TSTP Solution File: SYN486-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN486-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 23:55:51 EDT 2022
% Result : Unsatisfiable 1.35s 1.13s
% Output : Proof 1.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SYN486-1 : TPTP v8.1.0. Released v2.1.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 04:41:37 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.
% 1.35/1.13 % SZS status Unsatisfiable
% 1.35/1.13 % SZS output start Proof
% 1.35/1.13 tff(c2_1_type, type, (
% 1.35/1.13 c2_1: $i > $o)).
% 1.35/1.13 tff(a2186_type, type, (
% 1.35/1.13 a2186: $i)).
% 1.35/1.13 tff(c0_1_type, type, (
% 1.35/1.13 c0_1: $i > $o)).
% 1.35/1.13 tff(a2195_type, type, (
% 1.35/1.13 a2195: $i)).
% 1.35/1.13 tff(c1_1_type, type, (
% 1.35/1.13 c1_1: $i > $o)).
% 1.35/1.13 tff(c3_1_type, type, (
% 1.35/1.13 c3_1: $i > $o)).
% 1.35/1.13 tff(ndr1_0_type, type, (
% 1.35/1.13 ndr1_0: $o)).
% 1.35/1.13 tff(hskp0_type, type, (
% 1.35/1.13 hskp0: $o)).
% 1.35/1.13 tff(hskp16_type, type, (
% 1.35/1.13 hskp16: $o)).
% 1.35/1.13 tff(a2179_type, type, (
% 1.35/1.13 a2179: $i)).
% 1.35/1.13 tff(a2197_type, type, (
% 1.35/1.13 a2197: $i)).
% 1.35/1.13 tff(hskp21_type, type, (
% 1.35/1.13 hskp21: $o)).
% 1.35/1.13 tff(a2216_type, type, (
% 1.35/1.13 a2216: $i)).
% 1.35/1.13 tff(hskp18_type, type, (
% 1.35/1.13 hskp18: $o)).
% 1.35/1.13 tff(a2198_type, type, (
% 1.35/1.13 a2198: $i)).
% 1.35/1.13 tff(hskp17_type, type, (
% 1.35/1.13 hskp17: $o)).
% 1.35/1.13 tff(hskp26_type, type, (
% 1.35/1.13 hskp26: $o)).
% 1.35/1.13 tff(hskp24_type, type, (
% 1.35/1.13 hskp24: $o)).
% 1.35/1.13 tff(a2174_type, type, (
% 1.35/1.13 a2174: $i)).
% 1.35/1.13 tff(a2188_type, type, (
% 1.35/1.13 a2188: $i)).
% 1.35/1.13 tff(a2177_type, type, (
% 1.35/1.13 a2177: $i)).
% 1.35/1.13 tff(hskp3_type, type, (
% 1.35/1.13 hskp3: $o)).
% 1.35/1.13 tff(hskp13_type, type, (
% 1.35/1.13 hskp13: $o)).
% 1.35/1.13 tff(a2194_type, type, (
% 1.35/1.13 a2194: $i)).
% 1.35/1.13 tff(hskp10_type, type, (
% 1.35/1.13 hskp10: $o)).
% 1.35/1.13 tff(a2187_type, type, (
% 1.35/1.13 a2187: $i)).
% 1.35/1.13 tff(hskp11_type, type, (
% 1.35/1.13 hskp11: $o)).
% 1.35/1.13 tff(a2191_type, type, (
% 1.35/1.13 a2191: $i)).
% 1.35/1.13 tff(a2176_type, type, (
% 1.35/1.13 a2176: $i)).
% 1.35/1.13 tff(hskp7_type, type, (
% 1.35/1.13 hskp7: $o)).
% 1.35/1.13 tff(hskp28_type, type, (
% 1.35/1.13 hskp28: $o)).
% 1.35/1.13 tff(a2178_type, type, (
% 1.35/1.13 a2178: $i)).
% 1.35/1.13 tff(hskp27_type, type, (
% 1.35/1.13 hskp27: $o)).
% 1.35/1.13 tff(hskp22_type, type, (
% 1.35/1.13 hskp22: $o)).
% 1.35/1.13 tff(a2219_type, type, (
% 1.35/1.13 a2219: $i)).
% 1.35/1.13 tff(hskp15_type, type, (
% 1.35/1.13 hskp15: $o)).
% 1.35/1.13 tff(a2175_type, type, (
% 1.35/1.13 a2175: $i)).
% 1.35/1.13 tff(hskp1_type, type, (
% 1.35/1.13 hskp1: $o)).
% 1.35/1.13 tff(hskp30_type, type, (
% 1.35/1.13 hskp30: $o)).
% 1.35/1.13 tff(a2208_type, type, (
% 1.35/1.13 a2208: $i)).
% 1.35/1.13 tff(a2182_type, type, (
% 1.35/1.13 a2182: $i)).
% 1.35/1.13 tff(a2265_type, type, (
% 1.35/1.13 a2265: $i)).
% 1.35/1.13 tff(hskp25_type, type, (
% 1.35/1.13 hskp25: $o)).
% 1.35/1.13 tff(a2193_type, type, (
% 1.35/1.13 a2193: $i)).
% 1.35/1.13 tff(a2211_type, type, (
% 1.35/1.13 a2211: $i)).
% 1.35/1.13 tff(hskp19_type, type, (
% 1.35/1.13 hskp19: $o)).
% 1.35/1.13 tff(hskp14_type, type, (
% 1.35/1.13 hskp14: $o)).
% 1.35/1.13 tff(hskp9_type, type, (
% 1.35/1.13 hskp9: $o)).
% 1.35/1.13 tff(a2185_type, type, (
% 1.35/1.13 a2185: $i)).
% 1.35/1.13 tff(hskp2_type, type, (
% 1.35/1.13 hskp2: $o)).
% 1.35/1.13 tff(a2262_type, type, (
% 1.35/1.13 a2262: $i)).
% 1.35/1.13 tff(a2268_type, type, (
% 1.35/1.13 a2268: $i)).
% 1.35/1.13 tff(a2196_type, type, (
% 1.35/1.13 a2196: $i)).
% 1.35/1.13 tff(hskp29_type, type, (
% 1.35/1.13 hskp29: $o)).
% 1.35/1.13 tff(hskp4_type, type, (
% 1.35/1.13 hskp4: $o)).
% 1.35/1.13 tff(1,plain,
% 1.35/1.13 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.35/1.13 inference(bind,[status(th)],[])).
% 1.35/1.13 tff(2,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.13 inference(quant_intro,[status(thm)],[1])).
% 1.35/1.13 tff(3,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(4,plain,
% 1.35/1.13 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.35/1.13 inference(bind,[status(th)],[])).
% 1.35/1.13 tff(5,plain,
% 1.35/1.13 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.13 inference(quant_intro,[status(thm)],[4])).
% 1.35/1.13 tff(6,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.35/1.13 tff(7,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.35/1.13 tff(8,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.35/1.13 tff(9,plain,(
% 1.35/1.13 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.13 inference(skolemize,[status(sab)],[8])).
% 1.35/1.13 tff(10,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.35/1.13 tff(11,assumption,(~hskp16), introduced(assumption)).
% 1.35/1.13 tff(12,plain,
% 1.35/1.13 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.35/1.13 inference(bind,[status(th)],[])).
% 1.35/1.13 tff(13,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.35/1.13 inference(quant_intro,[status(thm)],[12])).
% 1.35/1.13 tff(14,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(15,plain,
% 1.35/1.13 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp18) <=> (((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.35/1.13 inference(bind,[status(th)],[])).
% 1.35/1.13 tff(16,plain,
% 1.35/1.13 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.35/1.13 inference(quant_intro,[status(thm)],[15])).
% 1.35/1.13 tff(17,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.35/1.13 tff(18,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.35/1.13 tff(19,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.35/1.13 tff(20,plain,(
% 1.35/1.13 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.35/1.13 inference(skolemize,[status(sab)],[19])).
% 1.35/1.13 tff(21,plain,
% 1.35/1.13 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.35/1.13 tff(22,assumption,(hskp21), introduced(assumption)).
% 1.35/1.13 tff(23,plain,
% 1.35/1.13 (((~hskp21) | (~c3_1(a2216))) <=> ((~hskp21) | (~c3_1(a2216)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(24,plain,
% 1.35/1.13 (((~c3_1(a2216)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a2216)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(25,axiom,((~c3_1(a2216)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.35/1.13 tff(26,plain,
% 1.35/1.13 ((~hskp21) | (~c3_1(a2216))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.35/1.13 tff(27,plain,
% 1.35/1.13 ((~hskp21) | (~c3_1(a2216))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[26, 23])).
% 1.35/1.13 tff(28,plain,
% 1.35/1.13 (~c3_1(a2216)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[27, 22])).
% 1.35/1.13 tff(29,plain,
% 1.35/1.13 (((~hskp21) | (~c2_1(a2216))) <=> ((~hskp21) | (~c2_1(a2216)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(30,plain,
% 1.35/1.13 (((~c2_1(a2216)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a2216)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(31,axiom,((~c2_1(a2216)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.35/1.13 tff(32,plain,
% 1.35/1.13 ((~hskp21) | (~c2_1(a2216))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.35/1.13 tff(33,plain,
% 1.35/1.13 ((~hskp21) | (~c2_1(a2216))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[32, 29])).
% 1.35/1.13 tff(34,plain,
% 1.35/1.13 (~c2_1(a2216)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[33, 22])).
% 1.35/1.13 tff(35,plain,
% 1.35/1.13 (((~hskp21) | c0_1(a2216)) <=> ((~hskp21) | c0_1(a2216))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(36,axiom,((~hskp21) | c0_1(a2216)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.35/1.13 tff(37,plain,
% 1.35/1.13 ((~hskp21) | c0_1(a2216)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.35/1.13 tff(38,plain,
% 1.35/1.13 ((~hskp21) | c0_1(a2216)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[37, 35])).
% 1.35/1.13 tff(39,plain,
% 1.35/1.13 ((~hskp21) | c0_1(a2216)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[38, 35])).
% 1.35/1.13 tff(40,plain,
% 1.35/1.13 ((~hskp21) | c0_1(a2216)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[39, 35])).
% 1.35/1.13 tff(41,plain,
% 1.35/1.13 ((~hskp21) | c0_1(a2216)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[40, 35])).
% 1.35/1.13 tff(42,plain,
% 1.35/1.13 ((~hskp21) | c0_1(a2216)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[41, 35])).
% 1.35/1.13 tff(43,plain,
% 1.35/1.13 ((~hskp21) | c0_1(a2216)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[42, 35])).
% 1.35/1.13 tff(44,plain,
% 1.35/1.13 ((~hskp21) | c0_1(a2216)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[43, 35])).
% 1.35/1.13 tff(45,plain,
% 1.35/1.13 (c0_1(a2216)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[44, 22])).
% 1.35/1.13 tff(46,plain,
% 1.35/1.13 (^[U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.35/1.13 inference(bind,[status(th)],[])).
% 1.35/1.13 tff(47,plain,
% 1.35/1.13 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.13 inference(quant_intro,[status(thm)],[46])).
% 1.35/1.13 tff(48,plain,
% 1.35/1.13 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(49,plain,
% 1.35/1.13 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.35/1.13 inference(bind,[status(th)],[])).
% 1.35/1.13 tff(50,plain,
% 1.35/1.13 (![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.13 inference(quant_intro,[status(thm)],[49])).
% 1.35/1.13 tff(51,axiom,(![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.35/1.13 tff(52,plain,
% 1.35/1.13 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.35/1.13 tff(53,plain,
% 1.35/1.13 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.35/1.13 tff(54,plain,(
% 1.35/1.13 ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.13 inference(skolemize,[status(sab)],[53])).
% 1.35/1.13 tff(55,plain,
% 1.35/1.13 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[54, 47])).
% 1.35/1.13 tff(56,assumption,(hskp18), introduced(assumption)).
% 1.35/1.13 tff(57,plain,
% 1.35/1.13 (((~hskp18) | (~c2_1(a2198))) <=> ((~hskp18) | (~c2_1(a2198)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(58,plain,
% 1.35/1.13 (((~c2_1(a2198)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a2198)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(59,axiom,((~c2_1(a2198)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.35/1.13 tff(60,plain,
% 1.35/1.13 ((~hskp18) | (~c2_1(a2198))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.35/1.13 tff(61,plain,
% 1.35/1.13 ((~hskp18) | (~c2_1(a2198))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[60, 57])).
% 1.35/1.13 tff(62,plain,
% 1.35/1.13 (~c2_1(a2198)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[61, 56])).
% 1.35/1.13 tff(63,plain,
% 1.35/1.13 (((~hskp18) | (~c1_1(a2198))) <=> ((~hskp18) | (~c1_1(a2198)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(64,plain,
% 1.35/1.13 (((~c1_1(a2198)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a2198)))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(65,axiom,((~c1_1(a2198)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.35/1.13 tff(66,plain,
% 1.35/1.13 ((~hskp18) | (~c1_1(a2198))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.35/1.13 tff(67,plain,
% 1.35/1.13 ((~hskp18) | (~c1_1(a2198))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[66, 63])).
% 1.35/1.13 tff(68,plain,
% 1.35/1.13 (~c1_1(a2198)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[67, 56])).
% 1.35/1.13 tff(69,plain,
% 1.35/1.13 (((~hskp18) | c0_1(a2198)) <=> ((~hskp18) | c0_1(a2198))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(70,axiom,((~hskp18) | c0_1(a2198)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.35/1.13 tff(71,plain,
% 1.35/1.13 ((~hskp18) | c0_1(a2198)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.35/1.13 tff(72,plain,
% 1.35/1.13 ((~hskp18) | c0_1(a2198)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[71, 69])).
% 1.35/1.13 tff(73,plain,
% 1.35/1.13 ((~hskp18) | c0_1(a2198)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[72, 69])).
% 1.35/1.13 tff(74,plain,
% 1.35/1.13 ((~hskp18) | c0_1(a2198)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[73, 69])).
% 1.35/1.13 tff(75,plain,
% 1.35/1.13 ((~hskp18) | c0_1(a2198)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[74, 69])).
% 1.35/1.13 tff(76,plain,
% 1.35/1.13 ((~hskp18) | c0_1(a2198)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[75, 69])).
% 1.35/1.13 tff(77,plain,
% 1.35/1.13 ((~hskp18) | c0_1(a2198)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[76, 69])).
% 1.35/1.13 tff(78,plain,
% 1.35/1.13 ((~hskp18) | c0_1(a2198)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[77, 69])).
% 1.35/1.13 tff(79,plain,
% 1.35/1.13 (c0_1(a2198)),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[78, 56])).
% 1.35/1.13 tff(80,assumption,(~ndr1_0), introduced(assumption)).
% 1.35/1.13 tff(81,plain,
% 1.35/1.13 ((ndr1_0 | (~hskp17)) <=> (ndr1_0 | (~hskp17))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(82,plain,
% 1.35/1.13 (((~hskp17) | ndr1_0) <=> (ndr1_0 | (~hskp17))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(83,axiom,((~hskp17) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause14')).
% 1.35/1.13 tff(84,plain,
% 1.35/1.13 (ndr1_0 | (~hskp17)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.35/1.13 tff(85,plain,
% 1.35/1.13 (ndr1_0 | (~hskp17)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[84, 81])).
% 1.35/1.13 tff(86,plain,
% 1.35/1.13 (~hskp17),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[85, 80])).
% 1.35/1.13 tff(87,plain,
% 1.35/1.13 ((ndr1_0 | (~hskp26)) <=> (ndr1_0 | (~hskp26))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(88,plain,
% 1.35/1.13 (((~hskp26) | ndr1_0) <=> (ndr1_0 | (~hskp26))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(89,axiom,((~hskp26) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 1.35/1.13 tff(90,plain,
% 1.35/1.13 (ndr1_0 | (~hskp26)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.35/1.13 tff(91,plain,
% 1.35/1.13 (ndr1_0 | (~hskp26)),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[90, 87])).
% 1.35/1.13 tff(92,plain,
% 1.35/1.13 (~hskp26),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[91, 80])).
% 1.35/1.14 tff(93,plain,
% 1.35/1.14 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(94,plain,
% 1.35/1.14 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(95,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 1.35/1.14 tff(96,plain,
% 1.35/1.14 (ndr1_0 | (~hskp24)),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.35/1.14 tff(97,plain,
% 1.35/1.14 (ndr1_0 | (~hskp24)),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[96, 93])).
% 1.35/1.14 tff(98,plain,
% 1.35/1.14 (~hskp24),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[97, 80])).
% 1.35/1.14 tff(99,plain,
% 1.35/1.14 ((hskp26 | hskp24 | hskp17) <=> (hskp26 | hskp24 | hskp17)),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(100,plain,
% 1.35/1.14 (((hskp24 | hskp26) | hskp17) <=> (hskp26 | hskp24 | hskp17)),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(101,axiom,((hskp24 | hskp26) | hskp17), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 1.35/1.14 tff(102,plain,
% 1.35/1.14 (hskp26 | hskp24 | hskp17),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[101, 100])).
% 1.35/1.14 tff(103,plain,
% 1.35/1.14 (hskp26 | hskp24 | hskp17),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[102, 99])).
% 1.35/1.14 tff(104,plain,
% 1.35/1.14 (hskp26 | hskp24 | hskp17),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[103, 99])).
% 1.35/1.14 tff(105,plain,
% 1.35/1.14 (hskp26 | hskp24 | hskp17),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[104, 99])).
% 1.35/1.14 tff(106,plain,
% 1.35/1.14 (hskp26 | hskp24 | hskp17),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[105, 99])).
% 1.35/1.14 tff(107,plain,
% 1.35/1.14 (hskp26 | hskp24 | hskp17),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[106, 99])).
% 1.35/1.14 tff(108,plain,
% 1.35/1.14 (hskp26 | hskp24 | hskp17),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[107, 99])).
% 1.35/1.14 tff(109,plain,
% 1.35/1.14 (hskp26 | hskp24 | hskp17),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[108, 99])).
% 1.35/1.14 tff(110,plain,
% 1.35/1.14 ($false),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[109, 98, 92, 86])).
% 1.35/1.14 tff(111,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.35/1.14 tff(112,plain,
% 1.35/1.14 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2198)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2198)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(113,plain,
% 1.35/1.14 ((hskp16 | (~ndr1_0) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198))) <=> (hskp16 | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2198)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(114,plain,
% 1.35/1.14 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2198))))),
% 1.35/1.14 inference(monotonicity,[status(thm)],[113])).
% 1.35/1.14 tff(115,plain,
% 1.35/1.14 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2198)))),
% 1.35/1.14 inference(transitivity,[status(thm)],[114, 112])).
% 1.35/1.14 tff(116,plain,
% 1.35/1.14 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)))),
% 1.35/1.14 inference(quant_inst,[status(thm)],[])).
% 1.35/1.14 tff(117,plain,
% 1.35/1.14 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2198))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[116, 115])).
% 1.35/1.14 tff(118,plain,
% 1.35/1.14 ($false),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[117, 111, 11, 79, 68, 62, 55])).
% 1.35/1.14 tff(119,plain,((~hskp18) | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.35/1.14 tff(120,plain,
% 1.35/1.14 (~hskp18),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[119, 11])).
% 1.35/1.14 tff(121,plain,
% 1.35/1.14 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp18 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(122,plain,
% 1.35/1.14 ((hskp18 | (~ndr1_0) | (~c0_1(a2216)) | c3_1(a2216) | (~c1_1(a2216)) | c2_1(a2216) | (~c1_1(a2216)) | (~c0_1(a2216))) <=> (hskp18 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(123,plain,
% 1.35/1.14 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2216)) | c3_1(a2216) | (~c1_1(a2216)) | c2_1(a2216) | (~c1_1(a2216)) | (~c0_1(a2216)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp18 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216))))),
% 1.35/1.14 inference(monotonicity,[status(thm)],[122])).
% 1.35/1.14 tff(124,plain,
% 1.35/1.14 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2216)) | c3_1(a2216) | (~c1_1(a2216)) | c2_1(a2216) | (~c1_1(a2216)) | (~c0_1(a2216)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 1.35/1.14 inference(transitivity,[status(thm)],[123, 121])).
% 1.35/1.14 tff(125,plain,
% 1.35/1.14 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2216)) | c3_1(a2216) | (~c1_1(a2216)) | c2_1(a2216) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 1.35/1.14 inference(quant_inst,[status(thm)],[])).
% 1.35/1.14 tff(126,plain,
% 1.35/1.14 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.35/1.14 tff(127,plain,
% 1.35/1.14 (~c1_1(a2216)),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[126, 111, 120, 45, 34, 28, 21])).
% 1.35/1.14 tff(128,plain,
% 1.35/1.14 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c2_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(129,plain,
% 1.35/1.14 ((hskp16 | (~ndr1_0) | c2_1(a2216) | c1_1(a2216) | (~c0_1(a2216))) <=> (hskp16 | c2_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(130,plain,
% 1.35/1.14 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2216) | c1_1(a2216) | (~c0_1(a2216)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c2_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216))))),
% 1.35/1.14 inference(monotonicity,[status(thm)],[129])).
% 1.35/1.14 tff(131,plain,
% 1.35/1.14 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2216) | c1_1(a2216) | (~c0_1(a2216)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 1.35/1.14 inference(transitivity,[status(thm)],[130, 128])).
% 1.35/1.14 tff(132,plain,
% 1.35/1.14 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2216) | c1_1(a2216) | (~c0_1(a2216)))),
% 1.35/1.14 inference(quant_inst,[status(thm)],[])).
% 1.35/1.14 tff(133,plain,
% 1.35/1.14 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[132, 131])).
% 1.35/1.14 tff(134,plain,
% 1.35/1.14 ($false),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[133, 111, 11, 45, 34, 55, 127])).
% 1.35/1.14 tff(135,plain,((~hskp21) | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.35/1.14 tff(136,plain,
% 1.35/1.14 (~hskp21),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[135, 11])).
% 1.35/1.14 tff(137,plain,
% 1.35/1.14 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(138,plain,
% 1.35/1.14 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[137])).
% 1.35/1.14 tff(139,plain,
% 1.35/1.14 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(140,plain,
% 1.35/1.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp21) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(141,plain,
% 1.35/1.14 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[140])).
% 1.35/1.14 tff(142,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.35/1.14 tff(143,plain,
% 1.35/1.14 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[142, 141])).
% 1.35/1.14 tff(144,plain,
% 1.35/1.14 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[143, 139])).
% 1.35/1.14 tff(145,plain,(
% 1.35/1.14 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.14 inference(skolemize,[status(sab)],[144])).
% 1.35/1.14 tff(146,plain,
% 1.35/1.14 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[145, 138])).
% 1.35/1.14 tff(147,assumption,(~c0_1(a2174)), introduced(assumption)).
% 1.35/1.14 tff(148,plain,
% 1.35/1.14 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(149,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[148])).
% 1.35/1.14 tff(150,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(151,plain,
% 1.35/1.14 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W))), ((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W)))), (((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W) | c2_1(W))), (((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W) | c2_1(W)))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), ((((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(152,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[151])).
% 1.35/1.14 tff(153,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 1.35/1.14 tff(154,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.35/1.14 tff(155,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[154, 150])).
% 1.35/1.14 tff(156,plain,(
% 1.35/1.14 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(skolemize,[status(sab)],[155])).
% 1.35/1.14 tff(157,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[156, 149])).
% 1.35/1.14 tff(158,assumption,(hskp17), introduced(assumption)).
% 1.35/1.14 tff(159,plain,
% 1.35/1.14 (((~hskp17) | (~c1_1(a2197))) <=> ((~hskp17) | (~c1_1(a2197)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(160,plain,
% 1.35/1.14 (((~c1_1(a2197)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a2197)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(161,axiom,((~c1_1(a2197)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.35/1.14 tff(162,plain,
% 1.35/1.14 ((~hskp17) | (~c1_1(a2197))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.35/1.14 tff(163,plain,
% 1.35/1.14 ((~hskp17) | (~c1_1(a2197))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[162, 159])).
% 1.35/1.14 tff(164,plain,
% 1.35/1.14 (~c1_1(a2197)),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[163, 158])).
% 1.35/1.14 tff(165,plain,
% 1.35/1.14 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(166,plain,
% 1.35/1.14 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[165])).
% 1.35/1.14 tff(167,plain,
% 1.35/1.14 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(168,plain,
% 1.35/1.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(169,plain,
% 1.35/1.14 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[168])).
% 1.35/1.14 tff(170,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 1.35/1.14 tff(171,plain,
% 1.35/1.14 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.35/1.14 tff(172,plain,
% 1.35/1.14 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[171, 167])).
% 1.35/1.14 tff(173,plain,(
% 1.35/1.14 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.35/1.14 inference(skolemize,[status(sab)],[172])).
% 1.35/1.14 tff(174,plain,
% 1.35/1.14 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[173, 166])).
% 1.35/1.14 tff(175,plain,
% 1.35/1.14 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(176,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[175])).
% 1.35/1.14 tff(177,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(178,plain,
% 1.35/1.14 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(179,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[178])).
% 1.35/1.14 tff(180,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 1.35/1.14 tff(181,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[180, 179])).
% 1.35/1.14 tff(182,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[181, 177])).
% 1.35/1.14 tff(183,plain,(
% 1.35/1.14 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(skolemize,[status(sab)],[182])).
% 1.35/1.14 tff(184,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[183, 176])).
% 1.35/1.14 tff(185,assumption,(~hskp10), introduced(assumption)).
% 1.35/1.14 tff(186,assumption,(~c3_1(a2191)), introduced(assumption)).
% 1.35/1.14 tff(187,assumption,(~c1_1(a2191)), introduced(assumption)).
% 1.35/1.14 tff(188,plain,
% 1.35/1.14 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_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) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(189,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_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) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[188])).
% 1.35/1.14 tff(190,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_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) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(191,plain,
% 1.35/1.14 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~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)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | 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)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(192,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[191])).
% 1.35/1.14 tff(193,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.35/1.14 tff(194,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.35/1.14 tff(195,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[194, 190])).
% 1.35/1.14 tff(196,plain,(
% 1.35/1.14 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.14 inference(skolemize,[status(sab)],[195])).
% 1.35/1.14 tff(197,plain,
% 1.35/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[196, 189])).
% 1.35/1.14 tff(198,assumption,(~c0_1(a2191)), introduced(assumption)).
% 1.35/1.14 tff(199,assumption,(~hskp28), introduced(assumption)).
% 1.35/1.14 tff(200,plain,
% 1.35/1.14 (^[U: $i] : refl((hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(201,plain,
% 1.35/1.14 (![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[200])).
% 1.35/1.14 tff(202,plain,
% 1.35/1.14 (![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(203,plain,
% 1.35/1.14 (^[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)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp22) <=> ((hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp22))), rewrite(((hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp22) <=> (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp22) <=> (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 1.35/1.14 inference(bind,[status(th)],[])).
% 1.35/1.14 tff(204,plain,
% 1.35/1.14 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp22) <=> ![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.35/1.14 inference(quant_intro,[status(thm)],[203])).
% 1.35/1.14 tff(205,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.35/1.15 tff(206,plain,
% 1.35/1.15 (![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[205, 204])).
% 1.35/1.15 tff(207,plain,
% 1.35/1.15 (![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[206, 202])).
% 1.35/1.15 tff(208,plain,(
% 1.35/1.15 ![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.35/1.15 inference(skolemize,[status(sab)],[207])).
% 1.35/1.15 tff(209,plain,
% 1.35/1.15 (![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[208, 201])).
% 1.35/1.15 tff(210,assumption,(~c1_1(a2219)), introduced(assumption)).
% 1.35/1.15 tff(211,assumption,(~c2_1(a2219)), introduced(assumption)).
% 1.35/1.15 tff(212,assumption,(~c3_1(a2219)), introduced(assumption)).
% 1.35/1.15 tff(213,assumption,(hskp11), introduced(assumption)).
% 1.35/1.15 tff(214,plain,
% 1.35/1.15 (((~hskp11) | (~c1_1(a2187))) <=> ((~hskp11) | (~c1_1(a2187)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(215,plain,
% 1.35/1.15 (((~c1_1(a2187)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a2187)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(216,axiom,((~c1_1(a2187)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.35/1.15 tff(217,plain,
% 1.35/1.15 ((~hskp11) | (~c1_1(a2187))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[216, 215])).
% 1.35/1.15 tff(218,plain,
% 1.35/1.15 ((~hskp11) | (~c1_1(a2187))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[217, 214])).
% 1.35/1.15 tff(219,plain,
% 1.35/1.15 (~c1_1(a2187)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[218, 213])).
% 1.35/1.15 tff(220,plain,
% 1.35/1.15 (((~hskp11) | c2_1(a2187)) <=> ((~hskp11) | c2_1(a2187))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(221,axiom,((~hskp11) | c2_1(a2187)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.35/1.15 tff(222,plain,
% 1.35/1.15 ((~hskp11) | c2_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[221, 220])).
% 1.35/1.15 tff(223,plain,
% 1.35/1.15 ((~hskp11) | c2_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[222, 220])).
% 1.35/1.15 tff(224,plain,
% 1.35/1.15 ((~hskp11) | c2_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[223, 220])).
% 1.35/1.15 tff(225,plain,
% 1.35/1.15 ((~hskp11) | c2_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[224, 220])).
% 1.35/1.15 tff(226,plain,
% 1.35/1.15 ((~hskp11) | c2_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[225, 220])).
% 1.35/1.15 tff(227,plain,
% 1.35/1.15 ((~hskp11) | c2_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[226, 220])).
% 1.35/1.15 tff(228,plain,
% 1.35/1.15 ((~hskp11) | c2_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[227, 220])).
% 1.35/1.15 tff(229,plain,
% 1.35/1.15 ((~hskp11) | c2_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[228, 220])).
% 1.35/1.15 tff(230,plain,
% 1.35/1.15 (c2_1(a2187)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[229, 213])).
% 1.35/1.15 tff(231,plain,
% 1.35/1.15 (((~hskp11) | c0_1(a2187)) <=> ((~hskp11) | c0_1(a2187))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(232,axiom,((~hskp11) | c0_1(a2187)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.35/1.15 tff(233,plain,
% 1.35/1.15 ((~hskp11) | c0_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[232, 231])).
% 1.35/1.15 tff(234,plain,
% 1.35/1.15 ((~hskp11) | c0_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[233, 231])).
% 1.35/1.15 tff(235,plain,
% 1.35/1.15 ((~hskp11) | c0_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[234, 231])).
% 1.35/1.15 tff(236,plain,
% 1.35/1.15 ((~hskp11) | c0_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[235, 231])).
% 1.35/1.15 tff(237,plain,
% 1.35/1.15 ((~hskp11) | c0_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[236, 231])).
% 1.35/1.15 tff(238,plain,
% 1.35/1.15 ((~hskp11) | c0_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[237, 231])).
% 1.35/1.15 tff(239,plain,
% 1.35/1.15 ((~hskp11) | c0_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[238, 231])).
% 1.35/1.15 tff(240,plain,
% 1.35/1.15 ((~hskp11) | c0_1(a2187)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[239, 231])).
% 1.35/1.15 tff(241,plain,
% 1.35/1.15 (c0_1(a2187)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[240, 213])).
% 1.35/1.15 tff(242,plain,
% 1.35/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(243,plain,
% 1.35/1.15 (((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191)) <=> (c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(244,plain,
% 1.35/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187))))),
% 1.35/1.15 inference(monotonicity,[status(thm)],[243])).
% 1.35/1.15 tff(245,plain,
% 1.35/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 1.35/1.15 inference(transitivity,[status(thm)],[244, 242])).
% 1.35/1.15 tff(246,plain,
% 1.35/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))),
% 1.35/1.15 inference(quant_inst,[status(thm)],[])).
% 1.35/1.15 tff(247,plain,
% 1.35/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[246, 245])).
% 1.35/1.15 tff(248,plain,
% 1.35/1.15 ($false),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[247, 111, 211, 198, 241, 230, 210, 212, 187, 186, 219, 197])).
% 1.35/1.15 tff(249,plain,((~hskp11) | c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.15 tff(250,plain,
% 1.35/1.15 (~hskp11),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[249, 212, 198, 210, 211, 187, 186])).
% 1.35/1.15 tff(251,plain,
% 1.35/1.15 (^[U: $i] : refl((hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) <=> (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(252,plain,
% 1.35/1.15 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[251])).
% 1.35/1.15 tff(253,plain,
% 1.35/1.15 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(254,plain,
% 1.35/1.15 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) | hskp11))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp11) | hskp10) <=> ((hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) | hskp10))), rewrite(((hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) | hskp10) <=> (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp11) | hskp10) <=> (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(255,plain,
% 1.35/1.15 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp11) | hskp10) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[254])).
% 1.35/1.15 tff(256,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp11) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.35/1.15 tff(257,plain,
% 1.35/1.15 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[256, 255])).
% 1.35/1.15 tff(258,plain,
% 1.35/1.15 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[257, 253])).
% 1.35/1.15 tff(259,plain,(
% 1.35/1.15 ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 1.35/1.15 inference(skolemize,[status(sab)],[258])).
% 1.35/1.15 tff(260,plain,
% 1.35/1.15 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[259, 252])).
% 1.35/1.15 tff(261,assumption,(hskp28), introduced(assumption)).
% 1.35/1.15 tff(262,plain,
% 1.35/1.15 (((~hskp28) | c2_1(a2188)) <=> ((~hskp28) | c2_1(a2188))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(263,axiom,((~hskp28) | c2_1(a2188)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 1.35/1.15 tff(264,plain,
% 1.35/1.15 ((~hskp28) | c2_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[263, 262])).
% 1.35/1.15 tff(265,plain,
% 1.35/1.15 ((~hskp28) | c2_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[264, 262])).
% 1.35/1.15 tff(266,plain,
% 1.35/1.15 ((~hskp28) | c2_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[265, 262])).
% 1.35/1.15 tff(267,plain,
% 1.35/1.15 ((~hskp28) | c2_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[266, 262])).
% 1.35/1.15 tff(268,plain,
% 1.35/1.15 ((~hskp28) | c2_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[267, 262])).
% 1.35/1.15 tff(269,plain,
% 1.35/1.15 ((~hskp28) | c2_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[268, 262])).
% 1.35/1.15 tff(270,plain,
% 1.35/1.15 ((~hskp28) | c2_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[269, 262])).
% 1.35/1.15 tff(271,plain,
% 1.35/1.15 ((~hskp28) | c2_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[270, 262])).
% 1.35/1.15 tff(272,plain,
% 1.35/1.15 (c2_1(a2188)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[271, 261])).
% 1.35/1.15 tff(273,plain,
% 1.35/1.15 (((~hskp28) | c0_1(a2188)) <=> ((~hskp28) | c0_1(a2188))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(274,axiom,((~hskp28) | c0_1(a2188)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.35/1.15 tff(275,plain,
% 1.35/1.15 ((~hskp28) | c0_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[274, 273])).
% 1.35/1.15 tff(276,plain,
% 1.35/1.15 ((~hskp28) | c0_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[275, 273])).
% 1.35/1.15 tff(277,plain,
% 1.35/1.15 ((~hskp28) | c0_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[276, 273])).
% 1.35/1.15 tff(278,plain,
% 1.35/1.15 ((~hskp28) | c0_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[277, 273])).
% 1.35/1.15 tff(279,plain,
% 1.35/1.15 ((~hskp28) | c0_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[278, 273])).
% 1.35/1.15 tff(280,plain,
% 1.35/1.15 ((~hskp28) | c0_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[279, 273])).
% 1.35/1.15 tff(281,plain,
% 1.35/1.15 ((~hskp28) | c0_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[280, 273])).
% 1.35/1.15 tff(282,plain,
% 1.35/1.15 ((~hskp28) | c0_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[281, 273])).
% 1.35/1.15 tff(283,plain,
% 1.35/1.15 (c0_1(a2188)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[282, 261])).
% 1.35/1.15 tff(284,assumption,(~hskp11), introduced(assumption)).
% 1.35/1.15 tff(285,plain,
% 1.35/1.15 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | hskp11 | hskp10 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(286,plain,
% 1.35/1.15 ((hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188)) <=> (hskp11 | hskp10 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(287,plain,
% 1.35/1.15 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188)))),
% 1.35/1.15 inference(monotonicity,[status(thm)],[286])).
% 1.35/1.15 tff(288,plain,
% 1.35/1.15 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | hskp11 | hskp10 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188))),
% 1.35/1.15 inference(transitivity,[status(thm)],[287, 285])).
% 1.35/1.15 tff(289,plain,
% 1.35/1.15 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188))),
% 1.35/1.15 inference(quant_inst,[status(thm)],[])).
% 1.35/1.15 tff(290,plain,
% 1.35/1.15 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | hskp11 | hskp10 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188)),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[289, 288])).
% 1.35/1.15 tff(291,plain,
% 1.35/1.15 (c3_1(a2188)),
% 1.35/1.15 inference(unit_resolution,[status(thm)],[290, 111, 284, 185, 283, 272, 260])).
% 1.35/1.15 tff(292,plain,
% 1.35/1.15 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(293,plain,
% 1.35/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[292])).
% 1.35/1.15 tff(294,plain,
% 1.35/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(295,plain,
% 1.35/1.15 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(296,plain,
% 1.35/1.15 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[295])).
% 1.35/1.15 tff(297,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 1.35/1.15 tff(298,plain,
% 1.35/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[297, 296])).
% 1.35/1.15 tff(299,plain,
% 1.35/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[298, 294])).
% 1.35/1.15 tff(300,plain,(
% 1.35/1.15 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(skolemize,[status(sab)],[299])).
% 1.35/1.15 tff(301,plain,
% 1.35/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[300, 293])).
% 1.35/1.15 tff(302,plain,
% 1.35/1.15 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(303,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[302])).
% 1.35/1.15 tff(304,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(305,plain,
% 1.35/1.15 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(306,plain,
% 1.35/1.15 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[305])).
% 1.35/1.15 tff(307,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.35/1.15 tff(308,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[307, 306])).
% 1.35/1.15 tff(309,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[308, 304])).
% 1.35/1.15 tff(310,plain,(
% 1.35/1.15 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.15 inference(skolemize,[status(sab)],[309])).
% 1.35/1.15 tff(311,plain,
% 1.35/1.15 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[310, 303])).
% 1.35/1.15 tff(312,assumption,(~hskp0), introduced(assumption)).
% 1.35/1.15 tff(313,plain,
% 1.35/1.15 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(314,plain,
% 1.35/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[313])).
% 1.35/1.15 tff(315,plain,
% 1.35/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(316,plain,
% 1.35/1.15 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(317,plain,
% 1.35/1.15 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[316])).
% 1.35/1.15 tff(318,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.35/1.15 tff(319,plain,
% 1.35/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[318, 317])).
% 1.35/1.15 tff(320,plain,
% 1.35/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[319, 315])).
% 1.35/1.15 tff(321,plain,(
% 1.35/1.15 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(skolemize,[status(sab)],[320])).
% 1.35/1.15 tff(322,plain,
% 1.35/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[321, 314])).
% 1.35/1.15 tff(323,assumption,(~c1_1(a2194)), introduced(assumption)).
% 1.35/1.15 tff(324,plain,
% 1.35/1.15 (^[U: $i] : refl((hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) <=> (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(325,plain,
% 1.35/1.15 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) <=> ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[324])).
% 1.35/1.15 tff(326,plain,
% 1.35/1.15 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) <=> ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(327,plain,
% 1.35/1.15 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp15) | hskp0) <=> ((hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) | hskp0))), rewrite(((hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) | hskp0) <=> (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp15) | hskp0) <=> (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))))),
% 1.35/1.15 inference(bind,[status(th)],[])).
% 1.35/1.15 tff(328,plain,
% 1.35/1.15 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp15) | hskp0) <=> ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 1.35/1.15 inference(quant_intro,[status(thm)],[327])).
% 1.35/1.15 tff(329,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp15) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.35/1.15 tff(330,plain,
% 1.35/1.15 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[329, 328])).
% 1.35/1.15 tff(331,plain,
% 1.35/1.15 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[330, 326])).
% 1.35/1.15 tff(332,plain,(
% 1.35/1.15 ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 1.35/1.15 inference(skolemize,[status(sab)],[331])).
% 1.35/1.15 tff(333,plain,
% 1.35/1.15 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 1.35/1.15 inference(modus_ponens,[status(thm)],[332, 325])).
% 1.35/1.15 tff(334,plain,
% 1.35/1.15 ((hskp13 | hskp10 | hskp0) <=> (hskp13 | hskp10 | hskp0)),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(335,plain,
% 1.35/1.15 (((hskp13 | hskp0) | hskp10) <=> (hskp13 | hskp10 | hskp0)),
% 1.35/1.15 inference(rewrite,[status(thm)],[])).
% 1.35/1.15 tff(336,plain,
% 1.35/1.16 ((hskp13 | hskp0) <=> (hskp13 | hskp0)),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(337,plain,
% 1.35/1.16 (((hskp13 | hskp0) | hskp10) <=> ((hskp13 | hskp0) | hskp10)),
% 1.35/1.16 inference(monotonicity,[status(thm)],[336])).
% 1.35/1.16 tff(338,plain,
% 1.35/1.16 (((hskp13 | hskp0) | hskp10) <=> (hskp13 | hskp10 | hskp0)),
% 1.35/1.16 inference(transitivity,[status(thm)],[337, 335])).
% 1.35/1.16 tff(339,axiom,((hskp13 | hskp0) | hskp10), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 1.35/1.16 tff(340,plain,
% 1.35/1.16 (hskp13 | hskp10 | hskp0),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[339, 338])).
% 1.35/1.16 tff(341,plain,
% 1.35/1.16 (hskp13 | hskp10 | hskp0),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[340, 334])).
% 1.35/1.16 tff(342,plain,
% 1.35/1.16 (hskp13 | hskp10 | hskp0),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[341, 334])).
% 1.35/1.16 tff(343,plain,
% 1.35/1.16 (hskp13 | hskp10 | hskp0),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[342, 334])).
% 1.35/1.16 tff(344,plain,
% 1.35/1.16 (hskp13 | hskp10 | hskp0),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[343, 334])).
% 1.35/1.16 tff(345,plain,
% 1.35/1.16 (hskp13 | hskp10 | hskp0),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[344, 334])).
% 1.35/1.16 tff(346,plain,
% 1.35/1.16 (hskp13 | hskp10 | hskp0),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[345, 334])).
% 1.35/1.16 tff(347,plain,
% 1.35/1.16 (hskp13 | hskp10 | hskp0),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[346, 334])).
% 1.35/1.16 tff(348,plain,
% 1.35/1.16 (hskp13),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[347, 312, 185])).
% 1.35/1.16 tff(349,plain,
% 1.35/1.16 (((~hskp13) | (~c3_1(a2191))) <=> ((~hskp13) | (~c3_1(a2191)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(350,plain,
% 1.35/1.16 (((~c3_1(a2191)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a2191)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(351,axiom,((~c3_1(a2191)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.35/1.16 tff(352,plain,
% 1.35/1.16 ((~hskp13) | (~c3_1(a2191))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[351, 350])).
% 1.35/1.16 tff(353,plain,
% 1.35/1.16 ((~hskp13) | (~c3_1(a2191))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[352, 349])).
% 1.35/1.16 tff(354,plain,
% 1.35/1.16 (~c3_1(a2191)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[353, 348])).
% 1.35/1.16 tff(355,plain,
% 1.35/1.16 (((~hskp13) | (~c1_1(a2191))) <=> ((~hskp13) | (~c1_1(a2191)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(356,plain,
% 1.35/1.16 (((~c1_1(a2191)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a2191)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(357,axiom,((~c1_1(a2191)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 1.35/1.16 tff(358,plain,
% 1.35/1.16 ((~hskp13) | (~c1_1(a2191))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[357, 356])).
