tff(979,plain,
% 2.81/2.05 (~c2_1(a2252)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[178, 978])).
% 2.81/2.05 tff(980,plain,
% 2.81/2.05 (c0_1(a2252)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[189, 978])).
% 2.81/2.05 tff(981,plain,
% 2.81/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c3_1(a2252) | (~c0_1(a2252)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(982,plain,
% 2.81/2.05 (((~ndr1_0) | c2_1(a2252) | c3_1(a2252) | (~c0_1(a2252)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241))) <=> (c2_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c3_1(a2252) | (~c0_1(a2252)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(983,plain,
% 2.81/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c3_1(a2252) | (~c0_1(a2252)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c3_1(a2252) | (~c0_1(a2252))))),
% 2.81/2.05 inference(monotonicity,[status(thm)],[982])).
% 2.81/2.05 tff(984,plain,
% 2.81/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c3_1(a2252) | (~c0_1(a2252)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c3_1(a2252) | (~c0_1(a2252)))),
% 2.81/2.05 inference(transitivity,[status(thm)],[983, 981])).
% 2.81/2.05 tff(985,plain,
% 2.81/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c3_1(a2252) | (~c0_1(a2252)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)))),
% 2.81/2.05 inference(quant_inst,[status(thm)],[])).
% 2.81/2.05 tff(986,plain,
% 2.81/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c3_1(a2252) | (~c0_1(a2252))),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[985, 984])).
% 2.81/2.05 tff(987,plain,
% 2.81/2.05 (c3_1(a2252)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[986, 159, 980, 959, 961, 960, 979, 964, 963, 51, 107])).
% 2.81/2.05 tff(988,plain,
% 2.81/2.05 (~c1_1(a2252)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[172, 978])).
% 2.81/2.05 tff(989,plain,
% 2.81/2.05 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | (~c3_1(a2252)) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | (~c3_1(a2252)) | (~c0_1(a2252)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(990,plain,
% 2.81/2.05 ((hskp32 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252))) <=> (hskp32 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | (~c3_1(a2252)) | (~c0_1(a2252)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(991,plain,
% 2.81/2.05 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | (~c3_1(a2252)) | (~c0_1(a2252))))),
% 2.81/2.05 inference(monotonicity,[status(thm)],[990])).
% 2.81/2.05 tff(992,plain,
% 2.81/2.05 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | (~c3_1(a2252)) | (~c0_1(a2252)))),
% 2.81/2.05 inference(transitivity,[status(thm)],[991, 989])).
% 2.81/2.05 tff(993,plain,
% 2.81/2.05 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))),
% 2.81/2.05 inference(quant_inst,[status(thm)],[])).
% 2.81/2.05 tff(994,plain,
% 2.81/2.05 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | (~c3_1(a2252)) | (~c0_1(a2252))),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[993, 992])).
% 2.81/2.05 tff(995,plain,
% 2.81/2.05 ($false),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[994, 159, 106, 980, 979, 988, 117, 987])).
% 2.81/2.05 tff(996,plain,((~c3_1(a2181)) | hskp32 | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.05 tff(997,plain,
% 2.81/2.05 (~c3_1(a2181)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[996, 976, 959, 961, 960])).
% 2.81/2.05 tff(998,plain,
% 2.81/2.05 (hskp32 | hskp2 | c3_1(a2181)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[225, 159, 965, 964, 219])).
% 2.81/2.05 tff(999,plain,
% 2.81/2.05 (hskp2),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[998, 997, 976])).
% 2.81/2.05 tff(1000,plain,
% 2.81/2.05 (~c2_1(a2187)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[232, 999])).
% 2.81/2.05 tff(1001,plain,
% 2.81/2.05 (c3_1(a2187)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[243, 999])).
% 2.81/2.05 tff(1002,plain,
% 2.81/2.05 (~c0_1(a2187)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[250, 159, 1001, 1000, 965, 964, 963, 209, 997])).
% 2.81/2.05 tff(1003,plain,
% 2.81/2.05 (hskp47),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[277, 159, 1001, 1000, 964, 963, 271, 997, 1002])).
% 2.81/2.05 tff(1004,plain,
% 2.81/2.05 (~c1_1(a2226)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[283, 1003])).
% 2.81/2.05 tff(1005,plain,
% 2.81/2.05 (c0_1(a2226)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[305, 1003])).
% 2.81/2.05 tff(1006,plain,
% 2.81/2.05 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | c1_1(a2226) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | c3_1(a2226) | (~c0_1(a2226)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | c1_1(a2226) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | c3_1(a2226) | (~c0_1(a2226)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(1007,plain,
% 2.81/2.05 ((hskp53 | (~ndr1_0) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181)) <=> (hskp53 | c1_1(a2226) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | c3_1(a2226) | (~c0_1(a2226)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(1008,plain,
% 2.81/2.05 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | c1_1(a2226) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | c3_1(a2226) | (~c0_1(a2226))))),
% 2.81/2.05 inference(monotonicity,[status(thm)],[1007])).
% 2.81/2.05 tff(1009,plain,
% 2.81/2.05 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | c1_1(a2226) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | c3_1(a2226) | (~c0_1(a2226)))),
% 2.81/2.05 inference(transitivity,[status(thm)],[1008, 1006])).
% 2.81/2.05 tff(1010,plain,
% 2.81/2.05 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))),
% 2.81/2.05 inference(quant_inst,[status(thm)],[])).
% 2.81/2.05 tff(1011,plain,
% 2.81/2.05 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | c1_1(a2226) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | c3_1(a2226) | (~c0_1(a2226))),
% 2.81/2.05 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 2.81/2.05 tff(1012,plain,
% 2.81/2.05 (c3_1(a2226)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[1011, 159, 522, 1005, 1004, 964, 963, 518, 997])).
% 2.81/2.05 tff(1013,plain,
% 2.81/2.05 (c1_1(a2187)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[294, 999])).
% 2.81/2.05 tff(1014,plain,
% 2.81/2.05 (c2_1(a2226)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[333, 1003])).
% 2.81/2.05 tff(1015,plain,
% 2.81/2.05 ($false),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[340, 159, 1014, 1005, 1001, 1013, 1000, 323, 1002, 1012])).
% 2.81/2.05 tff(1016,plain,(hskp53 | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.05 tff(1017,plain,
% 2.81/2.05 (hskp53),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[1016, 959, 961, 960])).
% 2.81/2.05 tff(1018,plain,
% 2.81/2.05 (c0_1(a2235)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[101, 1017])).
% 2.81/2.05 tff(1019,plain,
% 2.81/2.05 (c3_1(a2235)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[681, 1017])).
% 2.81/2.05 tff(1020,plain,
% 2.81/2.05 (c2_1(a2235)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[670, 1017])).
% 2.81/2.05 tff(1021,plain,
% 2.81/2.05 (~hskp34),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[803, 72, 1020, 1019, 1018])).
% 2.81/2.05 tff(1022,plain,
% 2.81/2.05 (~c3_1(a2181)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[996, 106, 959, 961, 960])).
% 2.81/2.05 tff(1023,plain,
% 2.81/2.05 (hskp2),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[998, 1022, 106])).
% 2.81/2.05 tff(1024,plain,
% 2.81/2.05 (~c2_1(a2187)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[232, 1023])).
% 2.81/2.05 tff(1025,plain,
% 2.81/2.05 (c3_1(a2187)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[243, 1023])).
% 2.81/2.05 tff(1026,plain,
% 2.81/2.05 (~c0_1(a2187)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[250, 159, 1025, 1024, 965, 964, 963, 209, 1022])).
% 2.81/2.05 tff(1027,plain,
% 2.81/2.05 (c1_1(a2187)),
% 2.81/2.05 inference(unit_resolution,[status(thm)],[294, 1023])).
% 2.81/2.05 tff(1028,plain,
% 2.81/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(1029,plain,
% 2.81/2.05 (((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187))) <=> (c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))),
% 2.81/2.05 inference(rewrite,[status(thm)],[])).
% 2.81/2.05 tff(1030,plain,
% 2.81/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235))))),
% 2.81/2.06 inference(monotonicity,[status(thm)],[1029])).
% 2.81/2.06 tff(1031,plain,
% 2.81/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))),
% 2.81/2.06 inference(transitivity,[status(thm)],[1030, 1028])).
% 2.81/2.06 tff(1032,plain,
% 2.81/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187)))),
% 2.81/2.06 inference(quant_inst,[status(thm)],[])).
% 2.81/2.06 tff(1033,plain,
% 2.81/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235))),
% 2.81/2.06 inference(modus_ponens,[status(thm)],[1032, 1031])).
% 2.81/2.06 tff(1034,plain,
% 2.81/2.06 ($false),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[1033, 159, 1018, 1020, 1019, 1025, 1027, 1024, 323, 1026])).
% 2.81/2.06 tff(1035,plain,(hskp32 | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.06 tff(1036,plain,
% 2.81/2.06 (hskp32),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[1035, 959, 961, 960])).
% 2.81/2.06 tff(1037,plain,
% 2.81/2.06 (~c2_1(a2186)),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[348, 1036])).
% 2.81/2.06 tff(1038,plain,
% 2.81/2.06 (~c3_1(a2186)),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[89, 1036])).
% 2.81/2.06 tff(1039,plain,
% 2.81/2.06 (~c1_1(a2186)),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[972, 159, 959, 961, 960, 1038, 1037, 965, 964, 963, 587])).
% 2.81/2.06 tff(1040,plain,
% 2.81/2.06 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))))),
% 2.81/2.06 inference(bind,[status(th)],[])).
% 2.81/2.06 tff(1041,plain,
% 2.81/2.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.81/2.06 inference(quant_intro,[status(thm)],[1040])).
% 2.81/2.06 tff(1042,plain,
% 2.81/2.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.81/2.06 inference(rewrite,[status(thm)],[])).
% 2.81/2.06 tff(1043,plain,
% 2.81/2.06 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | (~c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | (~c0_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) | c3_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) | c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))))),
% 2.81/2.06 inference(bind,[status(th)],[])).
% 2.81/2.06 tff(1044,plain,
% 2.81/2.06 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) | c3_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.81/2.06 inference(quant_intro,[status(thm)],[1043])).
% 2.81/2.06 tff(1045,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) | c3_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause288')).
% 2.81/2.06 tff(1046,plain,
% 2.81/2.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.81/2.06 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 2.81/2.06 tff(1047,plain,
% 2.81/2.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.81/2.06 inference(modus_ponens,[status(thm)],[1046, 1042])).
% 2.81/2.06 tff(1048,plain,(
% 2.81/2.06 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.81/2.06 inference(skolemize,[status(sab)],[1047])).
% 2.81/2.06 tff(1049,plain,
% 2.81/2.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.81/2.06 inference(modus_ponens,[status(thm)],[1048, 1041])).
% 2.81/2.06 tff(1050,plain,
% 2.81/2.06 (~hskp37),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[772, 72, 1020, 1019, 1018])).
% 2.81/2.06 tff(1051,plain,
% 2.81/2.06 (hskp6),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[615, 352, 1050])).
% 2.81/2.06 tff(1052,plain,
% 2.81/2.06 (~c1_1(a2197)),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[621, 1051])).
% 2.81/2.06 tff(1053,plain,
% 2.81/2.06 (~c0_1(a2197)),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[627, 1051])).
% 2.81/2.06 tff(1054,plain,
% 2.81/2.06 (c0_1(a2186)),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[83, 1036])).
% 2.81/2.06 tff(1055,plain,
% 2.81/2.06 (hskp37 | hskp7),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[549, 159, 1054, 1038, 1037, 543])).
% 2.81/2.06 tff(1056,plain,
% 2.81/2.06 (hskp7),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[1055, 1050])).
% 2.81/2.06 tff(1057,plain,
% 2.81/2.06 (~c3_1(a2198)),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[633, 1056])).
% 2.81/2.06 tff(1058,plain,
% 2.81/2.06 (c0_1(a2198)),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[561, 1056])).
% 2.81/2.06 tff(1059,plain,
% 2.81/2.06 (c2_1(a2198)),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[572, 1056])).
% 2.81/2.06 tff(1060,plain,
% 2.81/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | c1_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | c1_1(a2186) | (~c0_1(a2186)))),
% 2.81/2.06 inference(rewrite,[status(thm)],[])).
% 2.81/2.06 tff(1061,plain,
% 2.81/2.06 (((~ndr1_0) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c3_1(a2186) | c1_1(a2186) | (~c0_1(a2186))) <=> (c3_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | c1_1(a2186) | (~c0_1(a2186)))),
% 2.81/2.06 inference(rewrite,[status(thm)],[])).
% 2.81/2.06 tff(1062,plain,
% 2.81/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c3_1(a2186) | c1_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | c1_1(a2186) | (~c0_1(a2186))))),
% 2.81/2.06 inference(monotonicity,[status(thm)],[1061])).
% 2.81/2.06 tff(1063,plain,
% 2.81/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c3_1(a2186) | c1_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | c1_1(a2186) | (~c0_1(a2186)))),
% 2.81/2.06 inference(transitivity,[status(thm)],[1062, 1060])).
% 2.81/2.06 tff(1064,plain,
% 2.81/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c3_1(a2186) | c1_1(a2186) | (~c0_1(a2186)))),
% 2.81/2.06 inference(quant_inst,[status(thm)],[])).
% 2.81/2.06 tff(1065,plain,
% 2.81/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | c1_1(a2186) | (~c0_1(a2186))),
% 2.81/2.06 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 2.81/2.06 tff(1066,plain,
% 2.81/2.06 (~c2_1(a2197)),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[1065, 159, 1054, 1059, 1058, 1038, 1057, 1053, 1052, 1049, 1039])).
% 2.81/2.06 tff(1067,plain,
% 2.81/2.06 (((~hskp6) | (~c3_1(a2197))) <=> ((~hskp6) | (~c3_1(a2197)))),
% 2.81/2.06 inference(rewrite,[status(thm)],[])).
% 2.81/2.06 tff(1068,plain,
% 2.81/2.06 (((~c3_1(a2197)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a2197)))),
% 2.81/2.06 inference(rewrite,[status(thm)],[])).
% 2.81/2.06 tff(1069,axiom,((~c3_1(a2197)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause228')).
% 2.81/2.06 tff(1070,plain,
% 2.81/2.06 ((~hskp6) | (~c3_1(a2197))),
% 2.81/2.06 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 2.81/2.06 tff(1071,plain,
% 2.81/2.06 ((~hskp6) | (~c3_1(a2197))),
% 2.81/2.06 inference(modus_ponens,[status(thm)],[1070, 1067])).
% 2.81/2.06 tff(1072,plain,
% 2.81/2.06 (~c3_1(a2197)),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[1071, 1051])).
% 2.81/2.06 tff(1073,plain,
% 2.81/2.06 (hskp34 | c1_1(a2198)),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[576, 159, 72, 1059, 1058, 501])).
% 2.81/2.06 tff(1074,plain,
% 2.81/2.06 (c1_1(a2198)),
% 2.81/2.06 inference(unit_resolution,[status(thm)],[1073, 352])).
% 2.81/2.06 tff(1075,plain,
% 2.81/2.06 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | c3_1(a2198) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2198) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)))),
% 2.81/2.06 inference(rewrite,[status(thm)],[])).
% 2.81/2.06 tff(1076,plain,
% 2.81/2.06 ((hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181)) <=> (hskp38 | c3_1(a2198) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)))),
% 2.81/2.06 inference(rewrite,[status(thm)],[])).
% 2.81/2.06 tff(1077,plain,
% 2.81/2.06 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | c3_1(a2198) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198))))),
% 2.81/2.06 inference(monotonicity,[status(thm)],[1076])).
% 2.81/2.06 tff(1078,plain,
% 2.81/2.06 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2198) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)))),
% 2.88/2.06 inference(transitivity,[status(thm)],[1077, 1075])).
% 2.88/2.06 tff(1079,plain,
% 2.88/2.06 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181))),
% 2.88/2.06 inference(quant_inst,[status(thm)],[])).
% 2.88/2.06 tff(1080,plain,
% 2.88/2.06 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2198) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198))),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 2.88/2.06 tff(1081,plain,
% 2.88/2.06 (hskp38 | (~c1_1(a2198))),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[1080, 159, 1058, 1057, 965, 964, 963, 387])).
% 2.88/2.06 tff(1082,plain,
% 2.88/2.06 (hskp38),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[1081, 1074])).
% 2.88/2.06 tff(1083,plain,
% 2.88/2.06 (~c2_1(a2200)),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[400, 1082])).
% 2.88/2.06 tff(1084,plain,
% 2.88/2.06 (~c0_1(a2200)),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[406, 1082])).
% 2.88/2.06 tff(1085,assumption,(~hskp47), introduced(assumption)).
% 2.88/2.06 tff(1086,plain,
% 2.88/2.06 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c0_1(a2200) | c2_1(a2200) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c3_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c0_1(a2200) | c2_1(a2200) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c3_1(a2200)))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1087,plain,
% 2.88/2.06 ((hskp47 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c3_1(a2200)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197)) <=> (hskp47 | c0_1(a2200) | c2_1(a2200) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c3_1(a2200)))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1088,plain,
% 2.88/2.06 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c3_1(a2200)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c0_1(a2200) | c2_1(a2200) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c3_1(a2200))))),
% 2.88/2.06 inference(monotonicity,[status(thm)],[1087])).
% 2.88/2.06 tff(1089,plain,
% 2.88/2.06 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c3_1(a2200)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c0_1(a2200) | c2_1(a2200) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c3_1(a2200)))),
% 2.88/2.06 inference(transitivity,[status(thm)],[1088, 1086])).
% 2.88/2.06 tff(1090,plain,
% 2.88/2.06 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c3_1(a2200)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))),
% 2.88/2.06 inference(quant_inst,[status(thm)],[])).
% 2.88/2.06 tff(1091,plain,
% 2.88/2.06 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c0_1(a2200) | c2_1(a2200) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c3_1(a2200))),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 2.88/2.06 tff(1092,plain,
% 2.88/2.06 (~c3_1(a2200)),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[1091, 159, 1085, 1084, 1083, 1072, 1052, 271, 1066])).
% 2.88/2.06 tff(1093,plain,
% 2.88/2.06 (c1_1(a2200)),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[428, 1082])).
% 2.88/2.06 tff(1094,plain,
% 2.88/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2200) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c2_1(a2197) | (~c1_1(a2200)) | c3_1(a2200))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2200) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c2_1(a2197) | (~c1_1(a2200)) | c3_1(a2200))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1095,plain,
% 2.88/2.06 (((~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2197) | c2_1(a2197) | c1_1(a2197)) <=> (c2_1(a2200) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c2_1(a2197) | (~c1_1(a2200)) | c3_1(a2200))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1096,plain,
% 2.88/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2197) | c2_1(a2197) | c1_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2200) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c2_1(a2197) | (~c1_1(a2200)) | c3_1(a2200)))),
% 2.88/2.06 inference(monotonicity,[status(thm)],[1095])).
% 2.88/2.06 tff(1097,plain,
% 2.88/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2197) | c2_1(a2197) | c1_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2200) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c2_1(a2197) | (~c1_1(a2200)) | c3_1(a2200))),
% 2.88/2.06 inference(transitivity,[status(thm)],[1096, 1094])).
% 2.88/2.06 tff(1098,plain,
% 2.88/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2197) | c2_1(a2197) | c1_1(a2197))),
% 2.88/2.06 inference(quant_inst,[status(thm)],[])).
% 2.88/2.06 tff(1099,plain,
% 2.88/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2200) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c2_1(a2197) | (~c1_1(a2200)) | c3_1(a2200)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 2.88/2.06 tff(1100,plain,
% 2.88/2.06 ($false),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[1099, 159, 959, 961, 960, 1093, 1083, 1053, 1052, 587, 1092, 1066])).
% 2.88/2.06 tff(1101,plain,(hskp34 | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241)) | hskp47 | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.88/2.06 tff(1102,plain,
% 2.88/2.06 (hskp47),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[1101, 1021, 961, 960, 959, 72])).
% 2.88/2.06 tff(1103,plain,
% 2.88/2.06 (~c1_1(a2226)),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[283, 1102])).
% 2.88/2.06 tff(1104,plain,
% 2.88/2.06 (c0_1(a2226)),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[305, 1102])).
% 2.88/2.06 tff(1105,plain,
% 2.88/2.06 (c2_1(a2226)),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[333, 1102])).
% 2.88/2.06 tff(1106,plain,
% 2.88/2.06 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | c1_1(a2226) | (~ndr1_0) | (~c2_1(a2226)) | (~c0_1(a2226)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | c1_1(a2226) | (~ndr1_0) | (~c2_1(a2226)) | (~c0_1(a2226)))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1107,plain,
% 2.88/2.06 ((hskp34 | hskp33 | (~ndr1_0) | c1_1(a2226) | (~c0_1(a2226)) | (~c2_1(a2226))) <=> (hskp34 | hskp33 | c1_1(a2226) | (~ndr1_0) | (~c2_1(a2226)) | (~c0_1(a2226)))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1108,plain,
% 2.88/2.06 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2226) | (~c0_1(a2226)) | (~c2_1(a2226)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | c1_1(a2226) | (~ndr1_0) | (~c2_1(a2226)) | (~c0_1(a2226))))),
% 2.88/2.06 inference(monotonicity,[status(thm)],[1107])).
% 2.88/2.06 tff(1109,plain,
% 2.88/2.06 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2226) | (~c0_1(a2226)) | (~c2_1(a2226)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | c1_1(a2226) | (~ndr1_0) | (~c2_1(a2226)) | (~c0_1(a2226)))),
% 2.88/2.06 inference(transitivity,[status(thm)],[1108, 1106])).
% 2.88/2.06 tff(1110,plain,
% 2.88/2.06 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2226) | (~c0_1(a2226)) | (~c2_1(a2226)))),
% 2.88/2.06 inference(quant_inst,[status(thm)],[])).
% 2.88/2.06 tff(1111,plain,
% 2.88/2.06 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | c1_1(a2226) | (~ndr1_0) | (~c2_1(a2226)) | (~c0_1(a2226))),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 2.88/2.06 tff(1112,plain,
% 2.88/2.06 ($false),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[1111, 159, 1021, 72, 1105, 1104, 1103, 501])).
% 2.88/2.06 tff(1113,plain,(hskp33 | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241))), inference(lemma,lemma(discharge,[]))).
% 2.88/2.06 tff(1114,plain,
% 2.88/2.06 (hskp33),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[1113, 927, 916, 938])).
% 2.88/2.06 tff(1115,plain,
% 2.88/2.06 (((~hskp33) | (~c2_1(a2188))) <=> ((~hskp33) | (~c2_1(a2188)))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1116,plain,
% 2.88/2.06 (((~c2_1(a2188)) | (~hskp33)) <=> ((~hskp33) | (~c2_1(a2188)))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1117,axiom,((~c2_1(a2188)) | (~hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 2.88/2.06 tff(1118,plain,
% 2.88/2.06 ((~hskp33) | (~c2_1(a2188))),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 2.88/2.06 tff(1119,plain,
% 2.88/2.06 ((~hskp33) | (~c2_1(a2188))),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1118, 1115])).
% 2.88/2.06 tff(1120,plain,
% 2.88/2.06 (~c2_1(a2188)),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[1119, 1114])).
% 2.88/2.06 tff(1121,plain,
% 2.88/2.06 (((~hskp33) | (~c3_1(a2188))) <=> ((~hskp33) | (~c3_1(a2188)))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1122,plain,
% 2.88/2.06 (((~c3_1(a2188)) | (~hskp33)) <=> ((~hskp33) | (~c3_1(a2188)))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1123,axiom,((~c3_1(a2188)) | (~hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 2.88/2.06 tff(1124,plain,
% 2.88/2.06 ((~hskp33) | (~c3_1(a2188))),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 2.88/2.06 tff(1125,plain,
% 2.88/2.06 ((~hskp33) | (~c3_1(a2188))),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1124, 1121])).
% 2.88/2.06 tff(1126,plain,
% 2.88/2.06 (~c3_1(a2188)),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[1125, 1114])).
% 2.88/2.06 tff(1127,plain,
% 2.88/2.06 (((~hskp33) | c1_1(a2188)) <=> ((~hskp33) | c1_1(a2188))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1128,axiom,((~hskp33) | c1_1(a2188)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 2.88/2.06 tff(1129,plain,
% 2.88/2.06 ((~hskp33) | c1_1(a2188)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 2.88/2.06 tff(1130,plain,
% 2.88/2.06 ((~hskp33) | c1_1(a2188)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1129, 1127])).
% 2.88/2.06 tff(1131,plain,
% 2.88/2.06 ((~hskp33) | c1_1(a2188)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1130, 1127])).
% 2.88/2.06 tff(1132,plain,
% 2.88/2.06 ((~hskp33) | c1_1(a2188)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1131, 1127])).
% 2.88/2.06 tff(1133,plain,
% 2.88/2.06 ((~hskp33) | c1_1(a2188)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1132, 1127])).
% 2.88/2.06 tff(1134,plain,
% 2.88/2.06 ((~hskp33) | c1_1(a2188)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1133, 1127])).
% 2.88/2.06 tff(1135,plain,
% 2.88/2.06 ((~hskp33) | c1_1(a2188)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1134, 1127])).
% 2.88/2.06 tff(1136,plain,
% 2.88/2.06 ((~hskp33) | c1_1(a2188)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1135, 1127])).
% 2.88/2.06 tff(1137,plain,
% 2.88/2.06 (c1_1(a2188)),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[1136, 1114])).
% 2.88/2.06 tff(1138,plain,
% 2.88/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a2188) | c2_1(a2188) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2188)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2188) | c2_1(a2188) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2188)))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1139,plain,
% 2.88/2.06 (((~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181)) <=> (c3_1(a2188) | c2_1(a2188) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2188)))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1140,plain,
% 2.88/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a2188) | c2_1(a2188) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2188))))),
% 2.88/2.06 inference(monotonicity,[status(thm)],[1139])).
% 2.88/2.06 tff(1141,plain,
% 2.88/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2188) | c2_1(a2188) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2188)))),
% 2.88/2.06 inference(transitivity,[status(thm)],[1140, 1138])).
% 2.88/2.06 tff(1142,plain,
% 2.88/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))),
% 2.88/2.06 inference(quant_inst,[status(thm)],[])).
% 2.88/2.06 tff(1143,plain,
% 2.88/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2188) | c2_1(a2188) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2188))),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 2.88/2.06 tff(1144,plain,
% 2.88/2.06 ($false),
% 2.88/2.06 inference(unit_resolution,[status(thm)],[1143, 159, 938, 927, 916, 1137, 1126, 1120, 958, 957, 951, 587])).
% 2.88/2.06 tff(1145,plain,(~hskp55), inference(lemma,lemma(discharge,[]))).
% 2.88/2.06 tff(1146,assumption,(hskp26), introduced(assumption)).
% 2.88/2.06 tff(1147,plain,
% 2.88/2.06 (((~hskp26) | c2_1(a2178)) <=> ((~hskp26) | c2_1(a2178))),
% 2.88/2.06 inference(rewrite,[status(thm)],[])).
% 2.88/2.06 tff(1148,axiom,((~hskp26) | c2_1(a2178)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 2.88/2.06 tff(1149,plain,
% 2.88/2.06 ((~hskp26) | c2_1(a2178)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 2.88/2.06 tff(1150,plain,
% 2.88/2.06 ((~hskp26) | c2_1(a2178)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1149, 1147])).
% 2.88/2.06 tff(1151,plain,
% 2.88/2.06 ((~hskp26) | c2_1(a2178)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1150, 1147])).
% 2.88/2.06 tff(1152,plain,
% 2.88/2.06 ((~hskp26) | c2_1(a2178)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1151, 1147])).
% 2.88/2.06 tff(1153,plain,
% 2.88/2.06 ((~hskp26) | c2_1(a2178)),
% 2.88/2.06 inference(modus_ponens,[status(thm)],[1152, 1147])).
% 2.88/2.07 tff(1154,plain,
% 2.88/2.07 ((~hskp26) | c2_1(a2178)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1153, 1147])).
% 2.88/2.07 tff(1155,plain,
% 2.88/2.07 ((~hskp26) | c2_1(a2178)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1154, 1147])).
% 2.88/2.07 tff(1156,plain,
% 2.88/2.07 ((~hskp26) | c2_1(a2178)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1155, 1147])).
% 2.88/2.07 tff(1157,plain,
% 2.88/2.07 (c2_1(a2178)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1156, 1146])).
% 2.88/2.07 tff(1158,plain,
% 2.88/2.07 (((~hskp26) | c0_1(a2178)) <=> ((~hskp26) | c0_1(a2178))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1159,axiom,((~hskp26) | c0_1(a2178)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 2.88/2.07 tff(1160,plain,
% 2.88/2.07 ((~hskp26) | c0_1(a2178)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1159, 1158])).
% 2.88/2.07 tff(1161,plain,
% 2.88/2.07 ((~hskp26) | c0_1(a2178)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1160, 1158])).
% 2.88/2.07 tff(1162,plain,
% 2.88/2.07 ((~hskp26) | c0_1(a2178)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1161, 1158])).
% 2.88/2.07 tff(1163,plain,
% 2.88/2.07 ((~hskp26) | c0_1(a2178)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1162, 1158])).
% 2.88/2.07 tff(1164,plain,
% 2.88/2.07 ((~hskp26) | c0_1(a2178)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1163, 1158])).
% 2.88/2.07 tff(1165,plain,
% 2.88/2.07 ((~hskp26) | c0_1(a2178)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1164, 1158])).
% 2.88/2.07 tff(1166,plain,
% 2.88/2.07 ((~hskp26) | c0_1(a2178)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1165, 1158])).
% 2.88/2.07 tff(1167,plain,
% 2.88/2.07 ((~hskp26) | c0_1(a2178)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1166, 1158])).
% 2.88/2.07 tff(1168,plain,
% 2.88/2.07 (c0_1(a2178)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1167, 1146])).
% 2.88/2.07 tff(1169,plain,
% 2.88/2.07 (~hskp0),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[956, 904])).
% 2.88/2.07 tff(1170,plain,
% 2.88/2.07 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2178)) | (~c0_1(a2178)) | (~c2_1(a2178)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c1_1(a2178)) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1171,plain,
% 2.88/2.07 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2178)) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 2.88/2.07 inference(quant_inst,[status(thm)],[])).
% 2.88/2.07 tff(1172,plain,
% 2.88/2.07 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c1_1(a2178)) | (~c0_1(a2178)) | (~c2_1(a2178))),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 2.88/2.07 tff(1173,plain,
% 2.88/2.07 (~c1_1(a2178)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1172, 159, 1169, 1168, 1157, 824])).
% 2.88/2.07 tff(1174,plain,
% 2.88/2.07 (((~hskp26) | (~c3_1(a2178))) <=> ((~hskp26) | (~c3_1(a2178)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1175,plain,
% 2.88/2.07 (((~c3_1(a2178)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a2178)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1176,axiom,((~c3_1(a2178)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 2.88/2.07 tff(1177,plain,
% 2.88/2.07 ((~hskp26) | (~c3_1(a2178))),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 2.88/2.07 tff(1178,plain,
% 2.88/2.07 ((~hskp26) | (~c3_1(a2178))),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1177, 1174])).
% 2.88/2.07 tff(1179,plain,
% 2.88/2.07 (~c3_1(a2178)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1178, 1146])).
% 2.88/2.07 tff(1180,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c3_1(a2178) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c3_1(a2178) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1181,plain,
% 2.88/2.07 ((hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2178) | c3_1(a2178) | (~c0_1(a2178))) <=> (hskp33 | c3_1(a2178) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1182,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2178) | c3_1(a2178) | (~c0_1(a2178)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c3_1(a2178) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178))))),
% 2.88/2.07 inference(monotonicity,[status(thm)],[1181])).
% 2.88/2.07 tff(1183,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2178) | c3_1(a2178) | (~c0_1(a2178)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c3_1(a2178) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)))),
% 2.88/2.07 inference(transitivity,[status(thm)],[1182, 1180])).
% 2.88/2.07 tff(1184,plain,
% 2.88/2.07 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2178) | c3_1(a2178) | (~c0_1(a2178)))),
% 2.88/2.07 inference(quant_inst,[status(thm)],[])).