% 1.35/1.16 tff(359,plain,
% 1.35/1.16 ((~hskp13) | (~c1_1(a2191))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[358, 355])).
% 1.35/1.16 tff(360,plain,
% 1.35/1.16 (~c1_1(a2191)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[359, 348])).
% 1.35/1.16 tff(361,plain,
% 1.35/1.16 (((~hskp13) | c0_1(a2191)) <=> ((~hskp13) | c0_1(a2191))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(362,axiom,((~hskp13) | c0_1(a2191)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.35/1.16 tff(363,plain,
% 1.35/1.16 ((~hskp13) | c0_1(a2191)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[362, 361])).
% 1.35/1.16 tff(364,plain,
% 1.35/1.16 ((~hskp13) | c0_1(a2191)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[363, 361])).
% 1.35/1.16 tff(365,plain,
% 1.35/1.16 ((~hskp13) | c0_1(a2191)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[364, 361])).
% 1.35/1.16 tff(366,plain,
% 1.35/1.16 ((~hskp13) | c0_1(a2191)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[365, 361])).
% 1.35/1.16 tff(367,plain,
% 1.35/1.16 ((~hskp13) | c0_1(a2191)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[366, 361])).
% 1.35/1.16 tff(368,plain,
% 1.35/1.16 ((~hskp13) | c0_1(a2191)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[367, 361])).
% 1.35/1.16 tff(369,plain,
% 1.35/1.16 ((~hskp13) | c0_1(a2191)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[368, 361])).
% 1.35/1.16 tff(370,plain,
% 1.35/1.16 ((~hskp13) | c0_1(a2191)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[369, 361])).
% 1.35/1.16 tff(371,plain,
% 1.35/1.16 (c0_1(a2191)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[370, 348])).
% 1.35/1.16 tff(372,plain,
% 1.35/1.16 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | (hskp15 | hskp0 | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | hskp15 | hskp0 | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(373,plain,
% 1.35/1.16 ((hskp15 | hskp0 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191)) <=> (hskp15 | hskp0 | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(374,plain,
% 1.35/1.16 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | (hskp15 | hskp0 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | (hskp15 | hskp0 | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191))))),
% 1.35/1.16 inference(monotonicity,[status(thm)],[373])).
% 1.35/1.16 tff(375,plain,
% 1.35/1.16 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | (hskp15 | hskp0 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | hskp15 | hskp0 | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))),
% 1.35/1.16 inference(transitivity,[status(thm)],[374, 372])).
% 1.35/1.16 tff(376,plain,
% 1.35/1.16 ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | (hskp15 | hskp0 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191))),
% 1.35/1.16 inference(quant_inst,[status(thm)],[])).
% 1.35/1.16 tff(377,plain,
% 1.35/1.16 ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | hskp15 | hskp0 | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[376, 375])).
% 1.35/1.16 tff(378,plain,
% 1.35/1.16 (hskp15),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[377, 111, 312, 371, 360, 354, 333])).
% 1.35/1.16 tff(379,plain,
% 1.35/1.16 (((~hskp15) | (~c2_1(a2194))) <=> ((~hskp15) | (~c2_1(a2194)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(380,plain,
% 1.35/1.16 (((~c2_1(a2194)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a2194)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(381,axiom,((~c2_1(a2194)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.35/1.16 tff(382,plain,
% 1.35/1.16 ((~hskp15) | (~c2_1(a2194))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[381, 380])).
% 1.35/1.16 tff(383,plain,
% 1.35/1.16 ((~hskp15) | (~c2_1(a2194))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[382, 379])).
% 1.35/1.16 tff(384,plain,
% 1.35/1.16 (~c2_1(a2194)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[383, 378])).
% 1.35/1.16 tff(385,plain,
% 1.35/1.16 (((~hskp15) | c0_1(a2194)) <=> ((~hskp15) | c0_1(a2194))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(386,axiom,((~hskp15) | c0_1(a2194)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.35/1.16 tff(387,plain,
% 1.35/1.16 ((~hskp15) | c0_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[386, 385])).
% 1.35/1.16 tff(388,plain,
% 1.35/1.16 ((~hskp15) | c0_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[387, 385])).
% 1.35/1.16 tff(389,plain,
% 1.35/1.16 ((~hskp15) | c0_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[388, 385])).
% 1.35/1.16 tff(390,plain,
% 1.35/1.16 ((~hskp15) | c0_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[389, 385])).
% 1.35/1.16 tff(391,plain,
% 1.35/1.16 ((~hskp15) | c0_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[390, 385])).
% 1.35/1.16 tff(392,plain,
% 1.35/1.16 ((~hskp15) | c0_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[391, 385])).
% 1.35/1.16 tff(393,plain,
% 1.35/1.16 ((~hskp15) | c0_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[392, 385])).
% 1.35/1.16 tff(394,plain,
% 1.35/1.16 ((~hskp15) | c0_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[393, 385])).
% 1.35/1.16 tff(395,plain,
% 1.35/1.16 (c0_1(a2194)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[394, 378])).
% 1.35/1.16 tff(396,plain,
% 1.35/1.16 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(397,plain,
% 1.35/1.16 ((hskp16 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194))) <=> (hskp16 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(398,plain,
% 1.35/1.16 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194)))),
% 1.35/1.16 inference(monotonicity,[status(thm)],[397])).
% 1.35/1.16 tff(399,plain,
% 1.35/1.16 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))),
% 1.35/1.16 inference(transitivity,[status(thm)],[398, 396])).
% 1.35/1.16 tff(400,plain,
% 1.35/1.16 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194)))),
% 1.35/1.16 inference(quant_inst,[status(thm)],[])).
% 1.35/1.16 tff(401,plain,
% 1.35/1.16 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[400, 399])).
% 1.35/1.16 tff(402,plain,
% 1.35/1.16 (hskp16 | c1_1(a2194)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[401, 111, 395, 384, 55])).
% 1.35/1.16 tff(403,plain,
% 1.35/1.16 (hskp16),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[402, 323])).
% 1.35/1.16 tff(404,plain,
% 1.35/1.16 (((~hskp16) | (~c3_1(a2195))) <=> ((~hskp16) | (~c3_1(a2195)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(405,plain,
% 1.35/1.16 (((~c3_1(a2195)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a2195)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(406,axiom,((~c3_1(a2195)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.35/1.16 tff(407,plain,
% 1.35/1.16 ((~hskp16) | (~c3_1(a2195))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[406, 405])).
% 1.35/1.16 tff(408,plain,
% 1.35/1.16 ((~hskp16) | (~c3_1(a2195))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[407, 404])).
% 1.35/1.16 tff(409,plain,
% 1.35/1.16 (~c3_1(a2195)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[408, 403])).
% 1.35/1.16 tff(410,plain,
% 1.35/1.16 (((~hskp16) | (~c2_1(a2195))) <=> ((~hskp16) | (~c2_1(a2195)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(411,plain,
% 1.35/1.16 (((~c2_1(a2195)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a2195)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(412,axiom,((~c2_1(a2195)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.35/1.16 tff(413,plain,
% 1.35/1.16 ((~hskp16) | (~c2_1(a2195))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[412, 411])).
% 1.35/1.16 tff(414,plain,
% 1.35/1.16 ((~hskp16) | (~c2_1(a2195))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[413, 410])).
% 1.35/1.16 tff(415,plain,
% 1.35/1.16 (~c2_1(a2195)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[414, 403])).
% 1.35/1.16 tff(416,plain,
% 1.35/1.16 (((~hskp16) | (~c1_1(a2195))) <=> ((~hskp16) | (~c1_1(a2195)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(417,plain,
% 1.35/1.16 (((~c1_1(a2195)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a2195)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(418,axiom,((~c1_1(a2195)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.35/1.16 tff(419,plain,
% 1.35/1.16 ((~hskp16) | (~c1_1(a2195))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.35/1.16 tff(420,plain,
% 1.35/1.16 ((~hskp16) | (~c1_1(a2195))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[419, 416])).
% 1.35/1.16 tff(421,plain,
% 1.35/1.16 (~c1_1(a2195)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[420, 403])).
% 1.35/1.16 tff(422,plain,
% 1.35/1.16 (((~hskp15) | c3_1(a2194)) <=> ((~hskp15) | c3_1(a2194))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(423,axiom,((~hskp15) | c3_1(a2194)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.35/1.16 tff(424,plain,
% 1.35/1.16 ((~hskp15) | c3_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[423, 422])).
% 1.35/1.16 tff(425,plain,
% 1.35/1.16 ((~hskp15) | c3_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[424, 422])).
% 1.35/1.16 tff(426,plain,
% 1.35/1.16 ((~hskp15) | c3_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[425, 422])).
% 1.35/1.16 tff(427,plain,
% 1.35/1.16 ((~hskp15) | c3_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[426, 422])).
% 1.35/1.16 tff(428,plain,
% 1.35/1.16 ((~hskp15) | c3_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[427, 422])).
% 1.35/1.16 tff(429,plain,
% 1.35/1.16 ((~hskp15) | c3_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[428, 422])).
% 1.35/1.16 tff(430,plain,
% 1.35/1.16 ((~hskp15) | c3_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[429, 422])).
% 1.35/1.16 tff(431,plain,
% 1.35/1.16 ((~hskp15) | c3_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[430, 422])).
% 1.35/1.16 tff(432,plain,
% 1.35/1.16 (c3_1(a2194)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[431, 378])).
% 1.35/1.16 tff(433,plain,
% 1.35/1.16 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 1.35/1.16 inference(bind,[status(th)],[])).
% 1.35/1.16 tff(434,plain,
% 1.35/1.16 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.35/1.16 inference(quant_intro,[status(thm)],[433])).
% 1.35/1.16 tff(435,plain,
% 1.35/1.16 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(436,plain,
% 1.35/1.16 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 1.35/1.16 inference(bind,[status(th)],[])).
% 1.35/1.16 tff(437,plain,
% 1.35/1.16 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.35/1.16 inference(quant_intro,[status(thm)],[436])).
% 1.35/1.16 tff(438,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.35/1.16 tff(439,plain,
% 1.35/1.16 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[438, 437])).
% 1.35/1.16 tff(440,plain,
% 1.35/1.16 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[439, 435])).
% 1.35/1.16 tff(441,plain,(
% 1.35/1.16 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.35/1.16 inference(skolemize,[status(sab)],[440])).
% 1.35/1.16 tff(442,plain,
% 1.35/1.16 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[441, 434])).
% 1.35/1.16 tff(443,plain,
% 1.35/1.16 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(444,plain,
% 1.35/1.16 ((hskp28 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195)) <=> (hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(445,plain,
% 1.35/1.16 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191))))),
% 1.35/1.16 inference(monotonicity,[status(thm)],[444])).
% 1.35/1.16 tff(446,plain,
% 1.35/1.16 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))),
% 1.35/1.16 inference(transitivity,[status(thm)],[445, 443])).
% 1.35/1.16 tff(447,plain,
% 1.35/1.16 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))),
% 1.35/1.16 inference(quant_inst,[status(thm)],[])).
% 1.35/1.16 tff(448,plain,
% 1.35/1.16 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191))),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[447, 446])).
% 1.35/1.16 tff(449,plain,
% 1.35/1.16 (hskp28),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[448, 111, 371, 421, 415, 409, 360, 354, 442])).
% 1.35/1.16 tff(450,plain,
% 1.35/1.16 (c2_1(a2188)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[271, 449])).
% 1.35/1.16 tff(451,plain,
% 1.35/1.16 (c0_1(a2188)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[282, 449])).
% 1.35/1.16 tff(452,plain,
% 1.35/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2194))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2194))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(453,plain,
% 1.35/1.16 (((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2194))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(454,plain,
% 1.35/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2194)))),
% 1.35/1.16 inference(monotonicity,[status(thm)],[453])).
% 1.35/1.16 tff(455,plain,
% 1.35/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2194))),
% 1.35/1.16 inference(transitivity,[status(thm)],[454, 452])).
% 1.35/1.16 tff(456,plain,
% 1.35/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.35/1.16 inference(quant_inst,[status(thm)],[])).
% 1.35/1.16 tff(457,plain,
% 1.35/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2194)),
% 1.35/1.16 inference(modus_ponens,[status(thm)],[456, 455])).
% 1.35/1.16 tff(458,plain,
% 1.35/1.16 (~c3_1(a2188)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[457, 111, 451, 450, 395, 432, 421, 415, 409, 184, 323])).
% 1.35/1.16 tff(459,plain,
% 1.35/1.16 (hskp11),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[290, 111, 185, 451, 450, 260, 458])).
% 1.35/1.16 tff(460,plain,
% 1.35/1.16 (~c1_1(a2187)),
% 1.35/1.16 inference(unit_resolution,[status(thm)],[218, 459])).
% 1.35/1.16 tff(461,plain,
% 1.35/1.16 (^[U: $i] : refl((hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) <=> (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))))),
% 1.35/1.16 inference(bind,[status(th)],[])).
% 1.35/1.16 tff(462,plain,
% 1.35/1.16 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 1.35/1.16 inference(quant_intro,[status(thm)],[461])).
% 1.35/1.16 tff(463,plain,
% 1.35/1.16 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 1.35/1.16 inference(rewrite,[status(thm)],[])).
% 1.35/1.16 tff(464,plain,
% 1.35/1.16 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp22) <=> ((hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) | hskp22))), rewrite(((hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) | hskp22) <=> (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp22) <=> (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))))),
% 1.47/1.16 inference(bind,[status(th)],[])).
% 1.47/1.16 tff(465,plain,
% 1.47/1.16 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp22) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 1.47/1.16 inference(quant_intro,[status(thm)],[464])).
% 1.47/1.16 tff(466,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 1.47/1.16 tff(467,plain,
% 1.47/1.16 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[466, 465])).
% 1.47/1.16 tff(468,plain,
% 1.47/1.16 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[467, 463])).
% 1.47/1.16 tff(469,plain,(
% 1.47/1.16 ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 1.47/1.16 inference(skolemize,[status(sab)],[468])).
% 1.47/1.16 tff(470,plain,
% 1.47/1.16 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[469, 462])).
% 1.47/1.16 tff(471,plain,
% 1.47/1.16 (((~hskp28) | c1_1(a2188)) <=> ((~hskp28) | c1_1(a2188))),
% 1.47/1.16 inference(rewrite,[status(thm)],[])).
% 1.47/1.16 tff(472,axiom,((~hskp28) | c1_1(a2188)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 1.47/1.16 tff(473,plain,
% 1.47/1.16 ((~hskp28) | c1_1(a2188)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[472, 471])).
% 1.47/1.16 tff(474,plain,
% 1.47/1.16 ((~hskp28) | c1_1(a2188)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[473, 471])).
% 1.47/1.16 tff(475,plain,
% 1.47/1.16 ((~hskp28) | c1_1(a2188)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[474, 471])).
% 1.47/1.16 tff(476,plain,
% 1.47/1.16 ((~hskp28) | c1_1(a2188)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[475, 471])).
% 1.47/1.16 tff(477,plain,
% 1.47/1.16 ((~hskp28) | c1_1(a2188)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[476, 471])).
% 1.47/1.16 tff(478,plain,
% 1.47/1.16 ((~hskp28) | c1_1(a2188)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[477, 471])).
% 1.47/1.16 tff(479,plain,
% 1.47/1.16 ((~hskp28) | c1_1(a2188)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[478, 471])).
% 1.47/1.16 tff(480,plain,
% 1.47/1.16 ((~hskp28) | c1_1(a2188)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[479, 471])).
% 1.47/1.16 tff(481,plain,
% 1.47/1.16 (c1_1(a2188)),
% 1.47/1.16 inference(unit_resolution,[status(thm)],[480, 449])).
% 1.47/1.16 tff(482,plain,
% 1.47/1.16 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))) | hskp22 | hskp0 | (~ndr1_0) | (~c2_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)))),
% 1.47/1.16 inference(rewrite,[status(thm)],[])).
% 1.47/1.16 tff(483,plain,
% 1.47/1.16 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)))),
% 1.47/1.16 inference(quant_inst,[status(thm)],[])).
% 1.47/1.16 tff(484,plain,
% 1.47/1.16 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))) | hskp22 | hskp0 | (~ndr1_0) | (~c2_1(a2188)) | c3_1(a2188) | (~c1_1(a2188))),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[483, 482])).
% 1.47/1.16 tff(485,plain,
% 1.47/1.16 (hskp22),
% 1.47/1.16 inference(unit_resolution,[status(thm)],[484, 111, 312, 481, 450, 470, 458])).
% 1.47/1.16 tff(486,plain,
% 1.47/1.16 (((~hskp22) | (~c3_1(a2219))) <=> ((~hskp22) | (~c3_1(a2219)))),
% 1.47/1.16 inference(rewrite,[status(thm)],[])).
% 1.47/1.16 tff(487,plain,
% 1.47/1.16 (((~c3_1(a2219)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a2219)))),
% 1.47/1.16 inference(rewrite,[status(thm)],[])).
% 1.47/1.16 tff(488,axiom,((~c3_1(a2219)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.47/1.16 tff(489,plain,
% 1.47/1.16 ((~hskp22) | (~c3_1(a2219))),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[488, 487])).
% 1.47/1.16 tff(490,plain,
% 1.47/1.16 ((~hskp22) | (~c3_1(a2219))),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[489, 486])).
% 1.47/1.16 tff(491,plain,
% 1.47/1.16 (~c3_1(a2219)),
% 1.47/1.16 inference(unit_resolution,[status(thm)],[490, 485])).
% 1.47/1.16 tff(492,plain,
% 1.47/1.16 (c2_1(a2187)),
% 1.47/1.16 inference(unit_resolution,[status(thm)],[229, 459])).
% 1.47/1.16 tff(493,plain,
% 1.47/1.16 (c0_1(a2187)),
% 1.47/1.16 inference(unit_resolution,[status(thm)],[240, 459])).
% 1.47/1.16 tff(494,plain,
% 1.47/1.16 (((~hskp22) | c2_1(a2219)) <=> ((~hskp22) | c2_1(a2219))),
% 1.47/1.16 inference(rewrite,[status(thm)],[])).
% 1.47/1.16 tff(495,axiom,((~hskp22) | c2_1(a2219)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.47/1.16 tff(496,plain,
% 1.47/1.16 ((~hskp22) | c2_1(a2219)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[495, 494])).
% 1.47/1.16 tff(497,plain,
% 1.47/1.16 ((~hskp22) | c2_1(a2219)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[496, 494])).
% 1.47/1.16 tff(498,plain,
% 1.47/1.16 ((~hskp22) | c2_1(a2219)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[497, 494])).
% 1.47/1.16 tff(499,plain,
% 1.47/1.16 ((~hskp22) | c2_1(a2219)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[498, 494])).
% 1.47/1.16 tff(500,plain,
% 1.47/1.16 ((~hskp22) | c2_1(a2219)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[499, 494])).
% 1.47/1.16 tff(501,plain,
% 1.47/1.16 ((~hskp22) | c2_1(a2219)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[500, 494])).
% 1.47/1.16 tff(502,plain,
% 1.47/1.16 ((~hskp22) | c2_1(a2219)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[501, 494])).
% 1.47/1.16 tff(503,plain,
% 1.47/1.16 ((~hskp22) | c2_1(a2219)),
% 1.47/1.16 inference(modus_ponens,[status(thm)],[502, 494])).
% 1.47/1.16 tff(504,plain,
% 1.47/1.16 (c2_1(a2219)),
% 1.47/1.16 inference(unit_resolution,[status(thm)],[503, 485])).
% 1.47/1.16 tff(505,plain,
% 1.47/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2219) | c2_1(a2194) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2219) | c2_1(a2194) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c0_1(a2219) | (~c2_1(a2219)))),
% 1.47/1.16 inference(rewrite,[status(thm)],[])).
% 1.47/1.16 tff(506,plain,
% 1.47/1.16 (((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2219) | c0_1(a2219) | (~c2_1(a2219))) <=> (c3_1(a2219) | c2_1(a2194) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c0_1(a2219) | (~c2_1(a2219)))),
% 1.47/1.16 inference(rewrite,[status(thm)],[])).
% 1.47/1.16 tff(507,plain,
% 1.47/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2219) | c2_1(a2194) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c0_1(a2219) | (~c2_1(a2219))))),
% 1.47/1.16 inference(monotonicity,[status(thm)],[506])).
% 1.47/1.16 tff(508,plain,
% 1.47/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2219) | c2_1(a2194) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c0_1(a2219) | (~c2_1(a2219)))),
% 1.47/1.17 inference(transitivity,[status(thm)],[507, 505])).
% 1.47/1.17 tff(509,plain,
% 1.47/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))),
% 1.47/1.17 inference(quant_inst,[status(thm)],[])).
% 1.47/1.17 tff(510,plain,
% 1.47/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2219) | c2_1(a2194) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c0_1(a2219) | (~c2_1(a2219))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[509, 508])).
% 1.47/1.17 tff(511,plain,
% 1.47/1.17 (c0_1(a2219)),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[510, 111, 504, 395, 432, 493, 492, 491, 384, 460, 322])).
% 1.47/1.17 tff(512,plain,
% 1.47/1.17 (((~hskp22) | (~c1_1(a2219))) <=> ((~hskp22) | (~c1_1(a2219)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(513,plain,
% 1.47/1.17 (((~c1_1(a2219)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a2219)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(514,axiom,((~c1_1(a2219)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.47/1.17 tff(515,plain,
% 1.47/1.17 ((~hskp22) | (~c1_1(a2219))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[514, 513])).
% 1.47/1.17 tff(516,plain,
% 1.47/1.17 ((~hskp22) | (~c1_1(a2219))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[515, 512])).
% 1.47/1.17 tff(517,plain,
% 1.47/1.17 (~c1_1(a2219)),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[516, 485])).
% 1.47/1.17 tff(518,assumption,(~c3_1(a2188)), introduced(assumption)).
% 1.47/1.17 tff(519,plain,
% 1.47/1.17 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))))),
% 1.47/1.17 inference(bind,[status(th)],[])).
% 1.47/1.17 tff(520,plain,
% 1.47/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.47/1.17 inference(quant_intro,[status(thm)],[519])).
% 1.47/1.17 tff(521,plain,
% 1.47/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(522,plain,
% 1.47/1.17 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))))),
% 1.47/1.17 inference(bind,[status(th)],[])).
% 1.47/1.17 tff(523,plain,
% 1.47/1.17 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.47/1.17 inference(quant_intro,[status(thm)],[522])).
% 1.47/1.17 tff(524,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 1.47/1.17 tff(525,plain,
% 1.47/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[524, 523])).
% 1.47/1.17 tff(526,plain,
% 1.47/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[525, 521])).
% 1.47/1.17 tff(527,plain,(
% 1.47/1.17 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.47/1.17 inference(skolemize,[status(sab)],[526])).
% 1.47/1.17 tff(528,plain,
% 1.47/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[527, 520])).
% 1.47/1.17 tff(529,assumption,(c2_1(a2219)), introduced(assumption)).
% 1.47/1.17 tff(530,assumption,(c1_1(a2188)), introduced(assumption)).
% 1.47/1.17 tff(531,assumption,(c0_1(a2188)), introduced(assumption)).
% 1.47/1.17 tff(532,assumption,(hskp30), introduced(assumption)).
% 1.47/1.17 tff(533,plain,
% 1.47/1.17 (((~hskp30) | c3_1(a2208)) <=> ((~hskp30) | c3_1(a2208))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(534,axiom,((~hskp30) | c3_1(a2208)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.47/1.17 tff(535,plain,
% 1.47/1.17 ((~hskp30) | c3_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[534, 533])).
% 1.47/1.17 tff(536,plain,
% 1.47/1.17 ((~hskp30) | c3_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[535, 533])).
% 1.47/1.17 tff(537,plain,
% 1.47/1.17 ((~hskp30) | c3_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[536, 533])).
% 1.47/1.17 tff(538,plain,
% 1.47/1.17 ((~hskp30) | c3_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[537, 533])).
% 1.47/1.17 tff(539,plain,
% 1.47/1.17 ((~hskp30) | c3_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[538, 533])).
% 1.47/1.17 tff(540,plain,
% 1.47/1.17 ((~hskp30) | c3_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[539, 533])).
% 1.47/1.17 tff(541,plain,
% 1.47/1.17 ((~hskp30) | c3_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[540, 533])).
% 1.47/1.17 tff(542,plain,
% 1.47/1.17 ((~hskp30) | c3_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[541, 533])).
% 1.47/1.17 tff(543,plain,
% 1.47/1.17 (c3_1(a2208)),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[542, 532])).
% 1.47/1.17 tff(544,plain,
% 1.47/1.17 (((~hskp30) | c1_1(a2208)) <=> ((~hskp30) | c1_1(a2208))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(545,axiom,((~hskp30) | c1_1(a2208)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.47/1.17 tff(546,plain,
% 1.47/1.17 ((~hskp30) | c1_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[545, 544])).
% 1.47/1.17 tff(547,plain,
% 1.47/1.17 ((~hskp30) | c1_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[546, 544])).
% 1.47/1.17 tff(548,plain,
% 1.47/1.17 ((~hskp30) | c1_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[547, 544])).
% 1.47/1.17 tff(549,plain,
% 1.47/1.17 ((~hskp30) | c1_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[548, 544])).
% 1.47/1.17 tff(550,plain,
% 1.47/1.17 ((~hskp30) | c1_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[549, 544])).
% 1.47/1.17 tff(551,plain,
% 1.47/1.17 ((~hskp30) | c1_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[550, 544])).
% 1.47/1.17 tff(552,plain,
% 1.47/1.17 ((~hskp30) | c1_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[551, 544])).
% 1.47/1.17 tff(553,plain,
% 1.47/1.17 ((~hskp30) | c1_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[552, 544])).
% 1.47/1.17 tff(554,plain,
% 1.47/1.17 (c1_1(a2208)),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[553, 532])).
% 1.47/1.17 tff(555,plain,
% 1.47/1.17 (((~hskp30) | c0_1(a2208)) <=> ((~hskp30) | c0_1(a2208))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(556,axiom,((~hskp30) | c0_1(a2208)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.47/1.17 tff(557,plain,
% 1.47/1.17 ((~hskp30) | c0_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[556, 555])).
% 1.47/1.17 tff(558,plain,
% 1.47/1.17 ((~hskp30) | c0_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[557, 555])).
% 1.47/1.17 tff(559,plain,
% 1.47/1.17 ((~hskp30) | c0_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[558, 555])).
% 1.47/1.17 tff(560,plain,
% 1.47/1.17 ((~hskp30) | c0_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[559, 555])).
% 1.47/1.17 tff(561,plain,
% 1.47/1.17 ((~hskp30) | c0_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[560, 555])).
% 1.47/1.17 tff(562,plain,
% 1.47/1.17 ((~hskp30) | c0_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[561, 555])).
% 1.47/1.17 tff(563,plain,
% 1.47/1.17 ((~hskp30) | c0_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[562, 555])).
% 1.47/1.17 tff(564,plain,
% 1.47/1.17 ((~hskp30) | c0_1(a2208)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[563, 555])).
% 1.47/1.17 tff(565,plain,
% 1.47/1.17 (c0_1(a2208)),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[564, 532])).
% 1.47/1.17 tff(566,plain,
% 1.47/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2208)) | (~c0_1(a2208)) | (~c1_1(a2208)) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2208)) | (~c0_1(a2208)) | (~c1_1(a2208)) | (~c2_1(a2219)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(567,plain,
% 1.47/1.17 (((~ndr1_0) | (~c0_1(a2208)) | (~c3_1(a2208)) | (~c1_1(a2208)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2219) | c1_1(a2219) | (~c2_1(a2219))) <=> (c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2208)) | (~c0_1(a2208)) | (~c1_1(a2208)) | (~c2_1(a2219)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(568,plain,
% 1.47/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2208)) | (~c3_1(a2208)) | (~c1_1(a2208)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2219) | c1_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2208)) | (~c0_1(a2208)) | (~c1_1(a2208)) | (~c2_1(a2219))))),
% 1.47/1.17 inference(monotonicity,[status(thm)],[567])).
% 1.47/1.17 tff(569,plain,
% 1.47/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2208)) | (~c3_1(a2208)) | (~c1_1(a2208)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2219) | c1_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2208)) | (~c0_1(a2208)) | (~c1_1(a2208)) | (~c2_1(a2219)))),
% 1.47/1.17 inference(transitivity,[status(thm)],[568, 566])).
% 1.47/1.17 tff(570,plain,
% 1.47/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2208)) | (~c3_1(a2208)) | (~c1_1(a2208)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2219) | c1_1(a2219) | (~c2_1(a2219)))),
% 1.47/1.17 inference(quant_inst,[status(thm)],[])).
% 1.47/1.17 tff(571,plain,
% 1.47/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2208)) | (~c0_1(a2208)) | (~c1_1(a2208)) | (~c2_1(a2219))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[570, 569])).
% 1.47/1.17 tff(572,plain,
% 1.47/1.17 ($false),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[571, 111, 565, 554, 543, 531, 530, 529, 210, 212, 528, 518])).
% 1.47/1.17 tff(573,plain,((~hskp30) | (~c0_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2219)) | c1_1(a2219) | c3_1(a2219) | c3_1(a2188)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.17 tff(574,plain,
% 1.47/1.17 (~hskp30),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[573, 451, 481, 504, 517, 491, 458])).
% 1.47/1.17 tff(575,plain,
% 1.47/1.17 (^[U: $i] : refl((hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.47/1.17 inference(bind,[status(th)],[])).
% 1.47/1.17 tff(576,plain,
% 1.47/1.17 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.47/1.17 inference(quant_intro,[status(thm)],[575])).
% 1.47/1.17 tff(577,plain,
% 1.47/1.17 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(578,plain,
% 1.47/1.17 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp1) <=> ((hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp1))), rewrite(((hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp1) <=> (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp1) <=> (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.47/1.17 inference(bind,[status(th)],[])).
% 1.47/1.17 tff(579,plain,
% 1.47/1.17 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp1) <=> ![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.47/1.17 inference(quant_intro,[status(thm)],[578])).
% 1.47/1.17 tff(580,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.47/1.17 tff(581,plain,
% 1.47/1.17 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[580, 579])).
% 1.47/1.17 tff(582,plain,
% 1.47/1.17 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[581, 577])).
% 1.47/1.17 tff(583,plain,(
% 1.47/1.17 ![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.47/1.17 inference(skolemize,[status(sab)],[582])).
% 1.47/1.17 tff(584,plain,
% 1.47/1.17 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[583, 576])).
% 1.47/1.17 tff(585,plain,
% 1.47/1.17 (((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp1 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))) <=> ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp1 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(586,plain,
% 1.47/1.17 ((hskp30 | hskp1 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194))) <=> (hskp30 | hskp1 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(587,plain,
% 1.47/1.17 (((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp1 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194)))) <=> ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp1 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194)))),
% 1.47/1.17 inference(monotonicity,[status(thm)],[586])).
% 1.47/1.17 tff(588,plain,
% 1.47/1.17 (((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp1 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194)))) <=> ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp1 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))),
% 1.47/1.17 inference(transitivity,[status(thm)],[587, 585])).
% 1.47/1.17 tff(589,plain,
% 1.47/1.17 ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp1 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194)))),
% 1.47/1.17 inference(quant_inst,[status(thm)],[])).
% 1.47/1.17 tff(590,plain,
% 1.47/1.17 ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp1 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.47/1.17 tff(591,plain,
% 1.47/1.17 (hskp30 | hskp1 | c1_1(a2194)),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[590, 111, 395, 384, 584])).
% 1.47/1.17 tff(592,plain,
% 1.47/1.17 (hskp1),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[591, 574, 323])).
% 1.47/1.17 tff(593,plain,
% 1.47/1.17 (((~hskp1) | (~c3_1(a2175))) <=> ((~hskp1) | (~c3_1(a2175)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(594,plain,
% 1.47/1.17 (((~c3_1(a2175)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a2175)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(595,axiom,((~c3_1(a2175)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.47/1.17 tff(596,plain,
% 1.47/1.17 ((~hskp1) | (~c3_1(a2175))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[595, 594])).
% 1.47/1.17 tff(597,plain,
% 1.47/1.17 ((~hskp1) | (~c3_1(a2175))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[596, 593])).
% 1.47/1.17 tff(598,plain,
% 1.47/1.17 (~c3_1(a2175)),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[597, 592])).
% 1.47/1.17 tff(599,plain,
% 1.47/1.17 (((~hskp1) | (~c0_1(a2175))) <=> ((~hskp1) | (~c0_1(a2175)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(600,plain,
% 1.47/1.17 (((~c0_1(a2175)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a2175)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(601,axiom,((~c0_1(a2175)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.47/1.17 tff(602,plain,
% 1.47/1.17 ((~hskp1) | (~c0_1(a2175))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[601, 600])).
% 1.47/1.17 tff(603,plain,
% 1.47/1.17 ((~hskp1) | (~c0_1(a2175))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[602, 599])).
% 1.47/1.17 tff(604,plain,
% 1.47/1.17 (~c0_1(a2175)),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[603, 592])).
% 1.47/1.17 tff(605,plain,
% 1.47/1.17 (((~hskp1) | c2_1(a2175)) <=> ((~hskp1) | c2_1(a2175))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(606,axiom,((~hskp1) | c2_1(a2175)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.47/1.17 tff(607,plain,
% 1.47/1.17 ((~hskp1) | c2_1(a2175)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[606, 605])).
% 1.47/1.17 tff(608,plain,
% 1.47/1.17 ((~hskp1) | c2_1(a2175)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[607, 605])).
% 1.47/1.17 tff(609,plain,
% 1.47/1.17 ((~hskp1) | c2_1(a2175)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[608, 605])).
% 1.47/1.17 tff(610,plain,
% 1.47/1.17 ((~hskp1) | c2_1(a2175)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[609, 605])).
% 1.47/1.17 tff(611,plain,
% 1.47/1.17 ((~hskp1) | c2_1(a2175)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[610, 605])).
% 1.47/1.17 tff(612,plain,
% 1.47/1.17 ((~hskp1) | c2_1(a2175)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[611, 605])).
% 1.47/1.17 tff(613,plain,
% 1.47/1.17 ((~hskp1) | c2_1(a2175)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[612, 605])).
% 1.47/1.17 tff(614,plain,
% 1.47/1.17 ((~hskp1) | c2_1(a2175)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[613, 605])).
% 1.47/1.17 tff(615,plain,
% 1.47/1.17 (c2_1(a2175)),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[614, 592])).
% 1.47/1.17 tff(616,plain,
% 1.47/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2219) | c2_1(a2194) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c0_1(a2194)) | (~c3_1(a2194)) | (~c2_1(a2219)) | (~c0_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2219) | c2_1(a2194) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c0_1(a2194)) | (~c3_1(a2194)) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(617,plain,
% 1.47/1.17 (((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175))) <=> (c1_1(a2219) | c2_1(a2194) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c0_1(a2194)) | (~c3_1(a2194)) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(618,plain,
% 1.47/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2219) | c2_1(a2194) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c0_1(a2194)) | (~c3_1(a2194)) | (~c2_1(a2219)) | (~c0_1(a2219))))),
% 1.47/1.17 inference(monotonicity,[status(thm)],[617])).
% 1.47/1.17 tff(619,plain,
% 1.47/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2219) | c2_1(a2194) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c0_1(a2194)) | (~c3_1(a2194)) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.47/1.17 inference(transitivity,[status(thm)],[618, 616])).
% 1.47/1.17 tff(620,plain,
% 1.47/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)))),
% 1.47/1.17 inference(quant_inst,[status(thm)],[])).
% 1.47/1.17 tff(621,plain,
% 1.47/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2219) | c2_1(a2194) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c0_1(a2194)) | (~c3_1(a2194)) | (~c2_1(a2219)) | (~c0_1(a2219))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[620, 619])).
% 1.47/1.17 tff(622,plain,
% 1.47/1.17 ($false),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[621, 111, 504, 395, 432, 615, 517, 384, 604, 598, 322, 511])).
% 1.47/1.17 tff(623,plain,(c1_1(a2194) | hskp0 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.47/1.17 tff(624,plain,
% 1.47/1.17 (c1_1(a2194)),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[623, 312, 185])).
% 1.47/1.17 tff(625,plain,
% 1.47/1.17 (^[U: $i] : refl((hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 1.47/1.17 inference(bind,[status(th)],[])).
% 1.47/1.17 tff(626,plain,
% 1.47/1.17 (![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.17 inference(quant_intro,[status(thm)],[625])).
% 1.47/1.17 tff(627,plain,
% 1.47/1.17 (![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(628,plain,
% 1.47/1.17 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp10) <=> ((hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp10))), rewrite(((hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp10) <=> (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp10) <=> (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.47/1.17 inference(bind,[status(th)],[])).
% 1.47/1.17 tff(629,plain,
% 1.47/1.17 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp10) <=> ![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.17 inference(quant_intro,[status(thm)],[628])).
% 1.47/1.17 tff(630,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 1.47/1.17 tff(631,plain,
% 1.47/1.17 (![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[630, 629])).
% 1.47/1.17 tff(632,plain,
% 1.47/1.17 (![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[631, 627])).
% 1.47/1.17 tff(633,plain,(
% 1.47/1.17 ![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.17 inference(skolemize,[status(sab)],[632])).
% 1.47/1.17 tff(634,plain,
% 1.47/1.17 (![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[633, 626])).
% 1.47/1.17 tff(635,plain,
% 1.47/1.17 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | (~c1_1(a2194)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | (~c1_1(a2194)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(636,plain,
% 1.47/1.17 ((hskp17 | hskp10 | (~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c1_1(a2194))) <=> (hskp17 | hskp10 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | (~c1_1(a2194)))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(637,plain,
% 1.47/1.17 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c1_1(a2194)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | (~c1_1(a2194))))),
% 1.47/1.17 inference(monotonicity,[status(thm)],[636])).
% 1.47/1.17 tff(638,plain,
% 1.47/1.17 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c1_1(a2194)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | (~c1_1(a2194)))),
% 1.47/1.17 inference(transitivity,[status(thm)],[637, 635])).
% 1.47/1.17 tff(639,plain,
% 1.47/1.17 ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c1_1(a2194)))),
% 1.47/1.17 inference(quant_inst,[status(thm)],[])).
% 1.47/1.17 tff(640,plain,
% 1.47/1.17 ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | (~c1_1(a2194))),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[639, 638])).
% 1.47/1.17 tff(641,plain,
% 1.47/1.17 (hskp17 | (~c1_1(a2194))),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[640, 111, 185, 395, 384, 634])).
% 1.47/1.17 tff(642,plain,
% 1.47/1.17 (hskp17),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[641, 624])).
% 1.47/1.17 tff(643,plain,
% 1.47/1.17 (~c1_1(a2197)),
% 1.47/1.17 inference(unit_resolution,[status(thm)],[163, 642])).
% 1.47/1.17 tff(644,plain,
% 1.47/1.17 (((~hskp17) | c3_1(a2197)) <=> ((~hskp17) | c3_1(a2197))),
% 1.47/1.17 inference(rewrite,[status(thm)],[])).
% 1.47/1.17 tff(645,axiom,((~hskp17) | c3_1(a2197)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.47/1.17 tff(646,plain,
% 1.47/1.17 ((~hskp17) | c3_1(a2197)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[645, 644])).
% 1.47/1.17 tff(647,plain,
% 1.47/1.17 ((~hskp17) | c3_1(a2197)),
% 1.47/1.17 inference(modus_ponens,[status(thm)],[646, 644])).
% 1.47/1.18 tff(648,plain,
% 1.47/1.18 ((~hskp17) | c3_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[647, 644])).
% 1.47/1.18 tff(649,plain,
% 1.47/1.18 ((~hskp17) | c3_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[648, 644])).
% 1.47/1.18 tff(650,plain,
% 1.47/1.18 ((~hskp17) | c3_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[649, 644])).
% 1.47/1.18 tff(651,plain,
% 1.47/1.18 ((~hskp17) | c3_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[650, 644])).
% 1.47/1.18 tff(652,plain,
% 1.47/1.18 ((~hskp17) | c3_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[651, 644])).
% 1.47/1.18 tff(653,plain,
% 1.47/1.18 ((~hskp17) | c3_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[652, 644])).
% 1.47/1.18 tff(654,plain,
% 1.47/1.18 (c3_1(a2197)),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[653, 642])).
% 1.47/1.18 tff(655,plain,
% 1.47/1.18 (((~hskp17) | c2_1(a2197)) <=> ((~hskp17) | c2_1(a2197))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(656,axiom,((~hskp17) | c2_1(a2197)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.47/1.18 tff(657,plain,
% 1.47/1.18 ((~hskp17) | c2_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[656, 655])).
% 1.47/1.18 tff(658,plain,
% 1.47/1.18 ((~hskp17) | c2_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[657, 655])).
% 1.47/1.18 tff(659,plain,
% 1.47/1.18 ((~hskp17) | c2_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[658, 655])).
% 1.47/1.18 tff(660,plain,
% 1.47/1.18 ((~hskp17) | c2_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[659, 655])).
% 1.47/1.18 tff(661,plain,
% 1.47/1.18 ((~hskp17) | c2_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[660, 655])).
% 1.47/1.18 tff(662,plain,
% 1.47/1.18 ((~hskp17) | c2_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[661, 655])).
% 1.47/1.18 tff(663,plain,
% 1.47/1.18 ((~hskp17) | c2_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[662, 655])).
% 1.47/1.18 tff(664,plain,
% 1.47/1.18 ((~hskp17) | c2_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[663, 655])).
% 1.47/1.18 tff(665,plain,
% 1.47/1.18 (c2_1(a2197)),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[664, 642])).
% 1.47/1.18 tff(666,plain,
% 1.47/1.18 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(667,plain,
% 1.47/1.18 ((hskp10 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197))) <=> (hskp10 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(668,plain,
% 1.47/1.18 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197))))),
% 1.47/1.18 inference(monotonicity,[status(thm)],[667])).
% 1.47/1.18 tff(669,plain,
% 1.47/1.18 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.47/1.18 inference(transitivity,[status(thm)],[668, 666])).
% 1.47/1.18 tff(670,plain,
% 1.47/1.18 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197)))),
% 1.47/1.18 inference(quant_inst,[status(thm)],[])).
% 1.47/1.18 tff(671,plain,
% 1.47/1.18 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[670, 669])).
% 1.47/1.18 tff(672,plain,
% 1.47/1.18 (~c0_1(a2197)),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[671, 111, 185, 665, 654, 643, 311])).
% 1.47/1.18 tff(673,plain,
% 1.47/1.18 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a2197) | c2_1(a2194) | (~ndr1_0) | (~c3_1(a2194)) | (~c1_1(a2194)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a2197) | c2_1(a2194) | (~ndr1_0) | (~c3_1(a2194)) | (~c1_1(a2194)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(674,plain,
% 1.47/1.18 ((hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197))) <=> (hskp0 | c1_1(a2197) | c2_1(a2194) | (~ndr1_0) | (~c3_1(a2194)) | (~c1_1(a2194)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(675,plain,
% 1.47/1.18 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a2197) | c2_1(a2194) | (~ndr1_0) | (~c3_1(a2194)) | (~c1_1(a2194)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.47/1.18 inference(monotonicity,[status(thm)],[674])).
% 1.47/1.18 tff(676,plain,
% 1.47/1.18 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a2197) | c2_1(a2194) | (~ndr1_0) | (~c3_1(a2194)) | (~c1_1(a2194)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.47/1.18 inference(transitivity,[status(thm)],[675, 673])).
% 1.47/1.18 tff(677,plain,
% 1.47/1.18 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))),
% 1.47/1.18 inference(quant_inst,[status(thm)],[])).
% 1.47/1.18 tff(678,plain,
% 1.47/1.18 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a2197) | c2_1(a2194) | (~ndr1_0) | (~c3_1(a2194)) | (~c1_1(a2194)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[677, 676])).
% 1.47/1.18 tff(679,plain,
% 1.47/1.18 ($false),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[678, 111, 312, 654, 432, 643, 384, 174, 624, 672])).
% 1.47/1.18 tff(680,plain,(hskp0 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.47/1.18 tff(681,plain,
% 1.47/1.18 (hskp0),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[680, 185])).
% 1.47/1.18 tff(682,plain,
% 1.47/1.18 (((~hskp0) | (~c0_1(a2174))) <=> ((~hskp0) | (~c0_1(a2174)))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(683,plain,
% 1.47/1.18 (((~c0_1(a2174)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a2174)))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(684,axiom,((~c0_1(a2174)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 1.47/1.18 tff(685,plain,
% 1.47/1.18 ((~hskp0) | (~c0_1(a2174))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[684, 683])).
% 1.47/1.18 tff(686,plain,
% 1.47/1.18 ((~hskp0) | (~c0_1(a2174))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[685, 682])).
% 1.47/1.18 tff(687,plain,
% 1.47/1.18 (~c0_1(a2174)),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[686, 681])).
% 1.47/1.18 tff(688,plain,
% 1.47/1.18 (((~hskp0) | c2_1(a2174)) <=> ((~hskp0) | c2_1(a2174))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(689,axiom,((~hskp0) | c2_1(a2174)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 1.47/1.18 tff(690,plain,
% 1.47/1.18 ((~hskp0) | c2_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[689, 688])).
% 1.47/1.18 tff(691,plain,
% 1.47/1.18 ((~hskp0) | c2_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[690, 688])).
% 1.47/1.18 tff(692,plain,
% 1.47/1.18 ((~hskp0) | c2_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[691, 688])).
% 1.47/1.18 tff(693,plain,
% 1.47/1.18 ((~hskp0) | c2_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[692, 688])).
% 1.47/1.18 tff(694,plain,
% 1.47/1.18 ((~hskp0) | c2_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[693, 688])).
% 1.47/1.18 tff(695,plain,
% 1.47/1.18 ((~hskp0) | c2_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[694, 688])).
% 1.47/1.18 tff(696,plain,
% 1.47/1.18 ((~hskp0) | c2_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[695, 688])).
% 1.47/1.18 tff(697,plain,
% 1.47/1.18 ((~hskp0) | c2_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[696, 688])).
% 1.47/1.18 tff(698,plain,
% 1.47/1.18 (c2_1(a2174)),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[697, 681])).
% 1.47/1.18 tff(699,plain,
% 1.47/1.18 (((~hskp0) | c1_1(a2174)) <=> ((~hskp0) | c1_1(a2174))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(700,axiom,((~hskp0) | c1_1(a2174)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 1.47/1.18 tff(701,plain,
% 1.47/1.18 ((~hskp0) | c1_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[700, 699])).
% 1.47/1.18 tff(702,plain,
% 1.47/1.18 ((~hskp0) | c1_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[701, 699])).
% 1.47/1.18 tff(703,plain,
% 1.47/1.18 ((~hskp0) | c1_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[702, 699])).
% 1.47/1.18 tff(704,plain,
% 1.47/1.18 ((~hskp0) | c1_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[703, 699])).
% 1.47/1.18 tff(705,plain,
% 1.47/1.18 ((~hskp0) | c1_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[704, 699])).
% 1.47/1.18 tff(706,plain,
% 1.47/1.18 ((~hskp0) | c1_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[705, 699])).
% 1.47/1.18 tff(707,plain,
% 1.47/1.18 ((~hskp0) | c1_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[706, 699])).
% 1.47/1.18 tff(708,plain,
% 1.47/1.18 ((~hskp0) | c1_1(a2174)),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[707, 699])).
% 1.47/1.18 tff(709,plain,
% 1.47/1.18 (c1_1(a2174)),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[708, 681])).
% 1.47/1.18 tff(710,plain,
% 1.47/1.18 (c1_1(a2188)),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[480, 261])).
% 1.47/1.18 tff(711,plain,
% 1.47/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2191)))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(712,plain,
% 1.47/1.18 (((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191))) <=> (c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2191)))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(713,plain,
% 1.47/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2191))))),
% 1.47/1.18 inference(monotonicity,[status(thm)],[712])).
% 1.47/1.18 tff(714,plain,
% 1.47/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2191)))),
% 1.47/1.18 inference(transitivity,[status(thm)],[713, 711])).
% 1.47/1.18 tff(715,plain,
% 1.47/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))),
% 1.47/1.18 inference(quant_inst,[status(thm)],[])).
% 1.47/1.18 tff(716,plain,
% 1.47/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2191))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[715, 714])).
% 1.47/1.18 tff(717,plain,
% 1.47/1.18 ((~c3_1(a2188)) | (~c2_1(a2191))),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[716, 111, 283, 710, 198, 709, 698, 187, 687, 301])).
% 1.47/1.18 tff(718,plain,
% 1.47/1.18 (~c2_1(a2191)),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[717, 291])).
% 1.47/1.18 tff(719,plain,
% 1.47/1.18 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 1.47/1.18 inference(bind,[status(th)],[])).
% 1.47/1.18 tff(720,plain,
% 1.47/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.47/1.18 inference(quant_intro,[status(thm)],[719])).
% 1.47/1.18 tff(721,plain,
% 1.47/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(722,plain,
% 1.47/1.18 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 1.47/1.18 inference(bind,[status(th)],[])).
% 1.47/1.18 tff(723,plain,
% 1.47/1.18 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.47/1.18 inference(quant_intro,[status(thm)],[722])).
% 1.47/1.18 tff(724,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 1.47/1.18 tff(725,plain,
% 1.47/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[724, 723])).
% 1.47/1.18 tff(726,plain,
% 1.47/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[725, 721])).
% 1.47/1.18 tff(727,plain,(
% 1.47/1.18 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.47/1.18 inference(skolemize,[status(sab)],[726])).
% 1.47/1.18 tff(728,plain,
% 1.47/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[727, 720])).
% 1.47/1.18 tff(729,plain,
% 1.47/1.18 (^[U: $i] : refl((hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))),
% 1.47/1.18 inference(bind,[status(th)],[])).
% 1.47/1.18 tff(730,plain,
% 1.47/1.18 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.47/1.18 inference(quant_intro,[status(thm)],[729])).
% 1.47/1.18 tff(731,plain,
% 1.47/1.18 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(732,plain,
% 1.47/1.18 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp11))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp1) <=> ((hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp1))), rewrite(((hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp1) <=> (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp1) <=> (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.47/1.18 inference(bind,[status(th)],[])).
% 1.47/1.18 tff(733,plain,
% 1.47/1.18 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp1) <=> ![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.47/1.18 inference(quant_intro,[status(thm)],[732])).
% 1.47/1.18 tff(734,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.47/1.18 tff(735,plain,
% 1.47/1.18 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[734, 733])).
% 1.47/1.18 tff(736,plain,
% 1.47/1.18 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[735, 731])).
% 1.47/1.18 tff(737,plain,(
% 1.47/1.18 ![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.47/1.18 inference(skolemize,[status(sab)],[736])).
% 1.47/1.18 tff(738,plain,
% 1.47/1.18 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[737, 730])).
% 1.47/1.18 tff(739,plain,
% 1.47/1.18 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp1 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(740,plain,
% 1.47/1.18 ((hskp11 | hskp1 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188))) <=> (hskp11 | hskp1 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(741,plain,
% 1.47/1.18 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188))))),
% 1.47/1.18 inference(monotonicity,[status(thm)],[740])).
% 1.47/1.18 tff(742,plain,
% 1.47/1.18 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp1 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 1.47/1.18 inference(transitivity,[status(thm)],[741, 739])).
% 1.47/1.18 tff(743,plain,
% 1.47/1.18 ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)))),
% 1.47/1.18 inference(quant_inst,[status(thm)],[])).
% 1.47/1.18 tff(744,plain,
% 1.47/1.18 ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp1 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[743, 742])).
% 1.47/1.18 tff(745,plain,
% 1.47/1.18 (hskp1 | (~c3_1(a2188))),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[744, 111, 284, 283, 272, 738])).
% 1.47/1.18 tff(746,plain,
% 1.47/1.18 (hskp1),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[745, 291])).
% 1.47/1.18 tff(747,plain,
% 1.47/1.18 (~c3_1(a2175)),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[597, 746])).
% 1.47/1.18 tff(748,plain,
% 1.47/1.18 (~c0_1(a2175)),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[603, 746])).
% 1.47/1.18 tff(749,plain,
% 1.47/1.18 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.47/1.18 inference(bind,[status(th)],[])).
% 1.47/1.18 tff(750,plain,
% 1.47/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_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) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.18 inference(quant_intro,[status(thm)],[749])).
% 1.47/1.18 tff(751,plain,
% 1.47/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_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) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.18 tff(752,plain,
% 1.47/1.18 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_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) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.47/1.18 inference(bind,[status(th)],[])).
% 1.47/1.18 tff(753,plain,
% 1.47/1.18 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.18 inference(quant_intro,[status(thm)],[752])).
% 1.47/1.18 tff(754,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.47/1.18 tff(755,plain,
% 1.47/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[754, 753])).
% 1.47/1.18 tff(756,plain,
% 1.47/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[755, 751])).
% 1.47/1.18 tff(757,plain,(
% 1.47/1.18 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.18 inference(skolemize,[status(sab)],[756])).
% 1.47/1.18 tff(758,plain,
% 1.47/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[757, 750])).
% 1.47/1.18 tff(759,plain,
% 1.47/1.18 (c2_1(a2175)),
% 1.47/1.18 inference(unit_resolution,[status(thm)],[614, 746])).
% 1.47/1.18 tff(760,plain,
% 1.47/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)))),
% 1.47/1.18 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(761,plain,
% 1.47/1.19 (((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191)) <=> (c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(762,plain,
% 1.47/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175))))),
% 1.47/1.19 inference(monotonicity,[status(thm)],[761])).
% 1.47/1.19 tff(763,plain,
% 1.47/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)))),
% 1.47/1.19 inference(transitivity,[status(thm)],[762, 760])).
% 1.47/1.19 tff(764,plain,
% 1.47/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))),
% 1.47/1.19 inference(quant_inst,[status(thm)],[])).
% 1.47/1.19 tff(765,plain,
% 1.47/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[764, 763])).
% 1.47/1.19 tff(766,plain,
% 1.47/1.19 (~c3_1(a2174)),
% 1.47/1.19 inference(unit_resolution,[status(thm)],[765, 111, 198, 759, 709, 187, 186, 748, 747, 687, 758])).
% 1.47/1.19 tff(767,plain,
% 1.47/1.19 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 1.47/1.19 inference(bind,[status(th)],[])).
% 1.47/1.19 tff(768,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(quant_intro,[status(thm)],[767])).
% 1.47/1.19 tff(769,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(770,plain,
% 1.47/1.19 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 1.47/1.19 inference(bind,[status(th)],[])).
% 1.47/1.19 tff(771,plain,
% 1.47/1.19 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(quant_intro,[status(thm)],[770])).
% 1.47/1.19 tff(772,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.47/1.19 tff(773,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[772, 771])).
% 1.47/1.19 tff(774,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[773, 769])).
% 1.47/1.19 tff(775,plain,(
% 1.47/1.19 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(skolemize,[status(sab)],[774])).
% 1.47/1.19 tff(776,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[775, 768])).
% 1.47/1.19 tff(777,plain,
% 1.47/1.19 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(778,plain,
% 1.47/1.19 ((hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp7 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(779,plain,
% 1.47/1.19 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188))))),
% 1.47/1.19 inference(monotonicity,[status(thm)],[778])).
% 1.47/1.19 tff(780,plain,
% 1.47/1.19 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 1.47/1.19 inference(transitivity,[status(thm)],[779, 777])).
% 1.47/1.19 tff(781,plain,
% 1.47/1.19 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.47/1.19 inference(quant_inst,[status(thm)],[])).
% 1.47/1.19 tff(782,plain,
% 1.47/1.19 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[781, 780])).
% 1.47/1.19 tff(783,plain,
% 1.47/1.19 (hskp7),
% 1.47/1.19 inference(unit_resolution,[status(thm)],[782, 111, 283, 272, 709, 698, 776, 291, 766])).
% 1.47/1.19 tff(784,plain,
% 1.47/1.19 (((~hskp7) | (~c0_1(a2182))) <=> ((~hskp7) | (~c0_1(a2182)))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(785,plain,
% 1.47/1.19 (((~c0_1(a2182)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a2182)))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(786,axiom,((~c0_1(a2182)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.47/1.19 tff(787,plain,
% 1.47/1.19 ((~hskp7) | (~c0_1(a2182))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[786, 785])).
% 1.47/1.19 tff(788,plain,
% 1.47/1.19 ((~hskp7) | (~c0_1(a2182))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[787, 784])).
% 1.47/1.19 tff(789,plain,
% 1.47/1.19 (~c0_1(a2182)),
% 1.47/1.19 inference(unit_resolution,[status(thm)],[788, 783])).
% 1.47/1.19 tff(790,plain,
% 1.47/1.19 (((~hskp7) | c3_1(a2182)) <=> ((~hskp7) | c3_1(a2182))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(791,axiom,((~hskp7) | c3_1(a2182)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.47/1.19 tff(792,plain,
% 1.47/1.19 ((~hskp7) | c3_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[791, 790])).
% 1.47/1.19 tff(793,plain,
% 1.47/1.19 ((~hskp7) | c3_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[792, 790])).
% 1.47/1.19 tff(794,plain,
% 1.47/1.19 ((~hskp7) | c3_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[793, 790])).
% 1.47/1.19 tff(795,plain,
% 1.47/1.19 ((~hskp7) | c3_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[794, 790])).
% 1.47/1.19 tff(796,plain,
% 1.47/1.19 ((~hskp7) | c3_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[795, 790])).
% 1.47/1.19 tff(797,plain,
% 1.47/1.19 ((~hskp7) | c3_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[796, 790])).
% 1.47/1.19 tff(798,plain,
% 1.47/1.19 ((~hskp7) | c3_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[797, 790])).
% 1.47/1.19 tff(799,plain,
% 1.47/1.19 ((~hskp7) | c3_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[798, 790])).
% 1.47/1.19 tff(800,plain,
% 1.47/1.19 (c3_1(a2182)),
% 1.47/1.19 inference(unit_resolution,[status(thm)],[799, 783])).
% 1.47/1.19 tff(801,plain,
% 1.47/1.19 (((~hskp7) | c2_1(a2182)) <=> ((~hskp7) | c2_1(a2182))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(802,axiom,((~hskp7) | c2_1(a2182)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.47/1.19 tff(803,plain,
% 1.47/1.19 ((~hskp7) | c2_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[802, 801])).
% 1.47/1.19 tff(804,plain,
% 1.47/1.19 ((~hskp7) | c2_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[803, 801])).
% 1.47/1.19 tff(805,plain,
% 1.47/1.19 ((~hskp7) | c2_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[804, 801])).
% 1.47/1.19 tff(806,plain,
% 1.47/1.19 ((~hskp7) | c2_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[805, 801])).
% 1.47/1.19 tff(807,plain,
% 1.47/1.19 ((~hskp7) | c2_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[806, 801])).
% 1.47/1.19 tff(808,plain,
% 1.47/1.19 ((~hskp7) | c2_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[807, 801])).
% 1.47/1.19 tff(809,plain,
% 1.47/1.19 ((~hskp7) | c2_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[808, 801])).
% 1.47/1.19 tff(810,plain,
% 1.47/1.19 ((~hskp7) | c2_1(a2182)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[809, 801])).
% 1.47/1.19 tff(811,plain,
% 1.47/1.19 (c2_1(a2182)),
% 1.47/1.19 inference(unit_resolution,[status(thm)],[810, 783])).
% 1.47/1.19 tff(812,plain,
% 1.47/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a2191) | c1_1(a2191) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c2_1(a2191))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(813,plain,
% 1.47/1.19 (((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2191) | c0_1(a2191) | c2_1(a2191)) <=> (c0_1(a2191) | c1_1(a2191) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c2_1(a2191))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(814,plain,
% 1.47/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2191) | c0_1(a2191) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a2191) | c1_1(a2191) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c2_1(a2191)))),
% 1.47/1.19 inference(monotonicity,[status(thm)],[813])).
% 1.47/1.19 tff(815,plain,
% 1.47/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2191) | c0_1(a2191) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c2_1(a2191))),
% 1.47/1.19 inference(transitivity,[status(thm)],[814, 812])).
% 1.47/1.19 tff(816,plain,
% 1.47/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2191) | c0_1(a2191) | c2_1(a2191))),
% 1.47/1.19 inference(quant_inst,[status(thm)],[])).
% 1.47/1.19 tff(817,plain,
% 1.47/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c2_1(a2191)),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[816, 815])).
% 1.47/1.19 tff(818,plain,
% 1.47/1.19 ($false),
% 1.47/1.19 inference(unit_resolution,[status(thm)],[817, 111, 198, 811, 800, 759, 187, 789, 748, 747, 728, 718])).
% 1.47/1.19 tff(819,plain,((~hskp28) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | hskp11 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.47/1.19 tff(820,plain,
% 1.47/1.19 (~hskp28),
% 1.47/1.19 inference(unit_resolution,[status(thm)],[819, 250, 187, 186, 198, 185])).
% 1.47/1.19 tff(821,plain,
% 1.47/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(822,plain,
% 1.47/1.19 ((hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219)) <=> (hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(823,plain,
% 1.47/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2219))))),
% 1.47/1.19 inference(monotonicity,[status(thm)],[822])).
% 1.47/1.19 tff(824,plain,
% 1.47/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))),
% 1.47/1.19 inference(transitivity,[status(thm)],[823, 821])).
% 1.47/1.19 tff(825,plain,
% 1.47/1.19 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219))),
% 1.47/1.19 inference(quant_inst,[status(thm)],[])).
% 1.47/1.19 tff(826,plain,
% 1.47/1.19 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2219))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[825, 824])).
% 1.47/1.19 tff(827,plain,
% 1.47/1.19 (hskp28 | (~c0_1(a2219))),
% 1.47/1.19 inference(unit_resolution,[status(thm)],[826, 111, 211, 210, 212, 442])).
% 1.47/1.19 tff(828,plain,
% 1.47/1.19 (~c0_1(a2219)),
% 1.47/1.19 inference(unit_resolution,[status(thm)],[827, 199])).
% 1.47/1.19 tff(829,plain,
% 1.47/1.19 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.47/1.19 inference(bind,[status(th)],[])).
% 1.47/1.19 tff(830,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.19 inference(quant_intro,[status(thm)],[829])).
% 1.47/1.19 tff(831,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(832,plain,
% 1.47/1.19 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp28))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.47/1.19 inference(bind,[status(th)],[])).
% 1.47/1.19 tff(833,plain,
% 1.47/1.19 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.19 inference(quant_intro,[status(thm)],[832])).
% 1.47/1.19 tff(834,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 1.47/1.19 tff(835,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[834, 833])).
% 1.47/1.19 tff(836,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[835, 831])).
% 1.47/1.19 tff(837,plain,(
% 1.47/1.19 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.19 inference(skolemize,[status(sab)],[836])).
% 1.47/1.19 tff(838,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[837, 830])).
% 1.47/1.19 tff(839,plain,
% 1.47/1.19 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 1.47/1.19 inference(bind,[status(th)],[])).
% 1.47/1.19 tff(840,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(quant_intro,[status(thm)],[839])).
% 1.47/1.19 tff(841,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(842,plain,
% 1.47/1.19 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_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)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 1.47/1.19 inference(bind,[status(th)],[])).
% 1.47/1.19 tff(843,plain,
% 1.47/1.19 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(quant_intro,[status(thm)],[842])).
% 1.47/1.19 tff(844,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.47/1.19 tff(845,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[844, 843])).
% 1.47/1.19 tff(846,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[845, 841])).
% 1.47/1.19 tff(847,plain,(
% 1.47/1.19 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(skolemize,[status(sab)],[846])).
% 1.47/1.19 tff(848,plain,
% 1.47/1.19 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[847, 840])).
% 1.47/1.19 tff(849,plain,
% 1.47/1.19 (~hskp22),
% 1.47/1.19 inference(unit_resolution,[status(thm)],[503, 211])).
% 1.47/1.19 tff(850,assumption,(~hskp17), introduced(assumption)).
% 1.47/1.19 tff(851,plain,
% 1.47/1.19 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | c2_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(852,plain,
% 1.47/1.19 ((hskp17 | hskp10 | (~ndr1_0) | c2_1(a2216) | (~c0_1(a2216)) | (~c1_1(a2216))) <=> (hskp17 | hskp10 | c2_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(853,plain,
% 1.47/1.19 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2216) | (~c0_1(a2216)) | (~c1_1(a2216)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | c2_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216))))),
% 1.47/1.19 inference(monotonicity,[status(thm)],[852])).
% 1.47/1.19 tff(854,plain,
% 1.47/1.19 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2216) | (~c0_1(a2216)) | (~c1_1(a2216)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 1.47/1.19 inference(transitivity,[status(thm)],[853, 851])).
% 1.47/1.19 tff(855,plain,
% 1.47/1.19 ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2216) | (~c0_1(a2216)) | (~c1_1(a2216)))),
% 1.47/1.19 inference(quant_inst,[status(thm)],[])).
% 1.47/1.19 tff(856,plain,
% 1.47/1.19 ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216))),
% 1.47/1.19 inference(modus_ponens,[status(thm)],[855, 854])).
% 1.47/1.19 tff(857,plain,
% 1.47/1.19 (~c1_1(a2216)),
% 1.47/1.19 inference(unit_resolution,[status(thm)],[856, 111, 850, 185, 45, 34, 634])).
% 1.47/1.19 tff(858,plain,
% 1.47/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(859,plain,
% 1.47/1.19 ((hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219)) <=> (hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(860,plain,
% 1.47/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216))))),
% 1.47/1.19 inference(monotonicity,[status(thm)],[859])).
% 1.47/1.19 tff(861,plain,
% 1.47/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 1.47/1.19 inference(transitivity,[status(thm)],[860, 858])).
% 1.47/1.19 tff(862,plain,
% 1.47/1.19 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219))),
% 1.47/1.19 inference(quant_inst,[status(thm)],[])).
% 1.47/1.19 tff(863,plain,
% 1.47/1.19 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[862, 861])).
% 1.47/1.20 tff(864,plain,
% 1.47/1.20 ($false),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[863, 111, 199, 211, 45, 210, 212, 28, 442, 857])).
% 1.47/1.20 tff(865,plain,((~hskp21) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | hskp17 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.47/1.20 tff(866,plain,
% 1.47/1.20 (~hskp21),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[865, 199, 211, 210, 212, 850, 185])).
% 1.47/1.20 tff(867,plain,
% 1.47/1.20 ((hskp25 | hskp22 | hskp21) <=> (hskp25 | hskp22 | hskp21)),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(868,plain,
% 1.47/1.20 (((hskp21 | hskp25) | hskp22) <=> (hskp25 | hskp22 | hskp21)),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(869,axiom,((hskp21 | hskp25) | hskp22), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 1.47/1.20 tff(870,plain,
% 1.47/1.20 (hskp25 | hskp22 | hskp21),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[869, 868])).
% 1.47/1.20 tff(871,plain,
% 1.47/1.20 (hskp25 | hskp22 | hskp21),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[870, 867])).
% 1.47/1.20 tff(872,plain,
% 1.47/1.20 (hskp25 | hskp22 | hskp21),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[871, 867])).
% 1.47/1.20 tff(873,plain,
% 1.47/1.20 (hskp25 | hskp22 | hskp21),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[872, 867])).
% 1.47/1.20 tff(874,plain,
% 1.47/1.20 (hskp25 | hskp22 | hskp21),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[873, 867])).
% 1.47/1.20 tff(875,plain,
% 1.47/1.20 (hskp25 | hskp22 | hskp21),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[874, 867])).
% 1.47/1.20 tff(876,plain,
% 1.47/1.20 (hskp25 | hskp22 | hskp21),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[875, 867])).
% 1.47/1.20 tff(877,plain,
% 1.47/1.20 (hskp25 | hskp22 | hskp21),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[876, 867])).
% 1.47/1.20 tff(878,plain,
% 1.47/1.20 (hskp25),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[877, 866, 849])).
% 1.47/1.20 tff(879,plain,
% 1.47/1.20 (((~hskp25) | (~c2_1(a2265))) <=> ((~hskp25) | (~c2_1(a2265)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(880,plain,
% 1.47/1.20 (((~c2_1(a2265)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a2265)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(881,axiom,((~c2_1(a2265)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.47/1.20 tff(882,plain,
% 1.47/1.20 ((~hskp25) | (~c2_1(a2265))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[881, 880])).
% 1.47/1.20 tff(883,plain,
% 1.47/1.20 ((~hskp25) | (~c2_1(a2265))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[882, 879])).
% 1.47/1.20 tff(884,plain,
% 1.47/1.20 (~c2_1(a2265)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[883, 878])).
% 1.47/1.20 tff(885,plain,
% 1.47/1.20 (((~hskp25) | c3_1(a2265)) <=> ((~hskp25) | c3_1(a2265))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(886,axiom,((~hskp25) | c3_1(a2265)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.47/1.20 tff(887,plain,
% 1.47/1.20 ((~hskp25) | c3_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[886, 885])).
% 1.47/1.20 tff(888,plain,
% 1.47/1.20 ((~hskp25) | c3_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[887, 885])).
% 1.47/1.20 tff(889,plain,
% 1.47/1.20 ((~hskp25) | c3_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[888, 885])).
% 1.47/1.20 tff(890,plain,
% 1.47/1.20 ((~hskp25) | c3_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[889, 885])).
% 1.47/1.20 tff(891,plain,
% 1.47/1.20 ((~hskp25) | c3_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[890, 885])).
% 1.47/1.20 tff(892,plain,
% 1.47/1.20 ((~hskp25) | c3_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[891, 885])).
% 1.47/1.20 tff(893,plain,
% 1.47/1.20 ((~hskp25) | c3_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[892, 885])).
% 1.47/1.20 tff(894,plain,
% 1.47/1.20 ((~hskp25) | c3_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[893, 885])).
% 1.47/1.20 tff(895,plain,
% 1.47/1.20 (c3_1(a2265)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[894, 878])).
% 1.47/1.20 tff(896,plain,
% 1.47/1.20 (((~hskp25) | c1_1(a2265)) <=> ((~hskp25) | c1_1(a2265))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(897,axiom,((~hskp25) | c1_1(a2265)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 1.47/1.20 tff(898,plain,
% 1.47/1.20 ((~hskp25) | c1_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[897, 896])).
% 1.47/1.20 tff(899,plain,
% 1.47/1.20 ((~hskp25) | c1_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[898, 896])).
% 1.47/1.20 tff(900,plain,
% 1.47/1.20 ((~hskp25) | c1_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[899, 896])).
% 1.47/1.20 tff(901,plain,
% 1.47/1.20 ((~hskp25) | c1_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[900, 896])).
% 1.47/1.20 tff(902,plain,
% 1.47/1.20 ((~hskp25) | c1_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[901, 896])).
% 1.47/1.20 tff(903,plain,
% 1.47/1.20 ((~hskp25) | c1_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[902, 896])).
% 1.47/1.20 tff(904,plain,
% 1.47/1.20 ((~hskp25) | c1_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[903, 896])).
% 1.47/1.20 tff(905,plain,
% 1.47/1.20 ((~hskp25) | c1_1(a2265)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[904, 896])).
% 1.47/1.20 tff(906,plain,
% 1.47/1.20 (c1_1(a2265)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[905, 878])).
% 1.47/1.20 tff(907,plain,
% 1.47/1.20 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | c2_1(a2265) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2265)) | (~c1_1(a2265)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp27 | c2_1(a2265) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2265)) | (~c1_1(a2265)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(908,plain,
% 1.47/1.20 ((hskp27 | (~ndr1_0) | c2_1(a2265) | (~c3_1(a2265)) | (~c1_1(a2265)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp27 | c2_1(a2265) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2265)) | (~c1_1(a2265)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(909,plain,
% 1.47/1.20 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a2265) | (~c3_1(a2265)) | (~c1_1(a2265)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | c2_1(a2265) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2265)) | (~c1_1(a2265))))),
% 1.47/1.20 inference(monotonicity,[status(thm)],[908])).
% 1.47/1.20 tff(910,plain,
% 1.47/1.20 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a2265) | (~c3_1(a2265)) | (~c1_1(a2265)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp27 | c2_1(a2265) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2265)) | (~c1_1(a2265)))),
% 1.47/1.20 inference(transitivity,[status(thm)],[909, 907])).
% 1.47/1.20 tff(911,plain,
% 1.47/1.20 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a2265) | (~c3_1(a2265)) | (~c1_1(a2265)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.47/1.20 inference(quant_inst,[status(thm)],[])).
% 1.47/1.20 tff(912,plain,
% 1.47/1.20 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp27 | c2_1(a2265) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2265)) | (~c1_1(a2265))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[911, 910])).
% 1.47/1.20 tff(913,plain,
% 1.47/1.20 (hskp27),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[912, 111, 906, 895, 709, 698, 884, 687, 848])).
% 1.47/1.20 tff(914,plain,
% 1.47/1.20 (((~hskp27) | c3_1(a2178)) <=> ((~hskp27) | c3_1(a2178))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(915,axiom,((~hskp27) | c3_1(a2178)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 1.47/1.20 tff(916,plain,
% 1.47/1.20 ((~hskp27) | c3_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[915, 914])).
% 1.47/1.20 tff(917,plain,
% 1.47/1.20 ((~hskp27) | c3_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[916, 914])).
% 1.47/1.20 tff(918,plain,
% 1.47/1.20 ((~hskp27) | c3_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[917, 914])).
% 1.47/1.20 tff(919,plain,
% 1.47/1.20 ((~hskp27) | c3_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[918, 914])).
% 1.47/1.20 tff(920,plain,
% 1.47/1.20 ((~hskp27) | c3_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[919, 914])).
% 1.47/1.20 tff(921,plain,
% 1.47/1.20 ((~hskp27) | c3_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[920, 914])).
% 1.47/1.20 tff(922,plain,
% 1.47/1.20 ((~hskp27) | c3_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[921, 914])).
% 1.47/1.20 tff(923,plain,
% 1.47/1.20 ((~hskp27) | c3_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[922, 914])).
% 1.47/1.20 tff(924,plain,
% 1.47/1.20 (c3_1(a2178)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[923, 913])).
% 1.47/1.20 tff(925,plain,
% 1.47/1.20 (((~hskp27) | c2_1(a2178)) <=> ((~hskp27) | c2_1(a2178))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(926,axiom,((~hskp27) | c2_1(a2178)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 1.47/1.20 tff(927,plain,
% 1.47/1.20 ((~hskp27) | c2_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[926, 925])).
% 1.47/1.20 tff(928,plain,
% 1.47/1.20 ((~hskp27) | c2_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[927, 925])).
% 1.47/1.20 tff(929,plain,
% 1.47/1.20 ((~hskp27) | c2_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[928, 925])).
% 1.47/1.20 tff(930,plain,
% 1.47/1.20 ((~hskp27) | c2_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[929, 925])).
% 1.47/1.20 tff(931,plain,
% 1.47/1.20 ((~hskp27) | c2_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[930, 925])).
% 1.47/1.20 tff(932,plain,
% 1.47/1.20 ((~hskp27) | c2_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[931, 925])).
% 1.47/1.20 tff(933,plain,
% 1.47/1.20 ((~hskp27) | c2_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[932, 925])).
% 1.47/1.20 tff(934,plain,
% 1.47/1.20 ((~hskp27) | c2_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[933, 925])).
% 1.47/1.20 tff(935,plain,
% 1.47/1.20 (c2_1(a2178)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[934, 913])).
% 1.47/1.20 tff(936,plain,
% 1.47/1.20 (((~hskp27) | c0_1(a2178)) <=> ((~hskp27) | c0_1(a2178))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(937,axiom,((~hskp27) | c0_1(a2178)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.47/1.20 tff(938,plain,
% 1.47/1.20 ((~hskp27) | c0_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[937, 936])).
% 1.47/1.20 tff(939,plain,
% 1.47/1.20 ((~hskp27) | c0_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[938, 936])).
% 1.47/1.20 tff(940,plain,
% 1.47/1.20 ((~hskp27) | c0_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[939, 936])).
% 1.47/1.20 tff(941,plain,
% 1.47/1.20 ((~hskp27) | c0_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[940, 936])).
% 1.47/1.20 tff(942,plain,
% 1.47/1.20 ((~hskp27) | c0_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[941, 936])).
% 1.47/1.20 tff(943,plain,
% 1.47/1.20 ((~hskp27) | c0_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[942, 936])).
% 1.47/1.20 tff(944,plain,
% 1.47/1.20 ((~hskp27) | c0_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[943, 936])).
% 1.47/1.20 tff(945,plain,
% 1.47/1.20 ((~hskp27) | c0_1(a2178)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[944, 936])).
% 1.47/1.20 tff(946,plain,
% 1.47/1.20 (c0_1(a2178)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[945, 913])).
% 1.47/1.20 tff(947,plain,
% 1.47/1.20 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c2_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c2_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2219))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(948,plain,
% 1.47/1.20 ((hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2219) | c2_1(a2219) | c0_1(a2219)) <=> (hskp28 | c2_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2219))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(949,plain,
% 1.47/1.20 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2219) | c2_1(a2219) | c0_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c2_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2219)))),
% 1.47/1.20 inference(monotonicity,[status(thm)],[948])).
% 1.47/1.20 tff(950,plain,
% 1.47/1.20 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2219) | c2_1(a2219) | c0_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c2_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2219))),
% 1.47/1.20 inference(transitivity,[status(thm)],[949, 947])).
% 1.47/1.20 tff(951,plain,
% 1.47/1.20 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2219) | c2_1(a2219) | c0_1(a2219))),
% 1.47/1.20 inference(quant_inst,[status(thm)],[])).
% 1.47/1.20 tff(952,plain,
% 1.47/1.20 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c2_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2219)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[951, 950])).
% 1.47/1.20 tff(953,plain,
% 1.47/1.20 ($false),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[952, 111, 199, 946, 935, 924, 211, 212, 838, 828])).
% 1.47/1.20 tff(954,plain,(hskp28 | c2_1(a2219) | c3_1(a2219) | c1_1(a2219) | hskp17 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.47/1.20 tff(955,plain,
% 1.47/1.20 (hskp17),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[954, 820, 212, 210, 211, 185])).
% 1.47/1.20 tff(956,plain,
% 1.47/1.20 (~c1_1(a2197)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[163, 955])).
% 1.47/1.20 tff(957,plain,
% 1.47/1.20 (c2_1(a2197)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[664, 955])).
% 1.47/1.20 tff(958,plain,
% 1.47/1.20 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(959,plain,
% 1.47/1.20 ((hskp28 | hskp22 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197))) <=> (hskp28 | hskp22 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(960,plain,
% 1.47/1.20 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197))))),
% 1.47/1.20 inference(monotonicity,[status(thm)],[959])).
% 1.47/1.20 tff(961,plain,
% 1.47/1.20 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)))),
% 1.47/1.20 inference(transitivity,[status(thm)],[960, 958])).
% 1.47/1.20 tff(962,plain,
% 1.47/1.20 ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)))),
% 1.47/1.20 inference(quant_inst,[status(thm)],[])).
% 1.47/1.20 tff(963,plain,
% 1.47/1.20 ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[962, 961])).
% 1.47/1.20 tff(964,plain,
% 1.47/1.20 (~c0_1(a2197)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[963, 111, 820, 849, 957, 956, 209])).
% 1.47/1.20 tff(965,plain,
% 1.47/1.20 (c3_1(a2197)),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[653, 955])).
% 1.47/1.20 tff(966,plain,
% 1.47/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(967,plain,
% 1.51/1.20 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2219) | c1_1(a2219) | c2_1(a2219)) <=> (c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(968,plain,
% 1.51/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2219) | c1_1(a2219) | c2_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.51/1.20 inference(monotonicity,[status(thm)],[967])).
% 1.51/1.20 tff(969,plain,
% 1.51/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2219) | c1_1(a2219) | c2_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.51/1.20 inference(transitivity,[status(thm)],[968, 966])).
% 1.51/1.20 tff(970,plain,
% 1.51/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2219) | c1_1(a2219) | c2_1(a2219))),
% 1.51/1.20 inference(quant_inst,[status(thm)],[])).
% 1.51/1.20 tff(971,plain,
% 1.51/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[970, 969])).
% 1.51/1.20 tff(972,plain,
% 1.51/1.20 ($false),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[971, 111, 211, 965, 709, 698, 210, 212, 956, 687, 157, 964])).
% 1.51/1.20 tff(973,plain,(c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | hskp10 | c1_1(a2191) | c3_1(a2191) | c0_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.20 tff(974,plain,
% 1.51/1.20 (c3_1(a2219)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[973, 211, 210, 185, 187, 186, 198])).
% 1.51/1.20 tff(975,assumption,(c3_1(a2219)), introduced(assumption)).
% 1.51/1.20 tff(976,plain,
% 1.51/1.20 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(977,plain,
% 1.51/1.20 ((hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2216) | c2_1(a2216) | c1_1(a2216)) <=> (hskp28 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(978,plain,
% 1.51/1.20 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2216) | c2_1(a2216) | c1_1(a2216))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216))))),
% 1.51/1.20 inference(monotonicity,[status(thm)],[977])).
% 1.51/1.20 tff(979,plain,
% 1.51/1.20 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2216) | c2_1(a2216) | c1_1(a2216))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 1.51/1.20 inference(transitivity,[status(thm)],[978, 976])).
% 1.51/1.20 tff(980,plain,
% 1.51/1.20 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2216) | c2_1(a2216) | c1_1(a2216))),
% 1.51/1.20 inference(quant_inst,[status(thm)],[])).
% 1.51/1.20 tff(981,plain,
% 1.51/1.20 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[980, 979])).
% 1.51/1.20 tff(982,plain,
% 1.51/1.20 ($false),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[981, 111, 199, 45, 34, 28, 442, 857])).
% 1.51/1.20 tff(983,plain,((~hskp21) | hskp28 | hskp17 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.51/1.20 tff(984,plain,
% 1.51/1.20 (~hskp21),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[983, 850, 199, 185])).
% 1.51/1.20 tff(985,plain,
% 1.51/1.20 (hskp25),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[877, 984, 849])).
% 1.51/1.20 tff(986,plain,
% 1.51/1.20 (~c2_1(a2265)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[883, 985])).
% 1.51/1.20 tff(987,plain,
% 1.51/1.20 (c1_1(a2265)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[905, 985])).
% 1.51/1.20 tff(988,plain,
% 1.51/1.20 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | c2_1(a2265) | (~ndr1_0) | (~c0_1(a2265)) | (~c1_1(a2265)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2265) | (~ndr1_0) | (~c0_1(a2265)) | (~c1_1(a2265)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(989,plain,
% 1.51/1.20 ((hskp17 | hskp10 | (~ndr1_0) | c2_1(a2265) | (~c0_1(a2265)) | (~c1_1(a2265))) <=> (hskp17 | hskp10 | c2_1(a2265) | (~ndr1_0) | (~c0_1(a2265)) | (~c1_1(a2265)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(990,plain,
% 1.51/1.20 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2265) | (~c0_1(a2265)) | (~c1_1(a2265)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | c2_1(a2265) | (~ndr1_0) | (~c0_1(a2265)) | (~c1_1(a2265))))),
% 1.51/1.20 inference(monotonicity,[status(thm)],[989])).
% 1.51/1.20 tff(991,plain,
% 1.51/1.20 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2265) | (~c0_1(a2265)) | (~c1_1(a2265)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2265) | (~ndr1_0) | (~c0_1(a2265)) | (~c1_1(a2265)))),
% 1.51/1.20 inference(transitivity,[status(thm)],[990, 988])).
% 1.51/1.20 tff(992,plain,
% 1.51/1.20 ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2265) | (~c0_1(a2265)) | (~c1_1(a2265)))),
% 1.51/1.20 inference(quant_inst,[status(thm)],[])).
% 1.51/1.20 tff(993,plain,
% 1.51/1.20 ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2265) | (~ndr1_0) | (~c0_1(a2265)) | (~c1_1(a2265))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[992, 991])).
% 1.51/1.20 tff(994,plain,
% 1.51/1.20 (~c0_1(a2265)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[993, 111, 850, 185, 987, 986, 634])).
% 1.51/1.20 tff(995,plain,
% 1.51/1.20 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.51/1.20 inference(bind,[status(th)],[])).
% 1.51/1.20 tff(996,plain,
% 1.51/1.20 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.51/1.20 inference(quant_intro,[status(thm)],[995])).
% 1.51/1.20 tff(997,plain,
% 1.51/1.20 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(998,plain,
% 1.51/1.20 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.51/1.20 inference(bind,[status(th)],[])).
% 1.51/1.20 tff(999,plain,
% 1.51/1.20 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.51/1.20 inference(quant_intro,[status(thm)],[998])).
% 1.51/1.20 tff(1000,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 1.51/1.20 tff(1001,plain,
% 1.51/1.20 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[1000, 999])).
% 1.51/1.20 tff(1002,plain,
% 1.51/1.20 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[1001, 997])).
% 1.51/1.21 tff(1003,plain,(
% 1.51/1.21 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.51/1.21 inference(skolemize,[status(sab)],[1002])).
% 1.51/1.21 tff(1004,plain,
% 1.51/1.21 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[1003, 996])).
% 1.51/1.21 tff(1005,plain,
% 1.51/1.21 (c3_1(a2265)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[894, 985])).
% 1.51/1.21 tff(1006,plain,
% 1.51/1.21 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a2265) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2265) | (~c3_1(a2265)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2265) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2265) | (~c3_1(a2265)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1007,plain,
% 1.51/1.21 ((hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2265) | c0_1(a2265) | (~c3_1(a2265))) <=> (hskp10 | c2_1(a2265) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2265) | (~c3_1(a2265)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1008,plain,
% 1.51/1.21 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2265) | c0_1(a2265) | (~c3_1(a2265)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a2265) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2265) | (~c3_1(a2265))))),
% 1.51/1.21 inference(monotonicity,[status(thm)],[1007])).
% 1.51/1.21 tff(1009,plain,
% 1.51/1.21 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2265) | c0_1(a2265) | (~c3_1(a2265)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2265) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2265) | (~c3_1(a2265)))),
% 1.51/1.21 inference(transitivity,[status(thm)],[1008, 1006])).
% 1.51/1.21 tff(1010,plain,
% 1.51/1.21 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2265) | c0_1(a2265) | (~c3_1(a2265)))),
% 1.51/1.21 inference(quant_inst,[status(thm)],[])).
% 1.51/1.21 tff(1011,plain,
% 1.51/1.21 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2265) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2265) | (~c3_1(a2265))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 1.51/1.21 tff(1012,plain,
% 1.51/1.21 (~c2_1(a2191)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[1011, 111, 185, 1005, 986, 187, 186, 1004, 994])).
% 1.51/1.21 tff(1013,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | c0_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | c0_1(a2219))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1014,plain,
% 1.51/1.21 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191)) <=> (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | c0_1(a2219))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1015,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | c0_1(a2219)))),
% 1.51/1.21 inference(monotonicity,[status(thm)],[1014])).