% 2.88/2.07 tff(1185,plain,
% 2.88/2.07 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c3_1(a2178) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178))),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 2.88/2.07 tff(1186,plain,
% 2.88/2.07 ($false),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1185, 159, 72, 1168, 1179, 105, 904, 103, 261, 1173])).
% 2.88/2.07 tff(1187,plain,((~hskp26) | hskp33 | c0_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.88/2.07 tff(1188,plain,
% 2.88/2.07 (~hskp26),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1187, 105, 72, 103])).
% 2.88/2.07 tff(1189,assumption,(hskp48), introduced(assumption)).
% 2.88/2.07 tff(1190,plain,
% 2.88/2.07 (((~hskp48) | (~c0_1(a2228))) <=> ((~hskp48) | (~c0_1(a2228)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1191,plain,
% 2.88/2.07 (((~c0_1(a2228)) | (~hskp48)) <=> ((~hskp48) | (~c0_1(a2228)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1192,axiom,((~c0_1(a2228)) | (~hskp48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 2.88/2.07 tff(1193,plain,
% 2.88/2.07 ((~hskp48) | (~c0_1(a2228))),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 2.88/2.07 tff(1194,plain,
% 2.88/2.07 ((~hskp48) | (~c0_1(a2228))),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1193, 1190])).
% 2.88/2.07 tff(1195,plain,
% 2.88/2.07 (~c0_1(a2228)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1194, 1189])).
% 2.88/2.07 tff(1196,plain,
% 2.88/2.07 (((~hskp48) | c2_1(a2228)) <=> ((~hskp48) | c2_1(a2228))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1197,axiom,((~hskp48) | c2_1(a2228)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 2.88/2.07 tff(1198,plain,
% 2.88/2.07 ((~hskp48) | c2_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 2.88/2.07 tff(1199,plain,
% 2.88/2.07 ((~hskp48) | c2_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1198, 1196])).
% 2.88/2.07 tff(1200,plain,
% 2.88/2.07 ((~hskp48) | c2_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1199, 1196])).
% 2.88/2.07 tff(1201,plain,
% 2.88/2.07 ((~hskp48) | c2_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1200, 1196])).
% 2.88/2.07 tff(1202,plain,
% 2.88/2.07 ((~hskp48) | c2_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1201, 1196])).
% 2.88/2.07 tff(1203,plain,
% 2.88/2.07 ((~hskp48) | c2_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1202, 1196])).
% 2.88/2.07 tff(1204,plain,
% 2.88/2.07 ((~hskp48) | c2_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1203, 1196])).
% 2.88/2.07 tff(1205,plain,
% 2.88/2.07 ((~hskp48) | c2_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1204, 1196])).
% 2.88/2.07 tff(1206,plain,
% 2.88/2.07 (c2_1(a2228)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1205, 1189])).
% 2.88/2.07 tff(1207,plain,
% 2.88/2.07 (((~hskp48) | c3_1(a2228)) <=> ((~hskp48) | c3_1(a2228))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1208,axiom,((~hskp48) | c3_1(a2228)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 2.88/2.07 tff(1209,plain,
% 2.88/2.07 ((~hskp48) | c3_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 2.88/2.07 tff(1210,plain,
% 2.88/2.07 ((~hskp48) | c3_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1209, 1207])).
% 2.88/2.07 tff(1211,plain,
% 2.88/2.07 ((~hskp48) | c3_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1210, 1207])).
% 2.88/2.07 tff(1212,plain,
% 2.88/2.07 ((~hskp48) | c3_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1211, 1207])).
% 2.88/2.07 tff(1213,plain,
% 2.88/2.07 ((~hskp48) | c3_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1212, 1207])).
% 2.88/2.07 tff(1214,plain,
% 2.88/2.07 ((~hskp48) | c3_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1213, 1207])).
% 2.88/2.07 tff(1215,plain,
% 2.88/2.07 ((~hskp48) | c3_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1214, 1207])).
% 2.88/2.07 tff(1216,plain,
% 2.88/2.07 ((~hskp48) | c3_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1215, 1207])).
% 2.88/2.07 tff(1217,plain,
% 2.88/2.07 (c3_1(a2228)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1216, 1189])).
% 2.88/2.07 tff(1218,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c1_1(a2228)) | (~c3_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c1_1(a2228)) | (~c3_1(a2228)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1219,plain,
% 2.88/2.07 ((hskp33 | (~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c2_1(a2228)) | (~c1_1(a2228))) <=> (hskp33 | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c1_1(a2228)) | (~c3_1(a2228)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1220,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c2_1(a2228)) | (~c1_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c1_1(a2228)) | (~c3_1(a2228))))),
% 2.88/2.07 inference(monotonicity,[status(thm)],[1219])).
% 2.88/2.07 tff(1221,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c2_1(a2228)) | (~c1_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c1_1(a2228)) | (~c3_1(a2228)))),
% 2.88/2.07 inference(transitivity,[status(thm)],[1220, 1218])).
% 2.88/2.07 tff(1222,plain,
% 2.88/2.07 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c2_1(a2228)) | (~c1_1(a2228)))),
% 2.88/2.07 inference(quant_inst,[status(thm)],[])).
% 2.88/2.07 tff(1223,plain,
% 2.88/2.07 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c1_1(a2228)) | (~c3_1(a2228))),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 2.88/2.07 tff(1224,plain,
% 2.88/2.07 (~c1_1(a2228)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1223, 159, 72, 1217, 1206, 1195, 71])).
% 2.88/2.07 tff(1225,plain,
% 2.88/2.07 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 2.88/2.07 inference(bind,[status(th)],[])).
% 2.88/2.07 tff(1226,plain,
% 2.88/2.07 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.88/2.07 inference(quant_intro,[status(thm)],[1225])).
% 2.88/2.07 tff(1227,plain,
% 2.88/2.07 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1228,plain,
% 2.88/2.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp26))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 2.88/2.07 inference(bind,[status(th)],[])).
% 2.88/2.07 tff(1229,plain,
% 2.88/2.07 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.88/2.07 inference(quant_intro,[status(thm)],[1228])).
% 2.88/2.07 tff(1230,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause272')).
% 2.88/2.07 tff(1231,plain,
% 2.88/2.07 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1230, 1229])).
% 2.88/2.07 tff(1232,plain,
% 2.88/2.07 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1231, 1227])).
% 2.88/2.07 tff(1233,plain,(
% 2.88/2.07 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.88/2.07 inference(skolemize,[status(sab)],[1232])).
% 2.88/2.07 tff(1234,plain,
% 2.88/2.07 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1233, 1226])).
% 2.88/2.07 tff(1235,assumption,(c1_1(a2181)), introduced(assumption)).
% 2.88/2.07 tff(1236,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2228) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2228)) | c1_1(a2228))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2228)) | c1_1(a2228))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1237,plain,
% 2.88/2.07 ((hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228))) <=> (hskp26 | c0_1(a2228) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2228)) | c1_1(a2228))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1238,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2228) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2228)) | c1_1(a2228)))),
% 2.88/2.07 inference(monotonicity,[status(thm)],[1237])).
% 2.88/2.07 tff(1239,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2228)) | c1_1(a2228))),
% 2.88/2.07 inference(transitivity,[status(thm)],[1238, 1236])).
% 2.88/2.07 tff(1240,plain,
% 2.88/2.07 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))),
% 2.88/2.07 inference(quant_inst,[status(thm)],[])).
% 2.88/2.07 tff(1241,plain,
% 2.88/2.07 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2228)) | c1_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 2.88/2.07 tff(1242,plain,
% 2.88/2.07 (hskp26),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1241, 159, 1206, 1195, 105, 1235, 1234, 107, 1224])).
% 2.88/2.07 tff(1243,plain,
% 2.88/2.07 (~c3_1(a2178)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1178, 1242])).
% 2.88/2.07 tff(1244,plain,
% 2.88/2.07 (c2_1(a2178)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1156, 1242])).
% 2.88/2.07 tff(1245,plain,
% 2.88/2.07 (c0_1(a2178)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1167, 1242])).
% 2.88/2.07 tff(1246,plain,
% 2.88/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c0_1(a2228) | c3_1(a2178) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c2_1(a2228)) | c1_1(a2228))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c0_1(a2228) | c3_1(a2178) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c2_1(a2228)) | c1_1(a2228))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1247,plain,
% 2.88/2.07 (((~ndr1_0) | c1_1(a2228) | c0_1(a2228) | (~c2_1(a2228)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178))) <=> (c0_1(a2228) | c3_1(a2178) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c2_1(a2228)) | c1_1(a2228))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1248,plain,
% 2.88/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2228) | c0_1(a2228) | (~c2_1(a2228)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c0_1(a2228) | c3_1(a2178) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c2_1(a2228)) | c1_1(a2228)))),
% 2.88/2.07 inference(monotonicity,[status(thm)],[1247])).
% 2.88/2.07 tff(1249,plain,
% 2.88/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2228) | c0_1(a2228) | (~c2_1(a2228)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c0_1(a2228) | c3_1(a2178) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c2_1(a2228)) | c1_1(a2228))),
% 2.88/2.07 inference(transitivity,[status(thm)],[1248, 1246])).
% 2.88/2.07 tff(1250,plain,
% 2.88/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2228) | c0_1(a2228) | (~c2_1(a2228)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178)))),
% 2.88/2.07 inference(quant_inst,[status(thm)],[])).
% 2.88/2.07 tff(1251,plain,
% 2.88/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c0_1(a2228) | c3_1(a2178) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c2_1(a2228)) | c1_1(a2228)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 2.88/2.07 tff(1252,plain,
% 2.88/2.07 (c1_1(a2178)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1251, 159, 1206, 1245, 1244, 1195, 1243, 1049, 1224])).
% 2.88/2.07 tff(1253,plain,
% 2.88/2.07 (~hskp0),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[956, 1235])).
% 2.88/2.07 tff(1254,plain,
% 2.88/2.07 ($false),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1172, 159, 1253, 1245, 1244, 824, 1252])).
% 2.88/2.07 tff(1255,plain,((~hskp48) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.88/2.07 tff(1256,plain,
% 2.88/2.07 (~hskp48),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1255, 107, 904, 105, 72])).
% 2.88/2.07 tff(1257,assumption,(~hskp48), introduced(assumption)).
% 2.88/2.07 tff(1258,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2196) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2196)) | (~c1_1(a2196)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2196) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2196)) | (~c1_1(a2196)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1259,plain,
% 2.88/2.07 ((hskp48 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181))) <=> (hskp48 | c0_1(a2196) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2196)) | (~c1_1(a2196)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1260,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2196) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2196)) | (~c1_1(a2196))))),
% 2.88/2.07 inference(monotonicity,[status(thm)],[1259])).
% 2.88/2.07 tff(1261,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2196) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2196)) | (~c1_1(a2196)))),
% 2.88/2.07 inference(transitivity,[status(thm)],[1260, 1258])).
% 2.88/2.07 tff(1262,plain,
% 2.88/2.07 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))),
% 2.88/2.07 inference(quant_inst,[status(thm)],[])).
% 2.88/2.07 tff(1263,plain,
% 2.88/2.07 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2196) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2196)) | (~c1_1(a2196))),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 2.88/2.07 tff(1264,plain,
% 2.88/2.07 ($false),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1263, 159, 1257, 711, 700, 689, 105, 1235, 41, 107])).
% 2.88/2.07 tff(1265,plain,((~hskp37) | hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181))), inference(lemma,lemma(discharge,[]))).
% 2.88/2.07 tff(1266,plain,
% 2.88/2.07 (~hskp37),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1265, 1256, 105, 904, 107])).
% 2.88/2.07 tff(1267,plain,
% 2.88/2.07 (hskp6),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[615, 1266, 352])).
% 2.88/2.07 tff(1268,plain,
% 2.88/2.07 (~c1_1(a2197)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[621, 1267])).
% 2.88/2.07 tff(1269,plain,
% 2.88/2.07 (~c3_1(a2197)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1071, 1267])).
% 2.88/2.07 tff(1270,assumption,(hskp47), introduced(assumption)).
% 2.88/2.07 tff(1271,plain,
% 2.88/2.07 (~c1_1(a2226)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[283, 1270])).
% 2.88/2.07 tff(1272,plain,
% 2.88/2.07 (c0_1(a2226)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[305, 1270])).
% 2.88/2.07 tff(1273,plain,
% 2.88/2.07 (c2_1(a2226)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[333, 1270])).
% 2.88/2.07 tff(1274,plain,
% 2.88/2.07 ($false),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1111, 159, 352, 72, 1273, 1272, 1271, 501])).
% 2.88/2.07 tff(1275,plain,((~hskp47) | hskp34 | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.88/2.07 tff(1276,plain,
% 2.88/2.07 (~hskp47),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1275, 352, 72])).
% 2.88/2.07 tff(1277,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c3_1(a2197) | c1_1(a2197) | c0_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c3_1(a2197) | c1_1(a2197) | c0_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2197))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1278,plain,
% 2.88/2.07 ((hskp47 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c3_1(a2181)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197)) <=> (hskp47 | c3_1(a2197) | c1_1(a2197) | c0_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2197))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1279,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c3_1(a2181)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c3_1(a2197) | c1_1(a2197) | c0_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2197)))),
% 2.88/2.07 inference(monotonicity,[status(thm)],[1278])).
% 2.88/2.07 tff(1280,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c3_1(a2181)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c3_1(a2197) | c1_1(a2197) | c0_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2197))),
% 2.88/2.07 inference(transitivity,[status(thm)],[1279, 1277])).
% 2.88/2.07 tff(1281,plain,
% 2.88/2.07 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c3_1(a2181)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))),
% 2.88/2.07 inference(quant_inst,[status(thm)],[])).
% 2.88/2.07 tff(1282,plain,
% 2.88/2.07 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c3_1(a2197) | c1_1(a2197) | c0_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2197)),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 2.88/2.07 tff(1283,plain,
% 2.88/2.07 (c2_1(a2197)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1282, 159, 1276, 1269, 1268, 105, 103, 271, 107])).
% 2.88/2.07 tff(1284,plain,
% 2.88/2.07 (~c0_1(a2197)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[627, 1267])).
% 2.88/2.07 tff(1285,plain,
% 2.88/2.07 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1286,plain,
% 2.88/2.07 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 2.88/2.07 inference(quant_inst,[status(thm)],[])).
% 2.88/2.07 tff(1287,plain,
% 2.88/2.07 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178))),
% 2.88/2.07 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 2.88/2.07 tff(1288,plain,
% 2.88/2.07 (c1_1(a2178)),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1287, 159, 352, 72, 1168, 1157, 501])).
% 2.88/2.07 tff(1289,plain,
% 2.88/2.07 ($false),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1172, 159, 825, 1168, 1157, 824, 1288])).
% 2.88/2.07 tff(1290,plain,((~hskp26) | hskp0 | hskp34 | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.88/2.07 tff(1291,plain,
% 2.88/2.07 (~hskp26),
% 2.88/2.07 inference(unit_resolution,[status(thm)],[1290, 352, 1169, 72])).
% 2.88/2.07 tff(1292,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2197) | c1_1(a2197) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2197) | c1_1(a2197) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1293,plain,
% 2.88/2.07 ((hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197))) <=> (hskp26 | c0_1(a2197) | c1_1(a2197) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))),
% 2.88/2.07 inference(rewrite,[status(thm)],[])).
% 2.88/2.07 tff(1294,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2197) | c1_1(a2197) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197))))),
% 2.88/2.07 inference(monotonicity,[status(thm)],[1293])).
% 2.88/2.07 tff(1295,plain,
% 2.88/2.07 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2197) | c1_1(a2197) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))),
% 2.88/2.07 inference(transitivity,[status(thm)],[1294, 1292])).
% 2.88/2.07 tff(1296,plain,
% 2.88/2.07 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)))),
% 2.88/2.08 inference(quant_inst,[status(thm)],[])).
% 2.88/2.08 tff(1297,plain,
% 2.88/2.08 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2197) | c1_1(a2197) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197))),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 2.88/2.08 tff(1298,plain,
% 2.88/2.08 ($false),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1297, 159, 1291, 1284, 1268, 105, 904, 1234, 107, 1283])).
% 2.88/2.08 tff(1299,plain,((~c3_1(a2181)) | c0_1(a2181) | c2_1(a2181) | hskp34 | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.88/2.08 tff(1300,plain,
% 2.88/2.08 (~c3_1(a2181)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1299, 352, 103, 105, 72])).
% 2.88/2.08 tff(1301,plain,
% 2.88/2.08 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1302,plain,
% 2.88/2.08 ((hskp18 | (~ndr1_0) | c2_1(a2181) | c3_1(a2181) | (~c1_1(a2181))) <=> (hskp18 | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1303,plain,
% 2.88/2.08 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2181) | c3_1(a2181) | (~c1_1(a2181)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181)))),
% 2.88/2.08 inference(monotonicity,[status(thm)],[1302])).
% 2.88/2.08 tff(1304,plain,
% 2.88/2.08 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2181) | c3_1(a2181) | (~c1_1(a2181)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 2.88/2.08 inference(transitivity,[status(thm)],[1303, 1301])).
% 2.88/2.08 tff(1305,plain,
% 2.88/2.08 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2181) | c3_1(a2181) | (~c1_1(a2181)))),
% 2.88/2.08 inference(quant_inst,[status(thm)],[])).
% 2.88/2.08 tff(1306,plain,
% 2.88/2.08 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 2.88/2.08 tff(1307,plain,
% 2.88/2.08 (hskp18 | (~c1_1(a2181)) | c3_1(a2181)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1306, 159, 103, 61])).
% 2.88/2.08 tff(1308,plain,
% 2.88/2.08 (hskp18),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1307, 1300, 904])).
% 2.88/2.08 tff(1309,plain,
% 2.88/2.08 (~c2_1(a2222)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[376, 1308])).
% 2.88/2.08 tff(1310,plain,
% 2.88/2.08 (c3_1(a2222)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[417, 1308])).
% 2.88/2.08 tff(1311,plain,
% 2.88/2.08 (c0_1(a2222)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[456, 1308])).
% 2.88/2.08 tff(1312,plain,
% 2.88/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a2222) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a2222) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1313,plain,
% 2.88/2.08 (((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2181) | c2_1(a2181) | (~c1_1(a2181))) <=> (c2_1(a2222) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1314,plain,
% 2.88/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2181) | c2_1(a2181) | (~c1_1(a2181)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a2222) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222))))),
% 2.88/2.08 inference(monotonicity,[status(thm)],[1313])).
% 2.88/2.08 tff(1315,plain,
% 2.88/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2181) | c2_1(a2181) | (~c1_1(a2181)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a2222) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.88/2.08 inference(transitivity,[status(thm)],[1314, 1312])).
% 2.88/2.08 tff(1316,plain,
% 2.88/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2181) | c2_1(a2181) | (~c1_1(a2181)))),
% 2.88/2.08 inference(quant_inst,[status(thm)],[])).
% 2.88/2.08 tff(1317,plain,
% 2.88/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a2222) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 2.88/2.08 tff(1318,plain,
% 2.88/2.08 (~c1_1(a2222)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1317, 159, 1311, 1310, 1309, 105, 904, 103, 363])).
% 2.88/2.08 tff(1319,assumption,(hskp18), introduced(assumption)).
% 2.88/2.08 tff(1320,plain,
% 2.88/2.08 (~c2_1(a2222)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[376, 1319])).
% 2.88/2.08 tff(1321,plain,
% 2.88/2.08 (c3_1(a2222)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[417, 1319])).
% 2.88/2.08 tff(1322,plain,
% 2.88/2.08 (c0_1(a2222)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[456, 1319])).
% 2.88/2.08 tff(1323,plain,
% 2.88/2.08 (~c1_1(a2222)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1317, 159, 1322, 1321, 1320, 105, 1235, 103, 363])).
% 2.88/2.08 tff(1324,plain,
% 2.88/2.08 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1325,plain,
% 2.88/2.08 ((hskp32 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2222) | c2_1(a2222) | (~c0_1(a2222))) <=> (hskp32 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1326,plain,
% 2.88/2.08 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2222) | c2_1(a2222) | (~c0_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222))))),
% 2.88/2.08 inference(monotonicity,[status(thm)],[1325])).
% 2.88/2.08 tff(1327,plain,
% 2.88/2.08 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2222) | c2_1(a2222) | (~c0_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.88/2.08 inference(transitivity,[status(thm)],[1326, 1324])).
% 2.88/2.08 tff(1328,plain,
% 2.88/2.08 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2222) | c2_1(a2222) | (~c0_1(a2222)))),
% 2.88/2.08 inference(quant_inst,[status(thm)],[])).
% 2.88/2.08 tff(1329,plain,
% 2.88/2.08 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1328, 1327])).
% 2.88/2.08 tff(1330,plain,
% 2.88/2.08 ($false),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1329, 159, 106, 1322, 1321, 1320, 117, 1323])).
% 2.88/2.08 tff(1331,plain,((~hskp18) | hskp32 | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.88/2.08 tff(1332,plain,
% 2.88/2.08 (hskp32),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1331, 1308, 105, 904, 103])).
% 2.88/2.08 tff(1333,plain,
% 2.88/2.08 (~c2_1(a2186)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[348, 1332])).
% 2.88/2.08 tff(1334,plain,
% 2.88/2.08 (~c3_1(a2186)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[89, 1332])).
% 2.88/2.08 tff(1335,plain,
% 2.88/2.08 (c0_1(a2186)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[83, 1332])).
% 2.88/2.08 tff(1336,plain,
% 2.88/2.08 (hskp46 | c1_1(a2222)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[460, 159, 352, 1311, 1310, 446])).
% 2.88/2.08 tff(1337,plain,
% 2.88/2.08 (hskp46),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1336, 1318])).
% 2.88/2.08 tff(1338,plain,
% 2.88/2.08 (c2_1(a2218)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[472, 1337])).
% 2.88/2.08 tff(1339,plain,
% 2.88/2.08 (c0_1(a2218)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[483, 1337])).
% 2.88/2.08 tff(1340,plain,
% 2.88/2.08 (~c1_1(a2218)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[490, 159, 1339, 1338, 1335, 1310, 1334, 1333, 1309, 51, 1318])).
% 2.88/2.08 tff(1341,plain,
% 2.88/2.08 ($false),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[504, 159, 352, 72, 1339, 1338, 501, 1340])).
% 2.88/2.08 tff(1342,plain,(hskp34 | hskp33 | c0_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.88/2.08 tff(1343,plain,
% 2.88/2.08 (hskp34),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1342, 105, 72, 103])).
% 2.88/2.08 tff(1344,plain,
% 2.88/2.08 (~c0_1(a2189)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[763, 1343])).
% 2.88/2.08 tff(1345,plain,
% 2.88/2.08 (c3_1(a2189)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[739, 1343])).
% 2.88/2.08 tff(1346,plain,
% 2.88/2.08 (c1_1(a2189)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[750, 1343])).
% 2.88/2.08 tff(1347,plain,
% 2.88/2.08 (~hskp18),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1331, 106, 105, 904, 103])).
% 2.88/2.08 tff(1348,plain,
% 2.88/2.08 (c3_1(a2181)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1307, 1347, 904])).
% 2.88/2.08 tff(1349,plain,
% 2.88/2.08 (~hskp48),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1255, 1348, 904, 105, 72])).
% 2.88/2.08 tff(1350,assumption,(hskp21), introduced(assumption)).
% 2.88/2.08 tff(1351,plain,
% 2.88/2.08 (((~hskp21) | (~c0_1(a2239))) <=> ((~hskp21) | (~c0_1(a2239)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1352,plain,
% 2.88/2.08 (((~c0_1(a2239)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a2239)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1353,axiom,((~c0_1(a2239)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 2.88/2.08 tff(1354,plain,
% 2.88/2.08 ((~hskp21) | (~c0_1(a2239))),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 2.88/2.08 tff(1355,plain,
% 2.88/2.08 ((~hskp21) | (~c0_1(a2239))),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1354, 1351])).
% 2.88/2.08 tff(1356,plain,
% 2.88/2.08 (~c0_1(a2239)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1355, 1350])).
% 2.88/2.08 tff(1357,assumption,(~c0_1(a2189)), introduced(assumption)).
% 2.88/2.08 tff(1358,plain,
% 2.88/2.08 (((~hskp21) | c2_1(a2239)) <=> ((~hskp21) | c2_1(a2239))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1359,axiom,((~hskp21) | c2_1(a2239)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 2.88/2.08 tff(1360,plain,
% 2.88/2.08 ((~hskp21) | c2_1(a2239)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 2.88/2.08 tff(1361,plain,
% 2.88/2.08 ((~hskp21) | c2_1(a2239)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1360, 1358])).
% 2.88/2.08 tff(1362,plain,
% 2.88/2.08 ((~hskp21) | c2_1(a2239)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1361, 1358])).
% 2.88/2.08 tff(1363,plain,
% 2.88/2.08 ((~hskp21) | c2_1(a2239)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1362, 1358])).
% 2.88/2.08 tff(1364,plain,
% 2.88/2.08 ((~hskp21) | c2_1(a2239)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1363, 1358])).
% 2.88/2.08 tff(1365,plain,
% 2.88/2.08 ((~hskp21) | c2_1(a2239)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1364, 1358])).
% 2.88/2.08 tff(1366,plain,
% 2.88/2.08 ((~hskp21) | c2_1(a2239)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1365, 1358])).
% 2.88/2.08 tff(1367,plain,
% 2.88/2.08 ((~hskp21) | c2_1(a2239)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1366, 1358])).
% 2.88/2.08 tff(1368,plain,
% 2.88/2.08 (c2_1(a2239)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1367, 1350])).
% 2.88/2.08 tff(1369,assumption,(c3_1(a2189)), introduced(assumption)).
% 2.88/2.08 tff(1370,assumption,(c1_1(a2189)), introduced(assumption)).
% 2.88/2.08 tff(1371,plain,
% 2.88/2.08 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2239)) | (~c2_1(a2239)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1372,plain,
% 2.88/2.08 ((hskp48 | (~ndr1_0) | c0_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))) <=> (hskp48 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1373,plain,
% 2.88/2.08 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2239)) | (~c2_1(a2239))))),
% 2.88/2.08 inference(monotonicity,[status(thm)],[1372])).
% 2.88/2.08 tff(1374,plain,
% 2.88/2.08 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 2.88/2.08 inference(transitivity,[status(thm)],[1373, 1371])).
% 2.88/2.08 tff(1375,plain,
% 2.88/2.08 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.88/2.08 inference(quant_inst,[status(thm)],[])).
% 2.88/2.08 tff(1376,plain,
% 2.88/2.08 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2239)) | (~c2_1(a2239))),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 2.88/2.08 tff(1377,plain,
% 2.88/2.08 (~c1_1(a2239)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1376, 159, 1257, 1370, 1369, 1368, 1357, 1356, 41])).
% 2.88/2.08 tff(1378,assumption,(~hskp26), introduced(assumption)).
% 2.88/2.08 tff(1379,plain,
% 2.88/2.08 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | c1_1(a2239) | (~c2_1(a2239)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | c1_1(a2239) | (~c2_1(a2239)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1380,plain,
% 2.88/2.08 ((hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239))) <=> (hskp26 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | c1_1(a2239) | (~c2_1(a2239)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1381,plain,
% 2.88/2.08 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | c1_1(a2239) | (~c2_1(a2239))))),
% 2.88/2.08 inference(monotonicity,[status(thm)],[1380])).
% 2.88/2.08 tff(1382,plain,
% 2.88/2.08 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | c1_1(a2239) | (~c2_1(a2239)))),
% 2.88/2.08 inference(transitivity,[status(thm)],[1381, 1379])).
% 2.88/2.08 tff(1383,plain,
% 2.88/2.08 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239)))),
% 2.88/2.08 inference(quant_inst,[status(thm)],[])).
% 2.88/2.08 tff(1384,plain,
% 2.88/2.08 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | c1_1(a2239) | (~c2_1(a2239))),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 2.88/2.08 tff(1385,plain,
% 2.88/2.08 ($false),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1384, 159, 1378, 1370, 1369, 1368, 1357, 1356, 1234, 1377])).
% 2.88/2.08 tff(1386,plain,((~hskp21) | hskp26 | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2189) | hskp48), inference(lemma,lemma(discharge,[]))).
% 2.88/2.08 tff(1387,plain,
% 2.88/2.08 (~hskp21),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1386, 1349, 1346, 1345, 1344, 1188])).
% 2.88/2.08 tff(1388,plain,
% 2.88/2.08 (hskp54),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[157, 1387, 1145])).
% 2.88/2.08 tff(1389,plain,
% 2.88/2.08 (((~hskp54) | c0_1(a2240)) <=> ((~hskp54) | c0_1(a2240))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1390,axiom,((~hskp54) | c0_1(a2240)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 2.88/2.08 tff(1391,plain,
% 2.88/2.08 ((~hskp54) | c0_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 2.88/2.08 tff(1392,plain,
% 2.88/2.08 ((~hskp54) | c0_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1391, 1389])).
% 2.88/2.08 tff(1393,plain,
% 2.88/2.08 ((~hskp54) | c0_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1392, 1389])).
% 2.88/2.08 tff(1394,plain,
% 2.88/2.08 ((~hskp54) | c0_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1393, 1389])).
% 2.88/2.08 tff(1395,plain,
% 2.88/2.08 ((~hskp54) | c0_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1394, 1389])).
% 2.88/2.08 tff(1396,plain,
% 2.88/2.08 ((~hskp54) | c0_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1395, 1389])).
% 2.88/2.08 tff(1397,plain,
% 2.88/2.08 ((~hskp54) | c0_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1396, 1389])).
% 2.88/2.08 tff(1398,plain,
% 2.88/2.08 ((~hskp54) | c0_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1397, 1389])).
% 2.88/2.08 tff(1399,plain,
% 2.88/2.08 (c0_1(a2240)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1398, 1388])).
% 2.88/2.08 tff(1400,plain,
% 2.88/2.08 (((~hskp54) | c1_1(a2240)) <=> ((~hskp54) | c1_1(a2240))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1401,axiom,((~hskp54) | c1_1(a2240)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 2.88/2.08 tff(1402,plain,
% 2.88/2.08 ((~hskp54) | c1_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 2.88/2.08 tff(1403,plain,
% 2.88/2.08 ((~hskp54) | c1_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1402, 1400])).
% 2.88/2.08 tff(1404,plain,
% 2.88/2.08 ((~hskp54) | c1_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1403, 1400])).
% 2.88/2.08 tff(1405,plain,
% 2.88/2.08 ((~hskp54) | c1_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1404, 1400])).
% 2.88/2.08 tff(1406,plain,
% 2.88/2.08 ((~hskp54) | c1_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1405, 1400])).
% 2.88/2.08 tff(1407,plain,
% 2.88/2.08 ((~hskp54) | c1_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1406, 1400])).
% 2.88/2.08 tff(1408,plain,
% 2.88/2.08 ((~hskp54) | c1_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1407, 1400])).
% 2.88/2.08 tff(1409,plain,
% 2.88/2.08 ((~hskp54) | c1_1(a2240)),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1408, 1400])).
% 2.88/2.08 tff(1410,plain,
% 2.88/2.08 (c1_1(a2240)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1409, 1388])).
% 2.88/2.08 tff(1411,plain,
% 2.88/2.08 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | (~c2_1(a2240)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | (~c2_1(a2240)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1412,plain,
% 2.88/2.08 ((hskp0 | (~ndr1_0) | (~c1_1(a2240)) | (~c0_1(a2240)) | (~c2_1(a2240))) <=> (hskp0 | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | (~c2_1(a2240)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1413,plain,
% 2.88/2.08 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2240)) | (~c0_1(a2240)) | (~c2_1(a2240)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | (~c2_1(a2240))))),
% 2.88/2.08 inference(monotonicity,[status(thm)],[1412])).
% 2.88/2.08 tff(1414,plain,
% 2.88/2.08 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2240)) | (~c0_1(a2240)) | (~c2_1(a2240)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | (~c2_1(a2240)))),
% 2.88/2.08 inference(transitivity,[status(thm)],[1413, 1411])).