% 1.51/1.21 tff(1016,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | c0_1(a2219))),
% 1.51/1.21 inference(transitivity,[status(thm)],[1015, 1013])).
% 1.51/1.21 tff(1017,plain,
% 1.51/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191))),
% 1.51/1.21 inference(quant_inst,[status(thm)],[])).
% 1.51/1.21 tff(1018,plain,
% 1.51/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | c0_1(a2219)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 1.51/1.21 tff(1019,plain,
% 1.51/1.21 ((~c3_1(a2219)) | c2_1(a2191) | c0_1(a2219)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[1018, 111, 709, 698, 210, 187, 186, 687, 157])).
% 1.51/1.21 tff(1020,plain,
% 1.51/1.21 (c0_1(a2219)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[1019, 1012, 975])).
% 1.51/1.21 tff(1021,plain,
% 1.51/1.21 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c2_1(a2219) | c1_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2219) | c1_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1022,plain,
% 1.51/1.21 ((hskp16 | (~ndr1_0) | c2_1(a2219) | c1_1(a2219) | (~c0_1(a2219))) <=> (hskp16 | c2_1(a2219) | c1_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1023,plain,
% 1.51/1.21 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2219) | c1_1(a2219) | (~c0_1(a2219)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c2_1(a2219) | c1_1(a2219) | (~ndr1_0) | (~c0_1(a2219))))),
% 1.51/1.21 inference(monotonicity,[status(thm)],[1022])).
% 1.51/1.21 tff(1024,plain,
% 1.51/1.21 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2219) | c1_1(a2219) | (~c0_1(a2219)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2219) | c1_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))),
% 1.51/1.21 inference(transitivity,[status(thm)],[1023, 1021])).
% 1.51/1.21 tff(1025,plain,
% 1.51/1.21 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2219) | c1_1(a2219) | (~c0_1(a2219)))),
% 1.51/1.21 inference(quant_inst,[status(thm)],[])).
% 1.51/1.21 tff(1026,plain,
% 1.51/1.21 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2219) | c1_1(a2219) | (~ndr1_0) | (~c0_1(a2219))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 1.51/1.21 tff(1027,plain,
% 1.51/1.21 (hskp16 | c2_1(a2219) | (~c0_1(a2219))),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[1026, 111, 210, 55])).
% 1.51/1.21 tff(1028,plain,
% 1.51/1.21 (hskp16),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[1027, 1020, 211])).
% 1.51/1.21 tff(1029,plain,
% 1.51/1.21 (~c3_1(a2195)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[408, 1028])).
% 1.51/1.21 tff(1030,plain,
% 1.51/1.21 (~c2_1(a2195)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[414, 1028])).
% 1.51/1.21 tff(1031,plain,
% 1.51/1.21 (~c1_1(a2195)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[420, 1028])).
% 1.51/1.21 tff(1032,plain,
% 1.51/1.21 (hskp27),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[912, 111, 987, 1005, 709, 698, 986, 687, 848])).
% 1.51/1.21 tff(1033,plain,
% 1.51/1.21 (c3_1(a2178)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[923, 1032])).
% 1.51/1.21 tff(1034,plain,
% 1.51/1.21 (c2_1(a2178)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[934, 1032])).
% 1.51/1.21 tff(1035,plain,
% 1.51/1.21 (c0_1(a2178)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[945, 1032])).
% 1.51/1.21 tff(1036,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c0_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c0_1(a2219)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1037,plain,
% 1.51/1.21 (((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2219) | (~c3_1(a2219)) | (~c0_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c0_1(a2219)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1038,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2219) | (~c3_1(a2219)) | (~c0_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c0_1(a2219))))),
% 1.51/1.21 inference(monotonicity,[status(thm)],[1037])).
% 1.51/1.21 tff(1039,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2219) | (~c3_1(a2219)) | (~c0_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c0_1(a2219)))),
% 1.51/1.21 inference(transitivity,[status(thm)],[1038, 1036])).
% 1.51/1.21 tff(1040,plain,
% 1.51/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2219) | (~c3_1(a2219)) | (~c0_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.51/1.21 inference(quant_inst,[status(thm)],[])).
% 1.51/1.21 tff(1041,plain,
% 1.51/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c0_1(a2219))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[1040, 1039])).
% 1.51/1.21 tff(1042,plain,
% 1.51/1.21 ($false),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[1041, 111, 1035, 1034, 1033, 210, 975, 1031, 1030, 1029, 184, 1020])).
% 1.51/1.21 tff(1043,plain,(hskp17 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2219) | c1_1(a2191) | c3_1(a2191) | hskp10 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.51/1.21 tff(1044,plain,
% 1.51/1.21 (hskp17),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[1043, 199, 974, 211, 187, 186, 185, 210])).
% 1.51/1.21 tff(1045,plain,
% 1.51/1.21 (~c1_1(a2197)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[163, 1044])).
% 1.51/1.21 tff(1046,plain,
% 1.51/1.21 (c2_1(a2197)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[664, 1044])).
% 1.51/1.21 tff(1047,plain,
% 1.51/1.21 (~c0_1(a2197)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[963, 111, 199, 849, 1046, 1045, 209])).
% 1.51/1.21 tff(1048,plain,
% 1.51/1.21 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.51/1.21 inference(bind,[status(th)],[])).
% 1.51/1.21 tff(1049,plain,
% 1.51/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.51/1.21 inference(quant_intro,[status(thm)],[1048])).
% 1.51/1.21 tff(1050,plain,
% 1.51/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1051,plain,
% 1.51/1.21 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.51/1.21 inference(bind,[status(th)],[])).
% 1.51/1.21 tff(1052,plain,
% 1.51/1.21 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.51/1.21 inference(quant_intro,[status(thm)],[1051])).
% 1.51/1.21 tff(1053,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.51/1.21 tff(1054,plain,
% 1.51/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 1.51/1.21 tff(1055,plain,
% 1.51/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[1054, 1050])).
% 1.51/1.21 tff(1056,plain,(
% 1.51/1.21 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.51/1.21 inference(skolemize,[status(sab)],[1055])).
% 1.51/1.21 tff(1057,plain,
% 1.51/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[1056, 1049])).
% 1.51/1.21 tff(1058,plain,
% 1.51/1.21 (c3_1(a2197)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[653, 1044])).
% 1.51/1.21 tff(1059,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2197) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1060,plain,
% 1.51/1.21 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191)) <=> (c1_1(a2197) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1061,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2197) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.51/1.21 inference(monotonicity,[status(thm)],[1060])).
% 1.51/1.21 tff(1062,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.51/1.21 inference(transitivity,[status(thm)],[1061, 1059])).
% 1.51/1.21 tff(1063,plain,
% 1.51/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191))),
% 1.51/1.21 inference(quant_inst,[status(thm)],[])).
% 1.51/1.21 tff(1064,plain,
% 1.51/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 1.51/1.21 tff(1065,plain,
% 1.51/1.21 (c2_1(a2191)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[1064, 111, 1058, 709, 698, 1045, 187, 186, 687, 157, 1047])).
% 1.51/1.21 tff(1066,plain,
% 1.51/1.21 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2219))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1067,plain,
% 1.51/1.21 ((hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219))) <=> (hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2219))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1068,plain,
% 1.51/1.21 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2219)))),
% 1.51/1.21 inference(monotonicity,[status(thm)],[1067])).
% 1.51/1.21 tff(1069,plain,
% 1.51/1.21 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2219))),
% 1.51/1.21 inference(transitivity,[status(thm)],[1068, 1066])).
% 1.51/1.21 tff(1070,plain,
% 1.51/1.21 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219)))),
% 1.51/1.21 inference(quant_inst,[status(thm)],[])).
% 1.51/1.21 tff(1071,plain,
% 1.51/1.21 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2219)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 1.51/1.21 tff(1072,plain,
% 1.51/1.21 ((~c3_1(a2219)) | (~c2_1(a2191)) | c0_1(a2219)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[1071, 111, 185, 211, 187, 186, 1004])).
% 1.51/1.21 tff(1073,plain,
% 1.51/1.21 (c0_1(a2219)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[1072, 1065, 974])).
% 1.51/1.21 tff(1074,plain,
% 1.51/1.21 (hskp16),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[1027, 1073, 211])).
% 1.51/1.21 tff(1075,plain,
% 1.51/1.21 (~c3_1(a2195)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[408, 1074])).
% 1.51/1.21 tff(1076,plain,
% 1.51/1.21 (~c2_1(a2195)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[414, 1074])).
% 1.51/1.21 tff(1077,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1078,plain,
% 1.51/1.21 (((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2197)) | (~c2_1(a2197))) <=> (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(1079,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2197)) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.51/1.21 inference(monotonicity,[status(thm)],[1078])).
% 1.51/1.21 tff(1080,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2197)) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.51/1.21 inference(transitivity,[status(thm)],[1079, 1077])).
% 1.51/1.21 tff(1081,plain,
% 1.51/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2197)) | (~c2_1(a2197)))),
% 1.51/1.22 inference(quant_inst,[status(thm)],[])).
% 1.51/1.22 tff(1082,plain,
% 1.51/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.51/1.22 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 1.51/1.22 tff(1083,plain,
% 1.51/1.22 (~c0_1(a2195)),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[1082, 111, 1046, 1058, 1045, 1076, 1075, 1057, 1047])).
% 1.51/1.22 tff(1084,plain,
% 1.51/1.22 (~c1_1(a2195)),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[420, 1074])).
% 1.51/1.22 tff(1085,plain,
% 1.51/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a2191) | c1_1(a2195) | c2_1(a2195) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2191) | c1_1(a2195) | c2_1(a2195) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1086,plain,
% 1.51/1.22 (((~ndr1_0) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)) | c1_1(a2195) | c0_1(a2195) | c2_1(a2195)) <=> (c0_1(a2191) | c1_1(a2195) | c2_1(a2195) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1087,plain,
% 1.51/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)) | c1_1(a2195) | c0_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a2191) | c1_1(a2195) | c2_1(a2195) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.51/1.22 inference(monotonicity,[status(thm)],[1086])).
% 1.51/1.22 tff(1088,plain,
% 1.51/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)) | c1_1(a2195) | c0_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2191) | c1_1(a2195) | c2_1(a2195) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.51/1.22 inference(transitivity,[status(thm)],[1087, 1085])).
% 1.51/1.22 tff(1089,plain,
% 1.51/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)) | c1_1(a2195) | c0_1(a2195) | c2_1(a2195))),
% 1.51/1.22 inference(quant_inst,[status(thm)],[])).
% 1.51/1.22 tff(1090,plain,
% 1.51/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2191) | c1_1(a2195) | c2_1(a2195) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.51/1.22 inference(modus_ponens,[status(thm)],[1089, 1088])).
% 1.51/1.22 tff(1091,plain,
% 1.51/1.22 ($false),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[1090, 111, 1046, 1058, 198, 1084, 1076, 186, 728, 1065, 1047, 1083])).
% 1.51/1.22 tff(1092,plain,(hskp28 | c0_1(a2191) | c3_1(a2191) | c2_1(a2219) | c1_1(a2219) | hskp10 | c1_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.22 tff(1093,plain,
% 1.51/1.22 (hskp28),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[1092, 211, 186, 198, 210, 185, 187])).
% 1.51/1.22 tff(1094,plain,
% 1.51/1.22 (hskp11),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[819, 1093, 187, 186, 198, 185])).
% 1.51/1.22 tff(1095,plain,
% 1.51/1.22 (~c1_1(a2187)),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[218, 1094])).
% 1.51/1.22 tff(1096,plain,
% 1.51/1.22 (c2_1(a2187)),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[229, 1094])).
% 1.51/1.22 tff(1097,plain,
% 1.51/1.22 (c0_1(a2187)),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[240, 1094])).
% 1.51/1.22 tff(1098,plain,
% 1.51/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c2_1(a2191))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1099,plain,
% 1.51/1.22 (((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191)) <=> (c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c2_1(a2191))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1100,plain,
% 1.51/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c2_1(a2191)))),
% 1.51/1.22 inference(monotonicity,[status(thm)],[1099])).
% 1.51/1.22 tff(1101,plain,
% 1.51/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c2_1(a2191))),
% 1.51/1.22 inference(transitivity,[status(thm)],[1100, 1098])).
% 1.51/1.22 tff(1102,plain,
% 1.51/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))),
% 1.51/1.22 inference(quant_inst,[status(thm)],[])).
% 1.51/1.22 tff(1103,plain,
% 1.51/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c2_1(a2191)),
% 1.51/1.22 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 1.51/1.22 tff(1104,plain,
% 1.51/1.22 (c2_1(a2191)),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[1103, 111, 198, 1097, 1096, 187, 186, 1095, 197])).
% 1.51/1.22 tff(1105,plain,
% 1.51/1.22 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1106,plain,
% 1.51/1.22 ((hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187))) <=> (hskp10 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1107,plain,
% 1.51/1.22 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187))))),
% 1.51/1.22 inference(monotonicity,[status(thm)],[1106])).
% 1.51/1.22 tff(1108,plain,
% 1.51/1.22 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))),
% 1.51/1.22 inference(transitivity,[status(thm)],[1107, 1105])).
% 1.51/1.22 tff(1109,plain,
% 1.51/1.22 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)))),
% 1.51/1.22 inference(quant_inst,[status(thm)],[])).
% 1.51/1.22 tff(1110,plain,
% 1.51/1.22 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187))),
% 1.51/1.22 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 1.51/1.22 tff(1111,plain,
% 1.51/1.22 (~c3_1(a2187)),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[1110, 111, 185, 1097, 1096, 1095, 311])).
% 1.51/1.22 tff(1112,plain,
% 1.51/1.22 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2187) | (~ndr1_0) | c3_1(a2187) | (~c2_1(a2187)) | c0_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2187) | (~ndr1_0) | c3_1(a2187) | (~c2_1(a2187)) | c0_1(a2219))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1113,plain,
% 1.51/1.22 ((hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219))) <=> (hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2187) | (~ndr1_0) | c3_1(a2187) | (~c2_1(a2187)) | c0_1(a2219))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1114,plain,
% 1.51/1.22 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2187) | (~ndr1_0) | c3_1(a2187) | (~c2_1(a2187)) | c0_1(a2219)))),
% 1.51/1.22 inference(monotonicity,[status(thm)],[1113])).
% 1.51/1.22 tff(1115,plain,
% 1.51/1.22 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2187) | (~ndr1_0) | c3_1(a2187) | (~c2_1(a2187)) | c0_1(a2219))),
% 1.51/1.22 inference(transitivity,[status(thm)],[1114, 1112])).
% 1.51/1.22 tff(1116,plain,
% 1.51/1.22 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219)))),
% 1.51/1.22 inference(quant_inst,[status(thm)],[])).
% 1.51/1.22 tff(1117,plain,
% 1.51/1.22 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2187) | (~ndr1_0) | c3_1(a2187) | (~c2_1(a2187)) | c0_1(a2219)),
% 1.51/1.22 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 1.51/1.22 tff(1118,plain,
% 1.51/1.22 (c0_1(a2219)),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[1117, 111, 185, 211, 1096, 974, 1095, 1004, 1111])).
% 1.51/1.22 tff(1119,plain,
% 1.51/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a2219) | c0_1(a2191) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a2219) | c0_1(a2191) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2219)))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1120,plain,
% 1.51/1.22 (((~ndr1_0) | c2_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191))) <=> (c2_1(a2219) | c0_1(a2191) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2219)))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1121,plain,
% 1.51/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a2219) | c0_1(a2191) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2219))))),
% 1.51/1.22 inference(monotonicity,[status(thm)],[1120])).
% 1.51/1.22 tff(1122,plain,
% 1.51/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a2219) | c0_1(a2191) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2219)))),
% 1.51/1.22 inference(transitivity,[status(thm)],[1121, 1119])).
% 1.51/1.22 tff(1123,plain,
% 1.51/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))),
% 1.51/1.22 inference(quant_inst,[status(thm)],[])).
% 1.51/1.22 tff(1124,plain,
% 1.51/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a2219) | c0_1(a2191) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2219))),
% 1.51/1.22 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 1.51/1.22 tff(1125,plain,
% 1.51/1.22 ((~c2_1(a2191)) | (~c0_1(a2219))),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[1124, 111, 211, 198, 1097, 1096, 974, 186, 1095, 322])).
% 1.51/1.22 tff(1126,plain,
% 1.51/1.22 ($false),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[1125, 1118, 1104])).
% 1.51/1.22 tff(1127,plain,(c2_1(a2219) | c0_1(a2191) | c3_1(a2191) | hskp10 | c1_1(a2191) | c1_1(a2219)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.22 tff(1128,plain,
% 1.51/1.22 (c2_1(a2219)),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[1127, 210, 186, 185, 187, 198])).
% 1.51/1.22 tff(1129,plain,
% 1.51/1.22 (~hskp13),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[370, 198])).
% 1.51/1.22 tff(1130,assumption,(~c0_1(a2219)), introduced(assumption)).
% 1.51/1.22 tff(1131,assumption,(c2_1(a2174)), introduced(assumption)).
% 1.51/1.22 tff(1132,assumption,(c1_1(a2174)), introduced(assumption)).
% 1.51/1.22 tff(1133,plain,
% 1.51/1.22 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.51/1.22 inference(bind,[status(th)],[])).
% 1.51/1.22 tff(1134,plain,
% 1.51/1.22 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.51/1.22 inference(quant_intro,[status(thm)],[1133])).
% 1.51/1.22 tff(1135,plain,
% 1.51/1.22 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1136,plain,
% 1.51/1.22 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.51/1.22 inference(bind,[status(th)],[])).
% 1.51/1.22 tff(1137,plain,
% 1.51/1.22 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.51/1.22 inference(quant_intro,[status(thm)],[1136])).
% 1.51/1.22 tff(1138,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 1.51/1.22 tff(1139,plain,
% 1.51/1.22 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.51/1.22 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 1.51/1.22 tff(1140,plain,
% 1.51/1.22 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.51/1.22 inference(modus_ponens,[status(thm)],[1139, 1135])).
% 1.51/1.22 tff(1141,plain,(
% 1.51/1.22 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.51/1.22 inference(skolemize,[status(sab)],[1140])).
% 1.51/1.22 tff(1142,plain,
% 1.51/1.22 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.51/1.22 inference(modus_ponens,[status(thm)],[1141, 1134])).
% 1.51/1.22 tff(1143,plain,
% 1.51/1.22 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219) | (~c2_1(a2219)))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1144,plain,
% 1.51/1.22 ((hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219))) <=> (hskp27 | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219) | (~c2_1(a2219)))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1145,plain,
% 1.51/1.22 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219) | (~c2_1(a2219))))),
% 1.51/1.22 inference(monotonicity,[status(thm)],[1144])).
% 1.51/1.22 tff(1146,plain,
% 1.51/1.22 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219) | (~c2_1(a2219)))),
% 1.51/1.22 inference(transitivity,[status(thm)],[1145, 1143])).
% 1.51/1.22 tff(1147,plain,
% 1.51/1.22 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))),
% 1.51/1.22 inference(quant_inst,[status(thm)],[])).
% 1.51/1.22 tff(1148,plain,
% 1.51/1.22 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219) | (~c2_1(a2219))),
% 1.51/1.22 inference(modus_ponens,[status(thm)],[1147, 1146])).
% 1.51/1.22 tff(1149,plain,
% 1.51/1.22 (hskp27 | c0_1(a2219) | (~c2_1(a2219))),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[1148, 111, 1132, 1131, 210, 147, 1142])).
% 1.51/1.22 tff(1150,plain,
% 1.51/1.22 (hskp27),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[1149, 1130, 529])).
% 1.51/1.22 tff(1151,plain,
% 1.51/1.22 (c3_1(a2178)),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[923, 1150])).
% 1.51/1.22 tff(1152,plain,
% 1.51/1.22 (c0_1(a2178)),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[945, 1150])).
% 1.51/1.22 tff(1153,plain,
% 1.51/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2219) | (~c2_1(a2219)))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1154,plain,
% 1.51/1.22 (((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219))) <=> (c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2219) | (~c2_1(a2219)))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1155,plain,
% 1.51/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2219) | (~c2_1(a2219))))),
% 1.51/1.22 inference(monotonicity,[status(thm)],[1154])).
% 1.51/1.22 tff(1156,plain,
% 1.51/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2219) | (~c2_1(a2219)))),
% 1.51/1.22 inference(transitivity,[status(thm)],[1155, 1153])).
% 1.51/1.22 tff(1157,plain,
% 1.51/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))),
% 1.51/1.22 inference(quant_inst,[status(thm)],[])).
% 1.51/1.22 tff(1158,plain,
% 1.51/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2219) | (~c2_1(a2219))),
% 1.51/1.22 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 1.51/1.22 tff(1159,plain,
% 1.51/1.22 (~c1_1(a2178)),
% 1.51/1.22 inference(unit_resolution,[status(thm)],[1158, 111, 1152, 1151, 529, 1132, 1131, 210, 147, 301, 1130])).
% 1.51/1.22 tff(1160,plain,
% 1.51/1.22 (^[U: $i] : refl((hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 1.51/1.22 inference(bind,[status(th)],[])).
% 1.51/1.22 tff(1161,plain,
% 1.51/1.22 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.51/1.22 inference(quant_intro,[status(thm)],[1160])).
% 1.51/1.22 tff(1162,plain,
% 1.51/1.22 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.51/1.22 inference(rewrite,[status(thm)],[])).
% 1.51/1.22 tff(1163,plain,
% 1.51/1.22 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp16) <=> ((hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp16))), rewrite(((hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp16) <=> (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp16) <=> (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 1.51/1.23 inference(bind,[status(th)],[])).
% 1.51/1.23 tff(1164,plain,
% 1.51/1.23 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp16) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.51/1.23 inference(quant_intro,[status(thm)],[1163])).
% 1.51/1.23 tff(1165,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.51/1.23 tff(1166,plain,
% 1.51/1.23 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.51/1.23 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 1.51/1.23 tff(1167,plain,
% 1.51/1.23 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.51/1.23 inference(modus_ponens,[status(thm)],[1166, 1162])).
% 1.51/1.23 tff(1168,plain,(
% 1.51/1.23 ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.51/1.23 inference(skolemize,[status(sab)],[1167])).
% 1.51/1.23 tff(1169,plain,
% 1.51/1.23 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.51/1.23 inference(modus_ponens,[status(thm)],[1168, 1161])).
% 1.51/1.23 tff(1170,assumption,(~hskp13), introduced(assumption)).
% 1.51/1.23 tff(1171,plain,
% 1.51/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | (~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))),
% 1.51/1.23 inference(rewrite,[status(thm)],[])).
% 1.51/1.23 tff(1172,plain,
% 1.51/1.23 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c3_1(a2178))) <=> (hskp16 | hskp13 | (~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))),
% 1.51/1.23 inference(rewrite,[status(thm)],[])).
% 1.51/1.23 tff(1173,plain,
% 1.51/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c3_1(a2178)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178)))),
% 1.51/1.23 inference(monotonicity,[status(thm)],[1172])).
% 1.51/1.23 tff(1174,plain,
% 1.51/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c3_1(a2178)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | (~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))),
% 1.51/1.23 inference(transitivity,[status(thm)],[1173, 1171])).
% 1.51/1.23 tff(1175,plain,
% 1.51/1.23 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c3_1(a2178)))),
% 1.51/1.23 inference(quant_inst,[status(thm)],[])).
% 1.51/1.23 tff(1176,plain,
% 1.51/1.23 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | (~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178)),
% 1.51/1.23 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 1.51/1.23 tff(1177,plain,
% 1.51/1.23 (hskp16),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[1176, 111, 1170, 1152, 1151, 1169, 1159])).
% 1.51/1.23 tff(1178,plain,
% 1.51/1.23 (~c3_1(a2195)),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[408, 1177])).
% 1.51/1.23 tff(1179,plain,
% 1.51/1.23 (~c2_1(a2195)),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[414, 1177])).
% 1.51/1.23 tff(1180,plain,
% 1.51/1.23 (~c1_1(a2195)),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[420, 1177])).
% 1.51/1.23 tff(1181,plain,
% 1.51/1.23 (c2_1(a2178)),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[934, 1150])).
% 1.51/1.23 tff(1182,plain,
% 1.51/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))),
% 1.51/1.23 inference(rewrite,[status(thm)],[])).
% 1.51/1.23 tff(1183,plain,
% 1.51/1.23 (((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))),
% 1.51/1.23 inference(rewrite,[status(thm)],[])).
% 1.51/1.23 tff(1184,plain,
% 1.51/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178)))),
% 1.51/1.23 inference(monotonicity,[status(thm)],[1183])).
% 1.51/1.23 tff(1185,plain,
% 1.51/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))),
% 1.51/1.23 inference(transitivity,[status(thm)],[1184, 1182])).
% 1.51/1.23 tff(1186,plain,
% 1.51/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.51/1.23 inference(quant_inst,[status(thm)],[])).
% 1.51/1.23 tff(1187,plain,
% 1.51/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178)),
% 1.51/1.23 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 1.51/1.23 tff(1188,plain,
% 1.51/1.23 ($false),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[1187, 111, 1152, 1181, 1151, 1180, 1179, 1178, 184, 1159])).
% 1.51/1.23 tff(1189,plain,(c0_1(a2219) | hskp13 | (~c2_1(a2219)) | (~c1_1(a2174)) | (~c2_1(a2174)) | c1_1(a2219) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.23 tff(1190,plain,
% 1.51/1.23 (c0_1(a2219)),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[1189, 1128, 1129, 709, 698, 210, 687])).
% 1.51/1.23 tff(1191,plain,
% 1.51/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2191) | c1_1(a2219) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2219) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.51/1.23 inference(rewrite,[status(thm)],[])).
% 1.51/1.23 tff(1192,plain,
% 1.51/1.23 (((~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c2_1(a2219)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191)) <=> (c0_1(a2191) | c1_1(a2219) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.51/1.23 inference(rewrite,[status(thm)],[])).
% 1.51/1.23 tff(1193,plain,
% 1.51/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c2_1(a2219)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2191) | c1_1(a2219) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219))))),
% 1.51/1.23 inference(monotonicity,[status(thm)],[1192])).
% 1.51/1.23 tff(1194,plain,
% 1.51/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c2_1(a2219)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2219) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.51/1.23 inference(transitivity,[status(thm)],[1193, 1191])).
% 1.51/1.23 tff(1195,plain,
% 1.51/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c2_1(a2219)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))),
% 1.51/1.23 inference(quant_inst,[status(thm)],[])).
% 1.51/1.23 tff(1196,plain,
% 1.51/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2219) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219))),
% 1.51/1.23 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 1.51/1.23 tff(1197,plain,
% 1.51/1.23 (c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219))),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[1196, 111, 198, 210, 187, 186, 197])).
% 1.51/1.23 tff(1198,plain,
% 1.51/1.23 (c2_1(a2191)),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[1197, 1190, 1128])).
% 1.51/1.23 tff(1199,plain,
% 1.51/1.23 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2191)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2191)))),
% 1.51/1.23 inference(rewrite,[status(thm)],[])).
% 1.51/1.23 tff(1200,plain,
% 1.51/1.23 ((hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191))) <=> (hskp27 | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2191)))),
% 1.51/1.23 inference(rewrite,[status(thm)],[])).
% 1.51/1.23 tff(1201,plain,
% 1.51/1.23 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2191))))),
% 1.51/1.23 inference(monotonicity,[status(thm)],[1200])).
% 1.51/1.23 tff(1202,plain,
% 1.51/1.23 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2191)))),
% 1.51/1.23 inference(transitivity,[status(thm)],[1201, 1199])).
% 1.51/1.23 tff(1203,plain,
% 1.51/1.23 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))),
% 1.51/1.23 inference(quant_inst,[status(thm)],[])).
% 1.51/1.23 tff(1204,plain,
% 1.51/1.23 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2191))),
% 1.51/1.23 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 1.51/1.23 tff(1205,plain,
% 1.51/1.23 (hskp27 | c0_1(a2191) | (~c2_1(a2191))),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[1204, 111, 709, 698, 187, 687, 1142])).
% 1.51/1.23 tff(1206,plain,
% 1.51/1.23 (hskp27),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[1205, 1198, 198])).
% 1.51/1.23 tff(1207,plain,
% 1.51/1.23 (c3_1(a2178)),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[923, 1206])).
% 1.51/1.23 tff(1208,plain,
% 1.51/1.23 (c0_1(a2178)),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[945, 1206])).
% 1.51/1.23 tff(1209,plain,
% 1.51/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2191)))),
% 1.51/1.23 inference(rewrite,[status(thm)],[])).
% 1.51/1.23 tff(1210,plain,
% 1.51/1.23 (((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191))) <=> (c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2191)))),
% 1.51/1.23 inference(rewrite,[status(thm)],[])).
% 1.51/1.23 tff(1211,plain,
% 1.51/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2191))))),
% 1.51/1.23 inference(monotonicity,[status(thm)],[1210])).
% 1.51/1.23 tff(1212,plain,
% 1.51/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2191)))),
% 1.51/1.23 inference(transitivity,[status(thm)],[1211, 1209])).
% 1.51/1.23 tff(1213,plain,
% 1.51/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))),
% 1.51/1.23 inference(quant_inst,[status(thm)],[])).
% 1.51/1.23 tff(1214,plain,
% 1.51/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2191))),
% 1.51/1.23 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 1.51/1.23 tff(1215,plain,
% 1.51/1.23 (~c1_1(a2178)),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[1214, 111, 1208, 1207, 198, 709, 698, 187, 687, 301, 1198])).
% 1.51/1.23 tff(1216,plain,
% 1.51/1.23 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c1_1(a2219) | (~c3_1(a2219)) | (~ndr1_0) | (~c2_1(a2219)) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2219) | (~c3_1(a2219)) | (~ndr1_0) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.51/1.23 inference(rewrite,[status(thm)],[])).
% 1.51/1.23 tff(1217,plain,
% 1.51/1.23 ((hskp10 | (~ndr1_0) | c1_1(a2219) | (~c2_1(a2219)) | (~c3_1(a2219)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219))) <=> (hskp10 | c1_1(a2219) | (~c3_1(a2219)) | (~ndr1_0) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.51/1.23 inference(rewrite,[status(thm)],[])).
% 1.51/1.23 tff(1218,plain,
% 1.51/1.23 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2219) | (~c2_1(a2219)) | (~c3_1(a2219)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c1_1(a2219) | (~c3_1(a2219)) | (~ndr1_0) | (~c2_1(a2219)) | (~c0_1(a2219))))),
% 1.51/1.23 inference(monotonicity,[status(thm)],[1217])).
% 1.51/1.23 tff(1219,plain,
% 1.51/1.23 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2219) | (~c2_1(a2219)) | (~c3_1(a2219)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2219) | (~c3_1(a2219)) | (~ndr1_0) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.51/1.23 inference(transitivity,[status(thm)],[1218, 1216])).
% 1.51/1.23 tff(1220,plain,
% 1.51/1.23 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2219) | (~c2_1(a2219)) | (~c3_1(a2219)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.51/1.23 inference(quant_inst,[status(thm)],[])).
% 1.51/1.23 tff(1221,plain,
% 1.51/1.23 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2219) | (~c3_1(a2219)) | (~ndr1_0) | (~c2_1(a2219)) | (~c0_1(a2219))),
% 1.51/1.23 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 1.51/1.23 tff(1222,plain,
% 1.51/1.23 ((~c3_1(a2219)) | (~c2_1(a2219)) | (~c0_1(a2219))),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[1221, 111, 185, 210, 311])).
% 1.51/1.23 tff(1223,plain,
% 1.51/1.23 (~c3_1(a2219)),
% 1.51/1.23 inference(unit_resolution,[status(thm)],[1222, 1190, 1128])).
% 1.51/1.23 tff(1224,plain,
% 1.51/1.23 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 1.51/1.23 inference(bind,[status(th)],[])).
% 1.51/1.23 tff(1225,plain,
% 1.51/1.23 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.51/1.23 inference(quant_intro,[status(thm)],[1224])).
% 1.51/1.23 tff(1226,plain,
% 1.51/1.23 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.51/1.23 inference(rewrite,[status(thm)],[])).
% 1.51/1.23 tff(1227,plain,
% 1.51/1.23 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp18) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp18))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 1.51/1.23 inference(bind,[status(th)],[])).
% 1.51/1.23 tff(1228,plain,
% 1.51/1.23 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.51/1.23 inference(quant_intro,[status(thm)],[1227])).
% 1.51/1.23 tff(1229,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 1.51/1.23 tff(1230,plain,
% 1.51/1.23 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.51/1.23 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 1.51/1.23 tff(1231,plain,
% 1.51/1.23 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.51/1.23 inference(modus_ponens,[status(thm)],[1230, 1226])).
% 1.51/1.23 tff(1232,plain,(
% 1.51/1.23 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.54/1.23 inference(skolemize,[status(sab)],[1231])).
% 1.54/1.23 tff(1233,plain,
% 1.54/1.23 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[1232, 1225])).
% 1.54/1.23 tff(1234,plain,
% 1.54/1.23 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2219) | c3_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2219) | c3_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2219)))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(1235,plain,
% 1.54/1.23 ((hskp18 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp18 | c1_1(a2219) | c3_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2219)))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(1236,plain,
% 1.54/1.23 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2219) | c3_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2219))))),
% 1.54/1.23 inference(monotonicity,[status(thm)],[1235])).
% 1.54/1.23 tff(1237,plain,
% 1.54/1.23 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2219) | c3_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2219)))),
% 1.54/1.23 inference(transitivity,[status(thm)],[1236, 1234])).
% 1.54/1.23 tff(1238,plain,
% 1.54/1.23 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.54/1.23 inference(quant_inst,[status(thm)],[])).
% 1.54/1.23 tff(1239,plain,
% 1.54/1.23 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2219) | c3_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2219))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 1.54/1.23 tff(1240,plain,
% 1.54/1.23 (hskp18 | c3_1(a2219) | (~c0_1(a2219))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[1239, 111, 709, 698, 210, 687, 1233])).
% 1.54/1.23 tff(1241,plain,
% 1.54/1.23 (hskp18),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[1240, 1190, 1223])).
% 1.54/1.23 tff(1242,plain,
% 1.54/1.23 (~c2_1(a2198)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[61, 1241])).
% 1.54/1.23 tff(1243,plain,
% 1.54/1.23 (~c1_1(a2198)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[67, 1241])).
% 1.54/1.23 tff(1244,plain,
% 1.54/1.23 (c0_1(a2198)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[78, 1241])).
% 1.54/1.23 tff(1245,plain,
% 1.54/1.23 (hskp16),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[117, 111, 1244, 1243, 1242, 55])).
% 1.54/1.23 tff(1246,plain,
% 1.54/1.23 (~c3_1(a2195)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[408, 1245])).
% 1.54/1.23 tff(1247,plain,
% 1.54/1.23 (~c2_1(a2195)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[414, 1245])).
% 1.54/1.23 tff(1248,plain,
% 1.54/1.23 (~c1_1(a2195)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[420, 1245])).
% 1.54/1.23 tff(1249,plain,
% 1.54/1.23 (c2_1(a2178)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[934, 1206])).
% 1.54/1.23 tff(1250,plain,
% 1.54/1.23 ($false),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[1187, 111, 1208, 1249, 1207, 1248, 1247, 1246, 184, 1215])).
% 1.54/1.23 tff(1251,plain,(c1_1(a2219) | c0_1(a2191) | c1_1(a2191) | hskp10 | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.23 tff(1252,plain,
% 1.54/1.23 (c1_1(a2219)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[1251, 198, 187, 185, 186])).
% 1.54/1.24 tff(1253,plain,
% 1.54/1.24 (~hskp22),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[516, 1252])).
% 1.54/1.24 tff(1254,assumption,(~hskp27), introduced(assumption)).
% 1.54/1.24 tff(1255,assumption,(hskp25), introduced(assumption)).
% 1.54/1.24 tff(1256,plain,
% 1.54/1.24 (~c2_1(a2265)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[883, 1255])).
% 1.54/1.24 tff(1257,plain,
% 1.54/1.24 (c3_1(a2265)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[894, 1255])).
% 1.54/1.24 tff(1258,plain,
% 1.54/1.24 (c1_1(a2265)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[905, 1255])).
% 1.54/1.24 tff(1259,plain,
% 1.54/1.24 ($false),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[912, 111, 1254, 1258, 1257, 1132, 1131, 1256, 147, 848])).
% 1.54/1.24 tff(1260,plain,((~hskp25) | hskp27 | (~c1_1(a2174)) | (~c2_1(a2174)) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.24 tff(1261,plain,
% 1.54/1.24 (~hskp25),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1260, 1254, 709, 698, 687])).
% 1.54/1.24 tff(1262,plain,
% 1.54/1.24 (hskp21),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[877, 1261, 1253])).
% 1.54/1.24 tff(1263,plain,
% 1.54/1.24 (hskp17),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[983, 1262, 199, 185])).
% 1.54/1.24 tff(1264,plain,
% 1.54/1.24 (~c1_1(a2197)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[163, 1263])).
% 1.54/1.24 tff(1265,plain,
% 1.54/1.24 (c2_1(a2197)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[664, 1263])).
% 1.54/1.24 tff(1266,plain,
% 1.54/1.24 (~c0_1(a2197)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[963, 111, 199, 1253, 1265, 1264, 209])).
% 1.54/1.24 tff(1267,plain,
% 1.54/1.24 (~c2_1(a2191)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1205, 1254, 198])).
% 1.54/1.24 tff(1268,plain,
% 1.54/1.24 (c3_1(a2197)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[653, 1263])).
% 1.54/1.24 tff(1269,plain,
% 1.54/1.24 ($false),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1064, 111, 1268, 709, 698, 1264, 187, 186, 687, 157, 1267, 1266])).
% 1.54/1.24 tff(1270,plain,(hskp27 | c1_1(a2191) | c3_1(a2191) | hskp28 | hskp10 | c0_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.24 tff(1271,plain,
% 1.54/1.24 (hskp27),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1270, 199, 186, 187, 185, 198])).
% 1.54/1.24 tff(1272,plain,
% 1.54/1.24 (c2_1(a2178)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[934, 1271])).
% 1.54/1.24 tff(1273,plain,
% 1.54/1.24 (c0_1(a2178)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[945, 1271])).
% 1.54/1.24 tff(1274,plain,
% 1.54/1.24 (c3_1(a2178)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[923, 1271])).
% 1.54/1.24 tff(1275,assumption,(c3_1(a2178)), introduced(assumption)).
% 1.54/1.24 tff(1276,assumption,(c2_1(a2178)), introduced(assumption)).
% 1.54/1.24 tff(1277,assumption,(c0_1(a2178)), introduced(assumption)).
% 1.54/1.24 tff(1278,plain,
% 1.54/1.24 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c0_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c2_1(a2191))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c0_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c2_1(a2191))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1279,plain,
% 1.54/1.24 ((hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2191) | c2_1(a2191) | c0_1(a2191)) <=> (hskp28 | c0_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c2_1(a2191))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1280,plain,
% 1.54/1.24 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2191) | c2_1(a2191) | c0_1(a2191))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c0_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c2_1(a2191)))),
% 1.54/1.24 inference(monotonicity,[status(thm)],[1279])).
% 1.54/1.24 tff(1281,plain,
% 1.54/1.24 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2191) | c2_1(a2191) | c0_1(a2191))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c0_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c2_1(a2191))),
% 1.54/1.24 inference(transitivity,[status(thm)],[1280, 1278])).
% 1.54/1.24 tff(1282,plain,
% 1.54/1.24 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2191) | c2_1(a2191) | c0_1(a2191))),
% 1.54/1.24 inference(quant_inst,[status(thm)],[])).
% 1.54/1.24 tff(1283,plain,
% 1.54/1.24 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c0_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c2_1(a2191)),
% 1.54/1.24 inference(modus_ponens,[status(thm)],[1282, 1281])).
% 1.54/1.24 tff(1284,plain,
% 1.54/1.24 (hskp28 | c2_1(a2191)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1283, 111, 1277, 1276, 1275, 198, 186, 838])).
% 1.54/1.24 tff(1285,plain,
% 1.54/1.24 (c2_1(a2191)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1284, 199])).
% 1.54/1.24 tff(1286,assumption,(~hskp22), introduced(assumption)).
% 1.54/1.24 tff(1287,plain,
% 1.54/1.24 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | c1_1(a2178))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | c1_1(a2178))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1288,plain,
% 1.54/1.24 ((hskp28 | hskp22 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178))) <=> (hskp28 | hskp22 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | c1_1(a2178))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1289,plain,
% 1.54/1.24 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | c1_1(a2178)))),
% 1.54/1.24 inference(monotonicity,[status(thm)],[1288])).
% 1.54/1.24 tff(1290,plain,
% 1.54/1.24 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | c1_1(a2178))),
% 1.54/1.24 inference(transitivity,[status(thm)],[1289, 1287])).
% 1.54/1.24 tff(1291,plain,
% 1.54/1.24 ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 1.54/1.24 inference(quant_inst,[status(thm)],[])).
% 1.54/1.24 tff(1292,plain,
% 1.54/1.24 ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | c1_1(a2178)),
% 1.54/1.24 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 1.54/1.24 tff(1293,plain,
% 1.54/1.24 (hskp28 | c1_1(a2178)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1292, 111, 1286, 1277, 1276, 209])).
% 1.54/1.24 tff(1294,plain,
% 1.54/1.24 (c1_1(a2178)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1293, 199])).
% 1.54/1.24 tff(1295,plain,
% 1.54/1.24 ((~c1_1(a2178)) | (~c2_1(a2191))),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1214, 111, 1277, 1275, 198, 1132, 1131, 187, 147, 301])).
% 1.54/1.24 tff(1296,plain,
% 1.54/1.24 ($false),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1295, 1294, 1285])).
% 1.54/1.24 tff(1297,plain,(hskp28 | (~c0_1(a2178)) | (~c3_1(a2178)) | c0_1(a2191) | (~c1_1(a2174)) | (~c2_1(a2174)) | c1_1(a2191) | c0_1(a2174) | hskp22 | (~c2_1(a2178)) | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.24 tff(1298,plain,
% 1.54/1.24 ($false),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1297, 1274, 1273, 199, 198, 709, 698, 187, 687, 1253, 1272, 186])).
% 1.54/1.24 tff(1299,plain,(hskp28 | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.54/1.24 tff(1300,plain,
% 1.54/1.24 (hskp28),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1299, 198, 187, 186, 185])).
% 1.54/1.24 tff(1301,plain,
% 1.54/1.24 (hskp11),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[819, 1300, 187, 186, 198, 185])).
% 1.54/1.24 tff(1302,plain,
% 1.54/1.24 (~c1_1(a2187)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[218, 1301])).
% 1.54/1.24 tff(1303,plain,
% 1.54/1.24 (c2_1(a2187)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[229, 1301])).
% 1.54/1.24 tff(1304,plain,
% 1.54/1.24 (c0_1(a2187)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[240, 1301])).
% 1.54/1.24 tff(1305,plain,
% 1.54/1.24 (c2_1(a2191)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1103, 111, 198, 1304, 1303, 187, 186, 1302, 197])).
% 1.54/1.24 tff(1306,plain,
% 1.54/1.24 (~c3_1(a2187)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1110, 111, 185, 1304, 1303, 1302, 311])).
% 1.54/1.24 tff(1307,plain,
% 1.54/1.24 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1308,plain,
% 1.54/1.24 ((hskp18 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | c3_1(a2187) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp18 | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1309,plain,
% 1.54/1.24 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | c3_1(a2187) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187)))),
% 1.54/1.24 inference(monotonicity,[status(thm)],[1308])).
% 1.54/1.24 tff(1310,plain,
% 1.54/1.24 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | c3_1(a2187) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187))),
% 1.54/1.24 inference(transitivity,[status(thm)],[1309, 1307])).
% 1.54/1.24 tff(1311,plain,
% 1.54/1.24 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | c3_1(a2187) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.54/1.24 inference(quant_inst,[status(thm)],[])).
% 1.54/1.24 tff(1312,plain,
% 1.54/1.24 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187)),
% 1.54/1.24 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 1.54/1.24 tff(1313,plain,
% 1.54/1.24 (hskp18),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1312, 111, 1304, 709, 698, 1302, 687, 1233, 1306])).
% 1.54/1.24 tff(1314,plain,
% 1.54/1.24 (~c2_1(a2198)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[61, 1313])).
% 1.54/1.24 tff(1315,plain,
% 1.54/1.24 (c0_1(a2198)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[78, 1313])).
% 1.54/1.24 tff(1316,plain,
% 1.54/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2191) | c2_1(a2198) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2198)) | (~c3_1(a2198)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c2_1(a2198) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2198)) | (~c3_1(a2198)))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1317,plain,
% 1.54/1.24 (((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191))) <=> (c0_1(a2191) | c2_1(a2198) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2198)) | (~c3_1(a2198)))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1318,plain,
% 1.54/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2191) | c2_1(a2198) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2198)) | (~c3_1(a2198))))),
% 1.54/1.24 inference(monotonicity,[status(thm)],[1317])).
% 1.54/1.24 tff(1319,plain,
% 1.54/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c2_1(a2198) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2198)) | (~c3_1(a2198)))),
% 1.54/1.24 inference(transitivity,[status(thm)],[1318, 1316])).
% 1.54/1.24 tff(1320,plain,
% 1.54/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))),
% 1.54/1.24 inference(quant_inst,[status(thm)],[])).
% 1.54/1.24 tff(1321,plain,
% 1.54/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c2_1(a2198) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2198)) | (~c3_1(a2198))),
% 1.54/1.24 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 1.54/1.24 tff(1322,plain,
% 1.54/1.24 (~c3_1(a2198)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1321, 111, 1315, 198, 1304, 1303, 1314, 186, 1302, 322, 1305])).
% 1.54/1.24 tff(1323,plain,
% 1.54/1.24 (c1_1(a2188)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[480, 1300])).
% 1.54/1.24 tff(1324,plain,
% 1.54/1.24 (c0_1(a2188)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[282, 1300])).
% 1.54/1.24 tff(1325,plain,
% 1.54/1.24 ((~c3_1(a2188)) | (~c2_1(a2191))),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[716, 111, 1324, 1323, 198, 709, 698, 187, 687, 301])).
% 1.54/1.24 tff(1326,plain,
% 1.54/1.24 (~c3_1(a2188)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1325, 1305])).
% 1.54/1.24 tff(1327,plain,
% 1.54/1.24 (hskp27),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1205, 1305, 198])).
% 1.54/1.24 tff(1328,plain,
% 1.54/1.24 (c3_1(a2178)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[923, 1327])).
% 1.54/1.24 tff(1329,plain,
% 1.54/1.24 (c0_1(a2178)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[945, 1327])).
% 1.54/1.24 tff(1330,plain,
% 1.54/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2187) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2187) | (~c2_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2187) | (~c2_1(a2187)))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1331,plain,
% 1.54/1.24 (((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2187) | c1_1(a2187) | (~c2_1(a2187))) <=> (c1_1(a2187) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2187) | (~c2_1(a2187)))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1332,plain,
% 1.54/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2187) | c1_1(a2187) | (~c2_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2187) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2187) | (~c2_1(a2187))))),
% 1.54/1.24 inference(monotonicity,[status(thm)],[1331])).
% 1.54/1.24 tff(1333,plain,
% 1.54/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2187) | c1_1(a2187) | (~c2_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2187) | (~c2_1(a2187)))),
% 1.54/1.24 inference(transitivity,[status(thm)],[1332, 1330])).
% 1.54/1.24 tff(1334,plain,
% 1.54/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2187) | c1_1(a2187) | (~c2_1(a2187)))),
% 1.54/1.24 inference(quant_inst,[status(thm)],[])).
% 1.54/1.24 tff(1335,plain,
% 1.54/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2187) | (~c2_1(a2187))),
% 1.54/1.24 inference(modus_ponens,[status(thm)],[1334, 1333])).
% 1.54/1.24 tff(1336,plain,
% 1.54/1.24 (~c1_1(a2178)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1335, 111, 1324, 1323, 1329, 1328, 1303, 1302, 528, 1326, 1306])).
% 1.54/1.24 tff(1337,plain,
% 1.54/1.24 (~c1_1(a2198)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[67, 1313])).
% 1.54/1.24 tff(1338,plain,
% 1.54/1.24 (c2_1(a2178)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[934, 1327])).
% 1.54/1.24 tff(1339,plain,
% 1.54/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | c3_1(a2198))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | c3_1(a2198))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1340,plain,
% 1.54/1.24 (((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2198) | c1_1(a2198) | c2_1(a2198)) <=> (c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | c3_1(a2198))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1341,plain,
% 1.54/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2198) | c1_1(a2198) | c2_1(a2198))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | c3_1(a2198)))),
% 1.54/1.24 inference(monotonicity,[status(thm)],[1340])).
% 1.54/1.24 tff(1342,plain,
% 1.54/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2198) | c1_1(a2198) | c2_1(a2198))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | c3_1(a2198))),
% 1.54/1.24 inference(transitivity,[status(thm)],[1341, 1339])).
% 1.54/1.24 tff(1343,plain,
% 1.54/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2198) | c1_1(a2198) | c2_1(a2198))),
% 1.54/1.24 inference(quant_inst,[status(thm)],[])).
% 1.54/1.24 tff(1344,plain,
% 1.54/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | c3_1(a2198)),
% 1.54/1.24 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 1.54/1.24 tff(1345,plain,
% 1.54/1.24 ($false),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1344, 111, 1329, 1338, 1328, 1337, 1314, 184, 1336, 1322])).
% 1.54/1.24 tff(1346,plain,(c0_1(a2191) | c3_1(a2191) | c1_1(a2191) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.54/1.24 tff(1347,plain,
% 1.54/1.24 (c0_1(a2191)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1346, 187, 186, 185])).
% 1.54/1.24 tff(1348,plain,
% 1.54/1.24 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2191)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2191)))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1349,plain,
% 1.54/1.24 ((hskp18 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp18 | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2191)))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1350,plain,
% 1.54/1.24 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2191))))),
% 1.54/1.24 inference(monotonicity,[status(thm)],[1349])).
% 1.54/1.24 tff(1351,plain,
% 1.54/1.24 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2191)))),
% 1.54/1.24 inference(transitivity,[status(thm)],[1350, 1348])).
% 1.54/1.24 tff(1352,plain,
% 1.54/1.24 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.54/1.24 inference(quant_inst,[status(thm)],[])).
% 1.54/1.24 tff(1353,plain,
% 1.54/1.24 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2191))),
% 1.54/1.24 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 1.54/1.24 tff(1354,plain,
% 1.54/1.24 (hskp18 | (~c0_1(a2191))),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1353, 111, 709, 698, 187, 186, 687, 1233])).
% 1.54/1.24 tff(1355,plain,
% 1.54/1.24 (hskp18),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[1354, 1347])).
% 1.54/1.24 tff(1356,plain,
% 1.54/1.24 (~c2_1(a2198)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[61, 1355])).
% 1.54/1.24 tff(1357,plain,
% 1.54/1.24 (~c1_1(a2198)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[67, 1355])).
% 1.54/1.24 tff(1358,plain,
% 1.54/1.24 (c0_1(a2198)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[78, 1355])).
% 1.54/1.24 tff(1359,plain,
% 1.54/1.24 (hskp16),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[117, 111, 1358, 1357, 1356, 55])).
% 1.54/1.24 tff(1360,plain,
% 1.54/1.24 (~c3_1(a2195)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[408, 1359])).
% 1.54/1.24 tff(1361,plain,
% 1.54/1.24 (~c2_1(a2195)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[414, 1359])).
% 1.54/1.24 tff(1362,plain,
% 1.54/1.24 (~c1_1(a2195)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[420, 1359])).
% 1.54/1.24 tff(1363,plain,
% 1.54/1.24 (hskp28),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[448, 111, 1347, 1362, 1361, 1360, 187, 186, 442])).
% 1.54/1.24 tff(1364,plain,
% 1.54/1.24 (c2_1(a2188)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[271, 1363])).
% 1.54/1.24 tff(1365,plain,
% 1.54/1.24 (c0_1(a2188)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[282, 1363])).
% 1.54/1.24 tff(1366,plain,
% 1.54/1.24 (c1_1(a2188)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[480, 1363])).
% 1.54/1.24 tff(1367,assumption,(hskp7), introduced(assumption)).
% 1.54/1.24 tff(1368,plain,
% 1.54/1.24 (c2_1(a2182)),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[810, 1367])).
% 1.54/1.24 tff(1369,assumption,(c2_1(a2188)), introduced(assumption)).
% 1.54/1.24 tff(1370,assumption,(c0_1(a2198)), introduced(assumption)).
% 1.54/1.24 tff(1371,assumption,(~c2_1(a2198)), introduced(assumption)).
% 1.54/1.24 tff(1372,assumption,(~c1_1(a2198)), introduced(assumption)).
% 1.54/1.24 tff(1373,plain,
% 1.54/1.24 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.54/1.24 inference(bind,[status(th)],[])).
% 1.54/1.24 tff(1374,plain,
% 1.54/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.54/1.24 inference(quant_intro,[status(thm)],[1373])).
% 1.54/1.24 tff(1375,plain,
% 1.54/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(1376,plain,
% 1.54/1.24 (^[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)) | (~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))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.54/1.24 inference(bind,[status(th)],[])).
% 1.54/1.24 tff(1377,plain,
% 1.54/1.24 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.54/1.24 inference(quant_intro,[status(thm)],[1376])).
% 1.54/1.24 tff(1378,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 1.54/1.24 tff(1379,plain,
% 1.54/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 1.54/1.25 tff(1380,plain,
% 1.54/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1379, 1375])).
% 1.54/1.25 tff(1381,plain,(
% 1.54/1.25 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.54/1.25 inference(skolemize,[status(sab)],[1380])).
% 1.54/1.25 tff(1382,plain,
% 1.54/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1381, 1374])).
% 1.54/1.25 tff(1383,plain,
% 1.54/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2198) | c2_1(a2198) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188) | (~c0_1(a2198)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2198) | c2_1(a2198) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188) | (~c0_1(a2198)))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1384,plain,
% 1.54/1.25 (((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174))) <=> (c1_1(a2198) | c2_1(a2198) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188) | (~c0_1(a2198)))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1385,plain,
% 1.54/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2198) | c2_1(a2198) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188) | (~c0_1(a2198))))),
% 1.54/1.25 inference(monotonicity,[status(thm)],[1384])).
% 1.54/1.25 tff(1386,plain,
% 1.54/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2198) | c2_1(a2198) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188) | (~c0_1(a2198)))),
% 1.54/1.25 inference(transitivity,[status(thm)],[1385, 1383])).
% 1.54/1.25 tff(1387,plain,
% 1.54/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))),
% 1.54/1.25 inference(quant_inst,[status(thm)],[])).
% 1.54/1.25 tff(1388,plain,
% 1.54/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2198) | c2_1(a2198) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188) | (~c0_1(a2198))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 1.54/1.25 tff(1389,plain,
% 1.54/1.25 ((~c3_1(a2174)) | c3_1(a2188)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[1388, 111, 531, 1369, 1370, 698, 1372, 1371, 687, 1382])).
% 1.54/1.25 tff(1390,plain,
% 1.54/1.25 (~c3_1(a2174)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[1389, 518])).
% 1.54/1.25 tff(1391,plain,
% 1.54/1.25 (hskp11 | c3_1(a2188)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[290, 111, 185, 531, 1369, 260])).
% 1.54/1.25 tff(1392,plain,
% 1.54/1.25 (hskp11),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[1391, 518])).
% 1.54/1.25 tff(1393,plain,
% 1.54/1.25 (~c1_1(a2187)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[218, 1392])).
% 1.54/1.25 tff(1394,plain,
% 1.54/1.25 (c2_1(a2187)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[229, 1392])).
% 1.54/1.25 tff(1395,plain,
% 1.54/1.25 (c0_1(a2187)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[240, 1392])).
% 1.54/1.25 tff(1396,plain,
% 1.54/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a2198) | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2198)) | (~c3_1(a2198)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a2198) | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2198)) | (~c3_1(a2198)))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1397,plain,
% 1.54/1.25 (((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174))) <=> (c2_1(a2198) | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2198)) | (~c3_1(a2198)))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1398,plain,
% 1.54/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a2198) | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2198)) | (~c3_1(a2198))))),
% 1.54/1.25 inference(monotonicity,[status(thm)],[1397])).
% 1.54/1.25 tff(1399,plain,
% 1.54/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a2198) | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2198)) | (~c3_1(a2198)))),
% 1.54/1.25 inference(transitivity,[status(thm)],[1398, 1396])).
% 1.54/1.25 tff(1400,plain,
% 1.54/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)))),
% 1.54/1.25 inference(quant_inst,[status(thm)],[])).
% 1.54/1.25 tff(1401,plain,
% 1.54/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a2198) | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2198)) | (~c3_1(a2198))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 1.54/1.25 tff(1402,plain,
% 1.54/1.25 (~c3_1(a2198)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[1401, 111, 1370, 1395, 1394, 698, 1371, 1393, 687, 322, 1390])).
% 1.54/1.25 tff(1403,plain,
% 1.54/1.25 (hskp16),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[117, 111, 1370, 1372, 1371, 55])).
% 1.54/1.25 tff(1404,plain,
% 1.54/1.25 (~c3_1(a2195)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[408, 1403])).
% 1.54/1.25 tff(1405,plain,
% 1.54/1.25 (~c2_1(a2195)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[414, 1403])).
% 1.54/1.25 tff(1406,plain,
% 1.54/1.25 (~c1_1(a2195)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[420, 1403])).
% 1.54/1.25 tff(1407,plain,
% 1.54/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c0_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c0_1(a2195))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1408,plain,
% 1.54/1.25 (((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195) | c3_1(a2195) | c1_1(a2195) | c0_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c0_1(a2195))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1409,plain,
% 1.54/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195) | c3_1(a2195) | c1_1(a2195) | c0_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c0_1(a2195)))),
% 1.54/1.25 inference(monotonicity,[status(thm)],[1408])).
% 1.54/1.25 tff(1410,plain,
% 1.54/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195) | c3_1(a2195) | c1_1(a2195) | c0_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c0_1(a2195))),
% 1.54/1.25 inference(transitivity,[status(thm)],[1409, 1407])).
% 1.54/1.25 tff(1411,plain,
% 1.54/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195) | c3_1(a2195) | c1_1(a2195) | c0_1(a2195))),
% 1.54/1.25 inference(quant_inst,[status(thm)],[])).
% 1.54/1.25 tff(1412,plain,
% 1.54/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c0_1(a2195)),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 1.54/1.25 tff(1413,plain,
% 1.54/1.25 (c0_1(a2195)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[1412, 111, 1395, 1394, 1406, 1405, 1404, 1393, 197])).
% 1.54/1.25 tff(1414,plain,
% 1.54/1.25 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.54/1.25 inference(bind,[status(th)],[])).
% 1.54/1.25 tff(1415,plain,
% 1.54/1.25 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.25 inference(quant_intro,[status(thm)],[1414])).
% 1.54/1.25 tff(1416,plain,
% 1.54/1.25 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1417,plain,
% 1.54/1.25 (^[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)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.54/1.25 inference(bind,[status(th)],[])).
% 1.54/1.25 tff(1418,plain,
% 1.54/1.25 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.25 inference(quant_intro,[status(thm)],[1417])).
% 1.54/1.25 tff(1419,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 1.54/1.25 tff(1420,plain,
% 1.54/1.25 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1419, 1418])).
% 1.54/1.25 tff(1421,plain,
% 1.54/1.25 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1420, 1416])).
% 1.54/1.25 tff(1422,plain,(
% 1.54/1.25 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.25 inference(skolemize,[status(sab)],[1421])).
% 1.54/1.25 tff(1423,plain,
% 1.54/1.25 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1422, 1415])).
% 1.54/1.25 tff(1424,plain,
% 1.54/1.25 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2195)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2195)))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1425,plain,
% 1.54/1.25 ((hskp19 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c1_1(a2195) | (~c0_1(a2195))) <=> (hskp19 | c1_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2195)))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1426,plain,
% 1.54/1.25 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c1_1(a2195) | (~c0_1(a2195)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2195))))),
% 1.54/1.25 inference(monotonicity,[status(thm)],[1425])).
% 1.54/1.25 tff(1427,plain,
% 1.54/1.25 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c1_1(a2195) | (~c0_1(a2195)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2195)))),
% 1.54/1.25 inference(transitivity,[status(thm)],[1426, 1424])).
% 1.54/1.25 tff(1428,plain,
% 1.54/1.25 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c1_1(a2195) | (~c0_1(a2195)))),
% 1.54/1.25 inference(quant_inst,[status(thm)],[])).
% 1.54/1.25 tff(1429,plain,
% 1.54/1.25 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2195))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 1.54/1.25 tff(1430,plain,
% 1.54/1.25 (hskp19),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[1429, 111, 1395, 1394, 1406, 1404, 1393, 1423, 1413])).
% 1.54/1.25 tff(1431,plain,
% 1.54/1.25 (((~hskp19) | (~c3_1(a2211))) <=> ((~hskp19) | (~c3_1(a2211)))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1432,plain,
% 1.54/1.25 (((~c3_1(a2211)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a2211)))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1433,axiom,((~c3_1(a2211)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.54/1.25 tff(1434,plain,
% 1.54/1.25 ((~hskp19) | (~c3_1(a2211))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1433, 1432])).
% 1.54/1.25 tff(1435,plain,
% 1.54/1.25 ((~hskp19) | (~c3_1(a2211))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1434, 1431])).
% 1.54/1.25 tff(1436,plain,
% 1.54/1.25 (~c3_1(a2211)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[1435, 1430])).
% 1.54/1.25 tff(1437,plain,
% 1.54/1.25 (((~hskp19) | (~c0_1(a2211))) <=> ((~hskp19) | (~c0_1(a2211)))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1438,plain,
% 1.54/1.25 (((~c0_1(a2211)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a2211)))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1439,axiom,((~c0_1(a2211)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.54/1.25 tff(1440,plain,
% 1.54/1.25 ((~hskp19) | (~c0_1(a2211))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 1.54/1.25 tff(1441,plain,
% 1.54/1.25 ((~hskp19) | (~c0_1(a2211))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1440, 1437])).
% 1.54/1.25 tff(1442,plain,
% 1.54/1.25 (~c0_1(a2211)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[1441, 1430])).
% 1.54/1.25 tff(1443,plain,
% 1.54/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2211) | c3_1(a2211) | c1_1(a2198) | c2_1(a2198) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c1_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2211) | c3_1(a2211) | c1_1(a2198) | c2_1(a2198) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c1_1(a2211))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1444,plain,
% 1.54/1.25 (((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c2_1(a2198) | c1_1(a2198) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211)) <=> (c0_1(a2211) | c3_1(a2211) | c1_1(a2198) | c2_1(a2198) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c1_1(a2211))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1445,plain,
% 1.54/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c2_1(a2198) | c1_1(a2198) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2211) | c3_1(a2211) | c1_1(a2198) | c2_1(a2198) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c1_1(a2211)))),
% 1.54/1.25 inference(monotonicity,[status(thm)],[1444])).
% 1.54/1.25 tff(1446,plain,
% 1.54/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c2_1(a2198) | c1_1(a2198) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2211) | c3_1(a2211) | c1_1(a2198) | c2_1(a2198) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c1_1(a2211))),
% 1.54/1.25 inference(transitivity,[status(thm)],[1445, 1443])).
% 1.54/1.25 tff(1447,plain,
% 1.54/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c2_1(a2198) | c1_1(a2198) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))),
% 1.54/1.25 inference(quant_inst,[status(thm)],[])).
% 1.54/1.25 tff(1448,plain,
% 1.54/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2211) | c3_1(a2211) | c1_1(a2198) | c2_1(a2198) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c1_1(a2211)),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 1.54/1.25 tff(1449,plain,
% 1.54/1.25 (c1_1(a2211)),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[1448, 111, 1395, 1394, 1442, 1436, 1372, 1371, 1393, 197, 1402])).
% 1.54/1.25 tff(1450,plain,
% 1.54/1.25 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.54/1.25 inference(bind,[status(th)],[])).
% 1.54/1.25 tff(1451,plain,
% 1.54/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.54/1.25 inference(quant_intro,[status(thm)],[1450])).
% 1.54/1.25 tff(1452,plain,
% 1.54/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.54/1.25 inference(rewrite,[status(thm)],[])).
% 1.54/1.25 tff(1453,plain,
% 1.54/1.25 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.54/1.25 inference(bind,[status(th)],[])).
% 1.54/1.25 tff(1454,plain,
% 1.54/1.25 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.54/1.26 inference(quant_intro,[status(thm)],[1453])).
% 1.54/1.26 tff(1455,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.54/1.26 tff(1456,plain,
% 1.54/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 1.54/1.26 tff(1457,plain,
% 1.54/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1456, 1452])).
% 1.54/1.26 tff(1458,plain,(
% 1.54/1.26 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.54/1.26 inference(skolemize,[status(sab)],[1457])).
% 1.54/1.26 tff(1459,plain,
% 1.54/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1458, 1451])).
% 1.54/1.26 tff(1460,plain,
% 1.54/1.26 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.54/1.26 inference(bind,[status(th)],[])).
% 1.54/1.26 tff(1461,plain,
% 1.54/1.26 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.26 inference(quant_intro,[status(thm)],[1460])).
% 1.54/1.26 tff(1462,plain,
% 1.54/1.26 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1463,plain,
% 1.54/1.26 (^[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(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_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) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.54/1.26 inference(bind,[status(th)],[])).
% 1.54/1.26 tff(1464,plain,
% 1.54/1.26 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.26 inference(quant_intro,[status(thm)],[1463])).
% 1.54/1.26 tff(1465,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 1.54/1.26 tff(1466,plain,
% 1.54/1.26 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1465, 1464])).
% 1.54/1.26 tff(1467,plain,
% 1.54/1.26 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1466, 1462])).
% 1.54/1.26 tff(1468,plain,(
% 1.54/1.26 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.26 inference(skolemize,[status(sab)],[1467])).
% 1.54/1.26 tff(1469,plain,
% 1.54/1.26 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1468, 1461])).
% 1.54/1.26 tff(1470,plain,
% 1.54/1.26 (((~hskp19) | (~c2_1(a2211))) <=> ((~hskp19) | (~c2_1(a2211)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1471,plain,
% 1.54/1.26 (((~c2_1(a2211)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a2211)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1472,axiom,((~c2_1(a2211)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.54/1.26 tff(1473,plain,
% 1.54/1.26 ((~hskp19) | (~c2_1(a2211))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 1.54/1.26 tff(1474,plain,
% 1.54/1.26 ((~hskp19) | (~c2_1(a2211))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1473, 1470])).
% 1.54/1.26 tff(1475,plain,
% 1.54/1.26 (~c2_1(a2211)),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[1474, 1430])).
% 1.54/1.26 tff(1476,plain,
% 1.54/1.26 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c1_1(a2211)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp14 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c1_1(a2211)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1477,plain,
% 1.54/1.26 ((hskp14 | (~ndr1_0) | c2_1(a2211) | c3_1(a2211) | (~c1_1(a2211)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211))) <=> (hskp14 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c1_1(a2211)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1478,plain,
% 1.54/1.26 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2211) | c3_1(a2211) | (~c1_1(a2211)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c1_1(a2211))))),
% 1.54/1.26 inference(monotonicity,[status(thm)],[1477])).
% 1.54/1.26 tff(1479,plain,
% 1.54/1.26 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2211) | c3_1(a2211) | (~c1_1(a2211)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp14 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c1_1(a2211)))),
% 1.54/1.26 inference(transitivity,[status(thm)],[1478, 1476])).
% 1.54/1.26 tff(1480,plain,
% 1.54/1.26 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2211) | c3_1(a2211) | (~c1_1(a2211)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211)))),
% 1.54/1.26 inference(quant_inst,[status(thm)],[])).
% 1.54/1.26 tff(1481,plain,
% 1.54/1.26 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp14 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c1_1(a2211))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 1.54/1.26 tff(1482,plain,
% 1.54/1.26 (hskp14),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[1481, 111, 1442, 1475, 1436, 1469, 1449])).
% 1.54/1.26 tff(1483,plain,
% 1.54/1.26 (((~hskp14) | (~c1_1(a2193))) <=> ((~hskp14) | (~c1_1(a2193)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1484,plain,
% 1.54/1.26 (((~c1_1(a2193)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a2193)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1485,axiom,((~c1_1(a2193)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.54/1.26 tff(1486,plain,
% 1.54/1.26 ((~hskp14) | (~c1_1(a2193))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 1.54/1.26 tff(1487,plain,
% 1.54/1.26 ((~hskp14) | (~c1_1(a2193))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1486, 1483])).
% 1.54/1.26 tff(1488,plain,
% 1.54/1.26 (~c1_1(a2193)),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[1487, 1482])).
% 1.54/1.26 tff(1489,plain,
% 1.54/1.26 (((~hskp14) | c3_1(a2193)) <=> ((~hskp14) | c3_1(a2193))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1490,axiom,((~hskp14) | c3_1(a2193)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.54/1.26 tff(1491,plain,
% 1.54/1.26 ((~hskp14) | c3_1(a2193)),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1490, 1489])).
% 1.54/1.26 tff(1492,plain,
% 1.54/1.26 ((~hskp14) | c3_1(a2193)),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1491, 1489])).
% 1.54/1.26 tff(1493,plain,
% 1.54/1.26 ((~hskp14) | c3_1(a2193)),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1492, 1489])).
% 1.54/1.26 tff(1494,plain,
% 1.54/1.26 ((~hskp14) | c3_1(a2193)),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1493, 1489])).
% 1.54/1.26 tff(1495,plain,
% 1.54/1.26 ((~hskp14) | c3_1(a2193)),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1494, 1489])).
% 1.54/1.26 tff(1496,plain,
% 1.54/1.26 ((~hskp14) | c3_1(a2193)),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1495, 1489])).
% 1.54/1.26 tff(1497,plain,
% 1.54/1.26 ((~hskp14) | c3_1(a2193)),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1496, 1489])).
% 1.54/1.26 tff(1498,plain,
% 1.54/1.26 ((~hskp14) | c3_1(a2193)),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1497, 1489])).
% 1.54/1.26 tff(1499,plain,
% 1.54/1.26 (c3_1(a2193)),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[1498, 1482])).
% 1.54/1.26 tff(1500,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2211) | c3_1(a2211) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2193)) | (~c3_1(a2193)) | (~c1_1(a2211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2211) | c3_1(a2211) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2193)) | (~c3_1(a2193)) | (~c1_1(a2211)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1501,plain,
% 1.54/1.26 (((~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211))) <=> (c0_1(a2211) | c3_1(a2211) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2193)) | (~c3_1(a2193)) | (~c1_1(a2211)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1502,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2211) | c3_1(a2211) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2193)) | (~c3_1(a2193)) | (~c1_1(a2211))))),
% 1.54/1.26 inference(monotonicity,[status(thm)],[1501])).
% 1.54/1.26 tff(1503,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2211) | c3_1(a2211) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2193)) | (~c3_1(a2193)) | (~c1_1(a2211)))),
% 1.54/1.26 inference(transitivity,[status(thm)],[1502, 1500])).
% 1.54/1.26 tff(1504,plain,
% 1.54/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211)))),
% 1.54/1.26 inference(quant_inst,[status(thm)],[])).
% 1.54/1.26 tff(1505,plain,
% 1.54/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2211) | c3_1(a2211) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2193)) | (~c3_1(a2193)) | (~c1_1(a2211))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 1.54/1.26 tff(1506,plain,
% 1.54/1.26 (~c0_1(a2193)),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[1505, 111, 1499, 709, 698, 1442, 1436, 1488, 687, 1459, 1449])).
% 1.54/1.26 tff(1507,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2193) | (~c3_1(a2193)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1508,plain,
% 1.54/1.26 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1509,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2193) | (~c3_1(a2193))))),
% 1.54/1.26 inference(monotonicity,[status(thm)],[1508])).
% 1.54/1.26 tff(1510,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.54/1.26 inference(transitivity,[status(thm)],[1509, 1507])).
% 1.54/1.26 tff(1511,plain,
% 1.54/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.54/1.26 inference(quant_inst,[status(thm)],[])).
% 1.54/1.26 tff(1512,plain,
% 1.54/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2193) | (~c3_1(a2193))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1511, 1510])).
% 1.54/1.26 tff(1513,plain,
% 1.54/1.26 ($false),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[1512, 111, 1499, 709, 698, 1406, 1405, 1404, 1488, 687, 157, 1506])).
% 1.54/1.26 tff(1514,plain,(c3_1(a2188) | c1_1(a2198) | c2_1(a2198) | (~c0_1(a2198)) | hskp10 | (~c0_1(a2188)) | (~c2_1(a2188))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.26 tff(1515,plain,
% 1.54/1.26 (c3_1(a2188)),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[1514, 1372, 1371, 1370, 185, 531, 1369])).
% 1.54/1.26 tff(1516,plain,
% 1.54/1.26 (~c0_1(a2182)),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[788, 1367])).
% 1.54/1.26 tff(1517,plain,
% 1.54/1.26 (c3_1(a2182)),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[799, 1367])).
% 1.54/1.26 tff(1518,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1519,plain,
% 1.54/1.26 (((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1520,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187))))),
% 1.54/1.26 inference(monotonicity,[status(thm)],[1519])).
% 1.54/1.26 tff(1521,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))),
% 1.54/1.26 inference(transitivity,[status(thm)],[1520, 1518])).
% 1.54/1.26 tff(1522,plain,
% 1.54/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.54/1.26 inference(quant_inst,[status(thm)],[])).
% 1.54/1.26 tff(1523,plain,
% 1.54/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 1.54/1.26 tff(1524,plain,
% 1.54/1.26 (~c3_1(a2187)),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[1523, 111, 241, 230, 1406, 1405, 1404, 219, 184])).
% 1.54/1.26 tff(1525,assumption,(~c0_1(a2182)), introduced(assumption)).
% 1.54/1.26 tff(1526,assumption,(c3_1(a2182)), introduced(assumption)).
% 1.54/1.26 tff(1527,assumption,(c2_1(a2182)), introduced(assumption)).
% 1.54/1.26 tff(1528,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2198) | c2_1(a2198) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2198)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2198) | c2_1(a2198) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2198)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1529,plain,
% 1.54/1.26 (((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182))) <=> (c1_1(a2198) | c2_1(a2198) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2198)))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1530,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2198) | c2_1(a2198) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2198))))),
% 1.54/1.26 inference(monotonicity,[status(thm)],[1529])).
% 1.54/1.26 tff(1531,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2198) | c2_1(a2198) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2198)))),
% 1.54/1.26 inference(transitivity,[status(thm)],[1530, 1528])).
% 1.54/1.26 tff(1532,plain,
% 1.54/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182)))),
% 1.54/1.26 inference(quant_inst,[status(thm)],[])).
% 1.54/1.26 tff(1533,plain,
% 1.54/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2198) | c2_1(a2198) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2198))),
% 1.54/1.26 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 1.54/1.26 tff(1534,plain,
% 1.54/1.26 ($false),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[1533, 111, 1370, 241, 230, 1527, 1526, 1372, 1371, 1525, 1382, 1524])).
% 1.54/1.26 tff(1535,plain,((~hskp11) | (~c0_1(a2198)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c1_1(a2198) | c2_1(a2198) | c0_1(a2182)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.26 tff(1536,plain,
% 1.54/1.26 (~hskp11),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[1535, 1368, 1370, 1517, 1372, 1371, 1516])).
% 1.54/1.26 tff(1537,plain,
% 1.54/1.26 (hskp11 | hskp1 | (~c3_1(a2188))),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[744, 111, 531, 1369, 738])).
% 1.54/1.26 tff(1538,plain,
% 1.54/1.26 (hskp1),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[1537, 1536, 1515])).
% 1.54/1.26 tff(1539,plain,
% 1.54/1.26 (~c3_1(a2175)),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[597, 1538])).
% 1.54/1.26 tff(1540,plain,
% 1.54/1.26 (~c0_1(a2175)),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[603, 1538])).
% 1.54/1.26 tff(1541,assumption,(c3_1(a2188)), introduced(assumption)).
% 1.54/1.26 tff(1542,plain,
% 1.54/1.26 (c2_1(a2197)),
% 1.54/1.26 inference(unit_resolution,[status(thm)],[664, 158])).
% 1.54/1.26 tff(1543,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2197)) | c0_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2197)) | c0_1(a2197))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1544,plain,
% 1.54/1.26 (((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197))) <=> (c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2197)) | c0_1(a2197))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(1545,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2197)) | c0_1(a2197)))),
% 1.54/1.26 inference(monotonicity,[status(thm)],[1544])).
% 1.54/1.26 tff(1546,plain,
% 1.54/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2197)) | c0_1(a2197))),
% 1.54/1.26 inference(transitivity,[status(thm)],[1545, 1543])).
% 1.54/1.26 tff(1547,plain,
% 1.54/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)))),
% 1.54/1.26 inference(quant_inst,[status(thm)],[])).
% 1.54/1.26 tff(1548,plain,
% 1.54/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2197)) | c0_1(a2197)),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 1.54/1.27 tff(1549,plain,
% 1.54/1.27 (c0_1(a2197)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1548, 111, 531, 530, 1542, 1132, 1131, 164, 147, 301, 1541])).
% 1.54/1.27 tff(1550,assumption,(~c3_1(a2195)), introduced(assumption)).
% 1.54/1.27 tff(1551,assumption,(~c2_1(a2195)), introduced(assumption)).
% 1.54/1.27 tff(1552,assumption,(~c1_1(a2195)), introduced(assumption)).
% 1.54/1.27 tff(1553,plain,
% 1.54/1.27 (c3_1(a2197)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[653, 158])).
% 1.54/1.27 tff(1554,plain,
% 1.54/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c3_1(a2197)) | (~c0_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1555,plain,
% 1.54/1.27 (((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2197) | (~c3_1(a2197)) | (~c0_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1556,plain,
% 1.54/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2197) | (~c3_1(a2197)) | (~c0_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c3_1(a2197)) | (~c0_1(a2197))))),
% 1.54/1.27 inference(monotonicity,[status(thm)],[1555])).
% 1.54/1.27 tff(1557,plain,
% 1.54/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2197) | (~c3_1(a2197)) | (~c0_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.54/1.27 inference(transitivity,[status(thm)],[1556, 1554])).
% 1.54/1.27 tff(1558,plain,
% 1.54/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2197) | (~c3_1(a2197)) | (~c0_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.54/1.27 inference(quant_inst,[status(thm)],[])).
% 1.54/1.27 tff(1559,plain,
% 1.54/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c3_1(a2197)) | (~c0_1(a2197))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1558, 1557])).
% 1.54/1.27 tff(1560,plain,
% 1.54/1.27 ($false),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1559, 111, 531, 1369, 1553, 164, 1552, 1551, 1550, 184, 1541, 1549])).
% 1.54/1.27 tff(1561,plain,((~hskp17) | (~c0_1(a2188)) | (~c2_1(a2188)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c1_1(a2174)) | (~c2_1(a2174)) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.27 tff(1562,plain,
% 1.54/1.27 (~hskp17),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1561, 531, 1369, 1406, 1405, 1404, 1515, 530, 709, 698, 687])).
% 1.54/1.27 tff(1563,assumption,(hskp15), introduced(assumption)).
% 1.54/1.27 tff(1564,plain,
% 1.54/1.27 (~c2_1(a2194)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[383, 1563])).
% 1.54/1.27 tff(1565,plain,
% 1.54/1.27 (c0_1(a2194)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[394, 1563])).
% 1.54/1.27 tff(1566,plain,
% 1.54/1.27 (~c1_1(a2194)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[640, 111, 850, 185, 1565, 1564, 634])).
% 1.54/1.27 tff(1567,plain,
% 1.54/1.27 (c3_1(a2194)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[431, 1563])).
% 1.54/1.27 tff(1568,plain,
% 1.54/1.27 ($false),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[457, 111, 531, 1369, 1565, 1567, 1552, 1551, 1550, 184, 1541, 1566])).
% 1.54/1.27 tff(1569,plain,((~hskp15) | (~c0_1(a2188)) | (~c2_1(a2188)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~c3_1(a2188)) | hskp17 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.54/1.27 tff(1570,plain,
% 1.54/1.27 (~hskp15),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1569, 531, 1369, 1406, 1405, 1404, 1515, 1562, 185])).
% 1.54/1.27 tff(1571,plain,
% 1.54/1.27 (^[U: $i] : refl((hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.54/1.27 inference(bind,[status(th)],[])).
% 1.54/1.27 tff(1572,plain,
% 1.54/1.27 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.54/1.27 inference(quant_intro,[status(thm)],[1571])).
% 1.54/1.27 tff(1573,plain,
% 1.54/1.27 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1574,plain,
% 1.54/1.27 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp3) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp3))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp3) <=> (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.54/1.27 inference(bind,[status(th)],[])).
% 1.54/1.27 tff(1575,plain,
% 1.54/1.27 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp3) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.54/1.27 inference(quant_intro,[status(thm)],[1574])).
% 1.54/1.27 tff(1576,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 1.54/1.27 tff(1577,plain,
% 1.54/1.27 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 1.54/1.27 tff(1578,plain,
% 1.54/1.27 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1577, 1573])).
% 1.54/1.27 tff(1579,plain,(
% 1.54/1.27 ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.54/1.27 inference(skolemize,[status(sab)],[1578])).
% 1.54/1.27 tff(1580,plain,
% 1.54/1.27 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1579, 1572])).
% 1.54/1.27 tff(1581,plain,
% 1.54/1.27 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp3 | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp3 | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1582,plain,
% 1.54/1.27 ((hskp15 | hskp3 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp15 | hskp3 | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1583,plain,
% 1.54/1.27 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp3 | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174))))),
% 1.54/1.27 inference(monotonicity,[status(thm)],[1582])).
% 1.54/1.27 tff(1584,plain,
% 1.54/1.27 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp3 | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.54/1.27 inference(transitivity,[status(thm)],[1583, 1581])).
% 1.54/1.27 tff(1585,plain,
% 1.54/1.27 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.54/1.27 inference(quant_inst,[status(thm)],[])).
% 1.54/1.27 tff(1586,plain,
% 1.54/1.27 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp3 | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1585, 1584])).
% 1.54/1.27 tff(1587,plain,
% 1.54/1.27 (hskp15 | hskp3),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1586, 111, 709, 698, 687, 1580])).
% 1.54/1.27 tff(1588,plain,
% 1.54/1.27 (hskp3),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1587, 1570])).
% 1.54/1.27 tff(1589,plain,
% 1.54/1.27 (c2_1(a2175)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[614, 1538])).
% 1.54/1.27 tff(1590,assumption,(c1_1(a2182)), introduced(assumption)).
% 1.54/1.27 tff(1591,assumption,(hskp3), introduced(assumption)).
% 1.54/1.27 tff(1592,plain,
% 1.54/1.27 (((~hskp3) | (~c1_1(a2177))) <=> ((~hskp3) | (~c1_1(a2177)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1593,plain,
% 1.54/1.27 (((~c1_1(a2177)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a2177)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1594,axiom,((~c1_1(a2177)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.54/1.27 tff(1595,plain,
% 1.54/1.27 ((~hskp3) | (~c1_1(a2177))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 1.54/1.27 tff(1596,plain,
% 1.54/1.27 ((~hskp3) | (~c1_1(a2177))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1595, 1592])).
% 1.54/1.27 tff(1597,plain,
% 1.54/1.27 (~c1_1(a2177)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1596, 1591])).
% 1.54/1.27 tff(1598,plain,
% 1.54/1.27 (((~hskp3) | (~c0_1(a2177))) <=> ((~hskp3) | (~c0_1(a2177)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1599,plain,
% 1.54/1.27 (((~c0_1(a2177)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a2177)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1600,axiom,((~c0_1(a2177)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.54/1.27 tff(1601,plain,
% 1.54/1.27 ((~hskp3) | (~c0_1(a2177))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 1.54/1.27 tff(1602,plain,
% 1.54/1.27 ((~hskp3) | (~c0_1(a2177))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1601, 1598])).
% 1.54/1.27 tff(1603,plain,
% 1.54/1.27 (~c0_1(a2177)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1602, 1591])).
% 1.54/1.27 tff(1604,plain,
% 1.54/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | (~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)) | (~c2_1(a2182)) | (~c1_1(a2182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | (~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)) | (~c2_1(a2182)) | (~c1_1(a2182)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1605,plain,
% 1.54/1.27 (((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2182) | (~c2_1(a2182)) | (~c1_1(a2182)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177))) <=> (c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | (~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)) | (~c2_1(a2182)) | (~c1_1(a2182)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1606,plain,
% 1.54/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2182) | (~c2_1(a2182)) | (~c1_1(a2182)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | (~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)) | (~c2_1(a2182)) | (~c1_1(a2182))))),
% 1.54/1.27 inference(monotonicity,[status(thm)],[1605])).
% 1.54/1.27 tff(1607,plain,
% 1.54/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2182) | (~c2_1(a2182)) | (~c1_1(a2182)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | (~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)) | (~c2_1(a2182)) | (~c1_1(a2182)))),
% 1.54/1.27 inference(transitivity,[status(thm)],[1606, 1604])).
% 1.54/1.27 tff(1608,plain,
% 1.54/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2182) | (~c2_1(a2182)) | (~c1_1(a2182)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177)))),
% 1.54/1.27 inference(quant_inst,[status(thm)],[])).
% 1.54/1.27 tff(1609,plain,
% 1.54/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | (~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)) | (~c2_1(a2182)) | (~c1_1(a2182))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 1.54/1.27 tff(1610,plain,
% 1.54/1.27 (~c2_1(a2177)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1609, 111, 531, 530, 1527, 1525, 1603, 1597, 301, 1541, 1590])).
% 1.54/1.27 tff(1611,assumption,(~c3_1(a2175)), introduced(assumption)).
% 1.54/1.27 tff(1612,assumption,(~c0_1(a2175)), introduced(assumption)).
% 1.54/1.27 tff(1613,assumption,(c2_1(a2175)), introduced(assumption)).
% 1.54/1.27 tff(1614,plain,
% 1.54/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | c2_1(a2177) | (~c2_1(a2182)) | (~c3_1(a2182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | c2_1(a2177) | (~c2_1(a2182)) | (~c3_1(a2182)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1615,plain,
% 1.54/1.27 (((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2177) | c0_1(a2177) | c2_1(a2177)) <=> (c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | c2_1(a2177) | (~c2_1(a2182)) | (~c3_1(a2182)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1616,plain,
% 1.54/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2177) | c0_1(a2177) | c2_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | c2_1(a2177) | (~c2_1(a2182)) | (~c3_1(a2182))))),
% 1.54/1.27 inference(monotonicity,[status(thm)],[1615])).
% 1.54/1.27 tff(1617,plain,
% 1.54/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2177) | c0_1(a2177) | c2_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | c2_1(a2177) | (~c2_1(a2182)) | (~c3_1(a2182)))),
% 1.54/1.27 inference(transitivity,[status(thm)],[1616, 1614])).