% 2.88/2.08 tff(1415,plain,
% 2.88/2.08 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2240)) | (~c0_1(a2240)) | (~c2_1(a2240)))),
% 2.88/2.08 inference(quant_inst,[status(thm)],[])).
% 2.88/2.08 tff(1416,plain,
% 2.88/2.08 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | (~c2_1(a2240))),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 2.88/2.08 tff(1417,plain,
% 2.88/2.08 (~c2_1(a2240)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1416, 159, 1169, 1410, 1399, 824])).
% 2.88/2.08 tff(1418,plain,
% 2.88/2.08 (~c2_1(a2189)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[784, 159, 72, 1346, 1345, 1344, 71])).
% 2.88/2.08 tff(1419,assumption,(hskp58), introduced(assumption)).
% 2.88/2.08 tff(1420,plain,
% 2.88/2.08 (~c1_1(a2252)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[172, 1419])).
% 2.88/2.08 tff(1421,plain,
% 2.88/2.08 (~c2_1(a2252)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[178, 1419])).
% 2.88/2.08 tff(1422,plain,
% 2.88/2.08 (c0_1(a2252)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[189, 1419])).
% 2.88/2.08 tff(1423,plain,
% 2.88/2.08 (~c3_1(a2252)),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[994, 159, 106, 1422, 1421, 1420, 117])).
% 2.88/2.08 tff(1424,plain,
% 2.88/2.08 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c1_1(a2252) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2252) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2252) | (~c0_1(a2252)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1425,plain,
% 2.88/2.08 ((hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252))) <=> (hskp33 | c1_1(a2252) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2252) | (~c0_1(a2252)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1426,plain,
% 2.88/2.08 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c1_1(a2252) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2252) | (~c0_1(a2252))))),
% 2.88/2.08 inference(monotonicity,[status(thm)],[1425])).
% 2.88/2.08 tff(1427,plain,
% 2.88/2.08 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2252) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2252) | (~c0_1(a2252)))),
% 2.88/2.08 inference(transitivity,[status(thm)],[1426, 1424])).
% 2.88/2.08 tff(1428,plain,
% 2.88/2.08 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252)))),
% 2.88/2.08 inference(quant_inst,[status(thm)],[])).
% 2.88/2.08 tff(1429,plain,
% 2.88/2.08 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2252) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2252) | (~c0_1(a2252))),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 2.88/2.08 tff(1430,plain,
% 2.88/2.08 ($false),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1429, 159, 72, 1422, 1420, 105, 904, 103, 261, 1423])).
% 2.88/2.08 tff(1431,plain,((~hskp58) | hskp33 | c0_1(a2181) | c2_1(a2181) | hskp32), inference(lemma,lemma(discharge,[]))).
% 2.88/2.08 tff(1432,plain,
% 2.88/2.08 (~hskp58),
% 2.88/2.08 inference(unit_resolution,[status(thm)],[1431, 106, 105, 103, 72])).
% 2.88/2.08 tff(1433,assumption,(~hskp2), introduced(assumption)).
% 2.88/2.08 tff(1434,assumption,(~hskp58), introduced(assumption)).
% 2.88/2.08 tff(1435,plain,
% 2.88/2.08 (^[U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 2.88/2.08 inference(bind,[status(th)],[])).
% 2.88/2.08 tff(1436,plain,
% 2.88/2.08 (![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.88/2.08 inference(quant_intro,[status(thm)],[1435])).
% 2.88/2.08 tff(1437,plain,
% 2.88/2.08 (![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.88/2.08 inference(rewrite,[status(thm)],[])).
% 2.88/2.08 tff(1438,plain,
% 2.88/2.08 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 2.88/2.08 inference(bind,[status(th)],[])).
% 2.88/2.08 tff(1439,plain,
% 2.88/2.08 (![U: $i] : (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp17) <=> ![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.88/2.08 inference(quant_intro,[status(thm)],[1438])).
% 2.88/2.08 tff(1440,axiom,(![U: $i] : (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause255')).
% 2.88/2.08 tff(1441,plain,
% 2.88/2.08 (![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.88/2.08 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 2.88/2.09 tff(1442,plain,
% 2.88/2.09 (![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1441, 1437])).
% 2.88/2.09 tff(1443,plain,(
% 2.88/2.09 ![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.88/2.09 inference(skolemize,[status(sab)],[1442])).
% 2.88/2.09 tff(1444,plain,
% 2.88/2.09 (![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1443, 1436])).
% 2.88/2.09 tff(1445,assumption,(~c0_1(a2200)), introduced(assumption)).
% 2.88/2.09 tff(1446,assumption,(~c1_1(a2200)), introduced(assumption)).
% 2.88/2.09 tff(1447,plain,
% 2.88/2.09 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c1_1(a2200) | c0_1(a2200) | (~ndr1_0) | c3_1(a2200))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c1_1(a2200) | c0_1(a2200) | (~ndr1_0) | c3_1(a2200))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1448,plain,
% 2.88/2.09 ((hskp32 | hskp2 | (~ndr1_0) | c1_1(a2200) | c3_1(a2200) | c0_1(a2200)) <=> (hskp32 | hskp2 | c1_1(a2200) | c0_1(a2200) | (~ndr1_0) | c3_1(a2200))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1449,plain,
% 2.88/2.09 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2200) | c3_1(a2200) | c0_1(a2200))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c1_1(a2200) | c0_1(a2200) | (~ndr1_0) | c3_1(a2200)))),
% 2.88/2.09 inference(monotonicity,[status(thm)],[1448])).
% 2.88/2.09 tff(1450,plain,
% 2.88/2.09 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2200) | c3_1(a2200) | c0_1(a2200))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c1_1(a2200) | c0_1(a2200) | (~ndr1_0) | c3_1(a2200))),
% 2.88/2.09 inference(transitivity,[status(thm)],[1449, 1447])).
% 2.88/2.09 tff(1451,plain,
% 2.88/2.09 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2200) | c3_1(a2200) | c0_1(a2200))),
% 2.88/2.09 inference(quant_inst,[status(thm)],[])).
% 2.88/2.09 tff(1452,plain,
% 2.88/2.09 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c1_1(a2200) | c0_1(a2200) | (~ndr1_0) | c3_1(a2200)),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 2.88/2.09 tff(1453,plain,
% 2.88/2.09 (c1_1(a2200) | c3_1(a2200)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1452, 159, 106, 1433, 1445, 219])).
% 2.88/2.09 tff(1454,plain,
% 2.88/2.09 (c3_1(a2200)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1453, 1446])).
% 2.88/2.09 tff(1455,plain,
% 2.88/2.09 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c1_1(a2200) | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c1_1(a2200) | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1456,plain,
% 2.88/2.09 ((hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2200) | c1_1(a2200) | (~c2_1(a2200))) <=> (hskp26 | c1_1(a2200) | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1457,plain,
% 2.88/2.09 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2200) | c1_1(a2200) | (~c2_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c1_1(a2200) | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189))))),
% 2.88/2.09 inference(monotonicity,[status(thm)],[1456])).
% 2.88/2.09 tff(1458,plain,
% 2.88/2.09 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2200) | c1_1(a2200) | (~c2_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c1_1(a2200) | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.88/2.09 inference(transitivity,[status(thm)],[1457, 1455])).
% 2.88/2.09 tff(1459,plain,
% 2.88/2.09 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2200) | c1_1(a2200) | (~c2_1(a2200)))),
% 2.88/2.09 inference(quant_inst,[status(thm)],[])).
% 2.88/2.09 tff(1460,plain,
% 2.88/2.09 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c1_1(a2200) | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 2.88/2.09 tff(1461,plain,
% 2.88/2.09 (c1_1(a2200) | (~c2_1(a2200))),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1460, 159, 1378, 1370, 1369, 1445, 1357, 1234])).
% 2.88/2.09 tff(1462,plain,
% 2.88/2.09 (~c2_1(a2200)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1461, 1446])).
% 2.88/2.09 tff(1463,plain,
% 2.88/2.09 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c1_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c3_1(a2200)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c1_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c3_1(a2200)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1464,plain,
% 2.88/2.09 ((hskp58 | (~ndr1_0) | c2_1(a2200) | c1_1(a2200) | (~c3_1(a2200))) <=> (hskp58 | c1_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c3_1(a2200)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1465,plain,
% 2.88/2.09 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2200) | c1_1(a2200) | (~c3_1(a2200)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c1_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c3_1(a2200))))),
% 2.88/2.09 inference(monotonicity,[status(thm)],[1464])).
% 2.88/2.09 tff(1466,plain,
% 2.88/2.09 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2200) | c1_1(a2200) | (~c3_1(a2200)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c1_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c3_1(a2200)))),
% 2.88/2.09 inference(transitivity,[status(thm)],[1465, 1463])).
% 2.88/2.09 tff(1467,plain,
% 2.88/2.09 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2200) | c1_1(a2200) | (~c3_1(a2200)))),
% 2.88/2.09 inference(quant_inst,[status(thm)],[])).
% 2.88/2.09 tff(1468,plain,
% 2.88/2.09 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c1_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c3_1(a2200))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 2.88/2.09 tff(1469,plain,
% 2.88/2.09 ($false),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1468, 1434, 159, 1446, 1462, 127, 1454])).
% 2.88/2.09 tff(1470,plain,(c1_1(a2200) | hskp58 | hskp32 | hskp2 | c0_1(a2200) | hskp26 | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2189)), inference(lemma,lemma(discharge,[]))).
% 2.88/2.09 tff(1471,plain,
% 2.88/2.09 (c1_1(a2200)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1470, 1445, 106, 1433, 1434, 1378, 1370, 1369, 1357])).
% 2.88/2.09 tff(1472,plain,
% 2.88/2.09 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2200)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1473,plain,
% 2.88/2.09 ((hskp48 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))) <=> (hskp48 | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2200)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1474,plain,
% 2.88/2.09 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2200))))),
% 2.88/2.09 inference(monotonicity,[status(thm)],[1473])).
% 2.88/2.09 tff(1475,plain,
% 2.88/2.09 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2200)))),
% 2.88/2.09 inference(transitivity,[status(thm)],[1474, 1472])).
% 2.88/2.09 tff(1476,plain,
% 2.88/2.09 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.88/2.09 inference(quant_inst,[status(thm)],[])).
% 2.88/2.09 tff(1477,plain,
% 2.88/2.09 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2200))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 2.88/2.09 tff(1478,plain,
% 2.88/2.09 ((~c2_1(a2200)) | (~c1_1(a2200))),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1477, 159, 1257, 1370, 1369, 1445, 1357, 41])).
% 2.88/2.09 tff(1479,plain,
% 2.88/2.09 (~c2_1(a2200)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1478, 1471])).
% 2.88/2.09 tff(1480,assumption,(~hskp18), introduced(assumption)).
% 2.88/2.09 tff(1481,plain,
% 2.88/2.09 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c2_1(a2200) | (~ndr1_0) | (~c1_1(a2200)) | c3_1(a2200))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c2_1(a2200) | (~ndr1_0) | (~c1_1(a2200)) | c3_1(a2200))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1482,plain,
% 2.88/2.09 ((hskp18 | (~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200))) <=> (hskp18 | c2_1(a2200) | (~ndr1_0) | (~c1_1(a2200)) | c3_1(a2200))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1483,plain,
% 2.88/2.09 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c2_1(a2200) | (~ndr1_0) | (~c1_1(a2200)) | c3_1(a2200)))),
% 2.88/2.09 inference(monotonicity,[status(thm)],[1482])).
% 2.88/2.09 tff(1484,plain,
% 2.88/2.09 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c2_1(a2200) | (~ndr1_0) | (~c1_1(a2200)) | c3_1(a2200))),
% 2.88/2.09 inference(transitivity,[status(thm)],[1483, 1481])).
% 2.88/2.09 tff(1485,plain,
% 2.88/2.09 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)))),
% 2.88/2.09 inference(quant_inst,[status(thm)],[])).
% 2.88/2.09 tff(1486,plain,
% 2.88/2.09 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c2_1(a2200) | (~ndr1_0) | (~c1_1(a2200)) | c3_1(a2200)),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 2.88/2.09 tff(1487,plain,
% 2.88/2.09 (c3_1(a2200)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1486, 159, 1480, 1471, 1479, 61])).
% 2.88/2.09 tff(1488,assumption,(hskp54), introduced(assumption)).
% 2.88/2.09 tff(1489,plain,
% 2.88/2.09 (c0_1(a2240)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1398, 1488])).
% 2.88/2.09 tff(1490,plain,
% 2.88/2.09 (c1_1(a2240)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1409, 1488])).
% 2.88/2.09 tff(1491,plain,
% 2.88/2.09 (~c2_1(a2240)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1416, 159, 825, 1490, 1489, 824])).
% 2.88/2.09 tff(1492,assumption,(c3_1(a2200)), introduced(assumption)).
% 2.88/2.09 tff(1493,assumption,(~c2_1(a2200)), introduced(assumption)).
% 2.88/2.09 tff(1494,assumption,(c1_1(a2200)), introduced(assumption)).
% 2.88/2.09 tff(1495,plain,
% 2.88/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240) | (~c1_1(a2200)) | (~c3_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240) | (~c1_1(a2200)) | (~c3_1(a2200)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1496,plain,
% 2.88/2.09 (((~ndr1_0) | c2_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200))) <=> (c0_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240) | (~c1_1(a2200)) | (~c3_1(a2200)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1497,plain,
% 2.88/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240) | (~c1_1(a2200)) | (~c3_1(a2200))))),
% 2.88/2.09 inference(monotonicity,[status(thm)],[1496])).
% 2.88/2.09 tff(1498,plain,
% 2.88/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240) | (~c1_1(a2200)) | (~c3_1(a2200)))),
% 2.88/2.09 inference(transitivity,[status(thm)],[1497, 1495])).
% 2.88/2.09 tff(1499,plain,
% 2.88/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200)))),
% 2.88/2.09 inference(quant_inst,[status(thm)],[])).
% 2.88/2.09 tff(1500,plain,
% 2.88/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240) | (~c1_1(a2200)) | (~c3_1(a2200))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1499, 1498])).
% 2.88/2.09 tff(1501,plain,
% 2.88/2.09 ($false),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1500, 159, 1490, 1489, 1494, 1445, 1493, 363, 1492, 1491])).
% 2.88/2.09 tff(1502,plain,((~hskp54) | (~c1_1(a2200)) | c0_1(a2200) | c2_1(a2200) | (~c3_1(a2200)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.88/2.09 tff(1503,plain,
% 2.88/2.09 (~hskp54),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1502, 1471, 1445, 1479, 1487, 825])).
% 2.88/2.09 tff(1504,plain,
% 2.88/2.09 (hskp21),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[157, 1503, 1145])).
% 2.88/2.09 tff(1505,plain,
% 2.88/2.09 (((~hskp21) | (~c3_1(a2239))) <=> ((~hskp21) | (~c3_1(a2239)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1506,plain,
% 2.88/2.09 (((~c3_1(a2239)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a2239)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1507,axiom,((~c3_1(a2239)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 2.88/2.09 tff(1508,plain,
% 2.88/2.09 ((~hskp21) | (~c3_1(a2239))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1507, 1506])).
% 2.88/2.09 tff(1509,plain,
% 2.88/2.09 ((~hskp21) | (~c3_1(a2239))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1508, 1505])).
% 2.88/2.09 tff(1510,plain,
% 2.88/2.09 (~c3_1(a2239)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1509, 1504])).
% 2.88/2.09 tff(1511,plain,
% 2.88/2.09 (c2_1(a2239)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1367, 1504])).
% 2.88/2.09 tff(1512,assumption,(hskp17), introduced(assumption)).
% 2.88/2.09 tff(1513,plain,
% 2.88/2.09 (((~hskp17) | (~c3_1(a2221))) <=> ((~hskp17) | (~c3_1(a2221)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1514,plain,
% 2.88/2.09 (((~c3_1(a2221)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a2221)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1515,axiom,((~c3_1(a2221)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause205')).
% 2.88/2.09 tff(1516,plain,
% 2.88/2.09 ((~hskp17) | (~c3_1(a2221))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 2.88/2.09 tff(1517,plain,
% 2.88/2.09 ((~hskp17) | (~c3_1(a2221))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1516, 1513])).
% 2.88/2.09 tff(1518,plain,
% 2.88/2.09 (~c3_1(a2221)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1517, 1512])).
% 2.88/2.09 tff(1519,plain,
% 2.88/2.09 (((~hskp17) | (~c0_1(a2221))) <=> ((~hskp17) | (~c0_1(a2221)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1520,plain,
% 2.88/2.09 (((~c0_1(a2221)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a2221)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1521,axiom,((~c0_1(a2221)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 2.88/2.09 tff(1522,plain,
% 2.88/2.09 ((~hskp17) | (~c0_1(a2221))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 2.88/2.09 tff(1523,plain,
% 2.88/2.09 ((~hskp17) | (~c0_1(a2221))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1522, 1519])).
% 2.88/2.09 tff(1524,plain,
% 2.88/2.09 (~c0_1(a2221)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1523, 1512])).
% 2.88/2.09 tff(1525,plain,
% 2.88/2.09 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | c1_1(a2221))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | c1_1(a2221))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1526,plain,
% 2.88/2.09 ((hskp32 | hskp2 | (~ndr1_0) | c1_1(a2221) | c3_1(a2221) | c0_1(a2221)) <=> (hskp32 | hskp2 | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | c1_1(a2221))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1527,plain,
% 2.88/2.09 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2221) | c3_1(a2221) | c0_1(a2221))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | c1_1(a2221)))),
% 2.88/2.09 inference(monotonicity,[status(thm)],[1526])).
% 2.88/2.09 tff(1528,plain,
% 2.88/2.09 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2221) | c3_1(a2221) | c0_1(a2221))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | c1_1(a2221))),
% 2.88/2.09 inference(transitivity,[status(thm)],[1527, 1525])).
% 2.88/2.09 tff(1529,plain,
% 2.88/2.09 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2221) | c3_1(a2221) | c0_1(a2221))),
% 2.88/2.09 inference(quant_inst,[status(thm)],[])).
% 2.88/2.09 tff(1530,plain,
% 2.88/2.09 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | c1_1(a2221)),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1529, 1528])).
% 2.88/2.09 tff(1531,plain,
% 2.88/2.09 (c1_1(a2221)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1530, 159, 106, 1433, 1524, 1518, 219])).
% 2.88/2.09 tff(1532,plain,
% 2.88/2.09 (((~hskp17) | c2_1(a2221)) <=> ((~hskp17) | c2_1(a2221))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1533,axiom,((~hskp17) | c2_1(a2221)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 2.88/2.09 tff(1534,plain,
% 2.88/2.09 ((~hskp17) | c2_1(a2221)),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 2.88/2.09 tff(1535,plain,
% 2.88/2.09 ((~hskp17) | c2_1(a2221)),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1534, 1532])).
% 2.88/2.09 tff(1536,plain,
% 2.88/2.09 ((~hskp17) | c2_1(a2221)),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1535, 1532])).
% 2.88/2.09 tff(1537,plain,
% 2.88/2.09 ((~hskp17) | c2_1(a2221)),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1536, 1532])).
% 2.88/2.09 tff(1538,plain,
% 2.88/2.09 ((~hskp17) | c2_1(a2221)),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1537, 1532])).
% 2.88/2.09 tff(1539,plain,
% 2.88/2.09 ((~hskp17) | c2_1(a2221)),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1538, 1532])).
% 2.88/2.09 tff(1540,plain,
% 2.88/2.09 ((~hskp17) | c2_1(a2221)),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1539, 1532])).
% 2.88/2.09 tff(1541,plain,
% 2.88/2.09 ((~hskp17) | c2_1(a2221)),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1540, 1532])).
% 2.88/2.09 tff(1542,plain,
% 2.88/2.09 (c2_1(a2221)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1541, 1512])).
% 2.88/2.09 tff(1543,plain,
% 2.88/2.09 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2189) | c0_1(a2221) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2221)) | (~c2_1(a2221)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2221) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2221)) | (~c2_1(a2221)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1544,plain,
% 2.88/2.09 ((hskp48 | (~ndr1_0) | c0_1(a2221) | (~c1_1(a2221)) | (~c2_1(a2221)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))) <=> (hskp48 | c0_1(a2189) | c0_1(a2221) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2221)) | (~c2_1(a2221)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1545,plain,
% 2.88/2.09 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2221) | (~c1_1(a2221)) | (~c2_1(a2221)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2189) | c0_1(a2221) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2221)) | (~c2_1(a2221))))),
% 2.88/2.09 inference(monotonicity,[status(thm)],[1544])).
% 2.88/2.09 tff(1546,plain,
% 2.88/2.09 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2221) | (~c1_1(a2221)) | (~c2_1(a2221)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2221) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2221)) | (~c2_1(a2221)))),
% 2.88/2.09 inference(transitivity,[status(thm)],[1545, 1543])).
% 2.88/2.09 tff(1547,plain,
% 2.88/2.09 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2221) | (~c1_1(a2221)) | (~c2_1(a2221)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.88/2.09 inference(quant_inst,[status(thm)],[])).
% 2.88/2.09 tff(1548,plain,
% 2.88/2.09 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2221) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2221)) | (~c2_1(a2221))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 2.88/2.09 tff(1549,plain,
% 2.88/2.09 ($false),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1548, 159, 1257, 1370, 1369, 1542, 1357, 1524, 41, 1531])).
% 2.88/2.09 tff(1550,plain,((~hskp17) | hskp48 | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2189) | hskp32 | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.88/2.09 tff(1551,plain,
% 2.88/2.09 (~hskp17),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1550, 1433, 1370, 1369, 1357, 106, 1257])).
% 2.88/2.09 tff(1552,plain,
% 2.88/2.09 (((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | c3_1(a2239) | (~ndr1_0) | (~c1_1(a2239)) | (~c2_1(a2239)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | c3_1(a2239) | (~ndr1_0) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1553,plain,
% 2.88/2.09 ((hskp17 | (~ndr1_0) | c3_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239))) <=> (hskp17 | c3_1(a2239) | (~ndr1_0) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1554,plain,
% 2.88/2.09 (((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~ndr1_0) | c3_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | c3_1(a2239) | (~ndr1_0) | (~c1_1(a2239)) | (~c2_1(a2239))))),
% 2.88/2.09 inference(monotonicity,[status(thm)],[1553])).
% 2.88/2.09 tff(1555,plain,
% 2.88/2.09 (((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~ndr1_0) | c3_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | c3_1(a2239) | (~ndr1_0) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 2.88/2.09 inference(transitivity,[status(thm)],[1554, 1552])).
% 2.88/2.09 tff(1556,plain,
% 2.88/2.09 ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~ndr1_0) | c3_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 2.88/2.09 inference(quant_inst,[status(thm)],[])).
% 2.88/2.09 tff(1557,plain,
% 2.88/2.09 ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | c3_1(a2239) | (~ndr1_0) | (~c1_1(a2239)) | (~c2_1(a2239))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 2.88/2.09 tff(1558,plain,
% 2.88/2.09 (~c1_1(a2239)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1557, 159, 1551, 1511, 1510, 1444])).
% 2.88/2.09 tff(1559,plain,
% 2.88/2.09 (~c0_1(a2239)),
% 2.88/2.09 inference(unit_resolution,[status(thm)],[1355, 1504])).
% 2.88/2.09 tff(1560,plain,
% 2.88/2.09 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2200) | c0_1(a2239) | (~ndr1_0) | c1_1(a2239) | (~c2_1(a2239)) | (~c1_1(a2200)) | (~c3_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2200) | c0_1(a2239) | (~ndr1_0) | c1_1(a2239) | (~c2_1(a2239)) | (~c1_1(a2200)) | (~c3_1(a2200)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1561,plain,
% 2.88/2.09 ((hskp26 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239))) <=> (hskp26 | c0_1(a2200) | c0_1(a2239) | (~ndr1_0) | c1_1(a2239) | (~c2_1(a2239)) | (~c1_1(a2200)) | (~c3_1(a2200)))),
% 2.88/2.09 inference(rewrite,[status(thm)],[])).
% 2.88/2.09 tff(1562,plain,
% 2.88/2.09 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2200) | c0_1(a2239) | (~ndr1_0) | c1_1(a2239) | (~c2_1(a2239)) | (~c1_1(a2200)) | (~c3_1(a2200))))),
% 2.88/2.09 inference(monotonicity,[status(thm)],[1561])).
% 2.88/2.09 tff(1563,plain,
% 2.88/2.09 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2200) | c0_1(a2239) | (~ndr1_0) | c1_1(a2239) | (~c2_1(a2239)) | (~c1_1(a2200)) | (~c3_1(a2200)))),
% 2.88/2.09 inference(transitivity,[status(thm)],[1562, 1560])).
% 2.88/2.09 tff(1564,plain,
% 2.88/2.09 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239)))),
% 2.88/2.09 inference(quant_inst,[status(thm)],[])).
% 2.88/2.09 tff(1565,plain,
% 2.88/2.09 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2200) | c0_1(a2239) | (~ndr1_0) | c1_1(a2239) | (~c2_1(a2239)) | (~c1_1(a2200)) | (~c3_1(a2200))),
% 2.88/2.09 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 2.88/2.09 tff(1566,plain,
% 2.88/2.10 ($false),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[1565, 159, 1378, 1471, 1511, 1445, 1559, 1234, 1487, 1558])).
% 2.88/2.10 tff(1567,plain,(c0_1(a2200) | hskp26 | hskp0 | hskp18 | hskp48 | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2189) | hskp32 | hskp2 | hskp58), inference(lemma,lemma(discharge,[]))).
% 2.88/2.10 tff(1568,plain,
% 2.88/2.10 (c0_1(a2200)),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[1567, 1434, 1169, 1347, 1349, 1346, 1345, 1344, 106, 1433, 1378])).
% 2.88/2.10 tff(1569,assumption,(c0_1(a2200)), introduced(assumption)).
% 2.88/2.10 tff(1570,plain,
% 2.88/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~c0_1(a2200)) | c2_1(a2200) | c0_1(a2189) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c1_1(a2189)) | (~c1_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (~c0_1(a2200)) | c2_1(a2200) | c0_1(a2189) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c1_1(a2189)) | (~c1_1(a2200)))),
% 2.88/2.10 inference(rewrite,[status(thm)],[])).
% 2.88/2.10 tff(1571,plain,
% 2.88/2.10 (((~ndr1_0) | c2_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c2_1(a2200) | (~c0_1(a2200)) | (~c1_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189))) <=> ((~c0_1(a2200)) | c2_1(a2200) | c0_1(a2189) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c1_1(a2189)) | (~c1_1(a2200)))),
% 2.88/2.10 inference(rewrite,[status(thm)],[])).
% 2.88/2.10 tff(1572,plain,
% 2.88/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c2_1(a2200) | (~c0_1(a2200)) | (~c1_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~c0_1(a2200)) | c2_1(a2200) | c0_1(a2189) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c1_1(a2189)) | (~c1_1(a2200))))),
% 2.88/2.10 inference(monotonicity,[status(thm)],[1571])).
% 2.88/2.10 tff(1573,plain,
% 2.88/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c2_1(a2200) | (~c0_1(a2200)) | (~c1_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (~c0_1(a2200)) | c2_1(a2200) | c0_1(a2189) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c1_1(a2189)) | (~c1_1(a2200)))),
% 2.88/2.10 inference(transitivity,[status(thm)],[1572, 1570])).
% 2.88/2.10 tff(1574,plain,
% 2.88/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c2_1(a2200) | (~c0_1(a2200)) | (~c1_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))),
% 2.88/2.10 inference(quant_inst,[status(thm)],[])).
% 2.88/2.10 tff(1575,plain,
% 2.88/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (~c0_1(a2200)) | c2_1(a2200) | c0_1(a2189) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c1_1(a2189)) | (~c1_1(a2200))),
% 2.88/2.10 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 2.88/2.10 tff(1576,plain,
% 2.88/2.10 (~c1_1(a2200)),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[1575, 159, 1346, 1569, 1493, 1344, 904, 103, 363, 107, 1418])).
% 2.88/2.10 tff(1577,plain,
% 2.88/2.10 (~c3_1(a2200)),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[1468, 1434, 159, 1576, 1493, 127])).
% 2.88/2.10 tff(1578,plain,
% 2.88/2.10 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c1_1(a2200) | (~c0_1(a2200)) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2200))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2200) | (~c0_1(a2200)) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2200))),
% 2.88/2.10 inference(rewrite,[status(thm)],[])).
% 2.88/2.10 tff(1579,plain,
% 2.88/2.10 ((hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2200) | c3_1(a2200) | (~c0_1(a2200))) <=> (hskp33 | c1_1(a2200) | (~c0_1(a2200)) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2200))),
% 2.88/2.10 inference(rewrite,[status(thm)],[])).
% 2.88/2.10 tff(1580,plain,
% 2.88/2.10 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2200) | c3_1(a2200) | (~c0_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c1_1(a2200) | (~c0_1(a2200)) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2200)))),
% 2.88/2.10 inference(monotonicity,[status(thm)],[1579])).
% 2.88/2.10 tff(1581,plain,
% 2.88/2.10 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2200) | c3_1(a2200) | (~c0_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2200) | (~c0_1(a2200)) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2200))),
% 2.88/2.10 inference(transitivity,[status(thm)],[1580, 1578])).
% 2.88/2.10 tff(1582,plain,
% 2.88/2.10 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2200) | c3_1(a2200) | (~c0_1(a2200)))),
% 2.88/2.10 inference(quant_inst,[status(thm)],[])).
% 2.88/2.10 tff(1583,plain,
% 2.88/2.10 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2200) | (~c0_1(a2200)) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2200)),
% 2.88/2.10 inference(modus_ponens,[status(thm)],[1582, 1581])).
% 2.88/2.10 tff(1584,plain,
% 2.88/2.10 ($false),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[1583, 159, 72, 1576, 1569, 105, 904, 103, 261, 1577])).
% 2.88/2.10 tff(1585,plain,(c2_1(a2200) | hskp33 | (~c0_1(a2200)) | c0_1(a2181) | c2_1(a2181) | hskp58 | (~c3_1(a2181))), inference(lemma,lemma(discharge,[]))).
% 2.88/2.10 tff(1586,plain,
% 2.88/2.10 (c2_1(a2200)),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[1585, 1568, 72, 105, 103, 1434, 1348])).
% 2.88/2.10 tff(1587,plain,
% 2.88/2.10 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~c0_1(a2200)) | (~c2_1(a2200)) | (~ndr1_0) | (~c1_1(a2200)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~c0_1(a2200)) | (~c2_1(a2200)) | (~ndr1_0) | (~c1_1(a2200)))),
% 2.88/2.10 inference(rewrite,[status(thm)],[])).
% 2.88/2.10 tff(1588,plain,
% 2.88/2.10 ((hskp0 | (~ndr1_0) | (~c1_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200))) <=> (hskp0 | (~c0_1(a2200)) | (~c2_1(a2200)) | (~ndr1_0) | (~c1_1(a2200)))),
% 2.88/2.10 inference(rewrite,[status(thm)],[])).
% 2.88/2.10 tff(1589,plain,
% 2.88/2.10 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~c0_1(a2200)) | (~c2_1(a2200)) | (~ndr1_0) | (~c1_1(a2200))))),
% 2.88/2.10 inference(monotonicity,[status(thm)],[1588])).
% 2.88/2.10 tff(1590,plain,
% 2.88/2.10 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~c0_1(a2200)) | (~c2_1(a2200)) | (~ndr1_0) | (~c1_1(a2200)))),
% 2.88/2.10 inference(transitivity,[status(thm)],[1589, 1587])).
% 2.88/2.10 tff(1591,plain,
% 2.88/2.10 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)))),
% 2.88/2.10 inference(quant_inst,[status(thm)],[])).
% 2.88/2.10 tff(1592,plain,
% 2.88/2.10 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~c0_1(a2200)) | (~c2_1(a2200)) | (~ndr1_0) | (~c1_1(a2200))),
% 2.88/2.10 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 2.88/2.10 tff(1593,plain,
% 2.88/2.10 ((~c2_1(a2200)) | (~c1_1(a2200))),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[1592, 159, 1169, 1568, 824])).