% 1.54/1.27 tff(1618,plain,
% 1.54/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2177) | c0_1(a2177) | c2_1(a2177))),
% 1.54/1.27 inference(quant_inst,[status(thm)],[])).
% 1.54/1.27 tff(1619,plain,
% 1.54/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | c2_1(a2177) | (~c2_1(a2182)) | (~c3_1(a2182))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1618, 1617])).
% 1.54/1.27 tff(1620,plain,
% 1.54/1.27 ($false),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1619, 111, 1527, 1526, 1613, 1525, 1603, 1597, 1612, 1611, 728, 1610])).
% 1.54/1.27 tff(1621,plain,((~hskp3) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c2_1(a2175)) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~c0_1(a2188)) | (~c1_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2182))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.27 tff(1622,plain,
% 1.54/1.27 (~c1_1(a2182)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1621, 1589, 1588, 1517, 1516, 1540, 1539, 531, 530, 1515, 1368])).
% 1.54/1.27 tff(1623,plain,
% 1.54/1.27 (^[U: $i] : refl((hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.54/1.27 inference(bind,[status(th)],[])).
% 1.54/1.27 tff(1624,plain,
% 1.54/1.27 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.54/1.27 inference(quant_intro,[status(thm)],[1623])).
% 1.54/1.27 tff(1625,plain,
% 1.54/1.27 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1626,plain,
% 1.54/1.27 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp10) <=> ((hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp10))), rewrite(((hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp10) <=> (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp10) <=> (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.54/1.27 inference(bind,[status(th)],[])).
% 1.54/1.27 tff(1627,plain,
% 1.54/1.27 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp10) <=> ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.54/1.27 inference(quant_intro,[status(thm)],[1626])).
% 1.54/1.27 tff(1628,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.54/1.27 tff(1629,plain,
% 1.54/1.27 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 1.54/1.27 tff(1630,plain,
% 1.54/1.27 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1629, 1625])).
% 1.54/1.27 tff(1631,plain,(
% 1.54/1.27 ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.54/1.27 inference(skolemize,[status(sab)],[1630])).
% 1.54/1.27 tff(1632,plain,
% 1.54/1.27 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1631, 1624])).
% 1.54/1.27 tff(1633,assumption,(~c1_1(a2175)), introduced(assumption)).
% 1.54/1.27 tff(1634,plain,
% 1.54/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2175)) | c1_1(a2175) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2175)) | c1_1(a2175) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1635,plain,
% 1.54/1.27 (((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2175) | c0_1(a2175) | (~c2_1(a2175))) <=> (c0_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2175)) | c1_1(a2175) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1636,plain,
% 1.54/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2175) | c0_1(a2175) | (~c2_1(a2175)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2175)) | c1_1(a2175) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188))))),
% 1.54/1.27 inference(monotonicity,[status(thm)],[1635])).
% 1.54/1.27 tff(1637,plain,
% 1.54/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2175) | c0_1(a2175) | (~c2_1(a2175)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2175)) | c1_1(a2175) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))),
% 1.54/1.27 inference(transitivity,[status(thm)],[1636, 1634])).
% 1.54/1.27 tff(1638,plain,
% 1.54/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2175) | c0_1(a2175) | (~c2_1(a2175)))),
% 1.54/1.27 inference(quant_inst,[status(thm)],[])).
% 1.54/1.27 tff(1639,plain,
% 1.54/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2175)) | c1_1(a2175) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 1.54/1.27 tff(1640,plain,
% 1.54/1.27 ($false),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1639, 111, 531, 530, 1613, 1132, 1131, 1612, 147, 301, 1541, 1633])).
% 1.54/1.27 tff(1641,plain,(c1_1(a2175) | (~c0_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2175)) | (~c1_1(a2174)) | (~c2_1(a2174)) | c0_1(a2175) | c0_1(a2174) | (~c3_1(a2188))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.27 tff(1642,plain,
% 1.54/1.27 (c1_1(a2175)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1641, 1589, 530, 1540, 709, 698, 531, 687, 1515])).
% 1.54/1.27 tff(1643,assumption,(c1_1(a2175)), introduced(assumption)).
% 1.54/1.27 tff(1644,assumption,(hskp9), introduced(assumption)).
% 1.54/1.27 tff(1645,plain,
% 1.54/1.27 (((~hskp9) | (~c1_1(a2185))) <=> ((~hskp9) | (~c1_1(a2185)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1646,plain,
% 1.54/1.27 (((~c1_1(a2185)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a2185)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1647,axiom,((~c1_1(a2185)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.54/1.27 tff(1648,plain,
% 1.54/1.27 ((~hskp9) | (~c1_1(a2185))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1647, 1646])).
% 1.54/1.27 tff(1649,plain,
% 1.54/1.27 ((~hskp9) | (~c1_1(a2185))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1648, 1645])).
% 1.54/1.27 tff(1650,plain,
% 1.54/1.27 (~c1_1(a2185)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1649, 1644])).
% 1.54/1.27 tff(1651,plain,
% 1.54/1.27 (((~hskp9) | (~c0_1(a2185))) <=> ((~hskp9) | (~c0_1(a2185)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1652,plain,
% 1.54/1.27 (((~c0_1(a2185)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a2185)))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1653,axiom,((~c0_1(a2185)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.54/1.27 tff(1654,plain,
% 1.54/1.27 ((~hskp9) | (~c0_1(a2185))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1653, 1652])).
% 1.54/1.27 tff(1655,plain,
% 1.54/1.27 ((~hskp9) | (~c0_1(a2185))),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1654, 1651])).
% 1.54/1.27 tff(1656,plain,
% 1.54/1.27 (~c0_1(a2185)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1655, 1644])).
% 1.54/1.27 tff(1657,plain,
% 1.54/1.27 (((~hskp9) | c2_1(a2185)) <=> ((~hskp9) | c2_1(a2185))),
% 1.54/1.27 inference(rewrite,[status(thm)],[])).
% 1.54/1.27 tff(1658,axiom,((~hskp9) | c2_1(a2185)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.54/1.27 tff(1659,plain,
% 1.54/1.27 ((~hskp9) | c2_1(a2185)),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 1.54/1.27 tff(1660,plain,
% 1.54/1.27 ((~hskp9) | c2_1(a2185)),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1659, 1657])).
% 1.54/1.27 tff(1661,plain,
% 1.54/1.27 ((~hskp9) | c2_1(a2185)),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1660, 1657])).
% 1.54/1.27 tff(1662,plain,
% 1.54/1.27 ((~hskp9) | c2_1(a2185)),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1661, 1657])).
% 1.54/1.27 tff(1663,plain,
% 1.54/1.27 ((~hskp9) | c2_1(a2185)),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1662, 1657])).
% 1.54/1.27 tff(1664,plain,
% 1.54/1.27 ((~hskp9) | c2_1(a2185)),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1663, 1657])).
% 1.54/1.27 tff(1665,plain,
% 1.54/1.27 ((~hskp9) | c2_1(a2185)),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1664, 1657])).
% 1.54/1.27 tff(1666,plain,
% 1.54/1.27 ((~hskp9) | c2_1(a2185)),
% 1.54/1.27 inference(modus_ponens,[status(thm)],[1665, 1657])).
% 1.54/1.27 tff(1667,plain,
% 1.54/1.27 (c2_1(a2185)),
% 1.54/1.27 inference(unit_resolution,[status(thm)],[1666, 1644])).
% 1.54/1.27 tff(1668,plain,
% 1.54/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2185) | c1_1(a2185) | c0_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c1_1(a2175)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2185)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2185) | c1_1(a2185) | c0_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c1_1(a2175)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2185)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1669,plain,
% 1.54/1.28 (((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2175) | (~c2_1(a2175)) | (~c1_1(a2175)) | c1_1(a2185) | c0_1(a2185) | (~c2_1(a2185))) <=> (c0_1(a2185) | c1_1(a2185) | c0_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c1_1(a2175)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2185)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1670,plain,
% 1.54/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2175) | (~c2_1(a2175)) | (~c1_1(a2175)) | c1_1(a2185) | c0_1(a2185) | (~c2_1(a2185)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2185) | c1_1(a2185) | c0_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c1_1(a2175)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2185))))),
% 1.54/1.28 inference(monotonicity,[status(thm)],[1669])).
% 1.54/1.28 tff(1671,plain,
% 1.54/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2175) | (~c2_1(a2175)) | (~c1_1(a2175)) | c1_1(a2185) | c0_1(a2185) | (~c2_1(a2185)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2185) | c1_1(a2185) | c0_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c1_1(a2175)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2185)))),
% 1.54/1.28 inference(transitivity,[status(thm)],[1670, 1668])).
% 1.54/1.28 tff(1672,plain,
% 1.54/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2175) | (~c2_1(a2175)) | (~c1_1(a2175)) | c1_1(a2185) | c0_1(a2185) | (~c2_1(a2185)))),
% 1.54/1.28 inference(quant_inst,[status(thm)],[])).
% 1.54/1.28 tff(1673,plain,
% 1.54/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2185) | c1_1(a2185) | c0_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c1_1(a2175)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2185))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1672, 1671])).
% 1.54/1.28 tff(1674,plain,
% 1.54/1.28 ($false),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1673, 111, 531, 530, 1667, 1613, 1656, 1650, 1612, 301, 1541, 1643])).
% 1.54/1.28 tff(1675,plain,((~hskp9) | (~c0_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2175)) | c0_1(a2175) | (~c3_1(a2188)) | (~c1_1(a2175))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.28 tff(1676,plain,
% 1.54/1.28 (~hskp9),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1675, 1642, 530, 1589, 1540, 1515, 531])).
% 1.54/1.28 tff(1677,plain,
% 1.54/1.28 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | c0_1(a2182) | (~ndr1_0) | c1_1(a2182) | (~c3_1(a2182)))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp9 | c0_1(a2182) | (~ndr1_0) | c1_1(a2182) | (~c3_1(a2182)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1678,plain,
% 1.54/1.28 ((hskp10 | hskp9 | (~ndr1_0) | c1_1(a2182) | c0_1(a2182) | (~c3_1(a2182))) <=> (hskp10 | hskp9 | c0_1(a2182) | (~ndr1_0) | c1_1(a2182) | (~c3_1(a2182)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1679,plain,
% 1.54/1.28 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | (~ndr1_0) | c1_1(a2182) | c0_1(a2182) | (~c3_1(a2182)))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | c0_1(a2182) | (~ndr1_0) | c1_1(a2182) | (~c3_1(a2182))))),
% 1.54/1.28 inference(monotonicity,[status(thm)],[1678])).
% 1.54/1.28 tff(1680,plain,
% 1.54/1.28 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | (~ndr1_0) | c1_1(a2182) | c0_1(a2182) | (~c3_1(a2182)))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp9 | c0_1(a2182) | (~ndr1_0) | c1_1(a2182) | (~c3_1(a2182)))),
% 1.54/1.28 inference(transitivity,[status(thm)],[1679, 1677])).
% 1.54/1.28 tff(1681,plain,
% 1.54/1.28 ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | (~ndr1_0) | c1_1(a2182) | c0_1(a2182) | (~c3_1(a2182)))),
% 1.54/1.28 inference(quant_inst,[status(thm)],[])).
% 1.54/1.28 tff(1682,plain,
% 1.54/1.28 ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp9 | c0_1(a2182) | (~ndr1_0) | c1_1(a2182) | (~c3_1(a2182))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1681, 1680])).
% 1.54/1.28 tff(1683,plain,
% 1.54/1.28 ($false),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1682, 111, 185, 1676, 1517, 1516, 1632, 1622])).
% 1.54/1.28 tff(1684,plain,((~hskp7) | hskp10 | (~c1_1(a2188)) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c0_1(a2198)) | c1_1(a2198) | c2_1(a2198)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.28 tff(1685,plain,
% 1.54/1.28 (~hskp7),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1684, 1366, 185, 1365, 1364, 1358, 1357, 1356])).
% 1.54/1.28 tff(1686,plain,
% 1.54/1.28 (c3_1(a2188)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1514, 1357, 1356, 1358, 185, 1365, 1364])).
% 1.54/1.28 tff(1687,plain,
% 1.54/1.28 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.54/1.28 inference(bind,[status(th)],[])).
% 1.54/1.28 tff(1688,plain,
% 1.54/1.28 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.54/1.28 inference(quant_intro,[status(thm)],[1687])).
% 1.54/1.28 tff(1689,plain,
% 1.54/1.28 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1690,plain,
% 1.54/1.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.54/1.28 inference(bind,[status(th)],[])).
% 1.54/1.28 tff(1691,plain,
% 1.54/1.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.54/1.28 inference(quant_intro,[status(thm)],[1690])).
% 1.54/1.28 tff(1692,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.54/1.28 tff(1693,plain,
% 1.54/1.28 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1692, 1691])).
% 1.54/1.28 tff(1694,plain,
% 1.54/1.28 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1693, 1689])).
% 1.54/1.28 tff(1695,plain,(
% 1.54/1.28 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.54/1.28 inference(skolemize,[status(sab)],[1694])).
% 1.54/1.28 tff(1696,plain,
% 1.54/1.28 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1695, 1688])).
% 1.54/1.28 tff(1697,plain,
% 1.54/1.28 (~hskp17),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1561, 1365, 1364, 1362, 1361, 1360, 1686, 1366, 709, 698, 687])).
% 1.54/1.28 tff(1698,plain,
% 1.54/1.28 (~hskp15),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1569, 1365, 1364, 1362, 1361, 1360, 1686, 1697, 185])).
% 1.54/1.28 tff(1699,plain,
% 1.54/1.28 (hskp3),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1587, 1698])).
% 1.54/1.28 tff(1700,plain,
% 1.54/1.28 (((~hskp3) | (~c3_1(a2177))) <=> ((~hskp3) | (~c3_1(a2177)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1701,plain,
% 1.54/1.28 (((~c3_1(a2177)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a2177)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1702,axiom,((~c3_1(a2177)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.54/1.28 tff(1703,plain,
% 1.54/1.28 ((~hskp3) | (~c3_1(a2177))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 1.54/1.28 tff(1704,plain,
% 1.54/1.28 ((~hskp3) | (~c3_1(a2177))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1703, 1700])).
% 1.54/1.28 tff(1705,plain,
% 1.54/1.28 (~c3_1(a2177)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1704, 1699])).
% 1.54/1.28 tff(1706,plain,
% 1.54/1.28 (~c1_1(a2177)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1596, 1699])).
% 1.54/1.28 tff(1707,plain,
% 1.54/1.28 (~c0_1(a2177)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1602, 1699])).
% 1.54/1.28 tff(1708,plain,
% 1.54/1.28 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1709,plain,
% 1.54/1.28 ((hskp2 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177)) <=> (hskp2 | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1710,plain,
% 1.54/1.28 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188))))),
% 1.54/1.28 inference(monotonicity,[status(thm)],[1709])).
% 1.54/1.28 tff(1711,plain,
% 1.54/1.28 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 1.54/1.28 inference(transitivity,[status(thm)],[1710, 1708])).
% 1.54/1.28 tff(1712,plain,
% 1.54/1.28 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))),
% 1.54/1.28 inference(quant_inst,[status(thm)],[])).
% 1.54/1.28 tff(1713,plain,
% 1.54/1.28 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 1.54/1.28 tff(1714,plain,
% 1.54/1.28 (hskp2),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1713, 111, 1365, 1364, 1707, 1706, 1705, 1696, 1686])).
% 1.54/1.28 tff(1715,plain,
% 1.54/1.28 (((~hskp2) | (~c3_1(a2176))) <=> ((~hskp2) | (~c3_1(a2176)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1716,plain,
% 1.54/1.28 (((~c3_1(a2176)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a2176)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1717,axiom,((~c3_1(a2176)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.54/1.28 tff(1718,plain,
% 1.54/1.28 ((~hskp2) | (~c3_1(a2176))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 1.54/1.28 tff(1719,plain,
% 1.54/1.28 ((~hskp2) | (~c3_1(a2176))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1718, 1715])).
% 1.54/1.28 tff(1720,plain,
% 1.54/1.28 (~c3_1(a2176)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1719, 1714])).
% 1.54/1.28 tff(1721,plain,
% 1.54/1.28 (((~hskp2) | c1_1(a2176)) <=> ((~hskp2) | c1_1(a2176))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1722,axiom,((~hskp2) | c1_1(a2176)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.54/1.28 tff(1723,plain,
% 1.54/1.28 ((~hskp2) | c1_1(a2176)),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1722, 1721])).
% 1.54/1.28 tff(1724,plain,
% 1.54/1.28 ((~hskp2) | c1_1(a2176)),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1723, 1721])).
% 1.54/1.28 tff(1725,plain,
% 1.54/1.28 ((~hskp2) | c1_1(a2176)),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1724, 1721])).
% 1.54/1.28 tff(1726,plain,
% 1.54/1.28 ((~hskp2) | c1_1(a2176)),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1725, 1721])).
% 1.54/1.28 tff(1727,plain,
% 1.54/1.28 ((~hskp2) | c1_1(a2176)),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1726, 1721])).
% 1.54/1.28 tff(1728,plain,
% 1.54/1.28 ((~hskp2) | c1_1(a2176)),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1727, 1721])).
% 1.54/1.28 tff(1729,plain,
% 1.54/1.28 ((~hskp2) | c1_1(a2176)),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1728, 1721])).
% 1.54/1.28 tff(1730,plain,
% 1.54/1.28 ((~hskp2) | c1_1(a2176)),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1729, 1721])).
% 1.54/1.28 tff(1731,plain,
% 1.54/1.28 (c1_1(a2176)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1730, 1714])).
% 1.54/1.28 tff(1732,plain,
% 1.54/1.28 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | c3_1(a2176) | (~ndr1_0) | (~c2_1(a2176)) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2176)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c3_1(a2176) | (~ndr1_0) | (~c2_1(a2176)) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2176)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1733,plain,
% 1.54/1.28 ((hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2176) | (~c2_1(a2176)) | (~c1_1(a2176))) <=> (hskp7 | c3_1(a2176) | (~ndr1_0) | (~c2_1(a2176)) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2176)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1734,plain,
% 1.54/1.28 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2176) | (~c2_1(a2176)) | (~c1_1(a2176)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | c3_1(a2176) | (~ndr1_0) | (~c2_1(a2176)) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2176))))),
% 1.54/1.28 inference(monotonicity,[status(thm)],[1733])).
% 1.54/1.28 tff(1735,plain,
% 1.54/1.28 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2176) | (~c2_1(a2176)) | (~c1_1(a2176)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c3_1(a2176) | (~ndr1_0) | (~c2_1(a2176)) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2176)))),
% 1.54/1.28 inference(transitivity,[status(thm)],[1734, 1732])).
% 1.54/1.28 tff(1736,plain,
% 1.54/1.28 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2176) | (~c2_1(a2176)) | (~c1_1(a2176)))),
% 1.54/1.28 inference(quant_inst,[status(thm)],[])).
% 1.54/1.28 tff(1737,plain,
% 1.54/1.28 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c3_1(a2176) | (~ndr1_0) | (~c2_1(a2176)) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2176))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 1.54/1.28 tff(1738,plain,
% 1.54/1.28 (hskp7 | (~c2_1(a2176))),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1737, 111, 1365, 1364, 1731, 1720, 776, 1686])).
% 1.54/1.28 tff(1739,plain,
% 1.54/1.28 (~c2_1(a2176)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1738, 1685])).
% 1.54/1.28 tff(1740,plain,
% 1.54/1.28 (((~hskp2) | (~c0_1(a2176))) <=> ((~hskp2) | (~c0_1(a2176)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1741,plain,
% 1.54/1.28 (((~c0_1(a2176)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a2176)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1742,axiom,((~c0_1(a2176)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.54/1.28 tff(1743,plain,
% 1.54/1.28 ((~hskp2) | (~c0_1(a2176))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 1.54/1.28 tff(1744,plain,
% 1.54/1.28 ((~hskp2) | (~c0_1(a2176))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1743, 1740])).
% 1.54/1.28 tff(1745,plain,
% 1.54/1.28 (~c0_1(a2176)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1744, 1714])).
% 1.54/1.28 tff(1746,assumption,(hskp14), introduced(assumption)).
% 1.54/1.28 tff(1747,plain,
% 1.54/1.28 (~c1_1(a2193)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1487, 1746])).
% 1.54/1.28 tff(1748,plain,
% 1.54/1.28 (c3_1(a2193)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1498, 1746])).
% 1.54/1.28 tff(1749,plain,
% 1.54/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2193)) | (~c3_1(a2193)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1750,plain,
% 1.54/1.28 (((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2193) | (~c3_1(a2193)) | (~c0_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1751,plain,
% 1.54/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2193) | (~c3_1(a2193)) | (~c0_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2193)) | (~c3_1(a2193))))),
% 1.54/1.28 inference(monotonicity,[status(thm)],[1750])).
% 1.54/1.28 tff(1752,plain,
% 1.54/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2193) | (~c3_1(a2193)) | (~c0_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.54/1.28 inference(transitivity,[status(thm)],[1751, 1749])).
% 1.54/1.28 tff(1753,plain,
% 1.54/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2193) | (~c3_1(a2193)) | (~c0_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.54/1.28 inference(quant_inst,[status(thm)],[])).
% 1.54/1.28 tff(1754,plain,
% 1.54/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2193)) | (~c3_1(a2193))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 1.54/1.28 tff(1755,plain,
% 1.54/1.28 (~c0_1(a2193)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1754, 111, 531, 1369, 1748, 1552, 1551, 1550, 1747, 184, 1541])).
% 1.54/1.28 tff(1756,plain,
% 1.54/1.28 ($false),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1512, 111, 1748, 1132, 1131, 1552, 1551, 1550, 1747, 147, 157, 1755])).
% 1.54/1.28 tff(1757,plain,((~hskp14) | (~c1_1(a2174)) | (~c2_1(a2174)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.28 tff(1758,plain,
% 1.54/1.28 (~hskp14),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1757, 1362, 698, 709, 1361, 1360, 687, 1365, 1364, 1686])).
% 1.54/1.28 tff(1759,plain,
% 1.54/1.28 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | c0_1(a2176) | c3_1(a2176) | (~ndr1_0) | c2_1(a2176) | (~c1_1(a2176)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp14 | c0_1(a2176) | c3_1(a2176) | (~ndr1_0) | c2_1(a2176) | (~c1_1(a2176)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1760,plain,
% 1.54/1.28 ((hskp14 | (~ndr1_0) | c2_1(a2176) | c3_1(a2176) | (~c1_1(a2176)) | c3_1(a2176) | c0_1(a2176) | (~c1_1(a2176))) <=> (hskp14 | c0_1(a2176) | c3_1(a2176) | (~ndr1_0) | c2_1(a2176) | (~c1_1(a2176)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1761,plain,
% 1.54/1.28 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2176) | c3_1(a2176) | (~c1_1(a2176)) | c3_1(a2176) | c0_1(a2176) | (~c1_1(a2176)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | c0_1(a2176) | c3_1(a2176) | (~ndr1_0) | c2_1(a2176) | (~c1_1(a2176))))),
% 1.54/1.28 inference(monotonicity,[status(thm)],[1760])).
% 1.54/1.28 tff(1762,plain,
% 1.54/1.28 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2176) | c3_1(a2176) | (~c1_1(a2176)) | c3_1(a2176) | c0_1(a2176) | (~c1_1(a2176)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp14 | c0_1(a2176) | c3_1(a2176) | (~ndr1_0) | c2_1(a2176) | (~c1_1(a2176)))),
% 1.54/1.28 inference(transitivity,[status(thm)],[1761, 1759])).
% 1.54/1.28 tff(1763,plain,
% 1.54/1.28 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2176) | c3_1(a2176) | (~c1_1(a2176)) | c3_1(a2176) | c0_1(a2176) | (~c1_1(a2176)))),
% 1.54/1.28 inference(quant_inst,[status(thm)],[])).
% 1.54/1.28 tff(1764,plain,
% 1.54/1.28 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp14 | c0_1(a2176) | c3_1(a2176) | (~ndr1_0) | c2_1(a2176) | (~c1_1(a2176))),
% 1.54/1.28 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 1.54/1.28 tff(1765,plain,
% 1.54/1.28 ($false),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1764, 111, 1758, 1731, 1745, 1720, 1469, 1739])).
% 1.54/1.28 tff(1766,plain,(c1_1(a2191) | hskp10 | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.28 tff(1767,plain,
% 1.54/1.28 (c1_1(a2191)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1766, 186, 185])).
% 1.54/1.28 tff(1768,plain,
% 1.54/1.28 (~hskp13),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[359, 1767])).
% 1.54/1.28 tff(1769,assumption,(hskp27), introduced(assumption)).
% 1.54/1.28 tff(1770,plain,
% 1.54/1.28 (c3_1(a2178)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[923, 1769])).
% 1.54/1.28 tff(1771,plain,
% 1.54/1.28 (c0_1(a2178)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[945, 1769])).
% 1.54/1.28 tff(1772,plain,
% 1.54/1.28 (c1_1(a2178)),
% 1.54/1.28 inference(unit_resolution,[status(thm)],[1176, 111, 11, 1170, 1771, 1770, 1169])).
% 1.54/1.28 tff(1773,plain,
% 1.54/1.28 (^[U: $i] : refl((hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 1.54/1.28 inference(bind,[status(th)],[])).
% 1.54/1.28 tff(1774,plain,
% 1.54/1.28 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.28 inference(quant_intro,[status(thm)],[1773])).
% 1.54/1.28 tff(1775,plain,
% 1.54/1.28 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.28 inference(rewrite,[status(thm)],[])).
% 1.54/1.28 tff(1776,plain,
% 1.54/1.28 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp13))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp19) <=> ((hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp19))), rewrite(((hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp19) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp19) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.54/1.29 inference(bind,[status(th)],[])).
% 1.54/1.29 tff(1777,plain,
% 1.54/1.29 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp19) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.29 inference(quant_intro,[status(thm)],[1776])).
% 1.54/1.29 tff(1778,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.54/1.29 tff(1779,plain,
% 1.54/1.29 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 1.54/1.29 tff(1780,plain,
% 1.54/1.29 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1779, 1775])).
% 1.54/1.29 tff(1781,plain,(
% 1.54/1.29 ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.29 inference(skolemize,[status(sab)],[1780])).
% 1.54/1.29 tff(1782,plain,
% 1.54/1.29 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1781, 1774])).
% 1.54/1.29 tff(1783,plain,
% 1.54/1.29 (c2_1(a2178)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[934, 1769])).
% 1.54/1.29 tff(1784,plain,
% 1.54/1.29 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1785,plain,
% 1.54/1.29 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)))),
% 1.54/1.29 inference(quant_inst,[status(thm)],[])).
% 1.54/1.29 tff(1786,plain,
% 1.54/1.29 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1785, 1784])).
% 1.54/1.29 tff(1787,plain,
% 1.54/1.29 (hskp19),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1786, 111, 1170, 1783, 1770, 1782, 1772])).
% 1.54/1.29 tff(1788,plain,
% 1.54/1.29 (~c3_1(a2211)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1435, 1787])).
% 1.54/1.29 tff(1789,plain,
% 1.54/1.29 (~c2_1(a2211)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1474, 1787])).
% 1.54/1.29 tff(1790,plain,
% 1.54/1.29 (~c0_1(a2211)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1441, 1787])).
% 1.54/1.29 tff(1791,plain,
% 1.54/1.29 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1792,plain,
% 1.54/1.29 ((hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2211) | c2_1(a2211) | c0_1(a2211)) <=> (hskp28 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1793,plain,
% 1.54/1.29 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2211) | c2_1(a2211) | c0_1(a2211))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178))))),
% 1.54/1.29 inference(monotonicity,[status(thm)],[1792])).
% 1.54/1.29 tff(1794,plain,
% 1.54/1.29 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2211) | c2_1(a2211) | c0_1(a2211))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)))),
% 1.54/1.29 inference(transitivity,[status(thm)],[1793, 1791])).
% 1.54/1.29 tff(1795,plain,
% 1.54/1.29 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2211) | c2_1(a2211) | c0_1(a2211))),
% 1.54/1.29 inference(quant_inst,[status(thm)],[])).
% 1.54/1.29 tff(1796,plain,
% 1.54/1.29 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1795, 1794])).
% 1.54/1.29 tff(1797,plain,
% 1.54/1.29 ($false),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1796, 111, 199, 1771, 1783, 1770, 1790, 1789, 1788, 838])).
% 1.54/1.29 tff(1798,plain,((~hskp27) | hskp28 | hskp13 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.54/1.29 tff(1799,plain,
% 1.54/1.29 (~hskp27),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1798, 11, 1170, 199])).
% 1.54/1.29 tff(1800,plain,
% 1.54/1.29 (^[U: $i] : refl((hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 1.54/1.29 inference(bind,[status(th)],[])).
% 1.54/1.29 tff(1801,plain,
% 1.54/1.29 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.29 inference(quant_intro,[status(thm)],[1800])).
% 1.54/1.29 tff(1802,plain,
% 1.54/1.29 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1803,plain,
% 1.54/1.29 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp16) <=> ((hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp16))), rewrite(((hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp16) <=> (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp16) <=> (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.54/1.29 inference(bind,[status(th)],[])).
% 1.54/1.29 tff(1804,plain,
% 1.54/1.29 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp16) <=> ![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.29 inference(quant_intro,[status(thm)],[1803])).
% 1.54/1.29 tff(1805,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.54/1.29 tff(1806,plain,
% 1.54/1.29 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 1.54/1.29 tff(1807,plain,
% 1.54/1.29 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1806, 1802])).
% 1.54/1.29 tff(1808,plain,(
% 1.54/1.29 ![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.29 inference(skolemize,[status(sab)],[1807])).
% 1.54/1.29 tff(1809,plain,
% 1.54/1.29 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1808, 1801])).
% 1.54/1.29 tff(1810,plain,
% 1.54/1.29 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1811,plain,
% 1.54/1.29 ((hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174))) <=> (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1812,plain,
% 1.54/1.29 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174))))),
% 1.54/1.29 inference(monotonicity,[status(thm)],[1811])).
% 1.54/1.29 tff(1813,plain,
% 1.54/1.29 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)))),
% 1.54/1.29 inference(transitivity,[status(thm)],[1812, 1810])).
% 1.54/1.29 tff(1814,plain,
% 1.54/1.29 ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)))),
% 1.54/1.29 inference(quant_inst,[status(thm)],[])).
% 1.54/1.29 tff(1815,plain,
% 1.54/1.29 ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 1.54/1.29 tff(1816,plain,
% 1.54/1.29 (hskp27 | hskp16 | (~c3_1(a2174))),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1815, 111, 1132, 1131, 1809])).
% 1.54/1.29 tff(1817,plain,
% 1.54/1.29 (~c3_1(a2174)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1816, 1799, 11])).
% 1.54/1.29 tff(1818,plain,
% 1.54/1.29 (^[U: $i] : refl((hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.54/1.29 inference(bind,[status(th)],[])).
% 1.54/1.29 tff(1819,plain,
% 1.54/1.29 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.29 inference(quant_intro,[status(thm)],[1818])).
% 1.54/1.29 tff(1820,plain,
% 1.54/1.29 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1821,plain,
% 1.54/1.29 (^[U: $i] : 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(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp16))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.54/1.29 inference(bind,[status(th)],[])).
% 1.54/1.29 tff(1822,plain,
% 1.54/1.29 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.29 inference(quant_intro,[status(thm)],[1821])).
% 1.54/1.29 tff(1823,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.54/1.29 tff(1824,plain,
% 1.54/1.29 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1823, 1822])).
% 1.54/1.29 tff(1825,plain,
% 1.54/1.29 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1824, 1820])).
% 1.54/1.29 tff(1826,plain,(
% 1.54/1.29 ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.29 inference(skolemize,[status(sab)],[1825])).
% 1.54/1.29 tff(1827,plain,
% 1.54/1.29 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1826, 1819])).
% 1.54/1.29 tff(1828,plain,
% 1.54/1.29 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1829,plain,
% 1.54/1.29 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174))) <=> (hskp16 | hskp15 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1830,plain,
% 1.54/1.29 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174)))),
% 1.54/1.29 inference(monotonicity,[status(thm)],[1829])).
% 1.54/1.29 tff(1831,plain,
% 1.54/1.29 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))),
% 1.54/1.29 inference(transitivity,[status(thm)],[1830, 1828])).
% 1.54/1.29 tff(1832,plain,
% 1.54/1.29 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174)))),
% 1.54/1.29 inference(quant_inst,[status(thm)],[])).
% 1.54/1.29 tff(1833,plain,
% 1.54/1.29 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174)),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1832, 1831])).
% 1.54/1.29 tff(1834,plain,
% 1.54/1.29 (hskp16 | hskp15 | c3_1(a2174)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1833, 111, 1132, 147, 1827])).
% 1.54/1.29 tff(1835,plain,
% 1.54/1.29 (hskp15),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1834, 1817, 11])).
% 1.54/1.29 tff(1836,plain,
% 1.54/1.29 (~c2_1(a2194)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[383, 1835])).
% 1.54/1.29 tff(1837,plain,
% 1.54/1.29 (c3_1(a2194)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[431, 1835])).
% 1.54/1.29 tff(1838,plain,
% 1.54/1.29 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | c2_1(a2194) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2194)) | (~c1_1(a2194)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp27 | c2_1(a2194) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2194)) | (~c1_1(a2194)))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1839,plain,
% 1.54/1.29 ((hskp27 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp27 | c2_1(a2194) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2194)) | (~c1_1(a2194)))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1840,plain,
% 1.54/1.29 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | c2_1(a2194) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2194)) | (~c1_1(a2194))))),
% 1.54/1.29 inference(monotonicity,[status(thm)],[1839])).
% 1.54/1.29 tff(1841,plain,
% 1.54/1.29 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp27 | c2_1(a2194) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2194)) | (~c1_1(a2194)))),
% 1.54/1.29 inference(transitivity,[status(thm)],[1840, 1838])).
% 1.54/1.29 tff(1842,plain,
% 1.54/1.29 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.54/1.29 inference(quant_inst,[status(thm)],[])).
% 1.54/1.29 tff(1843,plain,
% 1.54/1.29 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp27 | c2_1(a2194) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2194)) | (~c1_1(a2194))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1842, 1841])).
% 1.54/1.29 tff(1844,plain,
% 1.54/1.29 (~c1_1(a2194)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1843, 111, 1799, 1837, 1132, 1131, 1836, 147, 848])).
% 1.54/1.29 tff(1845,plain,
% 1.54/1.29 (c0_1(a2194)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[394, 1835])).
% 1.54/1.29 tff(1846,plain,
% 1.54/1.29 ($false),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[401, 111, 11, 1845, 1836, 55, 1844])).
% 1.54/1.29 tff(1847,plain,(hskp16 | (~c1_1(a2174)) | (~c2_1(a2174)) | c0_1(a2174) | hskp13 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.54/1.29 tff(1848,plain,
% 1.54/1.29 (hskp16),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1847, 199, 698, 687, 1170, 709])).
% 1.54/1.29 tff(1849,plain,
% 1.54/1.29 (~c3_1(a2195)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[408, 1848])).
% 1.54/1.29 tff(1850,plain,
% 1.54/1.29 (~c1_1(a2195)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[420, 1848])).
% 1.54/1.29 tff(1851,plain,
% 1.54/1.29 (~c2_1(a2195)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[414, 1848])).
% 1.54/1.29 tff(1852,plain,
% 1.54/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1853,plain,
% 1.54/1.29 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1854,plain,
% 1.54/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219)))),
% 1.54/1.29 inference(monotonicity,[status(thm)],[1853])).
% 1.54/1.29 tff(1855,plain,
% 1.54/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219))),
% 1.54/1.29 inference(transitivity,[status(thm)],[1854, 1852])).
% 1.54/1.29 tff(1856,plain,
% 1.54/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.54/1.29 inference(quant_inst,[status(thm)],[])).
% 1.54/1.29 tff(1857,plain,
% 1.54/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219)),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1856, 1855])).
% 1.54/1.29 tff(1858,plain,
% 1.54/1.29 ((~c3_1(a2219)) | c0_1(a2219)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1857, 111, 1132, 1131, 210, 1552, 1551, 1550, 147, 157])).
% 1.54/1.29 tff(1859,plain,
% 1.54/1.29 (c0_1(a2219)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1858, 975])).
% 1.54/1.29 tff(1860,plain,
% 1.54/1.29 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1861,plain,
% 1.54/1.29 ((hskp28 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195)) <=> (hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1862,plain,
% 1.54/1.29 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195))))),
% 1.54/1.29 inference(monotonicity,[status(thm)],[1861])).
% 1.54/1.29 tff(1863,plain,
% 1.54/1.29 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))),
% 1.54/1.29 inference(transitivity,[status(thm)],[1862, 1860])).
% 1.54/1.29 tff(1864,plain,
% 1.54/1.29 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))),
% 1.54/1.29 inference(quant_inst,[status(thm)],[])).
% 1.54/1.29 tff(1865,plain,
% 1.54/1.29 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195))),
% 1.54/1.29 inference(modus_ponens,[status(thm)],[1864, 1863])).
% 1.54/1.29 tff(1866,plain,
% 1.54/1.29 (~c0_1(a2195)),
% 1.54/1.29 inference(unit_resolution,[status(thm)],[1865, 111, 199, 1552, 1551, 1550, 442])).
% 1.54/1.29 tff(1867,plain,
% 1.54/1.29 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.54/1.29 inference(bind,[status(th)],[])).
% 1.54/1.29 tff(1868,plain,
% 1.54/1.29 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.54/1.29 inference(quant_intro,[status(thm)],[1867])).
% 1.54/1.29 tff(1869,plain,
% 1.54/1.29 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.54/1.29 inference(rewrite,[status(thm)],[])).
% 1.54/1.29 tff(1870,plain,
% 1.54/1.29 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.54/1.30 inference(bind,[status(th)],[])).
% 1.54/1.30 tff(1871,plain,
% 1.54/1.30 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.54/1.30 inference(quant_intro,[status(thm)],[1870])).
% 1.54/1.30 tff(1872,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.54/1.30 tff(1873,plain,
% 1.54/1.30 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1872, 1871])).
% 1.54/1.30 tff(1874,plain,
% 1.54/1.30 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1873, 1869])).
% 1.54/1.30 tff(1875,plain,(
% 1.54/1.30 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.54/1.30 inference(skolemize,[status(sab)],[1874])).
% 1.54/1.30 tff(1876,plain,
% 1.54/1.30 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1875, 1868])).
% 1.54/1.30 tff(1877,plain,
% 1.54/1.30 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp11 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp11 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c0_1(a2219)))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1878,plain,
% 1.54/1.30 ((hskp11 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195)) <=> (hskp11 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c0_1(a2219)))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1879,plain,
% 1.54/1.30 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp11 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp11 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c0_1(a2219))))),
% 1.54/1.30 inference(monotonicity,[status(thm)],[1878])).
% 1.54/1.30 tff(1880,plain,
% 1.54/1.30 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp11 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp11 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c0_1(a2219)))),
% 1.54/1.30 inference(transitivity,[status(thm)],[1879, 1877])).
% 1.54/1.30 tff(1881,plain,
% 1.54/1.30 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp11 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195))),
% 1.54/1.30 inference(quant_inst,[status(thm)],[])).
% 1.54/1.30 tff(1882,plain,
% 1.54/1.30 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp11 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c0_1(a2219))),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1881, 1880])).
% 1.54/1.30 tff(1883,plain,
% 1.54/1.30 (hskp11 | (~c3_1(a2219)) | (~c0_1(a2219))),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1882, 111, 210, 1551, 1550, 1876, 1866])).
% 1.54/1.30 tff(1884,plain,
% 1.54/1.30 (hskp11),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1883, 975, 1859])).
% 1.54/1.30 tff(1885,plain,
% 1.54/1.30 (~c1_1(a2187)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[218, 1884])).
% 1.54/1.30 tff(1886,plain,
% 1.54/1.30 (c2_1(a2187)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[229, 1884])).
% 1.54/1.30 tff(1887,plain,
% 1.54/1.30 (c0_1(a2187)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[240, 1884])).
% 1.54/1.30 tff(1888,plain,
% 1.54/1.30 (~hskp22),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[490, 975])).
% 1.54/1.30 tff(1889,plain,
% 1.54/1.30 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1890,plain,
% 1.54/1.30 ((hskp28 | hskp22 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187))) <=> (hskp28 | hskp22 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1891,plain,
% 1.54/1.30 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187))))),
% 1.54/1.30 inference(monotonicity,[status(thm)],[1890])).
% 1.54/1.30 tff(1892,plain,
% 1.54/1.30 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 1.54/1.30 inference(transitivity,[status(thm)],[1891, 1889])).
% 1.54/1.30 tff(1893,plain,
% 1.54/1.30 ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 1.54/1.30 inference(quant_inst,[status(thm)],[])).
% 1.54/1.30 tff(1894,plain,
% 1.54/1.30 ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187))),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1893, 1892])).
% 1.54/1.30 tff(1895,plain,
% 1.54/1.30 ($false),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1894, 111, 199, 1888, 1887, 1886, 1885, 209])).
% 1.54/1.30 tff(1896,plain,((~c3_1(a2219)) | hskp28 | c1_1(a2219) | c2_1(a2195) | c3_1(a2195) | (~c1_1(a2174)) | (~c2_1(a2174)) | c1_1(a2195) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.30 tff(1897,plain,
% 1.54/1.30 (~c3_1(a2219)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1896, 210, 199, 1551, 1550, 709, 698, 1552, 687])).
% 1.54/1.30 tff(1898,plain,
% 1.54/1.30 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c1_1(a2219) | c3_1(a2219) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2219) | c3_1(a2219) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2219)))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1899,plain,
% 1.54/1.30 ((hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195)) <=> (hskp28 | c1_1(a2219) | c3_1(a2219) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2219)))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1900,plain,
% 1.54/1.30 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c1_1(a2219) | c3_1(a2219) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2219))))),
% 1.54/1.30 inference(monotonicity,[status(thm)],[1899])).
% 1.54/1.30 tff(1901,plain,
% 1.54/1.30 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2219) | c3_1(a2219) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2219)))),
% 1.54/1.30 inference(transitivity,[status(thm)],[1900, 1898])).
% 1.54/1.30 tff(1902,plain,
% 1.54/1.30 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))),
% 1.54/1.30 inference(quant_inst,[status(thm)],[])).
% 1.54/1.30 tff(1903,plain,
% 1.54/1.30 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2219) | c3_1(a2219) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2219))),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1902, 1901])).
% 1.54/1.30 tff(1904,plain,
% 1.54/1.30 (c3_1(a2219) | (~c0_1(a2219))),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1903, 111, 199, 210, 1552, 1551, 1550, 442])).
% 1.54/1.30 tff(1905,plain,
% 1.54/1.30 (~c0_1(a2219)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1904, 212])).
% 1.54/1.30 tff(1906,plain,
% 1.54/1.30 (c2_1(a2219)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[954, 212, 199, 210, 850, 185])).
% 1.54/1.30 tff(1907,plain,
% 1.54/1.30 ($false),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1189, 1906, 1905, 210, 709, 698, 1170, 687])).
% 1.54/1.30 tff(1908,plain,(c3_1(a2219) | c1_1(a2219) | hskp13 | hskp28 | hskp17 | hskp10 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.30 tff(1909,plain,
% 1.54/1.30 (hskp17),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1908, 1897, 1170, 199, 210, 185, 1552, 1551, 1550])).
% 1.54/1.30 tff(1910,plain,
% 1.54/1.30 (~c1_1(a2197)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[163, 1909])).
% 1.54/1.30 tff(1911,plain,
% 1.54/1.30 (c3_1(a2197)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[653, 1909])).
% 1.54/1.30 tff(1912,plain,
% 1.54/1.30 (~c0_1(a2219)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1904, 1897])).
% 1.54/1.30 tff(1913,plain,
% 1.54/1.30 (~c2_1(a2219)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1189, 1912, 210, 709, 698, 1170, 687])).
% 1.54/1.30 tff(1914,plain,
% 1.54/1.30 (c0_1(a2197)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[971, 111, 1913, 1911, 709, 698, 210, 1897, 1910, 687, 157])).
% 1.54/1.30 tff(1915,plain,
% 1.54/1.30 (c2_1(a2197)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[664, 1909])).
% 1.54/1.30 tff(1916,plain,
% 1.54/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)) | c0_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)) | c0_1(a2219))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1917,plain,
% 1.54/1.30 (((~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2219) | c0_1(a2219)) <=> (c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)) | c0_1(a2219))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1918,plain,
% 1.54/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2219) | c0_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)) | c0_1(a2219)))),
% 1.54/1.30 inference(monotonicity,[status(thm)],[1917])).
% 1.54/1.30 tff(1919,plain,
% 1.54/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2219) | c0_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)) | c0_1(a2219))),
% 1.54/1.30 inference(transitivity,[status(thm)],[1918, 1916])).
% 1.54/1.30 tff(1920,plain,
% 1.54/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2219) | c0_1(a2219))),
% 1.54/1.30 inference(quant_inst,[status(thm)],[])).
% 1.54/1.30 tff(1921,plain,
% 1.54/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)) | c0_1(a2219)),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1920, 1919])).
% 1.54/1.30 tff(1922,plain,
% 1.54/1.30 ($false),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1921, 111, 1913, 1915, 210, 1897, 1910, 197, 1912, 1914])).
% 1.54/1.30 tff(1923,plain,(c1_1(a2219) | hskp13 | hskp28 | hskp10 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.30 tff(1924,plain,
% 1.54/1.30 (c1_1(a2219)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1923, 1552, 199, 185, 1170, 1551, 1550])).
% 1.54/1.30 tff(1925,plain,
% 1.54/1.30 (~hskp22),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[516, 1924])).
% 1.54/1.30 tff(1926,assumption,(~c0_1(a2195)), introduced(assumption)).
% 1.54/1.30 tff(1927,plain,
% 1.54/1.30 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2195))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1928,plain,
% 1.54/1.30 ((hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195)) <=> (hskp28 | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2195))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1929,plain,
% 1.54/1.30 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2195)))),
% 1.54/1.30 inference(monotonicity,[status(thm)],[1928])).
% 1.54/1.30 tff(1930,plain,
% 1.54/1.30 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2195))),
% 1.54/1.30 inference(transitivity,[status(thm)],[1929, 1927])).
% 1.54/1.30 tff(1931,plain,
% 1.54/1.30 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195))),
% 1.54/1.30 inference(quant_inst,[status(thm)],[])).
% 1.54/1.30 tff(1932,plain,
% 1.54/1.30 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2195)),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1931, 1930])).
% 1.54/1.30 tff(1933,plain,
% 1.54/1.30 ($false),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1932, 111, 199, 1771, 1783, 1770, 1551, 1550, 838, 1926])).
% 1.54/1.30 tff(1934,plain,((~hskp27) | hskp28 | c2_1(a2195) | c3_1(a2195) | c0_1(a2195)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.30 tff(1935,plain,
% 1.54/1.30 (~hskp27),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1934, 1866, 1551, 1550, 199])).
% 1.54/1.30 tff(1936,plain,
% 1.54/1.30 (~hskp25),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1260, 1935, 709, 698, 687])).
% 1.54/1.30 tff(1937,plain,
% 1.54/1.30 (hskp21),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[877, 1936, 1925])).
% 1.54/1.30 tff(1938,plain,
% 1.54/1.30 (hskp17),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[983, 1937, 199, 185])).
% 1.54/1.30 tff(1939,plain,
% 1.54/1.30 (~c1_1(a2197)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[163, 1938])).
% 1.54/1.30 tff(1940,plain,
% 1.54/1.30 (c2_1(a2197)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[664, 1938])).
% 1.54/1.30 tff(1941,plain,
% 1.54/1.30 (~c0_1(a2197)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[963, 111, 199, 1925, 1940, 1939, 209])).
% 1.54/1.30 tff(1942,plain,
% 1.54/1.30 (c3_1(a2197)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[653, 1938])).
% 1.54/1.30 tff(1943,plain,
% 1.54/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1944,plain,
% 1.54/1.30 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1945,plain,
% 1.54/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.54/1.30 inference(monotonicity,[status(thm)],[1944])).
% 1.54/1.30 tff(1946,plain,
% 1.54/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.54/1.30 inference(transitivity,[status(thm)],[1945, 1943])).
% 1.54/1.30 tff(1947,plain,
% 1.54/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.54/1.30 inference(quant_inst,[status(thm)],[])).
% 1.54/1.30 tff(1948,plain,
% 1.54/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1947, 1946])).
% 1.54/1.30 tff(1949,plain,
% 1.54/1.30 ($false),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1948, 111, 1942, 709, 698, 1939, 1552, 1551, 1550, 687, 157, 1941])).
% 1.54/1.30 tff(1950,plain,(c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | hskp28 | hskp10 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.54/1.30 tff(1951,plain,
% 1.54/1.30 ($false),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1950, 1851, 1850, 1849, 199, 185, 1170])).
% 1.54/1.30 tff(1952,plain,(hskp28 | hskp10 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.54/1.30 tff(1953,plain,
% 1.54/1.30 (hskp28),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1952, 1170, 185])).
% 1.54/1.30 tff(1954,plain,
% 1.54/1.30 (c2_1(a2188)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[271, 1953])).
% 1.54/1.30 tff(1955,plain,
% 1.54/1.30 (c1_1(a2188)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[480, 1953])).
% 1.54/1.30 tff(1956,plain,
% 1.54/1.30 (c0_1(a2188)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[282, 1953])).
% 1.54/1.30 tff(1957,plain,
% 1.54/1.30 (hskp11 | c3_1(a2188)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[290, 111, 185, 1956, 1954, 260])).
% 1.54/1.30 tff(1958,plain,
% 1.54/1.30 (c3_1(a2188)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1957, 284])).
% 1.54/1.30 tff(1959,plain,
% 1.54/1.30 (hskp11 | hskp1 | (~c3_1(a2188))),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[744, 111, 1956, 1954, 738])).
% 1.54/1.30 tff(1960,plain,
% 1.54/1.30 (hskp1),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1959, 284, 1958])).
% 1.54/1.30 tff(1961,plain,
% 1.54/1.30 (~c3_1(a2175)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[597, 1960])).
% 1.54/1.30 tff(1962,plain,
% 1.54/1.30 (c2_1(a2175)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[614, 1960])).
% 1.54/1.30 tff(1963,plain,
% 1.54/1.30 (~c0_1(a2175)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[603, 1960])).
% 1.54/1.30 tff(1964,plain,
% 1.54/1.30 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1965,plain,
% 1.54/1.30 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))),
% 1.54/1.30 inference(quant_inst,[status(thm)],[])).
% 1.54/1.30 tff(1966,plain,
% 1.54/1.30 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188))),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1965, 1964])).
% 1.54/1.30 tff(1967,plain,
% 1.54/1.30 (hskp19 | hskp13 | (~c3_1(a2188))),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1966, 111, 530, 1369, 1782])).
% 1.54/1.30 tff(1968,plain,
% 1.54/1.30 (hskp19),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1967, 1170, 1541])).
% 1.54/1.30 tff(1969,plain,
% 1.54/1.30 (~c2_1(a2211)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1474, 1968])).
% 1.54/1.30 tff(1970,assumption,(~hskp14), introduced(assumption)).
% 1.54/1.30 tff(1971,plain,
% 1.54/1.30 (~c0_1(a2211)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1441, 1968])).
% 1.54/1.30 tff(1972,plain,
% 1.54/1.30 (~c3_1(a2211)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1435, 1968])).
% 1.54/1.30 tff(1973,assumption,(~c3_1(a2211)), introduced(assumption)).
% 1.54/1.30 tff(1974,assumption,(~c2_1(a2211)), introduced(assumption)).
% 1.54/1.30 tff(1975,assumption,(~c0_1(a2211)), introduced(assumption)).
% 1.54/1.30 tff(1976,plain,
% 1.54/1.30 (hskp14 | (~c1_1(a2211))),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1481, 111, 1975, 1974, 1973, 1469])).
% 1.54/1.30 tff(1977,plain,
% 1.54/1.30 (~c1_1(a2211)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1976, 1970])).
% 1.54/1.30 tff(1978,plain,
% 1.54/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2211) | c3_1(a2211) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)) | c1_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2211) | c3_1(a2211) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)) | c1_1(a2211))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1979,plain,
% 1.54/1.30 (((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211)) <=> (c0_1(a2211) | c3_1(a2211) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)) | c1_1(a2211))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1980,plain,
% 1.54/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2211) | c3_1(a2211) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)) | c1_1(a2211)))),
% 1.54/1.30 inference(monotonicity,[status(thm)],[1979])).
% 1.54/1.30 tff(1981,plain,
% 1.54/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2211) | c3_1(a2211) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)) | c1_1(a2211))),
% 1.54/1.30 inference(transitivity,[status(thm)],[1980, 1978])).
% 1.54/1.30 tff(1982,plain,
% 1.54/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))),
% 1.54/1.30 inference(quant_inst,[status(thm)],[])).
% 1.54/1.30 tff(1983,plain,
% 1.54/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2211) | c3_1(a2211) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)) | c1_1(a2211)),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1982, 1981])).
% 1.54/1.30 tff(1984,plain,
% 1.54/1.30 ((~c3_1(a2174)) | c1_1(a2211)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1983, 111, 1613, 1132, 1975, 1973, 1612, 1611, 147, 758])).
% 1.54/1.30 tff(1985,plain,
% 1.54/1.30 (~c3_1(a2174)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1984, 1977])).
% 1.54/1.30 tff(1986,plain,
% 1.54/1.30 ((hskp24 | hskp14 | hskp13) <=> (hskp24 | hskp14 | hskp13)),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1987,plain,
% 1.54/1.30 (((hskp13 | hskp24) | hskp14) <=> (hskp24 | hskp14 | hskp13)),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1988,axiom,((hskp13 | hskp24) | hskp14), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 1.54/1.30 tff(1989,plain,
% 1.54/1.30 (hskp24 | hskp14 | hskp13),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1988, 1987])).
% 1.54/1.30 tff(1990,plain,
% 1.54/1.30 (hskp24 | hskp14 | hskp13),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1989, 1986])).
% 1.54/1.30 tff(1991,plain,
% 1.54/1.30 (hskp24 | hskp14 | hskp13),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1990, 1986])).
% 1.54/1.30 tff(1992,plain,
% 1.54/1.30 (hskp24 | hskp14 | hskp13),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1991, 1986])).
% 1.54/1.30 tff(1993,plain,
% 1.54/1.30 (hskp24 | hskp14 | hskp13),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1992, 1986])).
% 1.54/1.30 tff(1994,plain,
% 1.54/1.30 (hskp24 | hskp14 | hskp13),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1993, 1986])).
% 1.54/1.30 tff(1995,plain,
% 1.54/1.30 (hskp24 | hskp14 | hskp13),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1994, 1986])).
% 1.54/1.30 tff(1996,plain,
% 1.54/1.30 (hskp24 | hskp14 | hskp13),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[1995, 1986])).
% 1.54/1.30 tff(1997,plain,
% 1.54/1.30 (hskp24),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[1996, 1970, 1170])).
% 1.54/1.30 tff(1998,plain,
% 1.54/1.30 (((~hskp24) | (~c0_1(a2262))) <=> ((~hskp24) | (~c0_1(a2262)))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(1999,plain,
% 1.54/1.30 (((~c0_1(a2262)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a2262)))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(2000,axiom,((~c0_1(a2262)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.54/1.30 tff(2001,plain,
% 1.54/1.30 ((~hskp24) | (~c0_1(a2262))),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[2000, 1999])).
% 1.54/1.30 tff(2002,plain,
% 1.54/1.30 ((~hskp24) | (~c0_1(a2262))),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[2001, 1998])).
% 1.54/1.30 tff(2003,plain,
% 1.54/1.30 (~c0_1(a2262)),
% 1.54/1.30 inference(unit_resolution,[status(thm)],[2002, 1997])).
% 1.54/1.30 tff(2004,plain,
% 1.54/1.30 (((~hskp24) | c3_1(a2262)) <=> ((~hskp24) | c3_1(a2262))),
% 1.54/1.30 inference(rewrite,[status(thm)],[])).
% 1.54/1.30 tff(2005,axiom,((~hskp24) | c3_1(a2262)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.54/1.30 tff(2006,plain,
% 1.54/1.30 ((~hskp24) | c3_1(a2262)),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[2005, 2004])).
% 1.54/1.30 tff(2007,plain,
% 1.54/1.30 ((~hskp24) | c3_1(a2262)),
% 1.54/1.30 inference(modus_ponens,[status(thm)],[2006, 2004])).
% 1.54/1.30 tff(2008,plain,
% 1.54/1.31 ((~hskp24) | c3_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2007, 2004])).
% 1.54/1.31 tff(2009,plain,
% 1.54/1.31 ((~hskp24) | c3_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2008, 2004])).
% 1.54/1.31 tff(2010,plain,
% 1.54/1.31 ((~hskp24) | c3_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2009, 2004])).
% 1.54/1.31 tff(2011,plain,
% 1.54/1.31 ((~hskp24) | c3_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2010, 2004])).
% 1.54/1.31 tff(2012,plain,
% 1.54/1.31 ((~hskp24) | c3_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2011, 2004])).
% 1.54/1.31 tff(2013,plain,
% 1.54/1.31 ((~hskp24) | c3_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2012, 2004])).
% 1.54/1.31 tff(2014,plain,
% 1.54/1.31 (c3_1(a2262)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2013, 1997])).
% 1.54/1.31 tff(2015,plain,
% 1.54/1.31 (((~hskp24) | c1_1(a2262)) <=> ((~hskp24) | c1_1(a2262))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2016,axiom,((~hskp24) | c1_1(a2262)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.54/1.31 tff(2017,plain,
% 1.54/1.31 ((~hskp24) | c1_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 1.54/1.31 tff(2018,plain,
% 1.54/1.31 ((~hskp24) | c1_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2017, 2015])).
% 1.54/1.31 tff(2019,plain,
% 1.54/1.31 ((~hskp24) | c1_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2018, 2015])).
% 1.54/1.31 tff(2020,plain,
% 1.54/1.31 ((~hskp24) | c1_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2019, 2015])).
% 1.54/1.31 tff(2021,plain,
% 1.54/1.31 ((~hskp24) | c1_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2020, 2015])).
% 1.54/1.31 tff(2022,plain,
% 1.54/1.31 ((~hskp24) | c1_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2021, 2015])).
% 1.54/1.31 tff(2023,plain,
% 1.54/1.31 ((~hskp24) | c1_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2022, 2015])).
% 1.54/1.31 tff(2024,plain,
% 1.54/1.31 ((~hskp24) | c1_1(a2262)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2023, 2015])).
% 1.54/1.31 tff(2025,plain,
% 1.54/1.31 (c1_1(a2262)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2024, 1997])).
% 1.54/1.31 tff(2026,plain,
% 1.54/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2262) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2211) | (~c3_1(a2262)) | (~c1_1(a2262)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2211) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2027,plain,
% 1.54/1.31 (((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211)) <=> (c0_1(a2262) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2211) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2028,plain,
% 1.54/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2262) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2211) | (~c3_1(a2262)) | (~c1_1(a2262))))),
% 1.54/1.31 inference(monotonicity,[status(thm)],[2027])).
% 1.54/1.31 tff(2029,plain,
% 1.54/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2211) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.54/1.31 inference(transitivity,[status(thm)],[2028, 2026])).
% 1.54/1.31 tff(2030,plain,
% 1.54/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))),
% 1.54/1.31 inference(quant_inst,[status(thm)],[])).
% 1.54/1.31 tff(2031,plain,
% 1.54/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2211) | (~c3_1(a2262)) | (~c1_1(a2262))),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2030, 2029])).
% 1.54/1.31 tff(2032,plain,
% 1.54/1.31 ($false),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2031, 111, 2025, 2014, 1131, 2003, 1975, 1973, 147, 758, 1985, 1977])).
% 1.54/1.31 tff(2033,plain,(hskp14 | (~c2_1(a2174)) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~c2_1(a2175)) | (~c1_1(a2174)) | c0_1(a2175) | c3_1(a2175) | c2_1(a2211) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.54/1.31 tff(2034,plain,
% 1.54/1.31 ($false),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2033, 1972, 1971, 1131, 1970, 147, 1613, 1132, 1612, 1611, 1969, 1170])).
% 1.54/1.31 tff(2035,plain,(hskp13 | (~c2_1(a2174)) | hskp14 | c0_1(a2174) | (~c2_1(a2175)) | (~c1_1(a2174)) | c0_1(a2175) | c3_1(a2175) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2188))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.31 tff(2036,plain,
% 1.54/1.31 (hskp14),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2035, 1963, 1170, 687, 698, 709, 1962, 1961, 1958, 1955, 1954])).
% 1.54/1.31 tff(2037,plain,
% 1.54/1.31 (~c1_1(a2193)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[1487, 2036])).
% 1.54/1.31 tff(2038,plain,
% 1.54/1.31 (c3_1(a2193)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[1498, 2036])).
% 1.54/1.31 tff(2039,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | c1_1(a2193) | (~ndr1_0) | (~c0_1(a2193)) | (~c3_1(a2193)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2193) | (~ndr1_0) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2040,plain,
% 1.54/1.31 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193))) <=> (hskp16 | hskp13 | c1_1(a2193) | (~ndr1_0) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2041,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | c1_1(a2193) | (~ndr1_0) | (~c0_1(a2193)) | (~c3_1(a2193))))),
% 1.54/1.31 inference(monotonicity,[status(thm)],[2040])).
% 1.54/1.31 tff(2042,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2193) | (~ndr1_0) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.54/1.31 inference(transitivity,[status(thm)],[2041, 2039])).
% 1.54/1.31 tff(2043,plain,
% 1.54/1.31 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.54/1.31 inference(quant_inst,[status(thm)],[])).
% 1.54/1.31 tff(2044,plain,
% 1.54/1.31 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2193) | (~ndr1_0) | (~c0_1(a2193)) | (~c3_1(a2193))),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2043, 2042])).
% 1.54/1.31 tff(2045,plain,
% 1.54/1.31 (~c0_1(a2193)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2044, 111, 11, 1170, 2038, 2037, 1169])).
% 1.54/1.31 tff(2046,plain,
% 1.54/1.31 (c1_1(a2175)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[1641, 1962, 1955, 1958, 709, 698, 1963, 687, 1956])).
% 1.54/1.31 tff(2047,plain,
% 1.54/1.31 (~hskp9),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[1675, 2046, 1955, 1962, 1963, 1958, 1956])).
% 1.54/1.31 tff(2048,plain,
% 1.54/1.31 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp9 | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2049,plain,
% 1.54/1.31 ((hskp10 | hskp9 | (~ndr1_0) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193))) <=> (hskp10 | hskp9 | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2050,plain,
% 1.54/1.31 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | (~ndr1_0) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193))))),
% 1.54/1.31 inference(monotonicity,[status(thm)],[2049])).
% 1.54/1.31 tff(2051,plain,
% 1.54/1.31 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | (~ndr1_0) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp9 | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.54/1.31 inference(transitivity,[status(thm)],[2050, 2048])).
% 1.54/1.31 tff(2052,plain,
% 1.54/1.31 ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | (~ndr1_0) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.54/1.31 inference(quant_inst,[status(thm)],[])).
% 1.54/1.31 tff(2053,plain,
% 1.54/1.31 ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp9 | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193))),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2052, 2051])).
% 1.54/1.31 tff(2054,plain,
% 1.54/1.31 ($false),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2053, 111, 185, 2047, 2038, 2037, 1632, 2045])).
% 1.54/1.31 tff(2055,plain,(hskp11 | hskp10 | hskp16 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.54/1.31 tff(2056,plain,
% 1.54/1.31 (hskp11),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2055, 11, 185, 1170])).
% 1.54/1.31 tff(2057,plain,
% 1.54/1.31 (~c1_1(a2187)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[218, 2056])).
% 1.54/1.31 tff(2058,plain,
% 1.54/1.31 (c0_1(a2187)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[240, 2056])).
% 1.54/1.31 tff(2059,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2060,plain,
% 1.54/1.31 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c3_1(a2187))) <=> (hskp16 | hskp13 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2061,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c3_1(a2187)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187))))),
% 1.54/1.31 inference(monotonicity,[status(thm)],[2060])).
% 1.54/1.31 tff(2062,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c3_1(a2187)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)))),
% 1.54/1.31 inference(transitivity,[status(thm)],[2061, 2059])).
% 1.54/1.31 tff(2063,plain,
% 1.54/1.31 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c3_1(a2187)))),
% 1.54/1.31 inference(quant_inst,[status(thm)],[])).
% 1.54/1.31 tff(2064,plain,
% 1.54/1.31 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187))),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2063, 2062])).
% 1.54/1.31 tff(2065,plain,
% 1.54/1.31 (~c3_1(a2187)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2064, 111, 11, 1170, 2058, 2057, 1169])).
% 1.54/1.31 tff(2066,plain,
% 1.54/1.31 ($false),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[1312, 111, 120, 2058, 709, 698, 2057, 687, 1233, 2065])).
% 1.54/1.31 tff(2067,plain,(hskp16 | hskp13 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.54/1.31 tff(2068,plain,
% 1.54/1.31 (hskp16),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2067, 1768, 185])).
% 1.54/1.31 tff(2069,plain,
% 1.54/1.31 (~c2_1(a2195)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[414, 2068])).
% 1.54/1.31 tff(2070,plain,
% 1.54/1.31 (~c3_1(a2195)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[408, 2068])).
% 1.54/1.31 tff(2071,plain,
% 1.54/1.31 (^[U: $i] : refl((hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.54/1.31 inference(bind,[status(th)],[])).
% 1.54/1.31 tff(2072,plain,
% 1.54/1.31 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.31 inference(quant_intro,[status(thm)],[2071])).
% 1.54/1.31 tff(2073,plain,
% 1.54/1.31 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2074,plain,
% 1.54/1.31 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp16) <=> ((hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp16))), rewrite(((hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp16) <=> (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp16) <=> (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.54/1.31 inference(bind,[status(th)],[])).
% 1.54/1.31 tff(2075,plain,
% 1.54/1.31 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp16) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.31 inference(quant_intro,[status(thm)],[2074])).
% 1.54/1.31 tff(2076,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 1.54/1.31 tff(2077,plain,
% 1.54/1.31 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2076, 2075])).
% 1.54/1.31 tff(2078,plain,
% 1.54/1.31 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2077, 2073])).
% 1.54/1.31 tff(2079,plain,(
% 1.54/1.31 ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.31 inference(skolemize,[status(sab)],[2078])).
% 1.54/1.31 tff(2080,plain,
% 1.54/1.31 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2079, 2072])).
% 1.54/1.31 tff(2081,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~c1_1(a2195)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | (~c1_1(a2195)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2082,plain,
% 1.54/1.31 ((hskp16 | hskp13 | (~ndr1_0) | c2_1(a2195) | c3_1(a2195) | (~c1_1(a2195))) <=> (hskp16 | hskp13 | (~c1_1(a2195)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2083,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2195) | c3_1(a2195) | (~c1_1(a2195)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~c1_1(a2195)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0)))),
% 1.54/1.31 inference(monotonicity,[status(thm)],[2082])).
% 1.54/1.31 tff(2084,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2195) | c3_1(a2195) | (~c1_1(a2195)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | (~c1_1(a2195)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0))),
% 1.54/1.31 inference(transitivity,[status(thm)],[2083, 2081])).
% 1.54/1.31 tff(2085,plain,
% 1.54/1.31 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2195) | c3_1(a2195) | (~c1_1(a2195)))),
% 1.54/1.31 inference(quant_inst,[status(thm)],[])).
% 1.54/1.31 tff(2086,plain,
% 1.54/1.31 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | (~c1_1(a2195)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2085, 2084])).
% 1.54/1.31 tff(2087,plain,
% 1.54/1.31 (hskp16 | (~c1_1(a2195)) | c2_1(a2195)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2086, 111, 1768, 1550, 2080])).
% 1.54/1.31 tff(2088,plain,
% 1.54/1.31 (~c1_1(a2195)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2087, 11, 1551])).
% 1.54/1.31 tff(2089,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2090,plain,
% 1.54/1.31 ((hskp16 | (~ndr1_0) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195))) <=> (hskp16 | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2091,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | (~c0_1(a2195))))),
% 1.54/1.31 inference(monotonicity,[status(thm)],[2090])).
% 1.54/1.31 tff(2092,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))),
% 1.54/1.31 inference(transitivity,[status(thm)],[2091, 2089])).
% 1.54/1.31 tff(2093,plain,
% 1.54/1.31 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)))),
% 1.54/1.31 inference(quant_inst,[status(thm)],[])).
% 1.54/1.31 tff(2094,plain,
% 1.54/1.31 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | (~c0_1(a2195))),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2093, 2092])).
% 1.54/1.31 tff(2095,plain,
% 1.54/1.31 (hskp16 | c1_1(a2195) | (~c0_1(a2195))),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2094, 111, 1551, 55])).
% 1.54/1.31 tff(2096,plain,
% 1.54/1.31 (~c0_1(a2195)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2095, 2088, 11])).
% 1.54/1.31 tff(2097,plain,
% 1.54/1.31 (hskp28),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[1952, 1768, 185])).
% 1.54/1.31 tff(2098,plain,
% 1.54/1.31 (c1_1(a2188)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[480, 2097])).
% 1.54/1.31 tff(2099,plain,
% 1.54/1.31 (c0_1(a2188)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[282, 2097])).
% 1.54/1.31 tff(2100,plain,
% 1.54/1.31 (c2_1(a2188)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[271, 2097])).
% 1.54/1.31 tff(2101,plain,
% 1.54/1.31 (hskp11 | c3_1(a2188)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[290, 111, 185, 2099, 2100, 260])).
% 1.54/1.31 tff(2102,plain,
% 1.54/1.31 (c3_1(a2188)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2101, 284])).
% 1.54/1.31 tff(2103,plain,
% 1.54/1.31 (~hskp17),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[1561, 2102, 2100, 2099, 1551, 1550, 2088, 2098, 709, 698, 687])).
% 1.54/1.31 tff(2104,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2105,plain,
% 1.54/1.31 ((hskp16 | hskp13 | (~ndr1_0) | c2_1(a2191) | c3_1(a2191) | (~c1_1(a2191))) <=> (hskp16 | hskp13 | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2106,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2191) | c3_1(a2191) | (~c1_1(a2191)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191)))),
% 1.54/1.31 inference(monotonicity,[status(thm)],[2105])).
% 1.54/1.31 tff(2107,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2191) | c3_1(a2191) | (~c1_1(a2191)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191))),
% 1.54/1.31 inference(transitivity,[status(thm)],[2106, 2104])).
% 1.54/1.31 tff(2108,plain,
% 1.54/1.31 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2191) | c3_1(a2191) | (~c1_1(a2191)))),
% 1.54/1.31 inference(quant_inst,[status(thm)],[])).
% 1.54/1.31 tff(2109,plain,
% 1.54/1.31 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2108, 2107])).
% 1.54/1.31 tff(2110,plain,
% 1.54/1.31 (hskp16 | hskp13 | (~c1_1(a2191)) | c2_1(a2191)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2109, 111, 186, 2080])).
% 1.54/1.31 tff(2111,plain,
% 1.54/1.31 (c2_1(a2191)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2110, 11, 1768, 1767])).
% 1.54/1.31 tff(2112,plain,
% 1.54/1.31 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | (~c0_1(a2191)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | hskp11 | hskp10 | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | (~c0_1(a2191)))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2113,plain,
% 1.54/1.31 ((hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2191)) | (~c2_1(a2191)) | c3_1(a2191)) <=> (hskp11 | hskp10 | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | (~c0_1(a2191)))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2114,plain,
% 1.54/1.31 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2191)) | (~c2_1(a2191)) | c3_1(a2191))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | (~c0_1(a2191))))),
% 1.54/1.31 inference(monotonicity,[status(thm)],[2113])).
% 1.54/1.31 tff(2115,plain,
% 1.54/1.31 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2191)) | (~c2_1(a2191)) | c3_1(a2191))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | hskp11 | hskp10 | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | (~c0_1(a2191)))),
% 1.54/1.31 inference(transitivity,[status(thm)],[2114, 2112])).
% 1.54/1.31 tff(2116,plain,
% 1.54/1.31 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2191)) | (~c2_1(a2191)) | c3_1(a2191))),
% 1.54/1.31 inference(quant_inst,[status(thm)],[])).
% 1.54/1.31 tff(2117,plain,
% 1.54/1.31 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | hskp11 | hskp10 | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | (~c0_1(a2191))),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 1.54/1.31 tff(2118,plain,
% 1.54/1.31 (hskp11 | (~c2_1(a2191)) | (~c0_1(a2191))),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2117, 111, 185, 186, 260])).
% 1.54/1.31 tff(2119,plain,
% 1.54/1.31 (~c0_1(a2191)),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2118, 284, 2111])).
% 1.54/1.31 tff(2120,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2121,plain,
% 1.54/1.31 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a2191) | c3_1(a2191) | (~c1_1(a2191))) <=> (hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0))),
% 1.54/1.31 inference(rewrite,[status(thm)],[])).
% 1.54/1.31 tff(2122,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2191) | c3_1(a2191) | (~c1_1(a2191)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0)))),
% 1.54/1.31 inference(monotonicity,[status(thm)],[2121])).
% 1.54/1.31 tff(2123,plain,
% 1.54/1.31 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2191) | c3_1(a2191) | (~c1_1(a2191)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0))),
% 1.54/1.31 inference(transitivity,[status(thm)],[2122, 2120])).
% 1.54/1.31 tff(2124,plain,
% 1.54/1.31 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2191) | c3_1(a2191) | (~c1_1(a2191)))),
% 1.54/1.31 inference(quant_inst,[status(thm)],[])).
% 1.54/1.31 tff(2125,plain,
% 1.54/1.31 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0)),
% 1.54/1.31 inference(modus_ponens,[status(thm)],[2124, 2123])).
% 1.54/1.31 tff(2126,plain,
% 1.54/1.31 (hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191))),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2125, 111, 186, 1827])).
% 1.54/1.31 tff(2127,plain,
% 1.54/1.31 (hskp15),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2126, 2119, 1767, 11])).
% 1.54/1.31 tff(2128,plain,
% 1.54/1.31 ($false),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[1569, 2127, 2102, 2100, 2099, 1551, 1550, 2088, 2103, 185])).
% 1.54/1.31 tff(2129,plain,(hskp11 | c2_1(a2195) | c3_1(a2195) | hskp10 | hskp16 | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.31 tff(2130,plain,
% 1.54/1.31 (hskp11),
% 1.54/1.31 inference(unit_resolution,[status(thm)],[2129, 11, 1550, 185, 1551, 186])).
% 1.54/1.32 tff(2131,plain,
% 1.54/1.32 (~c1_1(a2187)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[218, 2130])).
% 1.54/1.32 tff(2132,plain,
% 1.54/1.32 (c2_1(a2187)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[229, 2130])).
% 1.54/1.32 tff(2133,plain,
% 1.54/1.32 (c0_1(a2187)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[240, 2130])).
% 1.54/1.32 tff(2134,plain,
% 1.54/1.32 ($false),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1412, 111, 2133, 2132, 2088, 1551, 1550, 2131, 197, 2096])).
% 1.54/1.32 tff(2135,plain,(hskp16 | c2_1(a2195) | c3_1(a2195) | hskp10 | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.32 tff(2136,plain,
% 1.54/1.32 (hskp16),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2135, 1551, 1550, 185, 186])).
% 1.54/1.32 tff(2137,plain,
% 1.54/1.32 (~c1_1(a2195)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[420, 2136])).
% 1.54/1.32 tff(2138,plain,
% 1.54/1.32 (hskp1),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1959, 1958, 284])).
% 1.54/1.32 tff(2139,plain,
% 1.54/1.32 (~c3_1(a2175)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[597, 2138])).
% 1.54/1.32 tff(2140,plain,
% 1.54/1.32 (~hskp14),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1757, 1958, 698, 709, 1956, 1550, 687, 1551, 1954, 1552])).
% 1.54/1.32 tff(2141,plain,
% 1.54/1.32 (c2_1(a2175)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[614, 2138])).
% 1.54/1.32 tff(2142,plain,
% 1.54/1.32 (~c0_1(a2175)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[603, 2138])).
% 1.54/1.32 tff(2143,plain,
% 1.54/1.32 ($false),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2035, 2142, 2141, 1170, 687, 698, 709, 2140, 2139, 1958, 1955, 1954])).
% 1.54/1.32 tff(2144,plain,(hskp11 | hskp13 | c3_1(a2195) | c2_1(a2195) | c1_1(a2195) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.54/1.32 tff(2145,plain,
% 1.54/1.32 (hskp11),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2144, 1551, 1550, 1768, 2137, 185])).
% 1.54/1.32 tff(2146,plain,
% 1.54/1.32 (~c1_1(a2187)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[218, 2145])).
% 1.54/1.32 tff(2147,plain,
% 1.54/1.32 (c2_1(a2187)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[229, 2145])).
% 1.54/1.32 tff(2148,plain,
% 1.54/1.32 (c0_1(a2187)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[240, 2145])).
% 1.54/1.32 tff(2149,plain,
% 1.54/1.32 (c0_1(a2195)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1412, 111, 2148, 2147, 2137, 1551, 1550, 2146, 197])).
% 1.54/1.32 tff(2150,plain,
% 1.54/1.32 (~c3_1(a2187)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1523, 111, 2148, 2147, 2137, 1551, 1550, 2146, 184])).
% 1.54/1.32 tff(2151,plain,
% 1.54/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2195) | c2_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2195) | c2_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2195)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2152,plain,
% 1.54/1.32 (((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174))) <=> (c1_1(a2195) | c2_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2195)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2153,plain,
% 1.54/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2195) | c2_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2195))))),
% 1.54/1.32 inference(monotonicity,[status(thm)],[2152])).
% 1.54/1.32 tff(2154,plain,
% 1.54/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2195) | c2_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2195)))),
% 1.54/1.32 inference(transitivity,[status(thm)],[2153, 2151])).
% 1.54/1.32 tff(2155,plain,
% 1.54/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))),
% 1.54/1.32 inference(quant_inst,[status(thm)],[])).
% 1.54/1.32 tff(2156,plain,
% 1.54/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2195) | c2_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2195))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2155, 2154])).
% 1.54/1.32 tff(2157,plain,
% 1.54/1.32 ((~c3_1(a2174)) | (~c0_1(a2195))),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2156, 111, 2148, 2147, 698, 2137, 1551, 687, 1382, 2150])).
% 1.54/1.32 tff(2158,plain,
% 1.54/1.32 (~c3_1(a2174)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2157, 2149])).
% 1.54/1.32 tff(2159,plain,
% 1.54/1.32 (hskp18),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1312, 111, 2148, 709, 698, 2146, 687, 1233, 2150])).
% 1.54/1.32 tff(2160,plain,
% 1.54/1.32 (~c1_1(a2198)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[67, 2159])).
% 1.54/1.32 tff(2161,plain,
% 1.54/1.32 (c0_1(a2198)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[78, 2159])).
% 1.54/1.32 tff(2162,plain,
% 1.54/1.32 (~c2_1(a2198)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[61, 2159])).
% 1.54/1.32 tff(2163,plain,
% 1.54/1.32 (c3_1(a2188)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1514, 2162, 2099, 2161, 185, 2160, 2100])).
% 1.54/1.32 tff(2164,plain,
% 1.54/1.32 (~hskp17),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1561, 2163, 2100, 2099, 1551, 1550, 2137, 2098, 709, 698, 687])).
% 1.54/1.32 tff(2165,plain,
% 1.54/1.32 (~hskp15),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1569, 2163, 2100, 2099, 1551, 1550, 2137, 2164, 185])).
% 1.54/1.32 tff(2166,plain,
% 1.54/1.32 (hskp3),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1587, 2165])).
% 1.54/1.32 tff(2167,plain,
% 1.54/1.32 (~c3_1(a2177)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1704, 2166])).
% 1.54/1.32 tff(2168,plain,
% 1.54/1.32 (~c1_1(a2177)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1596, 2166])).
% 1.54/1.32 tff(2169,plain,
% 1.54/1.32 (~c0_1(a2177)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1602, 2166])).
% 1.54/1.32 tff(2170,plain,
% 1.54/1.32 (~hskp14),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1757, 2163, 698, 709, 2099, 1550, 687, 1551, 2100, 2137])).
% 1.54/1.32 tff(2171,plain,
% 1.54/1.32 (hskp24),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1996, 2170, 1768])).
% 1.54/1.32 tff(2172,plain,
% 1.54/1.32 (~c0_1(a2262)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2002, 2171])).
% 1.54/1.32 tff(2173,plain,
% 1.54/1.32 (c3_1(a2262)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2013, 2171])).
% 1.54/1.32 tff(2174,plain,
% 1.54/1.32 (c1_1(a2262)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2024, 2171])).
% 1.54/1.32 tff(2175,plain,
% 1.54/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2262)) | (~c1_1(a2262)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2176,plain,
% 1.54/1.32 (((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177)) <=> (c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2177,plain,
% 1.54/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2262)) | (~c1_1(a2262))))),
% 1.54/1.32 inference(monotonicity,[status(thm)],[2176])).
% 1.54/1.32 tff(2178,plain,
% 1.54/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.54/1.32 inference(transitivity,[status(thm)],[2177, 2175])).
% 1.54/1.32 tff(2179,plain,
% 1.54/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))),
% 1.54/1.32 inference(quant_inst,[status(thm)],[])).
% 1.54/1.32 tff(2180,plain,
% 1.54/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2262)) | (~c1_1(a2262))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2179, 2178])).
% 1.54/1.32 tff(2181,plain,
% 1.54/1.32 ($false),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2180, 111, 2174, 2173, 698, 2172, 2169, 2168, 2167, 687, 758, 2158])).
% 1.54/1.32 tff(2182,plain,(c2_1(a2195) | c3_1(a2195) | hskp10 | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.32 tff(2183,plain,
% 1.54/1.32 ($false),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2182, 2070, 2069, 185, 186])).
% 1.54/1.32 tff(2184,plain,(c3_1(a2191) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.54/1.32 tff(2185,plain,
% 1.54/1.32 (c3_1(a2191)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2184, 185])).
% 1.54/1.32 tff(2186,plain,
% 1.54/1.32 (~hskp13),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[353, 2185])).
% 1.54/1.32 tff(2187,plain,
% 1.54/1.32 (hskp16),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2067, 2186, 185])).
% 1.54/1.32 tff(2188,plain,
% 1.54/1.32 (~c1_1(a2195)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[420, 2187])).
% 1.54/1.32 tff(2189,plain,
% 1.54/1.32 (~c3_1(a2195)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[408, 2187])).
% 1.54/1.32 tff(2190,plain,
% 1.54/1.32 (~c2_1(a2195)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[414, 2187])).
% 1.54/1.32 tff(2191,plain,
% 1.54/1.32 (hskp11),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2144, 2190, 2189, 2186, 2188, 185])).
% 1.54/1.32 tff(2192,plain,
% 1.54/1.32 (~c1_1(a2187)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[218, 2191])).
% 1.54/1.32 tff(2193,plain,
% 1.54/1.32 (c2_1(a2187)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[229, 2191])).
% 1.54/1.32 tff(2194,plain,
% 1.54/1.32 (c0_1(a2187)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[240, 2191])).
% 1.54/1.32 tff(2195,plain,
% 1.54/1.32 (~c3_1(a2187)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1523, 111, 2194, 2193, 2188, 2190, 2189, 2192, 184])).
% 1.54/1.32 tff(2196,plain,
% 1.54/1.32 (c0_1(a2195)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1412, 111, 2194, 2193, 2188, 2190, 2189, 2192, 197])).
% 1.54/1.32 tff(2197,plain,
% 1.54/1.32 (~c3_1(a2174)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2156, 111, 2194, 2193, 698, 2188, 2190, 687, 1382, 2196, 2195])).
% 1.54/1.32 tff(2198,plain,
% 1.54/1.32 (hskp28),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1952, 2186, 185])).
% 1.54/1.32 tff(2199,plain,
% 1.54/1.32 (c1_1(a2188)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[480, 2198])).
% 1.54/1.32 tff(2200,plain,
% 1.54/1.32 (c0_1(a2188)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[282, 2198])).
% 1.54/1.32 tff(2201,plain,
% 1.54/1.32 (c2_1(a2188)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[271, 2198])).
% 1.54/1.32 tff(2202,plain,
% 1.54/1.32 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2195)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2195)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2203,plain,
% 1.54/1.32 ((hskp18 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp18 | c1_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2195)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2204,plain,
% 1.54/1.32 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2195))))),
% 1.54/1.32 inference(monotonicity,[status(thm)],[2203])).
% 1.54/1.32 tff(2205,plain,
% 1.54/1.32 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2195)))),
% 1.54/1.32 inference(transitivity,[status(thm)],[2204, 2202])).
% 1.54/1.32 tff(2206,plain,
% 1.54/1.32 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.54/1.32 inference(quant_inst,[status(thm)],[])).
% 1.54/1.32 tff(2207,plain,
% 1.54/1.32 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2195))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2206, 2205])).
% 1.54/1.32 tff(2208,plain,
% 1.54/1.32 (hskp18),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2207, 111, 709, 698, 2188, 2189, 687, 1233, 2196])).
% 1.54/1.32 tff(2209,plain,
% 1.54/1.32 (~c1_1(a2198)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[67, 2208])).
% 1.54/1.32 tff(2210,plain,
% 1.54/1.32 (c0_1(a2198)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[78, 2208])).
% 1.54/1.32 tff(2211,plain,
% 1.54/1.32 (~c2_1(a2198)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[61, 2208])).
% 1.54/1.32 tff(2212,plain,
% 1.54/1.32 (c3_1(a2188)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1514, 2211, 2200, 2210, 185, 2209, 2201])).
% 1.54/1.32 tff(2213,plain,
% 1.54/1.32 (~hskp17),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1561, 2212, 2201, 2200, 2190, 2189, 2188, 2199, 709, 698, 687])).
% 1.54/1.32 tff(2214,plain,
% 1.54/1.32 (~hskp15),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1569, 2212, 2201, 2200, 2190, 2189, 2188, 2213, 185])).
% 1.54/1.32 tff(2215,plain,
% 1.54/1.32 (hskp3),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1587, 2214])).
% 1.54/1.32 tff(2216,plain,
% 1.54/1.32 (~c3_1(a2177)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1704, 2215])).
% 1.54/1.32 tff(2217,plain,
% 1.54/1.32 (~c1_1(a2177)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1596, 2215])).
% 1.54/1.32 tff(2218,plain,
% 1.54/1.32 (~c0_1(a2177)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1602, 2215])).
% 1.54/1.32 tff(2219,plain,
% 1.54/1.32 (~hskp14),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1757, 2212, 698, 709, 2200, 2189, 687, 2190, 2201, 2188])).