% 2.88/2.10 tff(1594,plain,
% 2.88/2.10 (~c1_1(a2200)),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[1593, 1586])).
% 2.88/2.10 tff(1595,plain,
% 2.88/2.10 (c3_1(a2200)),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[1583, 159, 72, 1594, 1568, 105, 904, 103, 261])).
% 2.88/2.10 tff(1596,plain,
% 2.88/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c3_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c3_1(a2200)))),
% 2.88/2.10 inference(rewrite,[status(thm)],[])).
% 2.88/2.10 tff(1597,plain,
% 2.88/2.10 (((~ndr1_0) | (~c3_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189))) <=> ((~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c3_1(a2200)))),
% 2.88/2.10 inference(rewrite,[status(thm)],[])).
% 2.88/2.10 tff(1598,plain,
% 2.88/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c3_1(a2200))))),
% 2.88/2.10 inference(monotonicity,[status(thm)],[1597])).
% 2.88/2.10 tff(1599,plain,
% 2.88/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c3_1(a2200)))),
% 2.88/2.10 inference(transitivity,[status(thm)],[1598, 1596])).
% 2.88/2.10 tff(1600,plain,
% 2.88/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))),
% 2.88/2.10 inference(quant_inst,[status(thm)],[])).
% 2.88/2.10 tff(1601,plain,
% 2.88/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c3_1(a2200))),
% 2.88/2.10 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 2.88/2.10 tff(1602,plain,
% 2.88/2.10 ($false),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[1601, 159, 1346, 1345, 1568, 1586, 1344, 323, 1418, 1595])).
% 2.88/2.10 tff(1603,plain,(hskp58 | hskp33 | c0_1(a2181) | c2_1(a2181) | hskp32 | hskp2 | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.88/2.10 tff(1604,plain,
% 2.88/2.10 (hskp2),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[1603, 106, 105, 103, 1188, 72, 1432])).
% 2.88/2.10 tff(1605,plain,
% 2.88/2.10 (~c2_1(a2187)),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[232, 1604])).
% 2.88/2.10 tff(1606,plain,
% 2.88/2.10 (c1_1(a2187)),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[294, 1604])).
% 2.88/2.10 tff(1607,plain,
% 2.88/2.10 (c3_1(a2187)),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[243, 1604])).
% 2.88/2.10 tff(1608,plain,
% 2.88/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2189) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2189) | (~c1_1(a2189)) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2189) | (~c1_1(a2189)) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240))),
% 2.88/2.10 inference(rewrite,[status(thm)],[])).
% 2.88/2.10 tff(1609,plain,
% 2.88/2.10 (((~ndr1_0) | c2_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189))) <=> (c0_1(a2189) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2189) | (~c1_1(a2189)) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240))),
% 2.88/2.10 inference(rewrite,[status(thm)],[])).
% 2.88/2.10 tff(1610,plain,
% 2.88/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2189) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2189) | (~c1_1(a2189)) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240)))),
% 2.88/2.10 inference(monotonicity,[status(thm)],[1609])).
% 2.88/2.10 tff(1611,plain,
% 2.88/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2189) | (~c1_1(a2189)) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240))),
% 2.88/2.10 inference(transitivity,[status(thm)],[1610, 1608])).
% 2.88/2.10 tff(1612,plain,
% 2.88/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))),
% 2.88/2.10 inference(quant_inst,[status(thm)],[])).
% 2.88/2.10 tff(1613,plain,
% 2.88/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2189) | (~c1_1(a2189)) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240)),
% 2.88/2.10 inference(modus_ponens,[status(thm)],[1612, 1611])).
% 2.88/2.10 tff(1614,plain,
% 2.88/2.10 ($false),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[1613, 159, 1410, 1399, 1346, 1607, 1606, 1344, 1605, 363, 1418, 1417])).
% 2.88/2.10 tff(1615,plain,(hskp32 | c0_1(a2181) | hskp33 | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.88/2.10 tff(1616,plain,
% 2.88/2.10 (hskp32),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[1615, 105, 72, 103])).
% 2.88/2.10 tff(1617,plain,
% 2.88/2.10 (c0_1(a2186)),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[83, 1616])).
% 2.88/2.10 tff(1618,plain,
% 2.88/2.10 (~c3_1(a2186)),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[89, 1616])).
% 2.88/2.10 tff(1619,plain,
% 2.88/2.10 (~c2_1(a2186)),
% 2.88/2.10 inference(unit_resolution,[status(thm)],[348, 1616])).
% 2.88/2.10 tff(1620,plain,
% 2.88/2.10 (~c1_1(a2186)),
% 2.92/2.10 inference(unit_resolution,[status(thm)],[791, 159, 1346, 1345, 1617, 1344, 1619, 363, 1418])).
% 2.92/2.10 tff(1621,plain,
% 2.92/2.10 (hskp53),
% 2.92/2.10 inference(unit_resolution,[status(thm)],[530, 1620, 1619, 1618, 1617])).
% 2.92/2.10 tff(1622,plain,
% 2.92/2.10 (c0_1(a2235)),
% 2.92/2.10 inference(unit_resolution,[status(thm)],[101, 1621])).
% 2.92/2.10 tff(1623,plain,
% 2.92/2.10 (c2_1(a2235)),
% 2.92/2.10 inference(unit_resolution,[status(thm)],[670, 1621])).
% 2.92/2.10 tff(1624,plain,
% 2.92/2.10 (c3_1(a2235)),
% 2.92/2.10 inference(unit_resolution,[status(thm)],[681, 1621])).
% 2.92/2.10 tff(1625,plain,
% 2.92/2.10 ($false),
% 2.92/2.10 inference(unit_resolution,[status(thm)],[803, 1624, 1623, 72, 1343, 1622])).
% 2.92/2.10 tff(1626,plain,(c0_1(a2181) | hskp33 | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.92/2.10 tff(1627,plain,
% 2.92/2.10 (c0_1(a2181)),
% 2.92/2.10 inference(unit_resolution,[status(thm)],[1626, 103, 72])).
% 2.92/2.10 tff(1628,assumption,(c0_1(a2181)), introduced(assumption)).
% 2.92/2.10 tff(1629,plain,
% 2.92/2.10 (c3_1(a2181)),
% 2.92/2.10 inference(unit_resolution,[status(thm)],[1307, 1480, 1235])).
% 2.92/2.10 tff(1630,plain,
% 2.92/2.10 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 2.92/2.10 inference(bind,[status(th)],[])).
% 2.92/2.10 tff(1631,plain,
% 2.92/2.10 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.92/2.10 inference(quant_intro,[status(thm)],[1630])).
% 2.92/2.10 tff(1632,plain,
% 2.92/2.10 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.92/2.10 inference(rewrite,[status(thm)],[])).
% 2.92/2.10 tff(1633,plain,
% 2.92/2.10 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 2.92/2.10 inference(bind,[status(th)],[])).
% 2.92/2.10 tff(1634,plain,
% 2.92/2.10 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.92/2.10 inference(quant_intro,[status(thm)],[1633])).
% 2.92/2.10 tff(1635,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause281')).
% 2.92/2.10 tff(1636,plain,
% 2.92/2.10 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.92/2.10 inference(modus_ponens,[status(thm)],[1635, 1634])).
% 2.92/2.10 tff(1637,plain,
% 2.92/2.10 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.92/2.10 inference(modus_ponens,[status(thm)],[1636, 1632])).
% 2.92/2.10 tff(1638,plain,(
% 2.92/2.10 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.92/2.10 inference(skolemize,[status(sab)],[1637])).
% 2.92/2.10 tff(1639,plain,
% 2.92/2.10 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.92/2.10 inference(modus_ponens,[status(thm)],[1638, 1631])).
% 2.92/2.10 tff(1640,plain,
% 2.92/2.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.92/2.10 inference(rewrite,[status(thm)],[])).
% 2.92/2.10 tff(1641,plain,
% 2.92/2.10 ((hskp10 | (~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c2_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181))) <=> (hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.92/2.10 inference(rewrite,[status(thm)],[])).
% 2.92/2.10 tff(1642,plain,
% 2.92/2.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c2_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181))))),
% 2.92/2.10 inference(monotonicity,[status(thm)],[1641])).
% 2.92/2.10 tff(1643,plain,
% 2.92/2.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c2_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.92/2.10 inference(transitivity,[status(thm)],[1642, 1640])).
% 2.92/2.10 tff(1644,plain,
% 2.92/2.10 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c2_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))),
% 2.92/2.10 inference(quant_inst,[status(thm)],[])).
% 2.92/2.10 tff(1645,plain,
% 2.92/2.10 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181))),
% 2.92/2.10 inference(modus_ponens,[status(thm)],[1644, 1643])).
% 2.92/2.10 tff(1646,plain,
% 2.92/2.10 (hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c3_1(a2181))),
% 2.92/2.10 inference(unit_resolution,[status(thm)],[1645, 159, 103, 1639])).
% 2.92/2.10 tff(1647,plain,
% 2.92/2.10 (hskp10),
% 2.92/2.10 inference(unit_resolution,[status(thm)],[1646, 1629, 1235, 1628])).
% 2.92/2.10 tff(1648,plain,
% 2.92/2.10 (((~hskp10) | (~c3_1(a2206))) <=> ((~hskp10) | (~c3_1(a2206)))),
% 2.92/2.10 inference(rewrite,[status(thm)],[])).
% 2.92/2.10 tff(1649,plain,
% 2.92/2.10 (((~c3_1(a2206)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a2206)))),
% 2.92/2.10 inference(rewrite,[status(thm)],[])).
% 2.92/2.10 tff(1650,axiom,((~c3_1(a2206)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause220')).
% 2.92/2.10 tff(1651,plain,
% 2.92/2.10 ((~hskp10) | (~c3_1(a2206))),
% 2.92/2.10 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 2.92/2.10 tff(1652,plain,
% 2.92/2.10 ((~hskp10) | (~c3_1(a2206))),
% 2.92/2.10 inference(modus_ponens,[status(thm)],[1651, 1648])).
% 2.92/2.10 tff(1653,plain,
% 2.92/2.10 (~c3_1(a2206)),
% 2.92/2.10 inference(unit_resolution,[status(thm)],[1652, 1647])).
% 2.92/2.10 tff(1654,plain,
% 2.92/2.10 (((~hskp10) | (~c2_1(a2206))) <=> ((~hskp10) | (~c2_1(a2206)))),
% 2.92/2.10 inference(rewrite,[status(thm)],[])).
% 2.92/2.10 tff(1655,plain,
% 2.92/2.10 (((~c2_1(a2206)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a2206)))),
% 2.92/2.10 inference(rewrite,[status(thm)],[])).
% 2.92/2.10 tff(1656,axiom,((~c2_1(a2206)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause218')).
% 2.92/2.10 tff(1657,plain,
% 2.92/2.10 ((~hskp10) | (~c2_1(a2206))),
% 2.92/2.10 inference(modus_ponens,[status(thm)],[1656, 1655])).
% 2.92/2.10 tff(1658,plain,
% 2.92/2.10 ((~hskp10) | (~c2_1(a2206))),
% 2.92/2.10 inference(modus_ponens,[status(thm)],[1657, 1654])).
% 2.92/2.10 tff(1659,plain,
% 2.92/2.10 (~c2_1(a2206)),
% 2.92/2.10 inference(unit_resolution,[status(thm)],[1658, 1647])).
% 2.92/2.10 tff(1660,plain,
% 2.92/2.10 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c2_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c1_1(a2206)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c2_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c1_1(a2206)))),
% 2.92/2.10 inference(rewrite,[status(thm)],[])).
% 2.92/2.10 tff(1661,plain,
% 2.92/2.10 ((hskp18 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206))) <=> (hskp18 | c2_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c1_1(a2206)))),
% 2.92/2.10 inference(rewrite,[status(thm)],[])).
% 2.92/2.10 tff(1662,plain,
% 2.92/2.10 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c2_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c1_1(a2206))))),
% 2.92/2.10 inference(monotonicity,[status(thm)],[1661])).
% 2.92/2.10 tff(1663,plain,
% 2.92/2.10 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c2_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c1_1(a2206)))),
% 2.92/2.10 inference(transitivity,[status(thm)],[1662, 1660])).
% 2.92/2.10 tff(1664,plain,
% 2.92/2.10 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)))),
% 2.92/2.10 inference(quant_inst,[status(thm)],[])).
% 2.92/2.10 tff(1665,plain,
% 2.92/2.10 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c2_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c1_1(a2206))),
% 2.92/2.10 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 2.92/2.10 tff(1666,plain,
% 2.92/2.10 (~c1_1(a2206)),
% 2.92/2.10 inference(unit_resolution,[status(thm)],[1665, 159, 1480, 1659, 1653, 61])).
% 2.92/2.10 tff(1667,plain,
% 2.92/2.10 (((~hskp10) | (~c0_1(a2206))) <=> ((~hskp10) | (~c0_1(a2206)))),
% 2.92/2.10 inference(rewrite,[status(thm)],[])).
% 2.92/2.10 tff(1668,plain,
% 2.92/2.10 (((~c0_1(a2206)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a2206)))),
% 2.92/2.10 inference(rewrite,[status(thm)],[])).
% 2.92/2.10 tff(1669,axiom,((~c0_1(a2206)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause219')).
% 2.92/2.10 tff(1670,plain,
% 2.92/2.10 ((~hskp10) | (~c0_1(a2206))),
% 2.92/2.10 inference(modus_ponens,[status(thm)],[1669, 1668])).
% 2.92/2.11 tff(1671,plain,
% 2.92/2.11 ((~hskp10) | (~c0_1(a2206))),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1670, 1667])).
% 2.92/2.11 tff(1672,plain,
% 2.92/2.11 (~c0_1(a2206)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1671, 1647])).
% 2.92/2.11 tff(1673,plain,
% 2.92/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~c0_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~c0_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c1_1(a2206))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1674,plain,
% 2.92/2.11 (((~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206)) <=> (c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~c0_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c1_1(a2206))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1675,plain,
% 2.92/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~c0_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c1_1(a2206)))),
% 2.92/2.11 inference(monotonicity,[status(thm)],[1674])).
% 2.92/2.11 tff(1676,plain,
% 2.92/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~c0_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c1_1(a2206))),
% 2.92/2.11 inference(transitivity,[status(thm)],[1675, 1673])).
% 2.92/2.11 tff(1677,plain,
% 2.92/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))),
% 2.92/2.11 inference(quant_inst,[status(thm)],[])).
% 2.92/2.11 tff(1678,plain,
% 2.92/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~c0_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c1_1(a2206)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1677, 1676])).
% 2.92/2.11 tff(1679,plain,
% 2.92/2.11 ($false),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1678, 159, 1659, 1672, 1653, 1628, 103, 209, 1629, 1666])).
% 2.92/2.11 tff(1680,plain,(hskp18 | (~c0_1(a2181)) | c2_1(a2181) | (~c1_1(a2181))), inference(lemma,lemma(discharge,[]))).
% 2.92/2.11 tff(1681,plain,
% 2.92/2.11 (hskp18),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1680, 1627, 103, 904])).
% 2.92/2.11 tff(1682,plain,
% 2.92/2.11 (c0_1(a2222)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[456, 1681])).
% 2.92/2.11 tff(1683,plain,
% 2.92/2.11 (c3_1(a2222)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[417, 1681])).
% 2.92/2.11 tff(1684,plain,
% 2.92/2.11 (~c2_1(a2222)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[376, 1681])).
% 2.92/2.11 tff(1685,assumption,(c1_1(a2222)), introduced(assumption)).
% 2.92/2.11 tff(1686,assumption,(~c2_1(a2222)), introduced(assumption)).
% 2.92/2.11 tff(1687,assumption,(c3_1(a2222)), introduced(assumption)).
% 2.92/2.11 tff(1688,assumption,(c0_1(a2222)), introduced(assumption)).
% 2.92/2.11 tff(1689,plain,
% 2.92/2.11 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1690,plain,
% 2.92/2.11 ((hskp10 | (~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c3_1(a2222)) | (~c1_1(a2222))) <=> (hskp10 | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1691,plain,
% 2.92/2.11 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c3_1(a2222)) | (~c1_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222))))),
% 2.92/2.11 inference(monotonicity,[status(thm)],[1690])).
% 2.92/2.11 tff(1692,plain,
% 2.92/2.11 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c3_1(a2222)) | (~c1_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.92/2.11 inference(transitivity,[status(thm)],[1691, 1689])).
% 2.92/2.11 tff(1693,plain,
% 2.92/2.11 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c3_1(a2222)) | (~c1_1(a2222)))),
% 2.92/2.11 inference(quant_inst,[status(thm)],[])).
% 2.92/2.11 tff(1694,plain,
% 2.92/2.11 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 2.92/2.11 tff(1695,plain,
% 2.92/2.11 (hskp10 | (~c1_1(a2222))),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1694, 159, 1688, 1687, 1686, 1639])).
% 2.92/2.11 tff(1696,plain,
% 2.92/2.11 (hskp10),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1695, 1685])).
% 2.92/2.11 tff(1697,plain,
% 2.92/2.11 (~c3_1(a2206)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1652, 1696])).
% 2.92/2.11 tff(1698,plain,
% 2.92/2.11 (~c0_1(a2206)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1671, 1696])).
% 2.92/2.11 tff(1699,plain,
% 2.92/2.11 (~c2_1(a2206)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1658, 1696])).
% 2.92/2.11 tff(1700,plain,
% 2.92/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1701,plain,
% 2.92/2.11 (((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206)) <=> (c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1702,plain,
% 2.92/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206) | (~c3_1(a2222)) | (~c0_1(a2222))))),
% 2.92/2.11 inference(monotonicity,[status(thm)],[1701])).
% 2.92/2.11 tff(1703,plain,
% 2.92/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.92/2.11 inference(transitivity,[status(thm)],[1702, 1700])).
% 2.92/2.11 tff(1704,plain,
% 2.92/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))),
% 2.92/2.11 inference(quant_inst,[status(thm)],[])).
% 2.92/2.11 tff(1705,plain,
% 2.92/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1704, 1703])).
% 2.92/2.11 tff(1706,plain,
% 2.92/2.11 (c1_1(a2206)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1705, 159, 1688, 1687, 1686, 1699, 1698, 1697, 209])).
% 2.92/2.11 tff(1707,plain,
% 2.92/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | (~ndr1_0) | (~c1_1(a2206)) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | (~ndr1_0) | (~c1_1(a2206)) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1708,plain,
% 2.92/2.11 (((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2206) | c2_1(a2206) | (~c1_1(a2206))) <=> (c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | (~ndr1_0) | (~c1_1(a2206)) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1709,plain,
% 2.92/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2206) | c2_1(a2206) | (~c1_1(a2206)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | (~ndr1_0) | (~c1_1(a2206)) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222))))),
% 2.92/2.11 inference(monotonicity,[status(thm)],[1708])).
% 2.92/2.11 tff(1710,plain,
% 2.92/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2206) | c2_1(a2206) | (~c1_1(a2206)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | (~ndr1_0) | (~c1_1(a2206)) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.92/2.11 inference(transitivity,[status(thm)],[1709, 1707])).
% 2.92/2.11 tff(1711,plain,
% 2.92/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2206) | c2_1(a2206) | (~c1_1(a2206)))),
% 2.92/2.11 inference(quant_inst,[status(thm)],[])).
% 2.92/2.11 tff(1712,plain,
% 2.92/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | (~ndr1_0) | (~c1_1(a2206)) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 2.92/2.11 tff(1713,plain,
% 2.92/2.11 ($false),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1712, 159, 1688, 1687, 1686, 1699, 1698, 363, 1685, 1706])).
% 2.92/2.11 tff(1714,plain,((~c1_1(a2222)) | (~c0_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222)), inference(lemma,lemma(discharge,[]))).
% 2.92/2.11 tff(1715,plain,
% 2.92/2.11 (~c1_1(a2222)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1714, 1684, 1683, 1682])).
% 2.92/2.11 tff(1716,plain,
% 2.92/2.11 (^[V: $i, U: $i] : refl((hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 2.92/2.11 inference(bind,[status(th)],[])).
% 2.92/2.11 tff(1717,plain,
% 2.92/2.11 (![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.92/2.11 inference(quant_intro,[status(thm)],[1716])).
% 2.92/2.11 tff(1718,plain,
% 2.92/2.11 (![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1719,plain,
% 2.92/2.11 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp44) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp44))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp44) <=> (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp44) <=> (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 2.92/2.11 inference(bind,[status(th)],[])).
% 2.92/2.11 tff(1720,plain,
% 2.92/2.11 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp44) <=> ![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.92/2.11 inference(quant_intro,[status(thm)],[1719])).
% 2.92/2.11 tff(1721,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp44)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause278')).
% 2.92/2.11 tff(1722,plain,
% 2.92/2.11 (![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 2.92/2.11 tff(1723,plain,
% 2.92/2.11 (![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1722, 1718])).
% 2.92/2.11 tff(1724,plain,(
% 2.92/2.11 ![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.92/2.11 inference(skolemize,[status(sab)],[1723])).
% 2.92/2.11 tff(1725,plain,
% 2.92/2.11 (![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1724, 1717])).
% 2.92/2.11 tff(1726,plain,
% 2.92/2.11 (((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp44 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp44 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1727,plain,
% 2.92/2.11 ((hskp44 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c3_1(a2222))) <=> (hskp44 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1728,plain,
% 2.92/2.11 (((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp44 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c3_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp44 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222))))),
% 2.92/2.11 inference(monotonicity,[status(thm)],[1727])).
% 2.92/2.11 tff(1729,plain,
% 2.92/2.11 (((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp44 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c3_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp44 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 2.92/2.11 inference(transitivity,[status(thm)],[1728, 1726])).
% 2.92/2.11 tff(1730,plain,
% 2.92/2.11 ((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp44 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c3_1(a2222)))),
% 2.92/2.11 inference(quant_inst,[status(thm)],[])).
% 2.92/2.11 tff(1731,plain,
% 2.92/2.11 ((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp44 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 2.92/2.11 tff(1732,plain,
% 2.92/2.11 (hskp44),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1731, 159, 1682, 1683, 1684, 1725, 1715])).
% 2.92/2.11 tff(1733,plain,
% 2.92/2.11 (((~hskp44) | (~c0_1(a2215))) <=> ((~hskp44) | (~c0_1(a2215)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1734,plain,
% 2.92/2.11 (((~c0_1(a2215)) | (~hskp44)) <=> ((~hskp44) | (~c0_1(a2215)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1735,axiom,((~c0_1(a2215)) | (~hskp44)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 2.92/2.11 tff(1736,plain,
% 2.92/2.11 ((~hskp44) | (~c0_1(a2215))),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1735, 1734])).
% 2.92/2.11 tff(1737,plain,
% 2.92/2.11 ((~hskp44) | (~c0_1(a2215))),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1736, 1733])).
% 2.92/2.11 tff(1738,plain,
% 2.92/2.11 (~c0_1(a2215)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1737, 1732])).
% 2.92/2.11 tff(1739,plain,
% 2.92/2.11 (((~hskp44) | c1_1(a2215)) <=> ((~hskp44) | c1_1(a2215))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1740,axiom,((~hskp44) | c1_1(a2215)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 2.92/2.11 tff(1741,plain,
% 2.92/2.11 ((~hskp44) | c1_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1740, 1739])).
% 2.92/2.11 tff(1742,plain,
% 2.92/2.11 ((~hskp44) | c1_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1741, 1739])).
% 2.92/2.11 tff(1743,plain,
% 2.92/2.11 ((~hskp44) | c1_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1742, 1739])).
% 2.92/2.11 tff(1744,plain,
% 2.92/2.11 ((~hskp44) | c1_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1743, 1739])).
% 2.92/2.11 tff(1745,plain,
% 2.92/2.11 ((~hskp44) | c1_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1744, 1739])).
% 2.92/2.11 tff(1746,plain,
% 2.92/2.11 ((~hskp44) | c1_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1745, 1739])).
% 2.92/2.11 tff(1747,plain,
% 2.92/2.11 ((~hskp44) | c1_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1746, 1739])).
% 2.92/2.11 tff(1748,plain,
% 2.92/2.11 ((~hskp44) | c1_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1747, 1739])).
% 2.92/2.11 tff(1749,plain,
% 2.92/2.11 (c1_1(a2215)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1748, 1732])).
% 2.92/2.11 tff(1750,plain,
% 2.92/2.11 (((~hskp44) | c2_1(a2215)) <=> ((~hskp44) | c2_1(a2215))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1751,axiom,((~hskp44) | c2_1(a2215)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 2.92/2.11 tff(1752,plain,
% 2.92/2.11 ((~hskp44) | c2_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1751, 1750])).
% 2.92/2.11 tff(1753,plain,
% 2.92/2.11 ((~hskp44) | c2_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1752, 1750])).
% 2.92/2.11 tff(1754,plain,
% 2.92/2.11 ((~hskp44) | c2_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1753, 1750])).
% 2.92/2.11 tff(1755,plain,
% 2.92/2.11 ((~hskp44) | c2_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1754, 1750])).
% 2.92/2.11 tff(1756,plain,
% 2.92/2.11 ((~hskp44) | c2_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1755, 1750])).
% 2.92/2.11 tff(1757,plain,
% 2.92/2.11 ((~hskp44) | c2_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1756, 1750])).
% 2.92/2.11 tff(1758,plain,
% 2.92/2.11 ((~hskp44) | c2_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1757, 1750])).
% 2.92/2.11 tff(1759,plain,
% 2.92/2.11 ((~hskp44) | c2_1(a2215)),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1758, 1750])).
% 2.92/2.11 tff(1760,plain,
% 2.92/2.11 (c2_1(a2215)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1759, 1732])).
% 2.92/2.11 tff(1761,plain,
% 2.92/2.11 (~c1_1(a2222)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1714, 1322, 1321, 1320])).
% 2.92/2.11 tff(1762,plain,
% 2.92/2.11 ($false),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1329, 159, 106, 1322, 1321, 1320, 117, 1761])).
% 2.92/2.11 tff(1763,plain,((~hskp18) | hskp32), inference(lemma,lemma(discharge,[]))).
% 2.92/2.11 tff(1764,plain,
% 2.92/2.11 (hskp32),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[1763, 1681])).
% 2.92/2.11 tff(1765,plain,
% 2.92/2.11 (~c2_1(a2186)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[348, 1764])).
% 2.92/2.11 tff(1766,plain,
% 2.92/2.11 (~c3_1(a2186)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[89, 1764])).
% 2.92/2.11 tff(1767,plain,
% 2.92/2.11 (c0_1(a2186)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[83, 1764])).
% 2.92/2.11 tff(1768,plain,
% 2.92/2.11 (~hskp53),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[833, 352, 825, 72])).
% 2.92/2.11 tff(1769,plain,
% 2.92/2.11 (c1_1(a2186)),
% 2.92/2.11 inference(unit_resolution,[status(thm)],[530, 1768, 519, 520, 521])).
% 2.92/2.11 tff(1770,plain,
% 2.92/2.11 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 2.92/2.11 inference(bind,[status(th)],[])).
% 2.92/2.11 tff(1771,plain,
% 2.92/2.11 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.92/2.11 inference(quant_intro,[status(thm)],[1770])).
% 2.92/2.11 tff(1772,plain,
% 2.92/2.11 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1773,plain,
% 2.92/2.11 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 2.92/2.11 inference(bind,[status(th)],[])).
% 2.92/2.11 tff(1774,plain,
% 2.92/2.11 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.92/2.11 inference(quant_intro,[status(thm)],[1773])).
% 2.92/2.11 tff(1775,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause274')).
% 2.92/2.11 tff(1776,plain,
% 2.92/2.11 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 2.92/2.11 tff(1777,plain,
% 2.92/2.11 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1776, 1772])).
% 2.92/2.11 tff(1778,plain,(
% 2.92/2.11 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.92/2.11 inference(skolemize,[status(sab)],[1777])).
% 2.92/2.11 tff(1779,plain,
% 2.92/2.11 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.92/2.11 inference(modus_ponens,[status(thm)],[1778, 1771])).
% 2.92/2.11 tff(1780,assumption,(~c0_1(a2215)), introduced(assumption)).
% 2.92/2.11 tff(1781,assumption,(c1_1(a2215)), introduced(assumption)).
% 2.92/2.11 tff(1782,assumption,(c2_1(a2215)), introduced(assumption)).
% 2.92/2.11 tff(1783,plain,
% 2.92/2.11 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | c0_1(a2215) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)) | (~c2_1(a2215)) | (~c1_1(a2215)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a2215) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1784,plain,
% 2.92/2.11 ((hskp4 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | c0_1(a2215) | (~c2_1(a2215)) | (~c1_1(a2215))) <=> (hskp4 | c0_1(a2215) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 2.92/2.11 inference(rewrite,[status(thm)],[])).
% 2.92/2.11 tff(1785,plain,
% 2.92/2.11 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | c0_1(a2215) | (~c2_1(a2215)) | (~c1_1(a2215)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | c0_1(a2215) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)) | (~c2_1(a2215)) | (~c1_1(a2215))))),
% 2.92/2.11 inference(monotonicity,[status(thm)],[1784])).
% 2.92/2.11 tff(1786,plain,
% 2.92/2.11 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | c0_1(a2215) | (~c2_1(a2215)) | (~c1_1(a2215)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a2215) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 2.92/2.11 inference(transitivity,[status(thm)],[1785, 1783])).
% 2.92/2.11 tff(1787,plain,
% 2.92/2.11 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | c0_1(a2215) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 2.92/2.12 inference(quant_inst,[status(thm)],[])).
% 2.92/2.12 tff(1788,plain,
% 2.92/2.12 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a2215) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)) | (~c2_1(a2215)) | (~c1_1(a2215))),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1787, 1786])).
% 2.92/2.12 tff(1789,plain,
% 2.92/2.12 (hskp4 | (~c1_1(a2186))),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1788, 159, 1782, 1781, 1780, 520, 519, 1779])).
% 2.92/2.12 tff(1790,plain,
% 2.92/2.12 (hskp4),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1789, 1769])).
% 2.92/2.12 tff(1791,plain,
% 2.92/2.12 (((~hskp4) | (~c1_1(a2191))) <=> ((~hskp4) | (~c1_1(a2191)))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1792,plain,
% 2.92/2.12 (((~c1_1(a2191)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a2191)))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1793,axiom,((~c1_1(a2191)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause233')).
% 2.92/2.12 tff(1794,plain,
% 2.92/2.12 ((~hskp4) | (~c1_1(a2191))),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1793, 1792])).
% 2.92/2.12 tff(1795,plain,
% 2.92/2.12 ((~hskp4) | (~c1_1(a2191))),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1794, 1791])).
% 2.92/2.12 tff(1796,plain,
% 2.92/2.12 (~c1_1(a2191)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1795, 1790])).
% 2.92/2.12 tff(1797,plain,
% 2.92/2.12 (((~hskp4) | (~c2_1(a2191))) <=> ((~hskp4) | (~c2_1(a2191)))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1798,plain,
% 2.92/2.12 (((~c2_1(a2191)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a2191)))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1799,axiom,((~c2_1(a2191)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause232')).
% 2.92/2.12 tff(1800,plain,
% 2.92/2.12 ((~hskp4) | (~c2_1(a2191))),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1799, 1798])).
% 2.92/2.12 tff(1801,plain,
% 2.92/2.12 ((~hskp4) | (~c2_1(a2191))),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1800, 1797])).
% 2.92/2.12 tff(1802,plain,
% 2.92/2.12 (~c2_1(a2191)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1801, 1790])).
% 2.92/2.12 tff(1803,plain,
% 2.92/2.12 (((~hskp4) | c3_1(a2191)) <=> ((~hskp4) | c3_1(a2191))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1804,axiom,((~hskp4) | c3_1(a2191)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 2.92/2.12 tff(1805,plain,
% 2.92/2.12 ((~hskp4) | c3_1(a2191)),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1804, 1803])).
% 2.92/2.12 tff(1806,plain,
% 2.92/2.12 ((~hskp4) | c3_1(a2191)),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1805, 1803])).
% 2.92/2.12 tff(1807,plain,
% 2.92/2.12 ((~hskp4) | c3_1(a2191)),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1806, 1803])).
% 2.92/2.12 tff(1808,plain,
% 2.92/2.12 ((~hskp4) | c3_1(a2191)),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1807, 1803])).
% 2.92/2.12 tff(1809,plain,
% 2.92/2.12 ((~hskp4) | c3_1(a2191)),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1808, 1803])).
% 2.92/2.12 tff(1810,plain,
% 2.92/2.12 ((~hskp4) | c3_1(a2191)),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1809, 1803])).
% 2.92/2.12 tff(1811,plain,
% 2.92/2.12 ((~hskp4) | c3_1(a2191)),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1810, 1803])).
% 2.92/2.12 tff(1812,plain,
% 2.92/2.12 ((~hskp4) | c3_1(a2191)),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1811, 1803])).
% 2.92/2.12 tff(1813,plain,
% 2.92/2.12 (c3_1(a2191)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1812, 1790])).
% 2.92/2.12 tff(1814,assumption,(~c1_1(a2222)), introduced(assumption)).
% 2.92/2.12 tff(1815,plain,
% 2.92/2.12 (hskp46 | hskp34),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[460, 159, 1688, 1687, 446, 1814])).
% 2.92/2.12 tff(1816,plain,
% 2.92/2.12 (hskp46),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1815, 352])).
% 2.92/2.12 tff(1817,plain,
% 2.92/2.12 (c2_1(a2218)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[472, 1816])).
% 2.92/2.12 tff(1818,plain,
% 2.92/2.12 (c0_1(a2218)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[483, 1816])).
% 2.92/2.12 tff(1819,plain,
% 2.92/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1820,plain,
% 2.92/2.12 (((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2191) | c2_1(a2191) | (~c3_1(a2191)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218))) <=> (c3_1(a2186) | c2_1(a2186) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1821,plain,
% 2.92/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2191) | c2_1(a2191) | (~c3_1(a2191)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218))))),
% 2.92/2.12 inference(monotonicity,[status(thm)],[1820])).
% 2.92/2.12 tff(1822,plain,
% 2.92/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2191) | c2_1(a2191) | (~c3_1(a2191)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 2.92/2.12 inference(transitivity,[status(thm)],[1821, 1819])).
% 2.92/2.12 tff(1823,plain,
% 2.92/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2191) | c2_1(a2191) | (~c3_1(a2191)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))),
% 2.92/2.12 inference(quant_inst,[status(thm)],[])).
% 2.92/2.12 tff(1824,plain,
% 2.92/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218))),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1823, 1822])).
% 2.92/2.12 tff(1825,plain,
% 2.92/2.12 (~c1_1(a2218)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1824, 159, 1818, 1817, 521, 1813, 520, 519, 1802, 1796, 51])).
% 2.92/2.12 tff(1826,plain,
% 2.92/2.12 ($false),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[504, 159, 352, 72, 1818, 1817, 501, 1825])).
% 2.92/2.12 tff(1827,plain,(hskp34 | hskp33 | (~c0_1(a2186)) | c3_1(a2186) | c2_1(a2186) | (~c2_1(a2215)) | (~c1_1(a2215)) | c0_1(a2215) | (~c0_1(a2222)) | (~c3_1(a2222)) | c1_1(a2222) | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.92/2.12 tff(1828,plain,
% 2.92/2.12 (hskp34),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1827, 1767, 72, 1766, 1765, 1760, 1749, 1738, 1682, 1683, 1715, 1169])).
% 2.92/2.12 tff(1829,plain,
% 2.92/2.12 (c3_1(a2189)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[739, 1828])).
% 2.92/2.12 tff(1830,plain,
% 2.92/2.12 (c1_1(a2189)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[750, 1828])).
% 2.92/2.12 tff(1831,plain,
% 2.92/2.12 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2215) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2215) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1832,plain,
% 2.92/2.12 ((hskp33 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189))) <=> (hskp33 | c0_1(a2215) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1833,plain,
% 2.92/2.12 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2215) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215))))),
% 2.92/2.12 inference(monotonicity,[status(thm)],[1832])).
% 2.92/2.12 tff(1834,plain,
% 2.92/2.12 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2215) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 2.92/2.12 inference(transitivity,[status(thm)],[1833, 1831])).
% 2.92/2.12 tff(1835,plain,
% 2.92/2.12 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))),
% 2.92/2.12 inference(quant_inst,[status(thm)],[])).
% 2.92/2.12 tff(1836,plain,
% 2.92/2.12 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2215) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215))),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 2.92/2.12 tff(1837,plain,
% 2.92/2.12 (~c2_1(a2189)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1836, 159, 72, 1760, 1749, 1830, 1829, 1738, 71])).
% 2.92/2.12 tff(1838,plain,
% 2.92/2.12 (~c0_1(a2189)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[763, 1828])).
% 2.92/2.12 tff(1839,plain,
% 2.92/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2189) | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1840,plain,
% 2.92/2.12 (((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2181) | (~c0_1(a2181)) | (~c1_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189))) <=> (c0_1(a2189) | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1841,plain,
% 2.92/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2181) | (~c0_1(a2181)) | (~c1_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2189) | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))))),
% 2.92/2.12 inference(monotonicity,[status(thm)],[1840])).
% 2.92/2.12 tff(1842,plain,
% 2.92/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2181) | (~c0_1(a2181)) | (~c1_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.92/2.12 inference(transitivity,[status(thm)],[1841, 1839])).
% 2.92/2.12 tff(1843,plain,
% 2.92/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2181) | (~c0_1(a2181)) | (~c1_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))),
% 2.92/2.12 inference(quant_inst,[status(thm)],[])).
% 2.92/2.12 tff(1844,plain,
% 2.92/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 2.92/2.12 tff(1845,plain,
% 2.92/2.12 ($false),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1844, 159, 1830, 1829, 1838, 1627, 904, 103, 363, 1837])).
% 2.92/2.12 tff(1846,plain,(c2_1(a2181) | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.92/2.12 tff(1847,plain,
% 2.92/2.12 (c2_1(a2181)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1846, 72])).
% 2.92/2.12 tff(1848,plain,
% 2.92/2.12 (~hskp0),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[950, 1847])).
% 2.92/2.12 tff(1849,plain,
% 2.92/2.12 (hskp34),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[833, 91, 1848, 72])).
% 2.92/2.12 tff(1850,plain,
% 2.92/2.12 (c3_1(a2235)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[681, 91])).
% 2.92/2.12 tff(1851,plain,
% 2.92/2.12 ($false),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[803, 1850, 813, 72, 1849, 102])).
% 2.92/2.12 tff(1852,plain,((~hskp53) | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.92/2.12 tff(1853,plain,
% 2.92/2.12 (~hskp53),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1852, 72])).
% 2.92/2.12 tff(1854,plain,
% 2.92/2.12 (c1_1(a2186)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[530, 966, 1853, 90, 84])).
% 2.92/2.12 tff(1855,plain,
% 2.92/2.12 (hskp18),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[369, 159, 90, 966, 61, 1854])).
% 2.92/2.12 tff(1856,plain,
% 2.92/2.12 (c0_1(a2222)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[456, 1855])).
% 2.92/2.12 tff(1857,plain,
% 2.92/2.12 (~c2_1(a2222)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[376, 1855])).
% 2.92/2.12 tff(1858,plain,
% 2.92/2.12 (c3_1(a2222)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[417, 1855])).
% 2.92/2.12 tff(1859,plain,
% 2.92/2.12 (~c1_1(a2222)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1714, 1858, 1857, 1856])).
% 2.92/2.12 tff(1860,plain,
% 2.92/2.12 (hskp44),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1731, 159, 1856, 1858, 1857, 1725, 1859])).
% 2.92/2.12 tff(1861,plain,
% 2.92/2.12 (~c0_1(a2215)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1737, 1860])).
% 2.92/2.12 tff(1862,plain,
% 2.92/2.12 (c1_1(a2215)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1748, 1860])).
% 2.92/2.12 tff(1863,plain,
% 2.92/2.12 (c2_1(a2215)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1759, 1860])).
% 2.92/2.12 tff(1864,plain,
% 2.92/2.12 (hskp34),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1827, 1863, 1848, 84, 90, 966, 1862, 1861, 1856, 1858, 1859, 72])).
% 2.92/2.12 tff(1865,plain,
% 2.92/2.12 (c3_1(a2189)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[739, 1864])).
% 2.92/2.12 tff(1866,plain,
% 2.92/2.12 (c1_1(a2189)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[750, 1864])).
% 2.92/2.12 tff(1867,plain,
% 2.92/2.12 (~c2_1(a2189)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1836, 159, 72, 1863, 1862, 1866, 1865, 1861, 71])).
% 2.92/2.12 tff(1868,plain,
% 2.92/2.12 (~c0_1(a2189)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[763, 1864])).
% 2.92/2.12 tff(1869,plain,
% 2.92/2.12 ($false),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[791, 159, 1866, 1865, 84, 1868, 966, 363, 1854, 1867])).
% 2.92/2.12 tff(1870,plain,((~hskp32) | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.92/2.12 tff(1871,plain,
% 2.92/2.12 (~hskp32),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1870, 72])).
% 2.92/2.12 tff(1872,plain,
% 2.92/2.12 (~hskp26),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1290, 352, 1848, 72])).
% 2.92/2.12 tff(1873,assumption,(~c3_1(a2181)), introduced(assumption)).
% 2.92/2.12 tff(1874,plain,
% 2.92/2.12 (hskp32 | hskp2 | c1_1(a2181) | c3_1(a2181)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[225, 159, 105, 219])).
% 2.92/2.12 tff(1875,plain,
% 2.92/2.12 (hskp2),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1874, 1873, 106, 104])).
% 2.92/2.12 tff(1876,plain,
% 2.92/2.12 (~c2_1(a2187)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[232, 1875])).
% 2.92/2.12 tff(1877,plain,
% 2.92/2.12 (c1_1(a2187)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[294, 1875])).
% 2.92/2.12 tff(1878,plain,
% 2.92/2.12 (c3_1(a2187)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[243, 1875])).
% 2.92/2.12 tff(1879,plain,
% 2.92/2.12 (~hskp18),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1763, 106])).
% 2.92/2.12 tff(1880,assumption,(hskp10), introduced(assumption)).
% 2.92/2.12 tff(1881,plain,
% 2.92/2.12 (~c3_1(a2206)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1652, 1880])).
% 2.92/2.12 tff(1882,plain,
% 2.92/2.12 (~c2_1(a2206)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1658, 1880])).
% 2.92/2.12 tff(1883,plain,
% 2.92/2.12 (~c1_1(a2206)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1665, 159, 1480, 1882, 1881, 61])).
% 2.92/2.12 tff(1884,assumption,(~c2_1(a2187)), introduced(assumption)).
% 2.92/2.12 tff(1885,plain,
% 2.92/2.12 (~c0_1(a2206)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1671, 1880])).
% 2.92/2.12 tff(1886,assumption,(c3_1(a2187)), introduced(assumption)).
% 2.92/2.12 tff(1887,plain,
% 2.92/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | (~c0_1(a2187)) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | (~c0_1(a2187)) | c1_1(a2206))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1888,plain,
% 2.92/2.12 (((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206)) <=> (c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | (~c0_1(a2187)) | c1_1(a2206))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1889,plain,
% 2.92/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | (~c0_1(a2187)) | c1_1(a2206)))),
% 2.92/2.12 inference(monotonicity,[status(thm)],[1888])).
% 2.92/2.12 tff(1890,plain,
% 2.92/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | (~c0_1(a2187)) | c1_1(a2206))),
% 2.92/2.12 inference(transitivity,[status(thm)],[1889, 1887])).
% 2.92/2.12 tff(1891,plain,
% 2.92/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))),
% 2.92/2.12 inference(quant_inst,[status(thm)],[])).
% 2.92/2.12 tff(1892,plain,
% 2.92/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | (~c0_1(a2187)) | c1_1(a2206)),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 2.92/2.12 tff(1893,plain,
% 2.92/2.12 ((~c0_1(a2187)) | c1_1(a2206)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1892, 159, 1886, 1882, 1885, 1881, 1884, 209])).
% 2.92/2.12 tff(1894,plain,
% 2.92/2.12 (~c0_1(a2187)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1893, 1883])).
% 2.92/2.12 tff(1895,plain,
% 2.92/2.12 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c2_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c1_1(a2206))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c2_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c1_1(a2206))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1896,plain,
% 2.92/2.12 ((hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206)) <=> (hskp47 | c2_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c1_1(a2206))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1897,plain,
% 2.92/2.12 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c2_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c1_1(a2206)))),
% 2.92/2.12 inference(monotonicity,[status(thm)],[1896])).
% 2.92/2.12 tff(1898,plain,
% 2.92/2.12 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c2_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c1_1(a2206))),
% 2.92/2.12 inference(transitivity,[status(thm)],[1897, 1895])).
% 2.92/2.12 tff(1899,plain,
% 2.92/2.12 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206))),
% 2.92/2.12 inference(quant_inst,[status(thm)],[])).
% 2.92/2.12 tff(1900,plain,
% 2.92/2.12 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c2_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c1_1(a2206)),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 2.92/2.12 tff(1901,plain,
% 2.92/2.12 ($false),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1900, 159, 1085, 1886, 1882, 1881, 1884, 271, 1894, 1883])).
% 2.92/2.12 tff(1902,plain,((~hskp10) | hskp47 | (~c3_1(a2187)) | c2_1(a2187) | hskp18), inference(lemma,lemma(discharge,[]))).
% 2.92/2.12 tff(1903,plain,
% 2.92/2.12 (~hskp10),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1902, 1878, 1085, 1876, 1879])).
% 2.92/2.12 tff(1904,assumption,(~hskp10), introduced(assumption)).
% 2.92/2.12 tff(1905,assumption,(c1_1(a2187)), introduced(assumption)).
% 2.92/2.12 tff(1906,plain,
% 2.92/2.12 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | (~c0_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | (~c0_1(a2187)))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1907,plain,
% 2.92/2.12 ((hskp10 | (~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c2_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187))) <=> (hskp10 | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | (~c0_1(a2187)))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1908,plain,
% 2.92/2.12 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c2_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | (~c0_1(a2187))))),
% 2.92/2.12 inference(monotonicity,[status(thm)],[1907])).
% 2.92/2.12 tff(1909,plain,
% 2.92/2.12 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c2_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | (~c0_1(a2187)))),
% 2.92/2.12 inference(transitivity,[status(thm)],[1908, 1906])).
% 2.92/2.12 tff(1910,plain,
% 2.92/2.12 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c2_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187)))),
% 2.92/2.12 inference(quant_inst,[status(thm)],[])).
% 2.92/2.12 tff(1911,plain,
% 2.92/2.12 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | (~c0_1(a2187))),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 2.92/2.12 tff(1912,plain,
% 2.92/2.12 (hskp10 | (~c0_1(a2187))),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1911, 159, 1886, 1905, 1884, 1639])).
% 2.92/2.12 tff(1913,plain,
% 2.92/2.12 (~c0_1(a2187)),
% 2.92/2.12 inference(unit_resolution,[status(thm)],[1912, 1904])).
% 2.92/2.12 tff(1914,plain,
% 2.92/2.12 (^[U: $i] : refl((hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 2.92/2.12 inference(bind,[status(th)],[])).
% 2.92/2.12 tff(1915,plain,
% 2.92/2.12 (![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.92/2.12 inference(quant_intro,[status(thm)],[1914])).
% 2.92/2.12 tff(1916,plain,
% 2.92/2.12 (![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1917,plain,
% 2.92/2.12 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp41) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp41))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp41) <=> (hskp41 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp41) <=> (hskp41 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp41) | hskp10) <=> ((hskp41 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp10))), rewrite(((hskp41 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp10) <=> (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp41) | hskp10) <=> (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 2.92/2.12 inference(bind,[status(th)],[])).
% 2.92/2.12 tff(1918,plain,
% 2.92/2.12 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp41) | hskp10) <=> ![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.92/2.12 inference(quant_intro,[status(thm)],[1917])).
% 2.92/2.12 tff(1919,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp41) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause249')).
% 2.92/2.12 tff(1920,plain,
% 2.92/2.12 (![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1919, 1918])).
% 2.92/2.12 tff(1921,plain,
% 2.92/2.12 (![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1920, 1916])).
% 2.92/2.12 tff(1922,plain,(
% 2.92/2.12 ![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.92/2.12 inference(skolemize,[status(sab)],[1921])).
% 2.92/2.12 tff(1923,plain,
% 2.92/2.12 (![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.92/2.12 inference(modus_ponens,[status(thm)],[1922, 1915])).
% 2.92/2.12 tff(1924,assumption,(c2_1(a2181)), introduced(assumption)).
% 2.92/2.12 tff(1925,plain,
% 2.92/2.12 (((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp41 | hskp10 | c0_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))) <=> ((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp41 | hskp10 | c0_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1926,plain,
% 2.92/2.12 ((hskp41 | hskp10 | (~ndr1_0) | c3_1(a2181) | c0_1(a2181) | (~c2_1(a2181))) <=> (hskp41 | hskp10 | c0_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 2.92/2.12 inference(rewrite,[status(thm)],[])).
% 2.92/2.12 tff(1927,plain,
% 2.92/2.12 (((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp41 | hskp10 | (~ndr1_0) | c3_1(a2181) | c0_1(a2181) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp41 | hskp10 | c0_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181)))),
% 2.92/2.12 inference(monotonicity,[status(thm)],[1926])).
% 2.92/2.12 tff(1928,plain,
% 2.92/2.12 (((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp41 | hskp10 | (~ndr1_0) | c3_1(a2181) | c0_1(a2181) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp41 | hskp10 | c0_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 2.92/2.12 inference(transitivity,[status(thm)],[1927, 1925])).
% 2.92/2.13 tff(1929,plain,
% 2.92/2.13 ((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp41 | hskp10 | (~ndr1_0) | c3_1(a2181) | c0_1(a2181) | (~c2_1(a2181)))),
% 2.92/2.13 inference(quant_inst,[status(thm)],[])).
% 2.92/2.13 tff(1930,plain,
% 2.92/2.13 ((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp41 | hskp10 | c0_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1929, 1928])).
% 2.92/2.13 tff(1931,plain,
% 2.92/2.13 (hskp41 | hskp10 | c0_1(a2181) | c3_1(a2181)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1930, 159, 1924, 1923])).
% 2.92/2.13 tff(1932,plain,
% 2.92/2.13 (hskp41),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1931, 1904, 105, 1873])).
% 2.92/2.13 tff(1933,plain,
% 2.92/2.13 (((~hskp41) | (~c0_1(a2205))) <=> ((~hskp41) | (~c0_1(a2205)))),
% 2.92/2.13 inference(rewrite,[status(thm)],[])).
% 2.92/2.13 tff(1934,plain,
% 2.92/2.13 (((~c0_1(a2205)) | (~hskp41)) <=> ((~hskp41) | (~c0_1(a2205)))),
% 2.92/2.13 inference(rewrite,[status(thm)],[])).
% 2.92/2.13 tff(1935,axiom,((~c0_1(a2205)) | (~hskp41)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 2.92/2.13 tff(1936,plain,
% 2.92/2.13 ((~hskp41) | (~c0_1(a2205))),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1935, 1934])).
% 2.92/2.13 tff(1937,plain,
% 2.92/2.13 ((~hskp41) | (~c0_1(a2205))),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1936, 1933])).
% 2.92/2.13 tff(1938,plain,
% 2.92/2.13 (~c0_1(a2205)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1937, 1932])).
% 2.92/2.13 tff(1939,plain,
% 2.92/2.13 (((~hskp41) | c1_1(a2205)) <=> ((~hskp41) | c1_1(a2205))),
% 2.92/2.13 inference(rewrite,[status(thm)],[])).
% 2.92/2.13 tff(1940,axiom,((~hskp41) | c1_1(a2205)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 2.92/2.13 tff(1941,plain,
% 2.92/2.13 ((~hskp41) | c1_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 2.92/2.13 tff(1942,plain,
% 2.92/2.13 ((~hskp41) | c1_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1941, 1939])).
% 2.92/2.13 tff(1943,plain,
% 2.92/2.13 ((~hskp41) | c1_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1942, 1939])).
% 2.92/2.13 tff(1944,plain,
% 2.92/2.13 ((~hskp41) | c1_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1943, 1939])).
% 2.92/2.13 tff(1945,plain,
% 2.92/2.13 ((~hskp41) | c1_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1944, 1939])).
% 2.92/2.13 tff(1946,plain,
% 2.92/2.13 ((~hskp41) | c1_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1945, 1939])).
% 2.92/2.13 tff(1947,plain,
% 2.92/2.13 ((~hskp41) | c1_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1946, 1939])).
% 2.92/2.13 tff(1948,plain,
% 2.92/2.13 ((~hskp41) | c1_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1947, 1939])).
% 2.92/2.13 tff(1949,plain,
% 2.92/2.13 (c1_1(a2205)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1948, 1932])).
% 2.92/2.13 tff(1950,plain,
% 2.92/2.13 (((~hskp41) | c2_1(a2205)) <=> ((~hskp41) | c2_1(a2205))),
% 2.92/2.13 inference(rewrite,[status(thm)],[])).
% 2.92/2.13 tff(1951,axiom,((~hskp41) | c2_1(a2205)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 2.92/2.13 tff(1952,plain,
% 2.92/2.13 ((~hskp41) | c2_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 2.92/2.13 tff(1953,plain,
% 2.92/2.13 ((~hskp41) | c2_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1952, 1950])).
% 2.92/2.13 tff(1954,plain,
% 2.92/2.13 ((~hskp41) | c2_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1953, 1950])).
% 2.92/2.13 tff(1955,plain,
% 2.92/2.13 ((~hskp41) | c2_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1954, 1950])).
% 2.92/2.13 tff(1956,plain,
% 2.92/2.13 ((~hskp41) | c2_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1955, 1950])).
% 2.92/2.13 tff(1957,plain,
% 2.92/2.13 ((~hskp41) | c2_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1956, 1950])).
% 2.92/2.13 tff(1958,plain,
% 2.92/2.13 ((~hskp41) | c2_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1957, 1950])).
% 2.92/2.13 tff(1959,plain,
% 2.92/2.13 ((~hskp41) | c2_1(a2205)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1958, 1950])).
% 2.92/2.13 tff(1960,plain,
% 2.92/2.13 (c2_1(a2205)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1959, 1932])).
% 2.92/2.13 tff(1961,plain,
% 2.92/2.13 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2205) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2205)) | (~c1_1(a2205)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2205) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2205)) | (~c1_1(a2205)))),
% 2.92/2.13 inference(rewrite,[status(thm)],[])).
% 2.92/2.13 tff(1962,plain,
% 2.92/2.13 ((hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187))) <=> (hskp48 | c0_1(a2205) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2205)) | (~c1_1(a2205)))),
% 2.92/2.13 inference(rewrite,[status(thm)],[])).
% 2.92/2.13 tff(1963,plain,
% 2.92/2.13 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2205) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2205)) | (~c1_1(a2205))))),
% 2.92/2.13 inference(monotonicity,[status(thm)],[1962])).
% 2.92/2.13 tff(1964,plain,
% 2.92/2.13 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2205) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2205)) | (~c1_1(a2205)))),
% 2.92/2.13 inference(transitivity,[status(thm)],[1963, 1961])).
% 2.92/2.13 tff(1965,plain,
% 2.92/2.13 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187)))),
% 2.92/2.13 inference(quant_inst,[status(thm)],[])).
% 2.92/2.13 tff(1966,plain,
% 2.92/2.13 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2205) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2205)) | (~c1_1(a2205))),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1965, 1964])).
% 2.92/2.13 tff(1967,plain,
% 2.92/2.13 ($false),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1966, 159, 1257, 1960, 1949, 1886, 1905, 1938, 41, 1913])).
% 2.92/2.13 tff(1968,plain,(hskp10 | hskp48 | (~c3_1(a2187)) | (~c1_1(a2187)) | c2_1(a2187) | c0_1(a2181) | c3_1(a2181) | (~c2_1(a2181))), inference(lemma,lemma(discharge,[]))).
% 2.92/2.13 tff(1969,plain,
% 2.92/2.13 (hskp48),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1968, 1903, 1878, 1877, 1876, 105, 1873, 1847])).
% 2.92/2.13 tff(1970,plain,
% 2.92/2.13 (~c0_1(a2228)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1194, 1969])).
% 2.92/2.13 tff(1971,plain,
% 2.92/2.13 (c2_1(a2228)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1205, 1969])).
% 2.92/2.13 tff(1972,plain,
% 2.92/2.13 (c3_1(a2228)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1216, 1969])).
% 2.92/2.13 tff(1973,plain,
% 2.92/2.13 (~c1_1(a2228)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1223, 159, 72, 1972, 1971, 1970, 71])).
% 2.92/2.13 tff(1974,plain,
% 2.92/2.13 (hskp10 | (~c0_1(a2187))),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1911, 159, 1878, 1877, 1876, 1639])).
% 2.92/2.13 tff(1975,plain,
% 2.92/2.13 (~c0_1(a2187)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1974, 1903])).
% 2.92/2.13 tff(1976,plain,
% 2.92/2.13 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2228)) | c1_1(a2228))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2228)) | c1_1(a2228))),
% 2.92/2.13 inference(rewrite,[status(thm)],[])).
% 2.92/2.13 tff(1977,plain,
% 2.92/2.13 ((hskp26 | (~ndr1_0) | c0_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228))) <=> (hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2228)) | c1_1(a2228))),
% 2.92/2.13 inference(rewrite,[status(thm)],[])).
% 2.92/2.13 tff(1978,plain,
% 2.92/2.13 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2228)) | c1_1(a2228)))),
% 2.92/2.13 inference(monotonicity,[status(thm)],[1977])).
% 2.92/2.13 tff(1979,plain,
% 2.92/2.13 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2228)) | c1_1(a2228))),
% 2.92/2.13 inference(transitivity,[status(thm)],[1978, 1976])).
% 2.92/2.13 tff(1980,plain,
% 2.92/2.13 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))),
% 2.92/2.13 inference(quant_inst,[status(thm)],[])).
% 2.92/2.13 tff(1981,plain,
% 2.92/2.13 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2228)) | c1_1(a2228)),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1980, 1979])).
% 2.92/2.13 tff(1982,plain,
% 2.92/2.13 ($false),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1981, 159, 1378, 1971, 1878, 1877, 1970, 1234, 1975, 1973])).
% 2.92/2.13 tff(1983,plain,(c3_1(a2181) | hskp26 | hskp33 | c0_1(a2181) | hskp47 | hskp32 | c1_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.92/2.13 tff(1984,plain,
% 2.92/2.13 (c3_1(a2181)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1983, 1872, 72, 105, 1276, 106, 104])).
% 2.92/2.13 tff(1985,plain,
% 2.92/2.13 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 2.92/2.13 inference(bind,[status(th)],[])).
% 2.92/2.13 tff(1986,plain,
% 2.92/2.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.92/2.13 inference(quant_intro,[status(thm)],[1985])).
% 2.92/2.13 tff(1987,plain,
% 2.92/2.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.92/2.13 inference(rewrite,[status(thm)],[])).
% 2.92/2.13 tff(1988,plain,
% 2.92/2.13 (^[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) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 2.92/2.13 inference(bind,[status(th)],[])).
% 2.92/2.13 tff(1989,plain,
% 2.92/2.13 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.92/2.13 inference(quant_intro,[status(thm)],[1988])).
% 2.92/2.13 tff(1990,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause289')).
% 2.92/2.13 tff(1991,plain,
% 2.92/2.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1990, 1989])).
% 2.92/2.13 tff(1992,plain,
% 2.92/2.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1991, 1987])).
% 2.92/2.13 tff(1993,plain,(
% 2.92/2.13 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.92/2.13 inference(skolemize,[status(sab)],[1992])).
% 2.92/2.13 tff(1994,plain,
% 2.92/2.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1993, 1986])).
% 2.92/2.13 tff(1995,plain,
% 2.92/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c3_1(a2196) | (~c2_1(a2196)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c3_1(a2196) | (~c2_1(a2196)))),
% 2.92/2.13 inference(rewrite,[status(thm)],[])).
% 2.92/2.13 tff(1996,plain,
% 2.92/2.13 (((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | c0_1(a2196) | c3_1(a2196) | (~c2_1(a2196))) <=> (c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c3_1(a2196) | (~c2_1(a2196)))),
% 2.92/2.13 inference(rewrite,[status(thm)],[])).
% 2.92/2.13 tff(1997,plain,
% 2.92/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | c0_1(a2196) | c3_1(a2196) | (~c2_1(a2196)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c3_1(a2196) | (~c2_1(a2196))))),
% 2.92/2.13 inference(monotonicity,[status(thm)],[1996])).
% 2.92/2.13 tff(1998,plain,
% 2.92/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | c0_1(a2196) | c3_1(a2196) | (~c2_1(a2196)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c3_1(a2196) | (~c2_1(a2196)))),
% 2.92/2.13 inference(transitivity,[status(thm)],[1997, 1995])).
% 2.92/2.13 tff(1999,plain,
% 2.92/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | c0_1(a2196) | c3_1(a2196) | (~c2_1(a2196)))),
% 2.92/2.13 inference(quant_inst,[status(thm)],[])).
% 2.92/2.13 tff(2000,plain,
% 2.92/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c3_1(a2196) | (~c2_1(a2196))),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 2.92/2.13 tff(2001,plain,
% 2.92/2.13 (c3_1(a2196)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[2000, 159, 700, 689, 105, 104, 1924, 1994, 107])).
% 2.92/2.13 tff(2002,plain,
% 2.92/2.13 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2196)) | (~c3_1(a2196)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2196)) | (~c3_1(a2196)))),
% 2.92/2.13 inference(rewrite,[status(thm)],[])).
% 2.92/2.13 tff(2003,plain,
% 2.92/2.13 ((hskp26 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c3_1(a2196)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181))) <=> (hskp26 | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2196)) | (~c3_1(a2196)))),
% 2.92/2.13 inference(rewrite,[status(thm)],[])).
% 2.92/2.13 tff(2004,plain,
% 2.92/2.13 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c3_1(a2196)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2196)) | (~c3_1(a2196))))),
% 2.92/2.13 inference(monotonicity,[status(thm)],[2003])).
% 2.92/2.13 tff(2005,plain,
% 2.92/2.13 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c3_1(a2196)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2196)) | (~c3_1(a2196)))),
% 2.92/2.13 inference(transitivity,[status(thm)],[2004, 2002])).
% 2.92/2.13 tff(2006,plain,
% 2.92/2.13 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c3_1(a2196)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)))),
% 2.92/2.13 inference(quant_inst,[status(thm)],[])).
% 2.92/2.13 tff(2007,plain,
% 2.92/2.13 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2196)) | (~c3_1(a2196))),
% 2.92/2.13 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 2.92/2.13 tff(2008,plain,
% 2.92/2.13 ($false),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[2007, 159, 1378, 711, 689, 105, 104, 1924, 1234, 2001])).
% 2.92/2.13 tff(2009,plain,((~hskp37) | hskp26 | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~c3_1(a2181))), inference(lemma,lemma(discharge,[]))).
% 2.92/2.13 tff(2010,plain,
% 2.92/2.13 (~hskp37),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[2009, 1872, 105, 104, 1847, 1984])).
% 2.92/2.13 tff(2011,plain,
% 2.92/2.13 (hskp6),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[615, 2010, 352])).
% 2.92/2.13 tff(2012,plain,
% 2.92/2.13 (~c1_1(a2197)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[621, 2011])).
% 2.92/2.13 tff(2013,plain,
% 2.92/2.13 (~c3_1(a2197)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[1071, 2011])).
% 2.92/2.13 tff(2014,plain,
% 2.92/2.13 (~c0_1(a2197)),
% 2.92/2.13 inference(unit_resolution,[status(thm)],[627, 2011])).
% 2.92/2.13 tff(2015,plain,
% 2.92/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))),
% 2.95/2.13 inference(rewrite,[status(thm)],[])).
% 2.95/2.13 tff(2016,plain,
% 2.95/2.13 (((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c0_1(a2197) | c3_1(a2197) | (~c2_1(a2197))) <=> (c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))),
% 2.95/2.13 inference(rewrite,[status(thm)],[])).
% 2.95/2.13 tff(2017,plain,
% 2.95/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c0_1(a2197) | c3_1(a2197) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197))))),
% 2.95/2.13 inference(monotonicity,[status(thm)],[2016])).
% 2.95/2.13 tff(2018,plain,
% 2.95/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c0_1(a2197) | c3_1(a2197) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))),
% 2.95/2.13 inference(transitivity,[status(thm)],[2017, 2015])).
% 2.95/2.13 tff(2019,plain,
% 2.95/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c0_1(a2197) | c3_1(a2197) | (~c2_1(a2197)))),
% 2.95/2.13 inference(quant_inst,[status(thm)],[])).
% 2.95/2.13 tff(2020,plain,
% 2.95/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197))),
% 2.95/2.13 inference(modus_ponens,[status(thm)],[2019, 2018])).
% 2.95/2.13 tff(2021,plain,
% 2.95/2.13 (~c2_1(a2197)),
% 2.95/2.13 inference(unit_resolution,[status(thm)],[2020, 159, 2014, 2013, 2012, 104, 1847, 1994, 1984])).
% 2.95/2.13 tff(2022,assumption,(hskp6), introduced(assumption)).
% 2.95/2.13 tff(2023,plain,
% 2.95/2.13 (~c1_1(a2197)),
% 2.95/2.13 inference(unit_resolution,[status(thm)],[621, 2022])).
% 2.95/2.13 tff(2024,plain,
% 2.95/2.13 (~c3_1(a2197)),
% 2.95/2.13 inference(unit_resolution,[status(thm)],[1071, 2022])).
% 2.95/2.13 tff(2025,plain,
% 2.95/2.13 (~c0_1(a2197)),
% 2.95/2.13 inference(unit_resolution,[status(thm)],[627, 2022])).
% 2.95/2.13 tff(2026,plain,
% 2.95/2.13 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0))),
% 2.95/2.13 inference(rewrite,[status(thm)],[])).
% 2.95/2.13 tff(2027,plain,
% 2.95/2.13 ((hskp32 | hskp2 | (~ndr1_0) | c1_1(a2197) | c3_1(a2197) | c0_1(a2197)) <=> (hskp32 | hskp2 | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0))),
% 2.95/2.13 inference(rewrite,[status(thm)],[])).
% 2.95/2.13 tff(2028,plain,
% 2.95/2.13 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2197) | c3_1(a2197) | c0_1(a2197))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0)))),
% 2.95/2.13 inference(monotonicity,[status(thm)],[2027])).
% 2.95/2.13 tff(2029,plain,
% 2.95/2.13 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2197) | c3_1(a2197) | c0_1(a2197))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0))),
% 2.95/2.13 inference(transitivity,[status(thm)],[2028, 2026])).
% 2.95/2.13 tff(2030,plain,
% 2.95/2.13 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2197) | c3_1(a2197) | c0_1(a2197))),
% 2.95/2.13 inference(quant_inst,[status(thm)],[])).
% 2.95/2.13 tff(2031,plain,
% 2.95/2.13 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0)),
% 2.95/2.13 inference(modus_ponens,[status(thm)],[2030, 2029])).
% 2.95/2.13 tff(2032,plain,
% 2.95/2.13 ($false),
% 2.95/2.13 inference(unit_resolution,[status(thm)],[2031, 159, 106, 1433, 2025, 2024, 2023, 219])).
% 2.95/2.13 tff(2033,plain,((~hskp6) | hskp32 | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.95/2.13 tff(2034,plain,
% 2.95/2.13 (hskp2),
% 2.95/2.13 inference(unit_resolution,[status(thm)],[2033, 2011, 106])).
% 2.95/2.13 tff(2035,plain,
% 2.95/2.13 (~c2_1(a2187)),
% 2.95/2.13 inference(unit_resolution,[status(thm)],[232, 2034])).
% 2.95/2.13 tff(2036,plain,
% 2.95/2.13 (c1_1(a2187)),
% 2.95/2.13 inference(unit_resolution,[status(thm)],[294, 2034])).
% 2.95/2.13 tff(2037,plain,
% 2.95/2.13 (c3_1(a2187)),
% 2.95/2.13 inference(unit_resolution,[status(thm)],[243, 2034])).
% 2.95/2.13 tff(2038,plain,
% 2.95/2.13 (~hskp10),
% 2.95/2.13 inference(unit_resolution,[status(thm)],[1902, 2037, 1276, 2035, 1879])).
% 2.95/2.13 tff(2039,plain,
% 2.95/2.13 (~c0_1(a2187)),
% 2.95/2.13 inference(unit_resolution,[status(thm)],[1911, 159, 2038, 2037, 2036, 2035, 1639])).
% 2.95/2.13 tff(2040,plain,
% 2.95/2.13 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c3_1(a2197) | c1_1(a2197) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c3_1(a2197) | c1_1(a2197) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c2_1(a2197))),
% 2.95/2.13 inference(rewrite,[status(thm)],[])).
% 2.95/2.13 tff(2041,plain,
% 2.95/2.13 ((hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197)) <=> (hskp47 | c3_1(a2197) | c1_1(a2197) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c2_1(a2197))),
% 2.95/2.13 inference(rewrite,[status(thm)],[])).
% 2.95/2.13 tff(2042,plain,
% 2.95/2.13 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c3_1(a2197) | c1_1(a2197) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c2_1(a2197)))),
% 2.95/2.13 inference(monotonicity,[status(thm)],[2041])).
% 2.95/2.13 tff(2043,plain,
% 2.95/2.13 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c3_1(a2197) | c1_1(a2197) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c2_1(a2197))),
% 2.95/2.13 inference(transitivity,[status(thm)],[2042, 2040])).
% 2.95/2.13 tff(2044,plain,
% 2.95/2.13 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))),
% 2.95/2.13 inference(quant_inst,[status(thm)],[])).
% 2.95/2.13 tff(2045,plain,
% 2.95/2.13 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c3_1(a2197) | c1_1(a2197) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c2_1(a2197)),
% 2.95/2.13 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 2.95/2.13 tff(2046,plain,
% 2.95/2.13 (c0_1(a2187) | c2_1(a2197)),
% 2.95/2.13 inference(unit_resolution,[status(thm)],[2045, 159, 1276, 2037, 2013, 2012, 2035, 271])).
% 2.95/2.13 tff(2047,plain,
% 2.95/2.14 ($false),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2046, 2039, 2021])).
% 2.95/2.14 tff(2048,plain,(hskp34 | c1_1(a2181) | hskp32 | c0_1(a2181) | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.95/2.14 tff(2049,plain,
% 2.95/2.14 (hskp34),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2048, 104, 106, 105, 72])).
% 2.95/2.14 tff(2050,plain,
% 2.95/2.14 (~c0_1(a2189)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[763, 2049])).
% 2.95/2.14 tff(2051,plain,
% 2.95/2.14 (c3_1(a2189)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[739, 2049])).
% 2.95/2.14 tff(2052,plain,
% 2.95/2.14 (c1_1(a2189)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[750, 2049])).
% 2.95/2.14 tff(2053,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2189) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2189) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2054,plain,
% 2.95/2.14 ((hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181))) <=> (hskp26 | c0_1(a2189) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2055,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2189) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189))))),
% 2.95/2.14 inference(monotonicity,[status(thm)],[2054])).
% 2.95/2.14 tff(2056,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2189) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.95/2.14 inference(transitivity,[status(thm)],[2055, 2053])).
% 2.95/2.14 tff(2057,plain,
% 2.95/2.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)))),
% 2.95/2.14 inference(quant_inst,[status(thm)],[])).
% 2.95/2.14 tff(2058,plain,
% 2.95/2.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2189) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189))),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 2.95/2.14 tff(2059,plain,
% 2.95/2.14 (hskp26),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2058, 159, 2052, 2051, 2050, 105, 104, 1847, 1234])).
% 2.95/2.14 tff(2060,plain,
% 2.95/2.14 (c2_1(a2178)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1156, 2059])).
% 2.95/2.14 tff(2061,plain,
% 2.95/2.14 (c0_1(a2178)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1167, 2059])).
% 2.95/2.14 tff(2062,plain,
% 2.95/2.14 (~c1_1(a2178)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1172, 159, 1848, 2061, 2060, 824])).
% 2.95/2.14 tff(2063,plain,
% 2.95/2.14 (~c3_1(a2178)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1178, 2059])).
% 2.95/2.14 tff(2064,plain,
% 2.95/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a2178) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a2178) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2065,plain,
% 2.95/2.14 (((~ndr1_0) | c1_1(a2181) | c0_1(a2181) | (~c2_1(a2181)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178))) <=> (c3_1(a2178) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2066,plain,
% 2.95/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2181) | c0_1(a2181) | (~c2_1(a2181)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a2178) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178))))),
% 2.95/2.14 inference(monotonicity,[status(thm)],[2065])).
% 2.95/2.14 tff(2067,plain,
% 2.95/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2181) | c0_1(a2181) | (~c2_1(a2181)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a2178) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 2.95/2.14 inference(transitivity,[status(thm)],[2066, 2064])).
% 2.95/2.14 tff(2068,plain,
% 2.95/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2181) | c0_1(a2181) | (~c2_1(a2181)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178)))),
% 2.95/2.14 inference(quant_inst,[status(thm)],[])).
% 2.95/2.14 tff(2069,plain,
% 2.95/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a2178) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178))),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2068, 2067])).
% 2.95/2.14 tff(2070,plain,
% 2.95/2.14 ($false),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2069, 159, 2061, 2060, 2063, 105, 104, 1847, 1049, 2062])).
% 2.95/2.14 tff(2071,plain,(c1_1(a2181) | c0_1(a2181) | hskp32 | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.95/2.14 tff(2072,plain,
% 2.95/2.14 (c1_1(a2181)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2071, 106, 105, 72])).
% 2.95/2.14 tff(2073,plain,
% 2.95/2.14 (^[U: $i] : refl((hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 2.95/2.14 inference(bind,[status(th)],[])).
% 2.95/2.14 tff(2074,plain,
% 2.95/2.14 (![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.95/2.14 inference(quant_intro,[status(thm)],[2073])).
% 2.95/2.14 tff(2075,plain,
% 2.95/2.14 (![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2076,plain,
% 2.95/2.14 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp31) <=> ((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp31))), rewrite(((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp31) <=> (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp31) <=> (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 2.95/2.14 inference(bind,[status(th)],[])).
% 2.95/2.14 tff(2077,plain,
% 2.95/2.14 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp31) <=> ![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.95/2.14 inference(quant_intro,[status(thm)],[2076])).
% 2.95/2.14 tff(2078,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause260')).
% 2.95/2.14 tff(2079,plain,
% 2.95/2.14 (![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2078, 2077])).
% 2.95/2.14 tff(2080,plain,
% 2.95/2.14 (![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2079, 2075])).
% 2.95/2.14 tff(2081,plain,(
% 2.95/2.14 ![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.95/2.14 inference(skolemize,[status(sab)],[2080])).
% 2.95/2.14 tff(2082,plain,
% 2.95/2.14 (![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2081, 2074])).
% 2.95/2.14 tff(2083,plain,
% 2.95/2.14 (((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp31 | hskp18 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))) <=> ((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp31 | hskp18 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2084,plain,
% 2.95/2.14 ((hskp31 | hskp18 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181))) <=> (hskp31 | hskp18 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2085,plain,
% 2.95/2.14 (((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp31 | hskp18 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp31 | hskp18 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181)))),
% 2.95/2.14 inference(monotonicity,[status(thm)],[2084])).
% 2.95/2.14 tff(2086,plain,
% 2.95/2.14 (((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp31 | hskp18 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp31 | hskp18 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 2.95/2.14 inference(transitivity,[status(thm)],[2085, 2083])).
% 2.95/2.14 tff(2087,plain,
% 2.95/2.14 ((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp31 | hskp18 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)))),
% 2.95/2.14 inference(quant_inst,[status(thm)],[])).
% 2.95/2.14 tff(2088,plain,
% 2.95/2.14 ((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp31 | hskp18 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2087, 2086])).
% 2.95/2.14 tff(2089,plain,
% 2.95/2.14 (hskp31 | hskp18 | (~c1_1(a2181)) | c3_1(a2181)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2088, 159, 1847, 2082])).
% 2.95/2.14 tff(2090,plain,
% 2.95/2.14 (hskp31),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2089, 1873, 1879, 2072])).
% 2.95/2.14 tff(2091,plain,
% 2.95/2.14 (((~hskp31) | (~c2_1(a2185))) <=> ((~hskp31) | (~c2_1(a2185)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2092,plain,
% 2.95/2.14 (((~c2_1(a2185)) | (~hskp31)) <=> ((~hskp31) | (~c2_1(a2185)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2093,axiom,((~c2_1(a2185)) | (~hskp31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 2.95/2.14 tff(2094,plain,
% 2.95/2.14 ((~hskp31) | (~c2_1(a2185))),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2093, 2092])).
% 2.95/2.14 tff(2095,plain,
% 2.95/2.14 ((~hskp31) | (~c2_1(a2185))),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2094, 2091])).
% 2.95/2.14 tff(2096,plain,
% 2.95/2.14 (~c2_1(a2185)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2095, 2090])).
% 2.95/2.14 tff(2097,plain,
% 2.95/2.14 (((~hskp31) | c3_1(a2185)) <=> ((~hskp31) | c3_1(a2185))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2098,axiom,((~hskp31) | c3_1(a2185)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 2.95/2.14 tff(2099,plain,
% 2.95/2.14 ((~hskp31) | c3_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2098, 2097])).
% 2.95/2.14 tff(2100,plain,
% 2.95/2.14 ((~hskp31) | c3_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2099, 2097])).
% 2.95/2.14 tff(2101,plain,
% 2.95/2.14 ((~hskp31) | c3_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2100, 2097])).
% 2.95/2.14 tff(2102,plain,
% 2.95/2.14 ((~hskp31) | c3_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2101, 2097])).
% 2.95/2.14 tff(2103,plain,
% 2.95/2.14 ((~hskp31) | c3_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2102, 2097])).
% 2.95/2.14 tff(2104,plain,
% 2.95/2.14 ((~hskp31) | c3_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2103, 2097])).
% 2.95/2.14 tff(2105,plain,
% 2.95/2.14 ((~hskp31) | c3_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2104, 2097])).
% 2.95/2.14 tff(2106,plain,
% 2.95/2.14 ((~hskp31) | c3_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2105, 2097])).
% 2.95/2.14 tff(2107,plain,
% 2.95/2.14 (c3_1(a2185)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2106, 2090])).
% 2.95/2.14 tff(2108,plain,
% 2.95/2.14 (((~hskp31) | c1_1(a2185)) <=> ((~hskp31) | c1_1(a2185))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2109,axiom,((~hskp31) | c1_1(a2185)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 2.95/2.14 tff(2110,plain,
% 2.95/2.14 ((~hskp31) | c1_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 2.95/2.14 tff(2111,plain,
% 2.95/2.14 ((~hskp31) | c1_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2110, 2108])).
% 2.95/2.14 tff(2112,plain,
% 2.95/2.14 ((~hskp31) | c1_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2111, 2108])).
% 2.95/2.14 tff(2113,plain,
% 2.95/2.14 ((~hskp31) | c1_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2112, 2108])).
% 2.95/2.14 tff(2114,plain,
% 2.95/2.14 ((~hskp31) | c1_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2113, 2108])).
% 2.95/2.14 tff(2115,plain,
% 2.95/2.14 ((~hskp31) | c1_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2114, 2108])).
% 2.95/2.14 tff(2116,plain,
% 2.95/2.14 ((~hskp31) | c1_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2115, 2108])).
% 2.95/2.14 tff(2117,plain,
% 2.95/2.14 ((~hskp31) | c1_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2116, 2108])).
% 2.95/2.14 tff(2118,plain,
% 2.95/2.14 (c1_1(a2185)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2117, 2090])).
% 2.95/2.14 tff(2119,assumption,(~c2_1(a2185)), introduced(assumption)).
% 2.95/2.14 tff(2120,assumption,(c3_1(a2185)), introduced(assumption)).
% 2.95/2.14 tff(2121,assumption,(c1_1(a2185)), introduced(assumption)).
% 2.95/2.14 tff(2122,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c2_1(a2185) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | (~c0_1(a2185)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2185) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | (~c0_1(a2185)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2123,plain,
% 2.95/2.14 ((hskp10 | (~ndr1_0) | c2_1(a2185) | (~c3_1(a2185)) | (~c0_1(a2185)) | c2_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185))) <=> (hskp10 | c2_1(a2185) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | (~c0_1(a2185)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2124,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2185) | (~c3_1(a2185)) | (~c0_1(a2185)) | c2_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c2_1(a2185) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | (~c0_1(a2185))))),
% 2.95/2.14 inference(monotonicity,[status(thm)],[2123])).
% 2.95/2.14 tff(2125,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2185) | (~c3_1(a2185)) | (~c0_1(a2185)) | c2_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2185) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | (~c0_1(a2185)))),
% 2.95/2.14 inference(transitivity,[status(thm)],[2124, 2122])).
% 2.95/2.14 tff(2126,plain,
% 2.95/2.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2185) | (~c3_1(a2185)) | (~c0_1(a2185)) | c2_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185)))),
% 2.95/2.14 inference(quant_inst,[status(thm)],[])).
% 2.95/2.14 tff(2127,plain,
% 2.95/2.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2185) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | (~c0_1(a2185))),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2126, 2125])).
% 2.95/2.14 tff(2128,plain,
% 2.95/2.14 (hskp10 | (~c0_1(a2185))),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2127, 159, 2121, 2120, 2119, 1639])).
% 2.95/2.14 tff(2129,plain,
% 2.95/2.14 (~c0_1(a2185)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2128, 1904])).
% 2.95/2.14 tff(2130,plain,
% 2.95/2.14 (hskp41 | hskp10 | c0_1(a2181) | c3_1(a2181)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1930, 159, 1847, 1923])).
% 2.95/2.14 tff(2131,plain,
% 2.95/2.14 (hskp41),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2130, 1904, 105, 1873])).
% 2.95/2.14 tff(2132,plain,
% 2.95/2.14 (~c0_1(a2205)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1937, 2131])).
% 2.95/2.14 tff(2133,plain,
% 2.95/2.14 (c1_1(a2205)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1948, 2131])).
% 2.95/2.14 tff(2134,plain,
% 2.95/2.14 (c2_1(a2205)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1959, 2131])).
% 2.95/2.14 tff(2135,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2205) | (~ndr1_0) | (~c2_1(a2205)) | (~c1_1(a2205)) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2205) | (~ndr1_0) | (~c2_1(a2205)) | (~c1_1(a2205)) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2136,plain,
% 2.95/2.14 ((hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185))) <=> (hskp48 | c0_1(a2205) | (~ndr1_0) | (~c2_1(a2205)) | (~c1_1(a2205)) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2137,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2205) | (~ndr1_0) | (~c2_1(a2205)) | (~c1_1(a2205)) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185)))),
% 2.95/2.14 inference(monotonicity,[status(thm)],[2136])).
% 2.95/2.14 tff(2138,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2205) | (~ndr1_0) | (~c2_1(a2205)) | (~c1_1(a2205)) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185))),
% 2.95/2.14 inference(transitivity,[status(thm)],[2137, 2135])).
% 2.95/2.14 tff(2139,plain,
% 2.95/2.14 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185)))),
% 2.95/2.14 inference(quant_inst,[status(thm)],[])).
% 2.95/2.14 tff(2140,plain,
% 2.95/2.14 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2205) | (~ndr1_0) | (~c2_1(a2205)) | (~c1_1(a2205)) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2139, 2138])).
% 2.95/2.14 tff(2141,plain,
% 2.95/2.14 (hskp48),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2140, 159, 2134, 2133, 2121, 2120, 2132, 41, 2129])).
% 2.95/2.14 tff(2142,plain,
% 2.95/2.14 (~c0_1(a2228)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1194, 2141])).
% 2.95/2.14 tff(2143,plain,
% 2.95/2.14 (c2_1(a2228)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1205, 2141])).
% 2.95/2.14 tff(2144,plain,
% 2.95/2.14 (c3_1(a2228)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1216, 2141])).
% 2.95/2.14 tff(2145,plain,
% 2.95/2.14 (~c1_1(a2228)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1223, 159, 72, 2144, 2143, 2142, 71])).
% 2.95/2.14 tff(2146,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185) | (~c2_1(a2228)) | c1_1(a2228))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185) | (~c2_1(a2228)) | c1_1(a2228))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2147,plain,
% 2.95/2.14 ((hskp26 | (~ndr1_0) | c0_1(a2185) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228))) <=> (hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185) | (~c2_1(a2228)) | c1_1(a2228))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2148,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2185) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185) | (~c2_1(a2228)) | c1_1(a2228)))),
% 2.95/2.14 inference(monotonicity,[status(thm)],[2147])).
% 2.95/2.14 tff(2149,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2185) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185) | (~c2_1(a2228)) | c1_1(a2228))),
% 2.95/2.14 inference(transitivity,[status(thm)],[2148, 2146])).
% 2.95/2.14 tff(2150,plain,
% 2.95/2.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2185) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))),
% 2.95/2.14 inference(quant_inst,[status(thm)],[])).
% 2.95/2.14 tff(2151,plain,
% 2.95/2.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185) | (~c2_1(a2228)) | c1_1(a2228)),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2150, 2149])).
% 2.95/2.14 tff(2152,plain,
% 2.95/2.14 ($false),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2151, 159, 1378, 2143, 2121, 2120, 2142, 1234, 2129, 2145])).
% 2.95/2.14 tff(2153,plain,(hskp10 | hskp26 | (~c1_1(a2185)) | (~c3_1(a2185)) | hskp33 | c2_1(a2185) | c0_1(a2181) | c3_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.95/2.14 tff(2154,plain,
% 2.95/2.14 (hskp10),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2153, 1872, 2118, 2107, 72, 2096, 105, 1873])).
% 2.95/2.14 tff(2155,plain,
% 2.95/2.14 (~c3_1(a2206)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1652, 2154])).
% 2.95/2.14 tff(2156,plain,
% 2.95/2.14 (~c2_1(a2206)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1658, 2154])).
% 2.95/2.14 tff(2157,assumption,(hskp4), introduced(assumption)).
% 2.95/2.14 tff(2158,plain,
% 2.95/2.14 (~c1_1(a2191)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1795, 2157])).
% 2.95/2.14 tff(2159,plain,
% 2.95/2.14 (~c2_1(a2191)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1801, 2157])).
% 2.95/2.14 tff(2160,plain,
% 2.95/2.14 (c3_1(a2191)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1812, 2157])).
% 2.95/2.14 tff(2161,plain,
% 2.95/2.14 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2162,plain,
% 2.95/2.14 ((hskp58 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191))) <=> (hskp58 | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2163,plain,
% 2.95/2.14 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191))))),
% 2.95/2.14 inference(monotonicity,[status(thm)],[2162])).
% 2.95/2.14 tff(2164,plain,
% 2.95/2.14 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)))),
% 2.95/2.14 inference(transitivity,[status(thm)],[2163, 2161])).
% 2.95/2.14 tff(2165,plain,
% 2.95/2.14 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)))),
% 2.95/2.14 inference(quant_inst,[status(thm)],[])).
% 2.95/2.14 tff(2166,plain,
% 2.95/2.14 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191))),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2165, 2164])).
% 2.95/2.14 tff(2167,plain,
% 2.95/2.14 (hskp58),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2166, 159, 2160, 2159, 2158, 127])).
% 2.95/2.14 tff(2168,plain,
% 2.95/2.14 (~c1_1(a2252)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[172, 2167])).
% 2.95/2.14 tff(2169,plain,
% 2.95/2.14 (~c2_1(a2252)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[178, 2167])).
% 2.95/2.14 tff(2170,plain,
% 2.95/2.14 (c0_1(a2252)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[189, 2167])).
% 2.95/2.14 tff(2171,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2252) | c1_1(a2252) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2252)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2172,plain,
% 2.95/2.14 ((hskp32 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252))) <=> (hskp32 | c2_1(a2252) | c1_1(a2252) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2252)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2173,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2252) | c1_1(a2252) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2252))))),
% 2.95/2.14 inference(monotonicity,[status(thm)],[2172])).
% 2.95/2.14 tff(2174,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2252)))),
% 2.95/2.14 inference(transitivity,[status(thm)],[2173, 2171])).
% 2.95/2.14 tff(2175,plain,
% 2.95/2.14 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))),
% 2.95/2.14 inference(quant_inst,[status(thm)],[])).
% 2.95/2.14 tff(2176,plain,
% 2.95/2.14 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2252))),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2175, 2174])).
% 2.95/2.14 tff(2177,plain,
% 2.95/2.14 ($false),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2176, 159, 106, 2170, 2160, 2169, 2168, 2159, 2158, 117])).
% 2.95/2.14 tff(2178,plain,((~hskp4) | hskp32), inference(lemma,lemma(discharge,[]))).
% 2.95/2.14 tff(2179,plain,
% 2.95/2.14 (~hskp4),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2178, 106])).
% 2.95/2.14 tff(2180,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | c2_1(a2206) | c3_1(a2206) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2206)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp4 | c2_1(a2206) | c3_1(a2206) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2206)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2181,plain,
% 2.95/2.14 ((hskp4 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)) | c0_1(a2181) | (~c2_1(a2181)) | (~c1_1(a2181))) <=> (hskp4 | c2_1(a2206) | c3_1(a2206) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2206)))),
% 2.95/2.14 inference(rewrite,[status(thm)],[])).
% 2.95/2.14 tff(2182,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)) | c0_1(a2181) | (~c2_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | c2_1(a2206) | c3_1(a2206) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2206))))),
% 2.95/2.14 inference(monotonicity,[status(thm)],[2181])).
% 2.95/2.14 tff(2183,plain,
% 2.95/2.14 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)) | c0_1(a2181) | (~c2_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp4 | c2_1(a2206) | c3_1(a2206) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2206)))),
% 2.95/2.14 inference(transitivity,[status(thm)],[2182, 2180])).
% 2.95/2.14 tff(2184,plain,
% 2.95/2.14 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)) | c0_1(a2181) | (~c2_1(a2181)) | (~c1_1(a2181)))),
% 2.95/2.14 inference(quant_inst,[status(thm)],[])).
% 2.95/2.14 tff(2185,plain,
% 2.95/2.14 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp4 | c2_1(a2206) | c3_1(a2206) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2206))),
% 2.95/2.14 inference(modus_ponens,[status(thm)],[2184, 2183])).
% 2.95/2.14 tff(2186,plain,
% 2.95/2.14 (~c1_1(a2206)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[2185, 159, 2179, 2156, 2155, 105, 2072, 1847, 1779])).
% 2.95/2.14 tff(2187,plain,
% 2.95/2.14 (~c0_1(a2206)),
% 2.95/2.14 inference(unit_resolution,[status(thm)],[1671, 2154])).
% 2.95/2.14 tff(2188,plain,
% 2.95/2.14 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2189,plain,
% 2.95/2.15 ((hskp32 | hskp2 | (~ndr1_0) | c1_1(a2206) | c3_1(a2206) | c0_1(a2206)) <=> (hskp32 | hskp2 | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2190,plain,
% 2.95/2.15 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2206) | c3_1(a2206) | c0_1(a2206))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206)))),
% 2.95/2.15 inference(monotonicity,[status(thm)],[2189])).
% 2.95/2.15 tff(2191,plain,
% 2.95/2.15 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2206) | c3_1(a2206) | c0_1(a2206))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206))),
% 2.95/2.15 inference(transitivity,[status(thm)],[2190, 2188])).
% 2.95/2.15 tff(2192,plain,
% 2.95/2.15 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2206) | c3_1(a2206) | c0_1(a2206))),
% 2.95/2.15 inference(quant_inst,[status(thm)],[])).
% 2.95/2.15 tff(2193,plain,
% 2.95/2.15 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206)),
% 2.95/2.15 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 2.95/2.15 tff(2194,plain,
% 2.95/2.15 (hskp2),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2193, 159, 106, 2187, 2155, 219, 2186])).
% 2.95/2.15 tff(2195,plain,
% 2.95/2.15 (c3_1(a2187)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[243, 2194])).
% 2.95/2.15 tff(2196,plain,
% 2.95/2.15 (~c2_1(a2187)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[232, 2194])).
% 2.95/2.15 tff(2197,plain,
% 2.95/2.15 ($false),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1902, 2196, 2195, 1276, 2154, 1879])).
% 2.95/2.15 tff(2198,plain,(hskp34 | hskp32 | c0_1(a2181) | hskp33 | c3_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 2.95/2.15 tff(2199,plain,
% 2.95/2.15 (hskp34),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2198, 1873, 105, 72, 106])).
% 2.95/2.15 tff(2200,plain,
% 2.95/2.15 (~c0_1(a2189)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[763, 2199])).
% 2.95/2.15 tff(2201,plain,
% 2.95/2.15 (c3_1(a2189)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[739, 2199])).
% 2.95/2.15 tff(2202,plain,
% 2.95/2.15 (c1_1(a2189)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[750, 2199])).
% 2.95/2.15 tff(2203,plain,
% 2.95/2.15 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2189) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2204,plain,
% 2.95/2.15 ((hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))) <=> (hskp48 | c0_1(a2189) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2205,plain,
% 2.95/2.15 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2189) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189))))),
% 2.95/2.15 inference(monotonicity,[status(thm)],[2204])).
% 2.95/2.15 tff(2206,plain,
% 2.95/2.15 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.95/2.15 inference(transitivity,[status(thm)],[2205, 2203])).
% 2.95/2.15 tff(2207,plain,
% 2.95/2.15 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.95/2.15 inference(quant_inst,[status(thm)],[])).
% 2.95/2.15 tff(2208,plain,
% 2.95/2.15 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189))),
% 2.95/2.15 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 2.95/2.15 tff(2209,plain,
% 2.95/2.15 (hskp48),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2208, 159, 2202, 2201, 2200, 105, 2072, 1847, 41])).
% 2.95/2.15 tff(2210,plain,
% 2.95/2.15 (~c0_1(a2228)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1194, 2209])).
% 2.95/2.15 tff(2211,plain,
% 2.95/2.15 (c2_1(a2228)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1205, 2209])).
% 2.95/2.15 tff(2212,plain,
% 2.95/2.15 (c3_1(a2228)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1216, 2209])).
% 2.95/2.15 tff(2213,plain,
% 2.95/2.15 (~c1_1(a2228)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1223, 159, 72, 2212, 2211, 2210, 71])).
% 2.95/2.15 tff(2214,plain,
% 2.95/2.15 (((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2215,plain,
% 2.95/2.15 ((hskp17 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181))) <=> (hskp17 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2216,plain,
% 2.95/2.15 (((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181)))),
% 2.95/2.15 inference(monotonicity,[status(thm)],[2215])).
% 2.95/2.15 tff(2217,plain,
% 2.95/2.15 (((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 2.95/2.15 inference(transitivity,[status(thm)],[2216, 2214])).
% 2.95/2.15 tff(2218,plain,
% 2.95/2.15 ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)))),
% 2.95/2.15 inference(quant_inst,[status(thm)],[])).
% 2.95/2.15 tff(2219,plain,
% 2.95/2.15 ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181)),
% 2.95/2.15 inference(modus_ponens,[status(thm)],[2218, 2217])).
% 2.95/2.15 tff(2220,plain,
% 2.95/2.15 (hskp17 | (~c1_1(a2181)) | c3_1(a2181)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2219, 159, 1847, 1444])).
% 2.95/2.15 tff(2221,plain,
% 2.95/2.15 (hskp17),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2220, 1873, 2072])).
% 2.95/2.15 tff(2222,plain,
% 2.95/2.15 (~c3_1(a2221)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1517, 2221])).
% 2.95/2.15 tff(2223,plain,
% 2.95/2.15 (~c0_1(a2221)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1523, 2221])).
% 2.95/2.15 tff(2224,plain,
% 2.95/2.15 (c2_1(a2221)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1541, 2221])).
% 2.95/2.15 tff(2225,plain,
% 2.95/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2228) | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | (~c2_1(a2221)) | (~c2_1(a2228)) | c1_1(a2228) | (~c3_1(a2228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2228) | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | (~c2_1(a2221)) | (~c2_1(a2228)) | c1_1(a2228) | (~c3_1(a2228)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2226,plain,
% 2.95/2.15 (((~ndr1_0) | c1_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)) | c0_1(a2221) | c3_1(a2221) | (~c2_1(a2221))) <=> (c0_1(a2228) | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | (~c2_1(a2221)) | (~c2_1(a2228)) | c1_1(a2228) | (~c3_1(a2228)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2227,plain,
% 2.95/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)) | c0_1(a2221) | c3_1(a2221) | (~c2_1(a2221)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2228) | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | (~c2_1(a2221)) | (~c2_1(a2228)) | c1_1(a2228) | (~c3_1(a2228))))),
% 2.95/2.15 inference(monotonicity,[status(thm)],[2226])).
% 2.95/2.15 tff(2228,plain,
% 2.95/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)) | c0_1(a2221) | c3_1(a2221) | (~c2_1(a2221)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2228) | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | (~c2_1(a2221)) | (~c2_1(a2228)) | c1_1(a2228) | (~c3_1(a2228)))),
% 2.95/2.15 inference(transitivity,[status(thm)],[2227, 2225])).
% 2.95/2.15 tff(2229,plain,
% 2.95/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)) | c0_1(a2221) | c3_1(a2221) | (~c2_1(a2221)))),
% 2.95/2.15 inference(quant_inst,[status(thm)],[])).
% 2.95/2.15 tff(2230,plain,
% 2.95/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2228) | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | (~c2_1(a2221)) | (~c2_1(a2228)) | c1_1(a2228) | (~c3_1(a2228))),
% 2.95/2.15 inference(modus_ponens,[status(thm)],[2229, 2228])).
% 2.95/2.15 tff(2231,plain,
% 2.95/2.15 ($false),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2230, 159, 2212, 2211, 2224, 2210, 2223, 2222, 1994, 2213])).
% 2.95/2.15 tff(2232,plain,(c3_1(a2181) | hskp33 | c0_1(a2181) | hskp32), inference(lemma,lemma(discharge,[]))).
% 2.95/2.15 tff(2233,plain,
% 2.95/2.15 (c3_1(a2181)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2232, 106, 105, 72])).
% 2.95/2.15 tff(2234,plain,
% 2.95/2.15 (~hskp48),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1255, 2233, 105, 2072, 72])).
% 2.95/2.15 tff(2235,plain,
% 2.95/2.15 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2236,plain,
% 2.95/2.15 ((hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181))) <=> (hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2237,plain,
% 2.95/2.15 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181))))),
% 2.95/2.15 inference(monotonicity,[status(thm)],[2236])).
% 2.95/2.15 tff(2238,plain,
% 2.95/2.15 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)))),
% 2.95/2.15 inference(transitivity,[status(thm)],[2237, 2235])).
% 2.95/2.15 tff(2239,plain,
% 2.95/2.15 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))),
% 2.95/2.15 inference(quant_inst,[status(thm)],[])).
% 2.95/2.15 tff(2240,plain,
% 2.95/2.15 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181))),
% 2.95/2.15 inference(modus_ponens,[status(thm)],[2239, 2238])).
% 2.95/2.15 tff(2241,plain,
% 2.95/2.15 (hskp48 | (~c1_1(a2181)) | (~c3_1(a2181))),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2240, 159, 105, 1847, 41])).
% 2.95/2.15 tff(2242,plain,
% 2.95/2.15 ($false),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2241, 2234, 2233, 2072])).
% 2.95/2.15 tff(2243,plain,(hskp32 | c0_1(a2181) | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.95/2.15 tff(2244,plain,
% 2.95/2.15 (c0_1(a2181)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2243, 1871, 72])).
% 2.95/2.15 tff(2245,plain,
% 2.95/2.15 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2246,plain,
% 2.95/2.15 ((hskp0 | (~ndr1_0) | (~c1_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181))) <=> (hskp0 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2247,plain,
% 2.95/2.15 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0)))),
% 2.95/2.15 inference(monotonicity,[status(thm)],[2246])).
% 2.95/2.15 tff(2248,plain,
% 2.95/2.15 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0))),
% 2.95/2.15 inference(transitivity,[status(thm)],[2247, 2245])).
% 2.95/2.15 tff(2249,plain,
% 2.95/2.15 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)))),
% 2.95/2.15 inference(quant_inst,[status(thm)],[])).
% 2.95/2.15 tff(2250,plain,
% 2.95/2.15 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0)),
% 2.95/2.15 inference(modus_ponens,[status(thm)],[2249, 2248])).
% 2.95/2.15 tff(2251,plain,
% 2.95/2.15 ((~c0_1(a2181)) | (~c1_1(a2181))),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2250, 159, 1848, 1847, 824])).
% 2.95/2.15 tff(2252,plain,
% 2.95/2.15 (~c1_1(a2181)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2251, 2244])).
% 2.95/2.15 tff(2253,plain,
% 2.95/2.15 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~c0_1(a2181)) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~c0_1(a2181)) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2254,plain,
% 2.95/2.15 ((hskp34 | hskp33 | (~ndr1_0) | c1_1(a2181) | (~c0_1(a2181)) | (~c2_1(a2181))) <=> (hskp34 | hskp33 | (~c0_1(a2181)) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2255,plain,
% 2.95/2.15 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2181) | (~c0_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~c0_1(a2181)) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0)))),
% 2.95/2.15 inference(monotonicity,[status(thm)],[2254])).
% 2.95/2.15 tff(2256,plain,
% 2.95/2.15 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2181) | (~c0_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~c0_1(a2181)) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0))),
% 2.95/2.15 inference(transitivity,[status(thm)],[2255, 2253])).
% 2.95/2.15 tff(2257,plain,
% 2.95/2.15 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2181) | (~c0_1(a2181)) | (~c2_1(a2181)))),
% 2.95/2.15 inference(quant_inst,[status(thm)],[])).
% 2.95/2.15 tff(2258,plain,
% 2.95/2.15 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~c0_1(a2181)) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0)),
% 2.95/2.15 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 2.95/2.15 tff(2259,plain,
% 2.95/2.15 (hskp34 | (~c0_1(a2181)) | c1_1(a2181)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2258, 159, 72, 1847, 501])).
% 2.95/2.15 tff(2260,plain,
% 2.95/2.15 (hskp34),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2259, 2252, 2244])).
% 2.95/2.15 tff(2261,plain,
% 2.95/2.15 (~c0_1(a2189)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[763, 2260])).
% 2.95/2.15 tff(2262,plain,
% 2.95/2.15 (c3_1(a2189)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[739, 2260])).
% 2.95/2.15 tff(2263,plain,
% 2.95/2.15 (c1_1(a2189)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[750, 2260])).
% 2.95/2.15 tff(2264,plain,
% 2.95/2.15 (~c2_1(a2189)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[784, 159, 72, 2263, 2262, 2261, 71])).
% 2.95/2.15 tff(2265,plain,
% 2.95/2.15 (c3_1(a2181)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[875, 159, 72, 2263, 2261, 2244, 2252, 261, 2264])).
% 2.95/2.15 tff(2266,plain,
% 2.95/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a2189) | (~c0_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2189) | (~c0_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2267,plain,
% 2.95/2.15 (((~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189))) <=> (c0_1(a2189) | (~c0_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2268,plain,
% 2.95/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a2189) | (~c0_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))))),
% 2.95/2.15 inference(monotonicity,[status(thm)],[2267])).
% 2.95/2.15 tff(2269,plain,
% 2.95/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2189) | (~c0_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.95/2.15 inference(transitivity,[status(thm)],[2268, 2266])).
% 2.95/2.15 tff(2270,plain,
% 2.95/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))),
% 2.95/2.15 inference(quant_inst,[status(thm)],[])).
% 2.95/2.15 tff(2271,plain,
% 2.95/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2189) | (~c0_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))),
% 2.95/2.15 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 2.95/2.15 tff(2272,plain,
% 2.95/2.15 ($false),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2271, 159, 2263, 2262, 2261, 2244, 1847, 323, 2265, 2264])).
% 2.95/2.15 tff(2273,plain,(hskp33), inference(lemma,lemma(discharge,[]))).
% 2.95/2.15 tff(2274,plain,
% 2.95/2.15 (~c2_1(a2188)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1119, 2273])).
% 2.95/2.15 tff(2275,plain,
% 2.95/2.15 (~c3_1(a2188)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1125, 2273])).
% 2.95/2.15 tff(2276,plain,
% 2.95/2.15 (c1_1(a2188)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1136, 2273])).
% 2.95/2.15 tff(2277,plain,
% 2.95/2.15 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c3_1(a2188) | c2_1(a2188) | (~ndr1_0) | (~c1_1(a2188)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c3_1(a2188) | c2_1(a2188) | (~ndr1_0) | (~c1_1(a2188)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2278,plain,
% 2.95/2.15 ((hskp18 | (~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188))) <=> (hskp18 | c3_1(a2188) | c2_1(a2188) | (~ndr1_0) | (~c1_1(a2188)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2279,plain,
% 2.95/2.15 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c3_1(a2188) | c2_1(a2188) | (~ndr1_0) | (~c1_1(a2188))))),
% 2.95/2.15 inference(monotonicity,[status(thm)],[2278])).
% 2.95/2.15 tff(2280,plain,
% 2.95/2.15 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c3_1(a2188) | c2_1(a2188) | (~ndr1_0) | (~c1_1(a2188)))),
% 2.95/2.15 inference(transitivity,[status(thm)],[2279, 2277])).
% 2.95/2.15 tff(2281,plain,
% 2.95/2.15 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)))),
% 2.95/2.15 inference(quant_inst,[status(thm)],[])).
% 2.95/2.15 tff(2282,plain,
% 2.95/2.15 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c3_1(a2188) | c2_1(a2188) | (~ndr1_0) | (~c1_1(a2188))),
% 2.95/2.15 inference(modus_ponens,[status(thm)],[2281, 2280])).
% 2.95/2.15 tff(2283,plain,
% 2.95/2.15 (hskp18),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2282, 159, 2276, 2275, 2274, 61])).
% 2.95/2.15 tff(2284,plain,
% 2.95/2.15 (hskp32),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1763, 2283])).
% 2.95/2.15 tff(2285,plain,
% 2.95/2.15 (~c2_1(a2186)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[348, 2284])).
% 2.95/2.15 tff(2286,plain,
% 2.95/2.15 (~c3_1(a2186)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[89, 2284])).
% 2.95/2.15 tff(2287,plain,
% 2.95/2.15 (c0_1(a2222)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[456, 2283])).
% 2.95/2.15 tff(2288,plain,
% 2.95/2.15 (c3_1(a2222)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[417, 2283])).
% 2.95/2.15 tff(2289,plain,
% 2.95/2.15 (~c2_1(a2222)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[376, 2283])).
% 2.95/2.15 tff(2290,plain,
% 2.95/2.15 (~c1_1(a2222)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[1714, 2289, 2288, 2287])).
% 2.95/2.15 tff(2291,plain,
% 2.95/2.15 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2292,plain,
% 2.95/2.15 ((hskp58 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222))) <=> (hskp58 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2293,plain,
% 2.95/2.15 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222))))),
% 2.95/2.15 inference(monotonicity,[status(thm)],[2292])).
% 2.95/2.15 tff(2294,plain,
% 2.95/2.15 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)))),
% 2.95/2.15 inference(transitivity,[status(thm)],[2293, 2291])).
% 2.95/2.15 tff(2295,plain,
% 2.95/2.15 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)))),
% 2.95/2.15 inference(quant_inst,[status(thm)],[])).
% 2.95/2.15 tff(2296,plain,
% 2.95/2.15 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222))),
% 2.95/2.15 inference(modus_ponens,[status(thm)],[2295, 2294])).
% 2.95/2.15 tff(2297,plain,
% 2.95/2.15 (hskp58),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[2296, 159, 2288, 2289, 127, 2290])).
% 2.95/2.15 tff(2298,plain,
% 2.95/2.15 (~c1_1(a2252)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[172, 2297])).
% 2.95/2.15 tff(2299,plain,
% 2.95/2.15 (~c2_1(a2252)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[178, 2297])).
% 2.95/2.15 tff(2300,plain,
% 2.95/2.15 (c0_1(a2186)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[83, 2284])).
% 2.95/2.15 tff(2301,assumption,(hskp46), introduced(assumption)).
% 2.95/2.15 tff(2302,plain,
% 2.95/2.15 (c2_1(a2218)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[472, 2301])).
% 2.95/2.15 tff(2303,plain,
% 2.95/2.15 (c0_1(a2218)),
% 2.95/2.15 inference(unit_resolution,[status(thm)],[483, 2301])).
% 2.95/2.15 tff(2304,plain,
% 2.95/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c3_1(a2252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2252) | c1_1(a2252) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c3_1(a2252)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2305,plain,
% 2.95/2.15 (((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2252) | c2_1(a2252) | (~c3_1(a2252)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218))) <=> (c2_1(a2252) | c1_1(a2252) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c3_1(a2252)))),
% 2.95/2.15 inference(rewrite,[status(thm)],[])).
% 2.95/2.15 tff(2306,plain,
% 2.95/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2252) | c2_1(a2252) | (~c3_1(a2252)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c3_1(a2252))))),
% 2.95/2.15 inference(monotonicity,[status(thm)],[2305])).
% 2.95/2.15 tff(2307,plain,
% 2.95/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2252) | c2_1(a2252) | (~c3_1(a2252)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2252) | c1_1(a2252) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c3_1(a2252)))),
% 2.95/2.16 inference(transitivity,[status(thm)],[2306, 2304])).
% 2.95/2.16 tff(2308,plain,
% 2.95/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2252) | c2_1(a2252) | (~c3_1(a2252)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))),
% 2.95/2.16 inference(quant_inst,[status(thm)],[])).
% 2.95/2.16 tff(2309,plain,
% 2.95/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2252) | c1_1(a2252) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c3_1(a2252))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2308, 2307])).
% 2.95/2.16 tff(2310,plain,
% 2.95/2.16 (~c1_1(a2218)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2309, 159, 2303, 2302, 2300, 2299, 2298, 2286, 2285, 51, 21])).
% 2.95/2.16 tff(2311,plain,
% 2.95/2.16 (((~hskp46) | (~c3_1(a2218))) <=> ((~hskp46) | (~c3_1(a2218)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2312,plain,
% 2.95/2.16 (((~c3_1(a2218)) | (~hskp46)) <=> ((~hskp46) | (~c3_1(a2218)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2313,axiom,((~c3_1(a2218)) | (~hskp46)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 2.95/2.16 tff(2314,plain,
% 2.95/2.16 ((~hskp46) | (~c3_1(a2218))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2313, 2312])).
% 2.95/2.16 tff(2315,plain,
% 2.95/2.16 ((~hskp46) | (~c3_1(a2218))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2314, 2311])).
% 2.95/2.16 tff(2316,plain,
% 2.95/2.16 (~c3_1(a2218)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2315, 2301])).
% 2.95/2.16 tff(2317,plain,
% 2.95/2.16 (^[V: $i, U: $i] : refl((hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 2.95/2.16 inference(bind,[status(th)],[])).
% 2.95/2.16 tff(2318,plain,
% 2.95/2.16 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(quant_intro,[status(thm)],[2317])).
% 2.95/2.16 tff(2319,plain,
% 2.95/2.16 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2320,plain,
% 2.95/2.16 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp56) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp56))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp56) <=> (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp56) <=> (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 2.95/2.16 inference(bind,[status(th)],[])).
% 2.95/2.16 tff(2321,plain,
% 2.95/2.16 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp56) <=> ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(quant_intro,[status(thm)],[2320])).
% 2.95/2.16 tff(2322,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause276')).
% 2.95/2.16 tff(2323,plain,
% 2.95/2.16 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2322, 2321])).
% 2.95/2.16 tff(2324,plain,
% 2.95/2.16 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2323, 2319])).
% 2.95/2.16 tff(2325,plain,(
% 2.95/2.16 ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(skolemize,[status(sab)],[2324])).
% 2.95/2.16 tff(2326,plain,
% 2.95/2.16 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2325, 2318])).
% 2.95/2.16 tff(2327,plain,
% 2.95/2.16 (c0_1(a2252)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[189, 2297])).
% 2.95/2.16 tff(2328,plain,
% 2.95/2.16 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp56 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c0_1(a2252)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2329,plain,
% 2.95/2.16 ((hskp56 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252))) <=> (hskp56 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c0_1(a2252)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2330,plain,
% 2.95/2.16 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c0_1(a2252))))),
% 2.95/2.16 inference(monotonicity,[status(thm)],[2329])).
% 2.95/2.16 tff(2331,plain,
% 2.95/2.16 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp56 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c0_1(a2252)))),
% 2.95/2.16 inference(transitivity,[status(thm)],[2330, 2328])).
% 2.95/2.16 tff(2332,plain,
% 2.95/2.16 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))),
% 2.95/2.16 inference(quant_inst,[status(thm)],[])).
% 2.95/2.16 tff(2333,plain,
% 2.95/2.16 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp56 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c0_1(a2252))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2332, 2331])).
% 2.95/2.16 tff(2334,plain,
% 2.95/2.16 (hskp56),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2333, 159, 2327, 2303, 2302, 2299, 2298, 2326, 2310])).
% 2.95/2.16 tff(2335,plain,
% 2.95/2.16 (((~hskp56) | (~c1_1(a2242))) <=> ((~hskp56) | (~c1_1(a2242)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2336,plain,
% 2.95/2.16 (((~c1_1(a2242)) | (~hskp56)) <=> ((~hskp56) | (~c1_1(a2242)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2337,axiom,((~c1_1(a2242)) | (~hskp56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 2.95/2.16 tff(2338,plain,
% 2.95/2.16 ((~hskp56) | (~c1_1(a2242))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2337, 2336])).
% 2.95/2.16 tff(2339,plain,
% 2.95/2.16 ((~hskp56) | (~c1_1(a2242))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2338, 2335])).
% 2.95/2.16 tff(2340,plain,
% 2.95/2.16 (~c1_1(a2242)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2339, 2334])).
% 2.95/2.16 tff(2341,plain,
% 2.95/2.16 (((~hskp56) | c2_1(a2242)) <=> ((~hskp56) | c2_1(a2242))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2342,axiom,((~hskp56) | c2_1(a2242)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 2.95/2.16 tff(2343,plain,
% 2.95/2.16 ((~hskp56) | c2_1(a2242)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2342, 2341])).
% 2.95/2.16 tff(2344,plain,
% 2.95/2.16 ((~hskp56) | c2_1(a2242)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2343, 2341])).
% 2.95/2.16 tff(2345,plain,
% 2.95/2.16 ((~hskp56) | c2_1(a2242)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2344, 2341])).
% 2.95/2.16 tff(2346,plain,
% 2.95/2.16 ((~hskp56) | c2_1(a2242)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2345, 2341])).
% 2.95/2.16 tff(2347,plain,
% 2.95/2.16 ((~hskp56) | c2_1(a2242)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2346, 2341])).
% 2.95/2.16 tff(2348,plain,
% 2.95/2.16 ((~hskp56) | c2_1(a2242)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2347, 2341])).
% 2.95/2.16 tff(2349,plain,
% 2.95/2.16 ((~hskp56) | c2_1(a2242)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2348, 2341])).
% 2.95/2.16 tff(2350,plain,
% 2.95/2.16 ((~hskp56) | c2_1(a2242)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2349, 2341])).
% 2.95/2.16 tff(2351,plain,
% 2.95/2.16 (c2_1(a2242)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2350, 2334])).
% 2.95/2.16 tff(2352,plain,
% 2.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a2242) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c0_1(a2242) | (~c2_1(a2242)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a2242) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c0_1(a2242) | (~c2_1(a2242)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2353,plain,
% 2.95/2.16 (((~ndr1_0) | c1_1(a2242) | c0_1(a2242) | (~c2_1(a2242)) | c3_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c3_1(a2218) | c1_1(a2218) | (~c0_1(a2218))) <=> (c1_1(a2242) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c0_1(a2242) | (~c2_1(a2242)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2354,plain,
% 2.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2242) | c0_1(a2242) | (~c2_1(a2242)) | c3_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c3_1(a2218) | c1_1(a2218) | (~c0_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a2242) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c0_1(a2242) | (~c2_1(a2242))))),
% 2.95/2.16 inference(monotonicity,[status(thm)],[2353])).
% 2.95/2.16 tff(2355,plain,
% 2.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2242) | c0_1(a2242) | (~c2_1(a2242)) | c3_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c3_1(a2218) | c1_1(a2218) | (~c0_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a2242) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c0_1(a2242) | (~c2_1(a2242)))),
% 2.95/2.16 inference(transitivity,[status(thm)],[2354, 2352])).
% 2.95/2.16 tff(2356,plain,
% 2.95/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2242) | c0_1(a2242) | (~c2_1(a2242)) | c3_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c3_1(a2218) | c1_1(a2218) | (~c0_1(a2218)))),
% 2.95/2.16 inference(quant_inst,[status(thm)],[])).
% 2.95/2.16 tff(2357,plain,
% 2.95/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a2242) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c0_1(a2242) | (~c2_1(a2242))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 2.95/2.16 tff(2358,plain,
% 2.95/2.16 (c0_1(a2242)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2357, 159, 2351, 2303, 2302, 2340, 2316, 1049, 2310])).
% 2.95/2.16 tff(2359,plain,
% 2.95/2.16 (^[V: $i, U: $i] : refl((hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 2.95/2.16 inference(bind,[status(th)],[])).
% 2.95/2.16 tff(2360,plain,
% 2.95/2.16 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(quant_intro,[status(thm)],[2359])).
% 2.95/2.16 tff(2361,plain,
% 2.95/2.16 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2362,plain,
% 2.95/2.16 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp40) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp40))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp40) <=> (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp40) <=> (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 2.95/2.16 inference(bind,[status(th)],[])).
% 2.95/2.16 tff(2363,plain,
% 2.95/2.16 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp40) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(quant_intro,[status(thm)],[2362])).
% 2.95/2.16 tff(2364,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause267')).
% 2.95/2.16 tff(2365,plain,
% 2.95/2.16 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2364, 2363])).
% 2.95/2.16 tff(2366,plain,
% 2.95/2.16 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2365, 2361])).
% 2.95/2.16 tff(2367,plain,(
% 2.95/2.16 ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(skolemize,[status(sab)],[2366])).
% 2.95/2.16 tff(2368,plain,
% 2.95/2.16 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2367, 2360])).
% 2.95/2.16 tff(2369,plain,
% 2.95/2.16 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | c2_1(a2252) | c1_1(a2252) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c3_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp40 | c2_1(a2252) | c1_1(a2252) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c3_1(a2252)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2370,plain,
% 2.95/2.16 ((hskp40 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2218) | c3_1(a2218) | (~c0_1(a2218))) <=> (hskp40 | c2_1(a2252) | c1_1(a2252) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c3_1(a2252)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2371,plain,
% 2.95/2.16 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2218) | c3_1(a2218) | (~c0_1(a2218)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | c2_1(a2252) | c1_1(a2252) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c3_1(a2252))))),
% 2.95/2.16 inference(monotonicity,[status(thm)],[2370])).
% 2.95/2.16 tff(2372,plain,
% 2.95/2.16 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2218) | c3_1(a2218) | (~c0_1(a2218)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp40 | c2_1(a2252) | c1_1(a2252) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c3_1(a2252)))),
% 2.95/2.16 inference(transitivity,[status(thm)],[2371, 2369])).
% 2.95/2.16 tff(2373,plain,
% 2.95/2.16 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2218) | c3_1(a2218) | (~c0_1(a2218)))),
% 2.95/2.16 inference(quant_inst,[status(thm)],[])).
% 2.95/2.16 tff(2374,plain,
% 2.95/2.16 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp40 | c2_1(a2252) | c1_1(a2252) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c3_1(a2252))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2373, 2372])).
% 2.95/2.16 tff(2375,plain,
% 2.95/2.16 (hskp40),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2374, 159, 2303, 2299, 2298, 2316, 2368, 21, 2310])).
% 2.95/2.16 tff(2376,plain,
% 2.95/2.16 (((~hskp40) | (~c1_1(a2204))) <=> ((~hskp40) | (~c1_1(a2204)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2377,plain,
% 2.95/2.16 (((~c1_1(a2204)) | (~hskp40)) <=> ((~hskp40) | (~c1_1(a2204)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2378,axiom,((~c1_1(a2204)) | (~hskp40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 2.95/2.16 tff(2379,plain,
% 2.95/2.16 ((~hskp40) | (~c1_1(a2204))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2378, 2377])).
% 2.95/2.16 tff(2380,plain,
% 2.95/2.16 ((~hskp40) | (~c1_1(a2204))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2379, 2376])).
% 2.95/2.16 tff(2381,plain,
% 2.95/2.16 (~c1_1(a2204)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2380, 2375])).
% 2.95/2.16 tff(2382,plain,
% 2.95/2.16 (((~hskp56) | (~c3_1(a2242))) <=> ((~hskp56) | (~c3_1(a2242)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2383,plain,
% 2.95/2.16 (((~c3_1(a2242)) | (~hskp56)) <=> ((~hskp56) | (~c3_1(a2242)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2384,axiom,((~c3_1(a2242)) | (~hskp56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 2.95/2.16 tff(2385,plain,
% 2.95/2.16 ((~hskp56) | (~c3_1(a2242))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 2.95/2.16 tff(2386,plain,
% 2.95/2.16 ((~hskp56) | (~c3_1(a2242))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2385, 2382])).
% 2.95/2.16 tff(2387,plain,
% 2.95/2.16 (~c3_1(a2242)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2386, 2334])).
% 2.95/2.16 tff(2388,plain,
% 2.95/2.16 (((~hskp40) | c3_1(a2204)) <=> ((~hskp40) | c3_1(a2204))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2389,axiom,((~hskp40) | c3_1(a2204)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 2.95/2.16 tff(2390,plain,
% 2.95/2.16 ((~hskp40) | c3_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2389, 2388])).
% 2.95/2.16 tff(2391,plain,
% 2.95/2.16 ((~hskp40) | c3_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2390, 2388])).
% 2.95/2.16 tff(2392,plain,
% 2.95/2.16 ((~hskp40) | c3_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2391, 2388])).
% 2.95/2.16 tff(2393,plain,
% 2.95/2.16 ((~hskp40) | c3_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2392, 2388])).
% 2.95/2.16 tff(2394,plain,
% 2.95/2.16 ((~hskp40) | c3_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2393, 2388])).
% 2.95/2.16 tff(2395,plain,
% 2.95/2.16 ((~hskp40) | c3_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2394, 2388])).
% 2.95/2.16 tff(2396,plain,
% 2.95/2.16 ((~hskp40) | c3_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2395, 2388])).
% 2.95/2.16 tff(2397,plain,
% 2.95/2.16 ((~hskp40) | c3_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2396, 2388])).
% 2.95/2.16 tff(2398,plain,
% 2.95/2.16 (c3_1(a2204)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2397, 2375])).
% 2.95/2.16 tff(2399,plain,
% 2.95/2.16 (((~hskp40) | c2_1(a2204)) <=> ((~hskp40) | c2_1(a2204))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2400,axiom,((~hskp40) | c2_1(a2204)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 2.95/2.16 tff(2401,plain,
% 2.95/2.16 ((~hskp40) | c2_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2400, 2399])).
% 2.95/2.16 tff(2402,plain,
% 2.95/2.16 ((~hskp40) | c2_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2401, 2399])).
% 2.95/2.16 tff(2403,plain,
% 2.95/2.16 ((~hskp40) | c2_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2402, 2399])).
% 2.95/2.16 tff(2404,plain,
% 2.95/2.16 ((~hskp40) | c2_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2403, 2399])).
% 2.95/2.16 tff(2405,plain,
% 2.95/2.16 ((~hskp40) | c2_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2404, 2399])).
% 2.95/2.16 tff(2406,plain,
% 2.95/2.16 ((~hskp40) | c2_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2405, 2399])).
% 2.95/2.16 tff(2407,plain,
% 2.95/2.16 ((~hskp40) | c2_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2406, 2399])).
% 2.95/2.16 tff(2408,plain,
% 2.95/2.16 ((~hskp40) | c2_1(a2204)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2407, 2399])).
% 2.95/2.16 tff(2409,plain,
% 2.95/2.16 (c2_1(a2204)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2408, 2375])).
% 2.95/2.16 tff(2410,plain,
% 2.95/2.16 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp3 | c1_1(a2242) | c3_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2242)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp3 | c1_1(a2242) | c3_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2242)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2411,plain,
% 2.95/2.16 ((hskp3 | (~ndr1_0) | c1_1(a2242) | c3_1(a2242) | (~c2_1(a2242)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204))) <=> (hskp3 | c1_1(a2242) | c3_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2242)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2412,plain,
% 2.95/2.16 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2242) | c3_1(a2242) | (~c2_1(a2242)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp3 | c1_1(a2242) | c3_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2242))))),
% 2.95/2.16 inference(monotonicity,[status(thm)],[2411])).
% 2.95/2.16 tff(2413,plain,
% 2.95/2.16 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2242) | c3_1(a2242) | (~c2_1(a2242)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp3 | c1_1(a2242) | c3_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2242)))),
% 2.95/2.16 inference(transitivity,[status(thm)],[2412, 2410])).
% 2.95/2.16 tff(2414,plain,
% 2.95/2.16 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2242) | c3_1(a2242) | (~c2_1(a2242)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)))),
% 2.95/2.16 inference(quant_inst,[status(thm)],[])).
% 2.95/2.16 tff(2415,plain,
% 2.95/2.16 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp3 | c1_1(a2242) | c3_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2242))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 2.95/2.16 tff(2416,plain,
% 2.95/2.16 (hskp3),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2415, 159, 2351, 2409, 2398, 2340, 2387, 2381, 20])).
% 2.95/2.16 tff(2417,plain,
% 2.95/2.16 (((~hskp3) | (~c0_1(a2190))) <=> ((~hskp3) | (~c0_1(a2190)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2418,plain,
% 2.95/2.16 (((~c0_1(a2190)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a2190)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2419,axiom,((~c0_1(a2190)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause235')).
% 2.95/2.16 tff(2420,plain,
% 2.95/2.16 ((~hskp3) | (~c0_1(a2190))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2419, 2418])).
% 2.95/2.16 tff(2421,plain,
% 2.95/2.16 ((~hskp3) | (~c0_1(a2190))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2420, 2417])).
% 2.95/2.16 tff(2422,plain,
% 2.95/2.16 (~c0_1(a2190)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2421, 2416])).
% 2.95/2.16 tff(2423,plain,
% 2.95/2.16 (((~hskp3) | (~c1_1(a2190))) <=> ((~hskp3) | (~c1_1(a2190)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2424,plain,
% 2.95/2.16 (((~c1_1(a2190)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a2190)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2425,axiom,((~c1_1(a2190)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause234')).
% 2.95/2.16 tff(2426,plain,
% 2.95/2.16 ((~hskp3) | (~c1_1(a2190))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2425, 2424])).
% 2.95/2.16 tff(2427,plain,
% 2.95/2.16 ((~hskp3) | (~c1_1(a2190))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2426, 2423])).
% 2.95/2.16 tff(2428,plain,
% 2.95/2.16 (~c1_1(a2190)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2427, 2416])).
% 2.95/2.16 tff(2429,plain,
% 2.95/2.16 (((~hskp3) | c2_1(a2190)) <=> ((~hskp3) | c2_1(a2190))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2430,axiom,((~hskp3) | c2_1(a2190)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 2.95/2.16 tff(2431,plain,
% 2.95/2.16 ((~hskp3) | c2_1(a2190)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2430, 2429])).
% 2.95/2.16 tff(2432,plain,
% 2.95/2.16 ((~hskp3) | c2_1(a2190)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2431, 2429])).
% 2.95/2.16 tff(2433,plain,
% 2.95/2.16 ((~hskp3) | c2_1(a2190)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2432, 2429])).
% 2.95/2.16 tff(2434,plain,
% 2.95/2.16 ((~hskp3) | c2_1(a2190)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2433, 2429])).
% 2.95/2.16 tff(2435,plain,
% 2.95/2.16 ((~hskp3) | c2_1(a2190)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2434, 2429])).
% 2.95/2.16 tff(2436,plain,
% 2.95/2.16 ((~hskp3) | c2_1(a2190)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2435, 2429])).
% 2.95/2.16 tff(2437,plain,
% 2.95/2.16 ((~hskp3) | c2_1(a2190)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2436, 2429])).
% 2.95/2.16 tff(2438,plain,
% 2.95/2.16 ((~hskp3) | c2_1(a2190)),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2437, 2429])).
% 2.95/2.16 tff(2439,plain,
% 2.95/2.16 (c2_1(a2190)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2438, 2416])).
% 2.95/2.16 tff(2440,plain,
% 2.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2242) | c3_1(a2186) | c2_1(a2186) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c2_1(a2190)) | (~c0_1(a2186)) | (~c0_1(a2242)) | (~c2_1(a2242)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2242) | c3_1(a2186) | c2_1(a2186) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c2_1(a2190)) | (~c0_1(a2186)) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2441,plain,
% 2.95/2.16 (((~ndr1_0) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186))) <=> (c3_1(a2242) | c3_1(a2186) | c2_1(a2186) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c2_1(a2190)) | (~c0_1(a2186)) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2442,plain,
% 2.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2242) | c3_1(a2186) | c2_1(a2186) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c2_1(a2190)) | (~c0_1(a2186)) | (~c0_1(a2242)) | (~c2_1(a2242))))),
% 2.95/2.16 inference(monotonicity,[status(thm)],[2441])).
% 2.95/2.16 tff(2443,plain,
% 2.95/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2242) | c3_1(a2186) | c2_1(a2186) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c2_1(a2190)) | (~c0_1(a2186)) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 2.95/2.16 inference(transitivity,[status(thm)],[2442, 2440])).
% 2.95/2.16 tff(2444,plain,
% 2.95/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))),
% 2.95/2.16 inference(quant_inst,[status(thm)],[])).
% 2.95/2.16 tff(2445,plain,
% 2.95/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2242) | c3_1(a2186) | c2_1(a2186) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c2_1(a2190)) | (~c0_1(a2186)) | (~c0_1(a2242)) | (~c2_1(a2242))),
% 2.95/2.16 inference(modus_ponens,[status(thm)],[2444, 2443])).
% 2.95/2.16 tff(2446,plain,
% 2.95/2.16 ($false),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2445, 159, 2351, 2300, 2439, 2387, 2286, 2285, 2428, 2422, 604, 2358])).
% 2.95/2.16 tff(2447,plain,((~hskp46) | (~c3_1(a2252))), inference(lemma,lemma(discharge,[]))).
% 2.95/2.16 tff(2448,plain,
% 2.95/2.16 (~hskp46),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2447, 21])).
% 2.95/2.16 tff(2449,plain,
% 2.95/2.16 (hskp46 | hskp34),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[460, 159, 2287, 2288, 446, 2290])).
% 2.95/2.16 tff(2450,plain,
% 2.95/2.16 (hskp34),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[2449, 2448])).
% 2.95/2.16 tff(2451,plain,
% 2.95/2.16 (~c0_1(a2189)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[763, 2450])).
% 2.95/2.16 tff(2452,plain,
% 2.95/2.16 (hskp44),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[1731, 159, 2287, 2288, 2289, 1725, 2290])).
% 2.95/2.16 tff(2453,plain,
% 2.95/2.16 (~c0_1(a2215)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[1737, 2452])).
% 2.95/2.16 tff(2454,plain,
% 2.95/2.16 (c3_1(a2189)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[739, 2450])).
% 2.95/2.16 tff(2455,plain,
% 2.95/2.16 (c1_1(a2189)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[750, 2450])).
% 2.95/2.16 tff(2456,plain,
% 2.95/2.16 (c1_1(a2215)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[1748, 2452])).
% 2.95/2.16 tff(2457,plain,
% 2.95/2.16 (c2_1(a2215)),
% 2.95/2.16 inference(unit_resolution,[status(thm)],[1759, 2452])).
% 2.95/2.16 tff(2458,plain,
% 2.95/2.16 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2215) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2215) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2459,plain,
% 2.95/2.16 ((hskp48 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))) <=> (hskp48 | c0_1(a2215) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 2.95/2.16 inference(rewrite,[status(thm)],[])).
% 2.95/2.16 tff(2460,plain,
% 2.95/2.16 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2215) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215))))),
% 2.95/2.16 inference(monotonicity,[status(thm)],[2459])).
% 2.95/2.16 tff(2461,plain,
% 2.95/2.16 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2215) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 2.95/2.17 inference(transitivity,[status(thm)],[2460, 2458])).
% 2.95/2.17 tff(2462,plain,
% 2.95/2.17 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 2.95/2.17 inference(quant_inst,[status(thm)],[])).
% 2.95/2.17 tff(2463,plain,
% 2.95/2.17 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2215) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215))),
% 2.95/2.17 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 2.95/2.17 tff(2464,plain,
% 2.95/2.17 (hskp48),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2463, 159, 2457, 2456, 2455, 2454, 2453, 2451, 41])).
% 2.95/2.17 tff(2465,plain,
% 2.95/2.17 (~c0_1(a2228)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[1194, 2464])).
% 2.95/2.17 tff(2466,plain,
% 2.95/2.17 (c2_1(a2228)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[1205, 2464])).
% 2.95/2.17 tff(2467,plain,
% 2.95/2.17 (c3_1(a2228)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[1216, 2464])).
% 2.95/2.17 tff(2468,plain,
% 2.95/2.17 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp40 | c2_1(a2252) | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c3_1(a2252)) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp40 | c2_1(a2252) | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c3_1(a2252)) | (~c0_1(a2252)))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2469,plain,
% 2.95/2.17 ((hskp40 | (~ndr1_0) | c0_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c2_1(a2252) | (~c0_1(a2252)) | (~c3_1(a2252))) <=> (hskp40 | c2_1(a2252) | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c3_1(a2252)) | (~c0_1(a2252)))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2470,plain,
% 2.95/2.17 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp40 | (~ndr1_0) | c0_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c2_1(a2252) | (~c0_1(a2252)) | (~c3_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp40 | c2_1(a2252) | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c3_1(a2252)) | (~c0_1(a2252))))),
% 2.95/2.17 inference(monotonicity,[status(thm)],[2469])).
% 2.95/2.17 tff(2471,plain,
% 2.95/2.17 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp40 | (~ndr1_0) | c0_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c2_1(a2252) | (~c0_1(a2252)) | (~c3_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp40 | c2_1(a2252) | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c3_1(a2252)) | (~c0_1(a2252)))),
% 2.95/2.17 inference(transitivity,[status(thm)],[2470, 2468])).
% 2.95/2.17 tff(2472,plain,
% 2.95/2.17 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp40 | (~ndr1_0) | c0_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c2_1(a2252) | (~c0_1(a2252)) | (~c3_1(a2252)))),
% 2.95/2.17 inference(quant_inst,[status(thm)],[])).
% 2.95/2.17 tff(2473,plain,
% 2.95/2.17 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp40 | c2_1(a2252) | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c3_1(a2252)) | (~c0_1(a2252))),
% 2.95/2.17 inference(modus_ponens,[status(thm)],[2472, 2471])).
% 2.95/2.17 tff(2474,plain,
% 2.95/2.17 (hskp40),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2473, 159, 2327, 2467, 2466, 2299, 2465, 31, 21])).
% 2.95/2.17 tff(2475,plain,
% 2.95/2.17 (~c1_1(a2204)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2380, 2474])).
% 2.95/2.17 tff(2476,plain,
% 2.95/2.17 (c2_1(a2204)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2408, 2474])).
% 2.95/2.17 tff(2477,plain,
% 2.95/2.17 (c3_1(a2204)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2397, 2474])).
% 2.95/2.17 tff(2478,assumption,(~c0_1(a2204)), introduced(assumption)).
% 2.95/2.17 tff(2479,assumption,(~c1_1(a2204)), introduced(assumption)).
% 2.95/2.17 tff(2480,assumption,(c3_1(a2204)), introduced(assumption)).
% 2.95/2.17 tff(2481,assumption,(c2_1(a2204)), introduced(assumption)).
% 2.95/2.17 tff(2482,plain,
% 2.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | (~c0_1(a2252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | (~c0_1(a2252)))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2483,plain,
% 2.95/2.17 (((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | c1_1(a2204) | (~c2_1(a2204))) <=> (c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | (~c0_1(a2252)))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2484,plain,
% 2.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | c1_1(a2204) | (~c2_1(a2204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | (~c0_1(a2252))))),
% 2.95/2.17 inference(monotonicity,[status(thm)],[2483])).
% 2.95/2.17 tff(2485,plain,
% 2.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | c1_1(a2204) | (~c2_1(a2204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | (~c0_1(a2252)))),
% 2.95/2.17 inference(transitivity,[status(thm)],[2484, 2482])).
% 2.95/2.17 tff(2486,plain,
% 2.95/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | c1_1(a2204) | (~c2_1(a2204)))),
% 2.95/2.17 inference(quant_inst,[status(thm)],[])).
% 2.95/2.17 tff(2487,plain,
% 2.95/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | (~c0_1(a2252))),
% 2.95/2.17 inference(modus_ponens,[status(thm)],[2486, 2485])).
% 2.95/2.17 tff(2488,plain,
% 2.95/2.17 ($false),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2487, 159, 2327, 2481, 2480, 2299, 2298, 2479, 10, 2478])).
% 2.95/2.17 tff(2489,plain,(c0_1(a2204) | (~c2_1(a2204)) | (~c3_1(a2204)) | c1_1(a2204)), inference(lemma,lemma(discharge,[]))).
% 2.95/2.17 tff(2490,plain,
% 2.95/2.17 (c0_1(a2204)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2489, 2475, 2477, 2476])).
% 2.95/2.17 tff(2491,plain,
% 2.95/2.17 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp56 | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c0_1(a2252)))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2492,plain,
% 2.95/2.17 ((hskp56 | (~ndr1_0) | c1_1(a2204) | (~c0_1(a2204)) | (~c2_1(a2204)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252))) <=> (hskp56 | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c0_1(a2252)))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2493,plain,
% 2.95/2.17 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | (~ndr1_0) | c1_1(a2204) | (~c0_1(a2204)) | (~c2_1(a2204)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c0_1(a2252))))),
% 2.95/2.17 inference(monotonicity,[status(thm)],[2492])).
% 2.95/2.17 tff(2494,plain,
% 2.95/2.17 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | (~ndr1_0) | c1_1(a2204) | (~c0_1(a2204)) | (~c2_1(a2204)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp56 | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c0_1(a2252)))),
% 2.95/2.17 inference(transitivity,[status(thm)],[2493, 2491])).
% 2.95/2.17 tff(2495,plain,
% 2.95/2.17 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | (~ndr1_0) | c1_1(a2204) | (~c0_1(a2204)) | (~c2_1(a2204)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))),
% 2.95/2.17 inference(quant_inst,[status(thm)],[])).
% 2.95/2.17 tff(2496,plain,
% 2.95/2.17 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp56 | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c0_1(a2252))),
% 2.95/2.17 inference(modus_ponens,[status(thm)],[2495, 2494])).
% 2.95/2.17 tff(2497,plain,
% 2.95/2.17 (hskp56),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2496, 159, 2327, 2476, 2299, 2298, 2475, 2326, 2490])).
% 2.95/2.17 tff(2498,plain,
% 2.95/2.17 (~c3_1(a2242)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2386, 2497])).
% 2.95/2.17 tff(2499,plain,
% 2.95/2.17 (~c1_1(a2242)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2339, 2497])).
% 2.95/2.17 tff(2500,plain,
% 2.95/2.17 (c2_1(a2242)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2350, 2497])).
% 2.95/2.17 tff(2501,plain,
% 2.95/2.17 (hskp3),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2415, 159, 2500, 2476, 2477, 2499, 2498, 2475, 20])).
% 2.95/2.17 tff(2502,plain,
% 2.95/2.17 (~c0_1(a2190)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2421, 2501])).
% 2.95/2.17 tff(2503,plain,
% 2.95/2.17 (~c1_1(a2190)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2427, 2501])).
% 2.95/2.17 tff(2504,plain,
% 2.95/2.17 (c2_1(a2190)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2438, 2501])).
% 2.95/2.17 tff(2505,plain,
% 2.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c3_1(a2190)) | (~c2_1(a2190)) | (~c0_1(a2252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c3_1(a2190)) | (~c2_1(a2190)) | (~c0_1(a2252)))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2506,plain,
% 2.95/2.17 (((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2190) | (~c3_1(a2190)) | (~c2_1(a2190)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190))) <=> (c2_1(a2252) | c1_1(a2252) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c3_1(a2190)) | (~c2_1(a2190)) | (~c0_1(a2252)))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2507,plain,
% 2.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2190) | (~c3_1(a2190)) | (~c2_1(a2190)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c3_1(a2190)) | (~c2_1(a2190)) | (~c0_1(a2252))))),
% 2.95/2.17 inference(monotonicity,[status(thm)],[2506])).
% 2.95/2.17 tff(2508,plain,
% 2.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2190) | (~c3_1(a2190)) | (~c2_1(a2190)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c3_1(a2190)) | (~c2_1(a2190)) | (~c0_1(a2252)))),
% 2.95/2.17 inference(transitivity,[status(thm)],[2507, 2505])).
% 2.95/2.17 tff(2509,plain,
% 2.95/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2190) | (~c3_1(a2190)) | (~c2_1(a2190)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)))),
% 2.95/2.17 inference(quant_inst,[status(thm)],[])).
% 2.95/2.17 tff(2510,plain,
% 2.95/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c3_1(a2190)) | (~c2_1(a2190)) | (~c0_1(a2252))),
% 2.95/2.17 inference(modus_ponens,[status(thm)],[2509, 2508])).
% 2.95/2.17 tff(2511,plain,
% 2.95/2.17 (~c3_1(a2190)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2510, 159, 2327, 2504, 2299, 2298, 2503, 2502, 10])).
% 2.95/2.17 tff(2512,plain,
% 2.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c0_1(a2228) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2228)) | c1_1(a2228) | (~c0_1(a2252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c0_1(a2228) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2228)) | c1_1(a2228) | (~c0_1(a2252)))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2513,plain,
% 2.95/2.17 (((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228))) <=> (c2_1(a2252) | c1_1(a2252) | c0_1(a2228) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2228)) | c1_1(a2228) | (~c0_1(a2252)))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2514,plain,
% 2.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c0_1(a2228) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2228)) | c1_1(a2228) | (~c0_1(a2252))))),
% 2.95/2.17 inference(monotonicity,[status(thm)],[2513])).
% 2.95/2.17 tff(2515,plain,
% 2.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c0_1(a2228) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2228)) | c1_1(a2228) | (~c0_1(a2252)))),
% 2.95/2.17 inference(transitivity,[status(thm)],[2514, 2512])).
% 2.95/2.17 tff(2516,plain,
% 2.95/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))),
% 2.95/2.17 inference(quant_inst,[status(thm)],[])).
% 2.95/2.17 tff(2517,plain,
% 2.95/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c0_1(a2228) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2228)) | c1_1(a2228) | (~c0_1(a2252))),
% 2.95/2.17 inference(modus_ponens,[status(thm)],[2516, 2515])).
% 2.95/2.17 tff(2518,plain,
% 2.95/2.17 (c1_1(a2228)),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2517, 159, 2327, 2466, 2476, 2477, 2299, 2298, 2465, 2475, 10])).
% 2.95/2.17 tff(2519,plain,
% 2.95/2.17 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 2.95/2.17 inference(bind,[status(th)],[])).
% 2.95/2.17 tff(2520,plain,
% 2.95/2.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.95/2.17 inference(quant_intro,[status(thm)],[2519])).
% 2.95/2.17 tff(2521,plain,
% 2.95/2.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2522,plain,
% 2.95/2.17 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | (~c2_1(W)))), ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | (~c2_1(W))))), (((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(W)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 2.95/2.17 inference(bind,[status(th)],[])).
% 2.95/2.17 tff(2523,plain,
% 2.95/2.17 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(W)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.95/2.17 inference(quant_intro,[status(thm)],[2522])).
% 2.95/2.17 tff(2524,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(W)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause296')).
% 2.95/2.17 tff(2525,plain,
% 2.95/2.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.95/2.17 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 2.95/2.17 tff(2526,plain,
% 2.95/2.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.95/2.17 inference(modus_ponens,[status(thm)],[2525, 2521])).
% 2.95/2.17 tff(2527,plain,(
% 2.95/2.17 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.95/2.17 inference(skolemize,[status(sab)],[2526])).
% 2.95/2.17 tff(2528,plain,
% 2.95/2.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.95/2.17 inference(modus_ponens,[status(thm)],[2527, 2520])).
% 2.95/2.17 tff(2529,plain,
% 2.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2228) | c0_1(a2190) | (~ndr1_0) | c3_1(a2190) | (~c2_1(a2190)) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c1_1(a2228)) | (~c3_1(a2228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2228) | c0_1(a2190) | (~ndr1_0) | c3_1(a2190) | (~c2_1(a2190)) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c1_1(a2228)) | (~c3_1(a2228)))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2530,plain,
% 2.95/2.17 (((~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c3_1(a2228)) | (~c0_1(a2204)) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2190) | c3_1(a2190) | (~c2_1(a2190))) <=> (c0_1(a2228) | c0_1(a2190) | (~ndr1_0) | c3_1(a2190) | (~c2_1(a2190)) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c1_1(a2228)) | (~c3_1(a2228)))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2531,plain,
% 2.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c3_1(a2228)) | (~c0_1(a2204)) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2190) | c3_1(a2190) | (~c2_1(a2190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2228) | c0_1(a2190) | (~ndr1_0) | c3_1(a2190) | (~c2_1(a2190)) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c1_1(a2228)) | (~c3_1(a2228))))),
% 2.95/2.17 inference(monotonicity,[status(thm)],[2530])).
% 2.95/2.17 tff(2532,plain,
% 2.95/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c3_1(a2228)) | (~c0_1(a2204)) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2190) | c3_1(a2190) | (~c2_1(a2190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2228) | c0_1(a2190) | (~ndr1_0) | c3_1(a2190) | (~c2_1(a2190)) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c1_1(a2228)) | (~c3_1(a2228)))),
% 2.95/2.17 inference(transitivity,[status(thm)],[2531, 2529])).
% 2.95/2.17 tff(2533,plain,
% 2.95/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c3_1(a2228)) | (~c0_1(a2204)) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2190) | c3_1(a2190) | (~c2_1(a2190)))),
% 2.95/2.17 inference(quant_inst,[status(thm)],[])).
% 2.95/2.17 tff(2534,plain,
% 2.95/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2228) | c0_1(a2190) | (~ndr1_0) | c3_1(a2190) | (~c2_1(a2190)) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c1_1(a2228)) | (~c3_1(a2228))),
% 2.95/2.17 inference(modus_ponens,[status(thm)],[2533, 2532])).
% 2.95/2.17 tff(2535,plain,
% 2.95/2.17 ($false),
% 2.95/2.17 inference(unit_resolution,[status(thm)],[2534, 159, 2467, 2476, 2477, 2504, 2465, 2502, 2528, 2490, 2518, 2511])).
% 2.95/2.17 tff(2536,plain,(~c3_1(a2252)), inference(lemma,lemma(discharge,[]))).
% 2.95/2.17 tff(2537,plain,
% 2.95/2.17 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)))),
% 2.95/2.17 inference(bind,[status(th)],[])).
% 2.95/2.17 tff(2538,plain,
% 2.95/2.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 2.95/2.17 inference(quant_intro,[status(thm)],[2537])).
% 2.95/2.17 tff(2539,plain,
% 2.95/2.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 2.95/2.17 inference(rewrite,[status(thm)],[])).
% 2.95/2.17 tff(2540,plain,
% 2.95/2.17 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c3_1(W))), ((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c3_1(W)))), (((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c3_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c3_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c2_1(W) | c3_1(W))), (((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c2_1(W) | c3_1(W)))), ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c2_1(W) | c3_1(W)) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c2_1(W) | c3_1(W)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))), ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)))), (((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) | c0_1(W)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))), (((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) | c0_1(W)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))))),
% 2.95/2.18 inference(bind,[status(th)],[])).
% 2.95/2.18 tff(2541,plain,
% 2.95/2.18 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) | c0_1(W)) | c2_1(U)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 2.95/2.18 inference(quant_intro,[status(thm)],[2540])).
% 2.95/2.18 tff(2542,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) | c0_1(W)) | c2_1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause285')).
% 2.95/2.18 tff(2543,plain,
% 2.95/2.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 2.95/2.18 inference(modus_ponens,[status(thm)],[2542, 2541])).
% 2.95/2.18 tff(2544,plain,
% 2.95/2.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 2.95/2.18 inference(modus_ponens,[status(thm)],[2543, 2539])).
% 2.95/2.18 tff(2545,plain,(
% 2.95/2.18 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 2.95/2.18 inference(skolemize,[status(sab)],[2544])).
% 2.95/2.18 tff(2546,plain,
% 2.95/2.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 2.95/2.18 inference(modus_ponens,[status(thm)],[2545, 2538])).
% 2.95/2.18 tff(2547,plain,
% 2.95/2.18 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | c1_1(a2252) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp40 | c1_1(a2252) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2252) | (~c0_1(a2252)))),
% 2.95/2.18 inference(rewrite,[status(thm)],[])).
% 2.95/2.18 tff(2548,plain,
% 2.95/2.18 ((hskp40 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252))) <=> (hskp40 | c1_1(a2252) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2252) | (~c0_1(a2252)))),
% 2.95/2.18 inference(rewrite,[status(thm)],[])).
% 2.95/2.18 tff(2549,plain,
% 2.95/2.18 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | c1_1(a2252) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2252) | (~c0_1(a2252))))),
% 2.95/2.18 inference(monotonicity,[status(thm)],[2548])).
% 2.95/2.18 tff(2550,plain,
% 2.95/2.18 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp40 | c1_1(a2252) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2252) | (~c0_1(a2252)))),
% 2.95/2.18 inference(transitivity,[status(thm)],[2549, 2547])).
% 2.95/2.18 tff(2551,plain,
% 2.95/2.18 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252)))),
% 2.95/2.18 inference(quant_inst,[status(thm)],[])).
% 2.95/2.18 tff(2552,plain,
% 2.95/2.18 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp40 | c1_1(a2252) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2252) | (~c0_1(a2252))),
% 2.95/2.18 inference(modus_ponens,[status(thm)],[2551, 2550])).
% 2.95/2.18 tff(2553,plain,
% 2.95/2.18 (hskp40 | c3_1(a2252)),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[2552, 159, 2327, 2288, 2298, 2289, 2368, 2290])).
% 2.95/2.18 tff(2554,plain,
% 2.95/2.18 (hskp40),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[2553, 2536])).
% 2.95/2.18 tff(2555,plain,
% 2.95/2.18 (c2_1(a2204)),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[2408, 2554])).
% 2.95/2.18 tff(2556,plain,
% 2.95/2.18 (~c1_1(a2204)),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[2380, 2554])).
% 2.95/2.18 tff(2557,plain,
% 2.95/2.18 (c3_1(a2204)),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[2397, 2554])).
% 2.95/2.18 tff(2558,plain,
% 2.95/2.18 (c0_1(a2204)),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[2489, 2556, 2557, 2555])).
% 2.95/2.18 tff(2559,plain,
% 2.95/2.18 (hskp56),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[2496, 159, 2327, 2555, 2299, 2298, 2556, 2326, 2558])).
% 2.95/2.18 tff(2560,plain,
% 2.95/2.18 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 2.95/2.18 inference(bind,[status(th)],[])).
% 2.95/2.18 tff(2561,plain,
% 2.95/2.18 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.95/2.18 inference(quant_intro,[status(thm)],[2560])).
% 2.95/2.18 tff(2562,plain,
% 2.95/2.18 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.95/2.18 inference(rewrite,[status(thm)],[])).
% 2.95/2.18 tff(2563,plain,
% 2.95/2.18 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 2.95/2.18 inference(bind,[status(th)],[])).
% 2.95/2.18 tff(2564,plain,
% 2.95/2.18 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.95/2.18 inference(quant_intro,[status(thm)],[2563])).
% 2.95/2.18 tff(2565,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause275')).
% 2.95/2.18 tff(2566,plain,
% 2.95/2.18 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.95/2.18 inference(modus_ponens,[status(thm)],[2565, 2564])).
% 2.95/2.18 tff(2567,plain,
% 2.95/2.18 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.95/2.18 inference(modus_ponens,[status(thm)],[2566, 2562])).
% 2.95/2.18 tff(2568,plain,(
% 2.95/2.18 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.95/2.18 inference(skolemize,[status(sab)],[2567])).
% 2.95/2.18 tff(2569,plain,
% 2.95/2.18 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.95/2.18 inference(modus_ponens,[status(thm)],[2568, 2561])).
% 2.95/2.18 tff(2570,assumption,(hskp56), introduced(assumption)).
% 2.95/2.18 tff(2571,plain,
% 2.95/2.18 (~c3_1(a2242)),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[2386, 2570])).
% 2.95/2.18 tff(2572,plain,
% 2.95/2.18 (c2_1(a2242)),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[2350, 2570])).
% 2.95/2.18 tff(2573,plain,
% 2.95/2.18 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp10 | c3_1(a2242) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2242)) | (~c2_1(a2242)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp10 | c3_1(a2242) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 2.95/2.18 inference(rewrite,[status(thm)],[])).
% 2.95/2.18 tff(2574,plain,
% 2.95/2.18 ((hskp10 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242))) <=> (hskp10 | c3_1(a2242) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 2.95/2.18 inference(rewrite,[status(thm)],[])).
% 2.95/2.18 tff(2575,plain,
% 2.95/2.18 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp10 | c3_1(a2242) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2242)) | (~c2_1(a2242))))),
% 2.95/2.18 inference(monotonicity,[status(thm)],[2574])).
% 2.95/2.18 tff(2576,plain,
% 2.95/2.18 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp10 | c3_1(a2242) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 2.95/2.18 inference(transitivity,[status(thm)],[2575, 2573])).
% 2.95/2.18 tff(2577,plain,
% 2.95/2.18 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 2.95/2.18 inference(quant_inst,[status(thm)],[])).
% 2.95/2.18 tff(2578,plain,
% 2.95/2.18 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp10 | c3_1(a2242) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2242)) | (~c2_1(a2242))),
% 2.95/2.18 inference(modus_ponens,[status(thm)],[2577, 2576])).
% 2.95/2.18 tff(2579,plain,
% 2.95/2.18 (~c0_1(a2242)),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[2578, 159, 1904, 2572, 2288, 2571, 2289, 2569, 2290])).
% 2.95/2.18 tff(2580,plain,
% 2.95/2.18 (~c1_1(a2242)),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[2339, 2570])).
% 2.95/2.18 tff(2581,plain,
% 2.95/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c1_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | (~c2_1(a2242)) | (~c0_1(a2252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | (~c2_1(a2242)) | (~c0_1(a2252)))),
% 2.95/2.18 inference(rewrite,[status(thm)],[])).
% 2.95/2.18 tff(2582,plain,
% 2.95/2.18 (((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | c1_1(a2242) | (~c2_1(a2242))) <=> (c2_1(a2252) | c1_1(a2252) | c1_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | (~c2_1(a2242)) | (~c0_1(a2252)))),
% 2.95/2.18 inference(rewrite,[status(thm)],[])).
% 2.95/2.18 tff(2583,plain,
% 2.95/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | c1_1(a2242) | (~c2_1(a2242)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c1_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | (~c2_1(a2242)) | (~c0_1(a2252))))),
% 2.95/2.18 inference(monotonicity,[status(thm)],[2582])).
% 2.95/2.18 tff(2584,plain,
% 2.95/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | c1_1(a2242) | (~c2_1(a2242)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | (~c2_1(a2242)) | (~c0_1(a2252)))),
% 2.95/2.18 inference(transitivity,[status(thm)],[2583, 2581])).
% 2.95/2.18 tff(2585,plain,
% 2.95/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | c1_1(a2242) | (~c2_1(a2242)))),
% 2.95/2.18 inference(quant_inst,[status(thm)],[])).
% 2.95/2.18 tff(2586,plain,
% 2.95/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | (~c2_1(a2242)) | (~c0_1(a2252))),
% 2.95/2.18 inference(modus_ponens,[status(thm)],[2585, 2584])).
% 2.95/2.18 tff(2587,plain,
% 2.95/2.18 ($false),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[2586, 159, 2327, 2572, 2481, 2480, 2299, 2298, 2580, 2479, 10, 2579])).
% 2.95/2.18 tff(2588,plain,((~hskp56) | (~c2_1(a2204)) | (~c3_1(a2204)) | c1_1(a2204) | hskp10), inference(lemma,lemma(discharge,[]))).
% 2.95/2.18 tff(2589,plain,
% 2.95/2.18 (hskp10),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[2588, 2559, 2557, 2556, 2555])).
% 2.95/2.18 tff(2590,plain,
% 2.95/2.18 (~c3_1(a2206)),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[1652, 2589])).
% 2.95/2.18 tff(2591,plain,
% 2.95/2.18 (~c0_1(a2206)),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[1671, 2589])).
% 2.95/2.18 tff(2592,plain,
% 2.95/2.18 (~c2_1(a2206)),
% 2.95/2.18 inference(unit_resolution,[status(thm)],[1658, 2589])).
% 2.95/2.19 tff(2593,plain,
% 2.95/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | (c2_1(a2252) | c1_1(a2252) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c3_1(a2222)) | (~c0_1(a2222)) | c3_1(a2252))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | c2_1(a2252) | c1_1(a2252) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c3_1(a2222)) | (~c0_1(a2222)) | c3_1(a2252))),
% 2.95/2.19 inference(rewrite,[status(thm)],[])).
% 2.95/2.19 tff(2594,plain,
% 2.95/2.19 (((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c1_1(a2252) | c3_1(a2252) | c2_1(a2252) | c0_1(a2206) | c2_1(a2206) | c3_1(a2206)) <=> (c2_1(a2252) | c1_1(a2252) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c3_1(a2222)) | (~c0_1(a2222)) | c3_1(a2252))),
% 2.95/2.19 inference(rewrite,[status(thm)],[])).
% 2.95/2.19 tff(2595,plain,
% 2.95/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c1_1(a2252) | c3_1(a2252) | c2_1(a2252) | c0_1(a2206) | c2_1(a2206) | c3_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | (c2_1(a2252) | c1_1(a2252) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c3_1(a2222)) | (~c0_1(a2222)) | c3_1(a2252)))),
% 2.95/2.19 inference(monotonicity,[status(thm)],[2594])).
% 2.95/2.19 tff(2596,plain,
% 2.95/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c1_1(a2252) | c3_1(a2252) | c2_1(a2252) | c0_1(a2206) | c2_1(a2206) | c3_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | c2_1(a2252) | c1_1(a2252) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c3_1(a2222)) | (~c0_1(a2222)) | c3_1(a2252))),
% 2.95/2.19 inference(transitivity,[status(thm)],[2595, 2593])).
% 2.95/2.19 tff(2597,plain,
% 2.95/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c1_1(a2252) | c3_1(a2252) | c2_1(a2252) | c0_1(a2206) | c2_1(a2206) | c3_1(a2206))),
% 2.95/2.19 inference(quant_inst,[status(thm)],[])).
% 2.95/2.19 tff(2598,plain,
% 2.95/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | c2_1(a2252) | c1_1(a2252) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c3_1(a2222)) | (~c0_1(a2222)) | c3_1(a2252)),
% 2.95/2.19 inference(modus_ponens,[status(thm)],[2597, 2596])).
% 2.95/2.19 tff(2599,plain,
% 2.95/2.19 ($false),
% 2.95/2.19 inference(unit_resolution,[status(thm)],[2598, 159, 2287, 2288, 2299, 2298, 2289, 2592, 2591, 2590, 2546, 2536])).
% 2.95/2.19 % SZS output end Proof
%------------------------------------------------------------------------------