% 1.54/1.32 tff(2220,plain,
% 1.54/1.32 (hskp24),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1996, 2219, 2186])).
% 1.54/1.32 tff(2221,plain,
% 1.54/1.32 (~c0_1(a2262)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2002, 2220])).
% 1.54/1.32 tff(2222,plain,
% 1.54/1.32 (c3_1(a2262)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2013, 2220])).
% 1.54/1.32 tff(2223,plain,
% 1.54/1.32 (c1_1(a2262)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2024, 2220])).
% 1.54/1.32 tff(2224,plain,
% 1.54/1.32 ($false),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2180, 111, 2223, 2222, 698, 2221, 2218, 2217, 2216, 687, 758, 2197])).
% 1.54/1.32 tff(2225,plain,(hskp10), inference(lemma,lemma(discharge,[]))).
% 1.54/1.32 tff(2226,plain,
% 1.54/1.32 (((~hskp10) | (~c1_1(a2186))) <=> ((~hskp10) | (~c1_1(a2186)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2227,plain,
% 1.54/1.32 (((~c1_1(a2186)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a2186)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2228,axiom,((~c1_1(a2186)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.54/1.32 tff(2229,plain,
% 1.54/1.32 ((~hskp10) | (~c1_1(a2186))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2228, 2227])).
% 1.54/1.32 tff(2230,plain,
% 1.54/1.32 ((~hskp10) | (~c1_1(a2186))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2229, 2226])).
% 1.54/1.32 tff(2231,plain,
% 1.54/1.32 (~c1_1(a2186)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2230, 2225])).
% 1.54/1.32 tff(2232,plain,
% 1.54/1.32 (((~hskp10) | (~c0_1(a2186))) <=> ((~hskp10) | (~c0_1(a2186)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2233,plain,
% 1.54/1.32 (((~c0_1(a2186)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a2186)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2234,axiom,((~c0_1(a2186)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.54/1.32 tff(2235,plain,
% 1.54/1.32 ((~hskp10) | (~c0_1(a2186))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2234, 2233])).
% 1.54/1.32 tff(2236,plain,
% 1.54/1.32 ((~hskp10) | (~c0_1(a2186))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2235, 2232])).
% 1.54/1.32 tff(2237,plain,
% 1.54/1.32 (~c0_1(a2186)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2236, 2225])).
% 1.54/1.32 tff(2238,assumption,(~c1_1(a2174)), introduced(assumption)).
% 1.54/1.32 tff(2239,plain,
% 1.54/1.32 (~hskp0),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[708, 2238])).
% 1.54/1.32 tff(2240,plain,
% 1.54/1.32 (~c0_1(a2193)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2044, 111, 11, 1170, 1748, 1747, 1169])).
% 1.54/1.32 tff(2241,plain,
% 1.54/1.32 (((~hskp14) | (~c2_1(a2193))) <=> ((~hskp14) | (~c2_1(a2193)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2242,plain,
% 1.54/1.32 (((~c2_1(a2193)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a2193)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2243,axiom,((~c2_1(a2193)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.54/1.32 tff(2244,plain,
% 1.54/1.32 ((~hskp14) | (~c2_1(a2193))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2243, 2242])).
% 1.54/1.32 tff(2245,plain,
% 1.54/1.32 ((~hskp14) | (~c2_1(a2193))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2244, 2241])).
% 1.54/1.32 tff(2246,plain,
% 1.54/1.32 (~c2_1(a2193)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2245, 1746])).
% 1.54/1.32 tff(2247,plain,
% 1.54/1.32 ((hskp17 | hskp16 | hskp3) <=> (hskp17 | hskp16 | hskp3)),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2248,plain,
% 1.54/1.32 (((hskp17 | hskp3) | hskp16) <=> (hskp17 | hskp16 | hskp3)),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2249,axiom,((hskp17 | hskp3) | hskp16), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 1.54/1.32 tff(2250,plain,
% 1.54/1.32 (hskp17 | hskp16 | hskp3),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2249, 2248])).
% 1.54/1.32 tff(2251,plain,
% 1.54/1.32 (hskp17 | hskp16 | hskp3),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2250, 2247])).
% 1.54/1.32 tff(2252,plain,
% 1.54/1.32 (hskp17 | hskp16 | hskp3),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2251, 2247])).
% 1.54/1.32 tff(2253,plain,
% 1.54/1.32 (hskp17 | hskp16 | hskp3),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2252, 2247])).
% 1.54/1.32 tff(2254,plain,
% 1.54/1.32 (hskp17 | hskp16 | hskp3),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2253, 2247])).
% 1.54/1.32 tff(2255,plain,
% 1.54/1.32 (hskp17 | hskp16 | hskp3),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2254, 2247])).
% 1.54/1.32 tff(2256,plain,
% 1.54/1.32 (hskp17 | hskp16 | hskp3),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2255, 2247])).
% 1.54/1.32 tff(2257,plain,
% 1.54/1.32 (hskp17 | hskp16 | hskp3),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2256, 2247])).
% 1.54/1.32 tff(2258,plain,
% 1.54/1.32 (hskp3),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2257, 850, 11])).
% 1.54/1.32 tff(2259,plain,
% 1.54/1.32 (~c0_1(a2177)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[1602, 2258])).
% 1.54/1.32 tff(2260,assumption,(hskp26), introduced(assumption)).
% 1.54/1.32 tff(2261,plain,
% 1.54/1.32 (((~hskp26) | (~c2_1(a2268))) <=> ((~hskp26) | (~c2_1(a2268)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2262,plain,
% 1.54/1.32 (((~c2_1(a2268)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a2268)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2263,axiom,((~c2_1(a2268)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 1.54/1.32 tff(2264,plain,
% 1.54/1.32 ((~hskp26) | (~c2_1(a2268))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2263, 2262])).
% 1.54/1.32 tff(2265,plain,
% 1.54/1.32 ((~hskp26) | (~c2_1(a2268))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2264, 2261])).
% 1.54/1.32 tff(2266,plain,
% 1.54/1.32 (~c2_1(a2268)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2265, 2260])).
% 1.54/1.32 tff(2267,plain,
% 1.54/1.32 (((~hskp10) | c3_1(a2186)) <=> ((~hskp10) | c3_1(a2186))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2268,axiom,((~hskp10) | c3_1(a2186)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.54/1.32 tff(2269,plain,
% 1.54/1.32 ((~hskp10) | c3_1(a2186)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2268, 2267])).
% 1.54/1.32 tff(2270,plain,
% 1.54/1.32 ((~hskp10) | c3_1(a2186)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2269, 2267])).
% 1.54/1.32 tff(2271,plain,
% 1.54/1.32 ((~hskp10) | c3_1(a2186)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2270, 2267])).
% 1.54/1.32 tff(2272,plain,
% 1.54/1.32 ((~hskp10) | c3_1(a2186)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2271, 2267])).
% 1.54/1.32 tff(2273,plain,
% 1.54/1.32 ((~hskp10) | c3_1(a2186)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2272, 2267])).
% 1.54/1.32 tff(2274,plain,
% 1.54/1.32 ((~hskp10) | c3_1(a2186)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2273, 2267])).
% 1.54/1.32 tff(2275,plain,
% 1.54/1.32 ((~hskp10) | c3_1(a2186)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2274, 2267])).
% 1.54/1.32 tff(2276,plain,
% 1.54/1.32 ((~hskp10) | c3_1(a2186)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2275, 2267])).
% 1.54/1.32 tff(2277,plain,
% 1.54/1.32 (c3_1(a2186)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2276, 2225])).
% 1.54/1.32 tff(2278,plain,
% 1.54/1.32 (((~hskp26) | c1_1(a2268)) <=> ((~hskp26) | c1_1(a2268))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2279,axiom,((~hskp26) | c1_1(a2268)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 1.54/1.32 tff(2280,plain,
% 1.54/1.32 ((~hskp26) | c1_1(a2268)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2279, 2278])).
% 1.54/1.32 tff(2281,plain,
% 1.54/1.32 ((~hskp26) | c1_1(a2268)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2280, 2278])).
% 1.54/1.32 tff(2282,plain,
% 1.54/1.32 ((~hskp26) | c1_1(a2268)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2281, 2278])).
% 1.54/1.32 tff(2283,plain,
% 1.54/1.32 ((~hskp26) | c1_1(a2268)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2282, 2278])).
% 1.54/1.32 tff(2284,plain,
% 1.54/1.32 ((~hskp26) | c1_1(a2268)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2283, 2278])).
% 1.54/1.32 tff(2285,plain,
% 1.54/1.32 ((~hskp26) | c1_1(a2268)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2284, 2278])).
% 1.54/1.32 tff(2286,plain,
% 1.54/1.32 ((~hskp26) | c1_1(a2268)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2285, 2278])).
% 1.54/1.32 tff(2287,plain,
% 1.54/1.32 ((~hskp26) | c1_1(a2268)),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2286, 2278])).
% 1.54/1.32 tff(2288,plain,
% 1.54/1.32 (c1_1(a2268)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2287, 2260])).
% 1.54/1.32 tff(2289,plain,
% 1.54/1.32 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2268)) | (~c1_1(a2268)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2268)) | (~c1_1(a2268)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2290,plain,
% 1.54/1.32 ((hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (hskp0 | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2268)) | (~c1_1(a2268)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2291,plain,
% 1.54/1.32 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2268)) | (~c1_1(a2268))))),
% 1.54/1.32 inference(monotonicity,[status(thm)],[2290])).
% 1.54/1.32 tff(2292,plain,
% 1.54/1.32 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2268)) | (~c1_1(a2268)))),
% 1.54/1.32 inference(transitivity,[status(thm)],[2291, 2289])).
% 1.54/1.32 tff(2293,plain,
% 1.54/1.32 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.54/1.32 inference(quant_inst,[status(thm)],[])).
% 1.54/1.32 tff(2294,plain,
% 1.54/1.32 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2268)) | (~c1_1(a2268))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 1.54/1.32 tff(2295,plain,
% 1.54/1.32 (~c3_1(a2268)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2294, 111, 312, 2288, 2277, 2266, 2237, 2231, 174])).
% 1.54/1.32 tff(2296,plain,
% 1.54/1.32 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.54/1.32 inference(bind,[status(th)],[])).
% 1.54/1.32 tff(2297,plain,
% 1.54/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.54/1.32 inference(quant_intro,[status(thm)],[2296])).
% 1.54/1.32 tff(2298,plain,
% 1.54/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2299,plain,
% 1.54/1.32 (^[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))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.54/1.32 inference(bind,[status(th)],[])).
% 1.54/1.32 tff(2300,plain,
% 1.54/1.32 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.54/1.32 inference(quant_intro,[status(thm)],[2299])).
% 1.54/1.32 tff(2301,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 1.54/1.32 tff(2302,plain,
% 1.54/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2301, 2300])).
% 1.54/1.32 tff(2303,plain,
% 1.54/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2302, 2298])).
% 1.54/1.32 tff(2304,plain,(
% 1.54/1.32 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.54/1.32 inference(skolemize,[status(sab)],[2303])).
% 1.54/1.32 tff(2305,plain,
% 1.54/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2304, 2297])).
% 1.54/1.32 tff(2306,plain,
% 1.54/1.32 (((~hskp26) | (~c0_1(a2268))) <=> ((~hskp26) | (~c0_1(a2268)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2307,plain,
% 1.54/1.32 (((~c0_1(a2268)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a2268)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2308,axiom,((~c0_1(a2268)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.54/1.32 tff(2309,plain,
% 1.54/1.32 ((~hskp26) | (~c0_1(a2268))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2308, 2307])).
% 1.54/1.32 tff(2310,plain,
% 1.54/1.32 ((~hskp26) | (~c0_1(a2268))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2309, 2306])).
% 1.54/1.32 tff(2311,plain,
% 1.54/1.32 (~c0_1(a2268)),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2310, 2260])).
% 1.54/1.32 tff(2312,plain,
% 1.54/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a2268) | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a2268) | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2313,plain,
% 1.54/1.32 (((~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)) | c3_1(a2268) | c0_1(a2268) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (c0_1(a2268) | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.54/1.32 inference(rewrite,[status(thm)],[])).
% 1.54/1.32 tff(2314,plain,
% 1.54/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)) | c3_1(a2268) | c0_1(a2268) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a2268) | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | c3_1(a2268) | (~c1_1(a2268))))),
% 1.54/1.32 inference(monotonicity,[status(thm)],[2313])).
% 1.54/1.32 tff(2315,plain,
% 1.54/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)) | c3_1(a2268) | c0_1(a2268) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a2268) | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.54/1.32 inference(transitivity,[status(thm)],[2314, 2312])).
% 1.54/1.32 tff(2316,plain,
% 1.54/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)) | c3_1(a2268) | c0_1(a2268) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.54/1.32 inference(quant_inst,[status(thm)],[])).
% 1.54/1.32 tff(2317,plain,
% 1.54/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a2268) | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | c3_1(a2268) | (~c1_1(a2268))),
% 1.54/1.32 inference(modus_ponens,[status(thm)],[2316, 2315])).
% 1.54/1.32 tff(2318,plain,
% 1.54/1.32 ($false),
% 1.54/1.32 inference(unit_resolution,[status(thm)],[2317, 111, 2288, 2277, 2311, 2266, 2237, 2231, 2305, 2295])).
% 1.54/1.32 tff(2319,plain,((~hskp26) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.54/1.33 tff(2320,plain,
% 1.54/1.33 (~hskp26),
% 1.54/1.33 inference(unit_resolution,[status(thm)],[2319, 312])).
% 1.54/1.33 tff(2321,plain,
% 1.54/1.33 (hskp24),
% 1.54/1.33 inference(unit_resolution,[status(thm)],[109, 850, 2320])).
% 1.54/1.33 tff(2322,plain,
% 1.54/1.33 (~c1_1(a2177)),
% 1.54/1.33 inference(unit_resolution,[status(thm)],[1596, 2258])).
% 1.54/1.33 tff(2323,plain,
% 1.54/1.33 (~c3_1(a2177)),
% 1.54/1.33 inference(unit_resolution,[status(thm)],[1704, 2258])).
% 1.54/1.33 tff(2324,assumption,(~c3_1(a2177)), introduced(assumption)).
% 1.54/1.33 tff(2325,assumption,(~c1_1(a2177)), introduced(assumption)).
% 1.54/1.33 tff(2326,assumption,(~c0_1(a2177)), introduced(assumption)).
% 1.54/1.33 tff(2327,assumption,(hskp24), introduced(assumption)).
% 1.54/1.33 tff(2328,plain,
% 1.54/1.33 (~c0_1(a2262)),
% 1.54/1.33 inference(unit_resolution,[status(thm)],[2002, 2327])).
% 1.54/1.33 tff(2329,plain,
% 1.54/1.33 (c3_1(a2262)),
% 1.54/1.33 inference(unit_resolution,[status(thm)],[2013, 2327])).
% 1.54/1.33 tff(2330,plain,
% 1.54/1.33 (c1_1(a2262)),
% 1.54/1.33 inference(unit_resolution,[status(thm)],[2024, 2327])).
% 1.54/1.33 tff(2331,plain,
% 1.54/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2177)) | (~c3_1(a2262)) | (~c1_1(a2262)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2177)) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.54/1.33 inference(rewrite,[status(thm)],[])).
% 1.54/1.33 tff(2332,plain,
% 1.54/1.33 (((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177)) <=> (c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2177)) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.54/1.33 inference(rewrite,[status(thm)],[])).
% 1.54/1.33 tff(2333,plain,
% 1.54/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2177)) | (~c3_1(a2262)) | (~c1_1(a2262))))),
% 1.54/1.33 inference(monotonicity,[status(thm)],[2332])).
% 1.54/1.33 tff(2334,plain,
% 1.54/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2177)) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.54/1.33 inference(transitivity,[status(thm)],[2333, 2331])).
% 1.54/1.33 tff(2335,plain,
% 1.54/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))),
% 1.54/1.33 inference(quant_inst,[status(thm)],[])).
% 1.54/1.33 tff(2336,plain,
% 1.54/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2177)) | (~c3_1(a2262)) | (~c1_1(a2262))),
% 1.54/1.33 inference(modus_ponens,[status(thm)],[2335, 2334])).
% 1.54/1.33 tff(2337,plain,
% 1.54/1.33 (~c2_1(a2177)),
% 1.54/1.33 inference(unit_resolution,[status(thm)],[2336, 111, 2330, 2329, 2328, 2326, 2325, 2324, 758])).
% 1.54/1.33 tff(2338,plain,
% 1.54/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a2262) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | c2_1(a2177) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2262) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | c2_1(a2177) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.54/1.33 inference(rewrite,[status(thm)],[])).
% 1.54/1.33 tff(2339,plain,
% 1.54/1.33 (((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177)) <=> (c0_1(a2262) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | c2_1(a2177) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.54/1.33 inference(rewrite,[status(thm)],[])).
% 1.54/1.33 tff(2340,plain,
% 1.54/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a2262) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | c2_1(a2177) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262))))),
% 1.54/1.33 inference(monotonicity,[status(thm)],[2339])).
% 1.54/1.33 tff(2341,plain,
% 1.54/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2262) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | c2_1(a2177) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.54/1.33 inference(transitivity,[status(thm)],[2340, 2338])).
% 1.54/1.33 tff(2342,plain,
% 1.54/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177))),
% 1.54/1.33 inference(quant_inst,[status(thm)],[])).
% 1.54/1.33 tff(2343,plain,
% 1.54/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2262) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | c2_1(a2177) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262))),
% 1.54/1.33 inference(modus_ponens,[status(thm)],[2342, 2341])).
% 1.54/1.33 tff(2344,plain,
% 1.54/1.33 (c2_1(a2177) | (~c2_1(a2262))),
% 1.54/1.33 inference(unit_resolution,[status(thm)],[2343, 111, 2330, 2277, 2328, 2237, 2231, 2325, 2324, 157])).
% 1.54/1.33 tff(2345,plain,
% 1.54/1.33 (~c2_1(a2262)),
% 1.54/1.33 inference(unit_resolution,[status(thm)],[2344, 2337])).
% 1.54/1.33 tff(2346,plain,
% 1.54/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))),
% 1.54/1.33 inference(rewrite,[status(thm)],[])).
% 1.54/1.33 tff(2347,plain,
% 1.54/1.33 ((hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (hskp0 | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))),
% 1.54/1.33 inference(rewrite,[status(thm)],[])).
% 1.54/1.33 tff(2348,plain,
% 1.54/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262))))),
% 1.64/1.33 inference(monotonicity,[status(thm)],[2347])).
% 1.64/1.33 tff(2349,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))),
% 1.64/1.33 inference(transitivity,[status(thm)],[2348, 2346])).
% 1.64/1.33 tff(2350,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.64/1.33 inference(quant_inst,[status(thm)],[])).
% 1.64/1.33 tff(2351,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262))),
% 1.64/1.33 inference(modus_ponens,[status(thm)],[2350, 2349])).
% 1.64/1.33 tff(2352,plain,
% 1.64/1.33 ($false),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[2351, 111, 312, 2330, 2329, 2277, 2237, 2231, 174, 2345])).
% 1.64/1.33 tff(2353,plain,((~hskp24) | hskp0 | c1_1(a2177) | c3_1(a2177) | c0_1(a2177)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.33 tff(2354,plain,
% 1.64/1.33 ($false),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[2353, 2323, 2322, 312, 2321, 2259])).
% 1.64/1.33 tff(2355,plain,(hskp17 | hskp0 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.64/1.33 tff(2356,plain,
% 1.64/1.33 (hskp17),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[2355, 312, 11])).
% 1.64/1.33 tff(2357,plain,
% 1.64/1.33 (~c1_1(a2197)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[163, 2356])).
% 1.64/1.33 tff(2358,plain,
% 1.64/1.33 (c3_1(a2197)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[653, 2356])).
% 1.64/1.33 tff(2359,plain,
% 1.64/1.33 (c2_1(a2197)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[664, 2356])).
% 1.64/1.33 tff(2360,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2197) | c1_1(a2193) | c2_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c1_1(a2193) | c2_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(2361,plain,
% 1.64/1.33 ((hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2193) | c1_1(a2193) | c0_1(a2193)) <=> (hskp0 | c1_1(a2197) | c1_1(a2193) | c2_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(2362,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2193) | c1_1(a2193) | c0_1(a2193))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2197) | c1_1(a2193) | c2_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.64/1.33 inference(monotonicity,[status(thm)],[2361])).
% 1.64/1.33 tff(2363,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2193) | c1_1(a2193) | c0_1(a2193))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c1_1(a2193) | c2_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.33 inference(transitivity,[status(thm)],[2362, 2360])).
% 1.64/1.33 tff(2364,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2193) | c1_1(a2193) | c0_1(a2193))),
% 1.64/1.33 inference(quant_inst,[status(thm)],[])).
% 1.64/1.33 tff(2365,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c1_1(a2193) | c2_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.64/1.33 inference(modus_ponens,[status(thm)],[2364, 2363])).
% 1.64/1.33 tff(2366,plain,
% 1.64/1.33 ($false),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[2365, 111, 312, 2359, 2358, 2357, 1747, 2246, 10, 2240])).
% 1.64/1.33 tff(2367,plain,((~hskp14) | hskp0 | hskp16 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.64/1.33 tff(2368,plain,
% 1.64/1.33 (~hskp14),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[2367, 1170, 11, 2239])).
% 1.64/1.33 tff(2369,plain,
% 1.64/1.33 (hskp24),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1996, 2368, 1170])).
% 1.64/1.33 tff(2370,plain,
% 1.64/1.33 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c3_1(a2262)) | (~c2_1(a2262)) | (~c1_1(a2262)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp16 | (~ndr1_0) | (~c3_1(a2262)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(2371,plain,
% 1.64/1.33 ((hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2262)) | (~c3_1(a2262)) | (~c1_1(a2262))) <=> (hskp27 | hskp16 | (~ndr1_0) | (~c3_1(a2262)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(2372,plain,
% 1.64/1.33 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2262)) | (~c3_1(a2262)) | (~c1_1(a2262)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c3_1(a2262)) | (~c2_1(a2262)) | (~c1_1(a2262))))),
% 1.64/1.33 inference(monotonicity,[status(thm)],[2371])).
% 1.64/1.33 tff(2373,plain,
% 1.64/1.33 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2262)) | (~c3_1(a2262)) | (~c1_1(a2262)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp16 | (~ndr1_0) | (~c3_1(a2262)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.64/1.33 inference(transitivity,[status(thm)],[2372, 2370])).
% 1.64/1.33 tff(2374,plain,
% 1.64/1.33 ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2262)) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.64/1.33 inference(quant_inst,[status(thm)],[])).
% 1.64/1.33 tff(2375,plain,
% 1.64/1.33 ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp16 | (~ndr1_0) | (~c3_1(a2262)) | (~c2_1(a2262)) | (~c1_1(a2262))),
% 1.64/1.33 inference(modus_ponens,[status(thm)],[2374, 2373])).
% 1.64/1.33 tff(2376,plain,
% 1.64/1.33 (~c2_1(a2262)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[2375, 111, 1254, 11, 2330, 2329, 1809])).
% 1.64/1.33 tff(2377,plain,
% 1.64/1.33 ($false),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[2351, 111, 312, 2330, 2329, 2277, 2237, 2231, 174, 2376])).
% 1.64/1.33 tff(2378,plain,((~hskp24) | hskp0 | hskp27 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.64/1.33 tff(2379,plain,
% 1.64/1.33 (hskp27),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[2378, 2369, 11, 2239])).
% 1.64/1.33 tff(2380,plain,
% 1.64/1.33 (c3_1(a2178)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[923, 2379])).
% 1.64/1.33 tff(2381,plain,
% 1.64/1.33 (c0_1(a2178)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[945, 2379])).
% 1.64/1.33 tff(2382,plain,
% 1.64/1.33 (c1_1(a2178)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[1176, 111, 11, 1170, 2381, 2380, 1169])).
% 1.64/1.33 tff(2383,plain,
% 1.64/1.33 (~c0_1(a2262)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[2002, 2369])).
% 1.64/1.33 tff(2384,assumption,(~c2_1(a2174)), introduced(assumption)).
% 1.64/1.33 tff(2385,plain,
% 1.64/1.33 (~hskp0),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[697, 2384])).
% 1.64/1.33 tff(2386,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2186)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(2387,plain,
% 1.64/1.33 ((hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (hskp0 | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2186)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(2388,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2186))))),
% 1.64/1.33 inference(monotonicity,[status(thm)],[2387])).
% 1.64/1.33 tff(2389,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2186)))),
% 1.64/1.33 inference(transitivity,[status(thm)],[2388, 2386])).
% 1.64/1.33 tff(2390,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.64/1.33 inference(quant_inst,[status(thm)],[])).
% 1.64/1.33 tff(2391,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2186))),
% 1.64/1.33 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 1.64/1.33 tff(2392,plain,
% 1.64/1.33 ((~c1_1(a2174)) | (~c3_1(a2174))),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[2391, 111, 2385, 2277, 2384, 2237, 2231, 174])).
% 1.64/1.33 tff(2393,plain,
% 1.64/1.33 (~c3_1(a2174)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[2392, 1132])).
% 1.64/1.33 tff(2394,plain,
% 1.64/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(2395,plain,
% 1.64/1.33 (((~ndr1_0) | c2_1(a2174) | c3_1(a2174) | (~c1_1(a2174)) | c3_1(a2174) | c0_1(a2174) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(2396,plain,
% 1.64/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2174) | c3_1(a2174) | (~c1_1(a2174)) | c3_1(a2174) | c0_1(a2174) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c3_1(a2186))))),
% 1.64/1.33 inference(monotonicity,[status(thm)],[2395])).
% 1.64/1.33 tff(2397,plain,
% 1.64/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2174) | c3_1(a2174) | (~c1_1(a2174)) | c3_1(a2174) | c0_1(a2174) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))),
% 1.64/1.33 inference(transitivity,[status(thm)],[2396, 2394])).
% 1.64/1.33 tff(2398,plain,
% 1.64/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2174) | c3_1(a2174) | (~c1_1(a2174)) | c3_1(a2174) | c0_1(a2174) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.64/1.33 inference(quant_inst,[status(thm)],[])).
% 1.64/1.33 tff(2399,plain,
% 1.64/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c3_1(a2186))),
% 1.64/1.33 inference(modus_ponens,[status(thm)],[2398, 2397])).
% 1.64/1.33 tff(2400,plain,
% 1.64/1.33 ($false),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[2399, 111, 2277, 1132, 2384, 2237, 2231, 147, 2305, 2393])).
% 1.64/1.33 tff(2401,plain,((~c1_1(a2174)) | c2_1(a2174) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.33 tff(2402,plain,
% 1.64/1.33 (~c1_1(a2174)),
% 1.64/1.33 inference(unit_resolution,[status(thm)],[2401, 2384, 147])).
% 1.64/1.33 tff(2403,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(2404,plain,
% 1.64/1.33 ((hskp0 | (~ndr1_0) | c1_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174)) <=> (hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.64/1.33 inference(rewrite,[status(thm)],[])).
% 1.64/1.33 tff(2405,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186))))),
% 1.64/1.33 inference(monotonicity,[status(thm)],[2404])).
% 1.64/1.33 tff(2406,plain,
% 1.64/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.64/1.33 inference(transitivity,[status(thm)],[2405, 2403])).
% 1.64/1.33 tff(2407,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174))),
% 1.64/1.33 inference(quant_inst,[status(thm)],[])).
% 1.64/1.33 tff(2408,plain,
% 1.64/1.33 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2407, 2406])).
% 1.64/1.34 tff(2409,plain,
% 1.64/1.34 (c1_1(a2174) | (~c2_1(a2186))),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2408, 111, 2385, 2277, 2384, 2231, 147, 10])).
% 1.64/1.34 tff(2410,plain,
% 1.64/1.34 (~c2_1(a2186)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2409, 2238])).
% 1.64/1.34 tff(2411,plain,
% 1.64/1.34 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2412,plain,
% 1.64/1.34 ((hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174)) <=> (hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2413,plain,
% 1.64/1.34 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.64/1.34 inference(monotonicity,[status(thm)],[2412])).
% 1.64/1.34 tff(2414,plain,
% 1.64/1.34 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.34 inference(transitivity,[status(thm)],[2413, 2411])).
% 1.64/1.34 tff(2415,plain,
% 1.64/1.34 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174))),
% 1.64/1.34 inference(quant_inst,[status(thm)],[])).
% 1.64/1.34 tff(2416,plain,
% 1.64/1.34 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2415, 2414])).
% 1.64/1.34 tff(2417,plain,
% 1.64/1.34 ($false),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2416, 111, 2385, 1542, 1553, 2238, 2384, 164, 147, 10])).
% 1.64/1.34 tff(2418,plain,((~hskp17) | c1_1(a2174) | c2_1(a2174) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.34 tff(2419,plain,
% 1.64/1.34 (~hskp17),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2418, 2238, 2384, 147])).
% 1.64/1.34 tff(2420,assumption,(~c2_1(a2186)), introduced(assumption)).
% 1.64/1.34 tff(2421,plain,
% 1.64/1.34 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.64/1.34 inference(bind,[status(th)],[])).
% 1.64/1.34 tff(2422,plain,
% 1.64/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_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)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.64/1.34 inference(quant_intro,[status(thm)],[2421])).
% 1.64/1.34 tff(2423,plain,
% 1.64/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_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)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2424,plain,
% 1.64/1.34 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.64/1.34 inference(bind,[status(th)],[])).
% 1.64/1.34 tff(2425,plain,
% 1.64/1.34 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.64/1.34 inference(quant_intro,[status(thm)],[2424])).
% 1.64/1.34 tff(2426,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 1.64/1.34 tff(2427,plain,
% 1.64/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2426, 2425])).
% 1.64/1.34 tff(2428,plain,
% 1.64/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2427, 2423])).
% 1.64/1.34 tff(2429,plain,(
% 1.64/1.34 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.64/1.34 inference(skolemize,[status(sab)],[2428])).
% 1.64/1.34 tff(2430,plain,
% 1.64/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2429, 2422])).
% 1.64/1.34 tff(2431,plain,
% 1.64/1.34 (hskp3),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2257, 11, 850])).
% 1.64/1.34 tff(2432,plain,
% 1.64/1.34 (~c0_1(a2177)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1602, 2431])).
% 1.64/1.34 tff(2433,plain,
% 1.64/1.34 (~c3_1(a2177)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1704, 2431])).
% 1.64/1.34 tff(2434,plain,
% 1.64/1.34 (~c1_1(a2177)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1596, 2431])).
% 1.64/1.34 tff(2435,plain,
% 1.64/1.34 (~hskp24),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2353, 2434, 312, 2433, 2432])).
% 1.64/1.34 tff(2436,assumption,(~hskp24), introduced(assumption)).
% 1.64/1.34 tff(2437,plain,
% 1.64/1.34 (hskp14),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1996, 2436, 1170])).
% 1.64/1.34 tff(2438,plain,
% 1.64/1.34 (~c1_1(a2193)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1487, 2437])).
% 1.64/1.34 tff(2439,plain,
% 1.64/1.34 (hskp26),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[109, 2436, 850])).
% 1.64/1.34 tff(2440,plain,
% 1.64/1.34 (c3_1(a2193)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[1498, 2437])).
% 1.64/1.34 tff(2441,plain,
% 1.64/1.34 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c2_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2442,plain,
% 1.64/1.34 ((hskp16 | hskp13 | (~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268))) <=> (hskp16 | hskp13 | c2_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2443,plain,
% 1.64/1.34 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c2_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268))))),
% 1.64/1.34 inference(monotonicity,[status(thm)],[2442])).
% 1.64/1.34 tff(2444,plain,
% 1.64/1.34 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.64/1.34 inference(transitivity,[status(thm)],[2443, 2441])).
% 1.64/1.34 tff(2445,plain,
% 1.64/1.34 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.64/1.34 inference(quant_inst,[status(thm)],[])).
% 1.64/1.34 tff(2446,plain,
% 1.64/1.34 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2445, 2444])).
% 1.64/1.34 tff(2447,plain,
% 1.64/1.34 (c3_1(a2268)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2446, 111, 11, 1170, 2288, 2266, 2080])).
% 1.64/1.34 tff(2448,assumption,(~c1_1(a2193)), introduced(assumption)).
% 1.64/1.34 tff(2449,assumption,(c3_1(a2193)), introduced(assumption)).
% 1.64/1.34 tff(2450,plain,
% 1.64/1.34 (~c0_1(a2193)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2044, 111, 11, 1170, 2449, 2448, 1169])).
% 1.64/1.34 tff(2451,plain,
% 1.64/1.34 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2268) | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)) | (~c3_1(a2268)) | (~c1_1(a2268)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2268) | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)) | (~c3_1(a2268)) | (~c1_1(a2268)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2452,plain,
% 1.64/1.34 ((hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193))) <=> (hskp0 | c2_1(a2268) | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)) | (~c3_1(a2268)) | (~c1_1(a2268)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2453,plain,
% 1.64/1.34 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2268) | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)) | (~c3_1(a2268)) | (~c1_1(a2268))))),
% 1.64/1.34 inference(monotonicity,[status(thm)],[2452])).
% 1.64/1.34 tff(2454,plain,
% 1.64/1.34 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2268) | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)) | (~c3_1(a2268)) | (~c1_1(a2268)))),
% 1.64/1.34 inference(transitivity,[status(thm)],[2453, 2451])).
% 1.64/1.34 tff(2455,plain,
% 1.64/1.34 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.64/1.34 inference(quant_inst,[status(thm)],[])).
% 1.64/1.34 tff(2456,plain,
% 1.64/1.34 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2268) | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)) | (~c3_1(a2268)) | (~c1_1(a2268))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2455, 2454])).
% 1.64/1.34 tff(2457,plain,
% 1.64/1.34 ($false),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2456, 111, 312, 2288, 2449, 2266, 2448, 174, 2450, 2447])).
% 1.64/1.34 tff(2458,plain,((~hskp26) | hskp0 | (~c3_1(a2193)) | c1_1(a2193) | hskp16 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.64/1.34 tff(2459,plain,
% 1.64/1.34 ($false),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2458, 2440, 2439, 312, 2438, 11, 1170])).
% 1.64/1.34 tff(2460,plain,(hskp24 | hskp0 | hskp16 | hskp13 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.64/1.34 tff(2461,plain,
% 1.64/1.34 (hskp13),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2460, 2435, 11, 312, 850])).
% 1.64/1.34 tff(2462,plain,
% 1.64/1.34 (~c3_1(a2191)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[353, 2461])).
% 1.64/1.34 tff(2463,plain,
% 1.64/1.34 (~c1_1(a2191)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[359, 2461])).
% 1.64/1.34 tff(2464,plain,
% 1.64/1.34 (c0_1(a2191)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[370, 2461])).
% 1.64/1.34 tff(2465,plain,
% 1.64/1.34 (hskp15),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[377, 111, 312, 2464, 2463, 2462, 333])).
% 1.64/1.34 tff(2466,plain,
% 1.64/1.34 (~c2_1(a2194)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[383, 2465])).
% 1.64/1.34 tff(2467,plain,
% 1.64/1.34 (c3_1(a2194)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[431, 2465])).
% 1.64/1.34 tff(2468,plain,
% 1.64/1.34 (c0_1(a2194)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[394, 2465])).
% 1.64/1.34 tff(2469,plain,
% 1.64/1.34 (hskp26),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[109, 2435, 850])).
% 1.64/1.34 tff(2470,plain,
% 1.64/1.34 (~c2_1(a2268)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2265, 2469])).
% 1.64/1.34 tff(2471,plain,
% 1.64/1.34 (c1_1(a2268)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2287, 2469])).
% 1.64/1.34 tff(2472,plain,
% 1.64/1.34 (~c3_1(a2268)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2294, 111, 312, 2471, 2277, 2470, 2237, 2231, 174])).
% 1.64/1.34 tff(2473,plain,
% 1.64/1.34 (^[U: $i] : refl((hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.64/1.34 inference(bind,[status(th)],[])).
% 1.64/1.34 tff(2474,plain,
% 1.64/1.34 (![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.64/1.34 inference(quant_intro,[status(thm)],[2473])).
% 1.64/1.34 tff(2475,plain,
% 1.64/1.34 (![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2476,plain,
% 1.64/1.34 (^[U: $i] : 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(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp29))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp17) <=> ((hskp29 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp17))), rewrite(((hskp29 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp17) <=> (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp17) <=> (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.64/1.34 inference(bind,[status(th)],[])).
% 1.64/1.34 tff(2477,plain,
% 1.64/1.34 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp17) <=> ![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.64/1.34 inference(quant_intro,[status(thm)],[2476])).
% 1.64/1.34 tff(2478,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.64/1.34 tff(2479,plain,
% 1.64/1.34 (![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2478, 2477])).
% 1.64/1.34 tff(2480,plain,
% 1.64/1.34 (![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2479, 2475])).
% 1.64/1.34 tff(2481,plain,(
% 1.64/1.34 ![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.64/1.34 inference(skolemize,[status(sab)],[2480])).
% 1.64/1.34 tff(2482,plain,
% 1.64/1.34 (![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2481, 2474])).
% 1.64/1.34 tff(2483,plain,
% 1.64/1.34 (~c0_1(a2268)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2310, 2469])).
% 1.64/1.34 tff(2484,plain,
% 1.64/1.34 (((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | c0_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp29 | hskp17 | c0_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2485,plain,
% 1.64/1.34 ((hskp29 | hskp17 | (~ndr1_0) | c0_1(a2268) | c3_1(a2268) | (~c1_1(a2268))) <=> (hskp29 | hskp17 | c0_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2486,plain,
% 1.64/1.34 (((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | (~ndr1_0) | c0_1(a2268) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | c0_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268))))),
% 1.64/1.34 inference(monotonicity,[status(thm)],[2485])).
% 1.64/1.34 tff(2487,plain,
% 1.64/1.34 (((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | (~ndr1_0) | c0_1(a2268) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp29 | hskp17 | c0_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.64/1.34 inference(transitivity,[status(thm)],[2486, 2484])).
% 1.64/1.34 tff(2488,plain,
% 1.64/1.34 ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | (~ndr1_0) | c0_1(a2268) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.64/1.34 inference(quant_inst,[status(thm)],[])).
% 1.64/1.34 tff(2489,plain,
% 1.64/1.34 ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp29 | hskp17 | c0_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2488, 2487])).
% 1.64/1.34 tff(2490,plain,
% 1.64/1.34 (hskp29 | c3_1(a2268)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2489, 111, 850, 2471, 2483, 2482])).
% 1.64/1.34 tff(2491,plain,
% 1.64/1.34 (hskp29),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2490, 2472])).
% 1.64/1.34 tff(2492,plain,
% 1.64/1.34 (((~hskp29) | c3_1(a2196)) <=> ((~hskp29) | c3_1(a2196))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2493,axiom,((~hskp29) | c3_1(a2196)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.64/1.34 tff(2494,plain,
% 1.64/1.34 ((~hskp29) | c3_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2493, 2492])).
% 1.64/1.34 tff(2495,plain,
% 1.64/1.34 ((~hskp29) | c3_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2494, 2492])).
% 1.64/1.34 tff(2496,plain,
% 1.64/1.34 ((~hskp29) | c3_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2495, 2492])).
% 1.64/1.34 tff(2497,plain,
% 1.64/1.34 ((~hskp29) | c3_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2496, 2492])).
% 1.64/1.34 tff(2498,plain,
% 1.64/1.34 ((~hskp29) | c3_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2497, 2492])).
% 1.64/1.34 tff(2499,plain,
% 1.64/1.34 ((~hskp29) | c3_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2498, 2492])).
% 1.64/1.34 tff(2500,plain,
% 1.64/1.34 ((~hskp29) | c3_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2499, 2492])).
% 1.64/1.34 tff(2501,plain,
% 1.64/1.34 ((~hskp29) | c3_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2500, 2492])).
% 1.64/1.34 tff(2502,plain,
% 1.64/1.34 (c3_1(a2196)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2501, 2491])).
% 1.64/1.34 tff(2503,plain,
% 1.64/1.34 (((~hskp29) | c2_1(a2196)) <=> ((~hskp29) | c2_1(a2196))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2504,axiom,((~hskp29) | c2_1(a2196)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.64/1.34 tff(2505,plain,
% 1.64/1.34 ((~hskp29) | c2_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2504, 2503])).
% 1.64/1.34 tff(2506,plain,
% 1.64/1.34 ((~hskp29) | c2_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2505, 2503])).
% 1.64/1.34 tff(2507,plain,
% 1.64/1.34 ((~hskp29) | c2_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2506, 2503])).
% 1.64/1.34 tff(2508,plain,
% 1.64/1.34 ((~hskp29) | c2_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2507, 2503])).
% 1.64/1.34 tff(2509,plain,
% 1.64/1.34 ((~hskp29) | c2_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2508, 2503])).
% 1.64/1.34 tff(2510,plain,
% 1.64/1.34 ((~hskp29) | c2_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2509, 2503])).
% 1.64/1.34 tff(2511,plain,
% 1.64/1.34 ((~hskp29) | c2_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2510, 2503])).
% 1.64/1.34 tff(2512,plain,
% 1.64/1.34 ((~hskp29) | c2_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2511, 2503])).
% 1.64/1.34 tff(2513,plain,
% 1.64/1.34 (c2_1(a2196)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2512, 2491])).
% 1.64/1.34 tff(2514,plain,
% 1.64/1.34 (((~hskp29) | c1_1(a2196)) <=> ((~hskp29) | c1_1(a2196))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2515,axiom,((~hskp29) | c1_1(a2196)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.64/1.34 tff(2516,plain,
% 1.64/1.34 ((~hskp29) | c1_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2515, 2514])).
% 1.64/1.34 tff(2517,plain,
% 1.64/1.34 ((~hskp29) | c1_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2516, 2514])).
% 1.64/1.34 tff(2518,plain,
% 1.64/1.34 ((~hskp29) | c1_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2517, 2514])).
% 1.64/1.34 tff(2519,plain,
% 1.64/1.34 ((~hskp29) | c1_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2518, 2514])).
% 1.64/1.34 tff(2520,plain,
% 1.64/1.34 ((~hskp29) | c1_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2519, 2514])).
% 1.64/1.34 tff(2521,plain,
% 1.64/1.34 ((~hskp29) | c1_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2520, 2514])).
% 1.64/1.34 tff(2522,plain,
% 1.64/1.34 ((~hskp29) | c1_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2521, 2514])).
% 1.64/1.34 tff(2523,plain,
% 1.64/1.34 ((~hskp29) | c1_1(a2196)),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2522, 2514])).
% 1.64/1.34 tff(2524,plain,
% 1.64/1.34 (c1_1(a2196)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2523, 2491])).
% 1.64/1.34 tff(2525,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2194) | c0_1(a2186) | (~ndr1_0) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c3_1(a2186)) | c2_1(a2186) | (~c0_1(a2194)) | (~c3_1(a2194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2194) | c0_1(a2186) | (~ndr1_0) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c3_1(a2186)) | c2_1(a2186) | (~c0_1(a2194)) | (~c3_1(a2194)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2526,plain,
% 1.64/1.34 (((~ndr1_0) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c1_1(a2196)) | c2_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c0_1(a2186) | c2_1(a2186) | (~c3_1(a2186))) <=> (c2_1(a2194) | c0_1(a2186) | (~ndr1_0) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c3_1(a2186)) | c2_1(a2186) | (~c0_1(a2194)) | (~c3_1(a2194)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2527,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c1_1(a2196)) | c2_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c0_1(a2186) | c2_1(a2186) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2194) | c0_1(a2186) | (~ndr1_0) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c3_1(a2186)) | c2_1(a2186) | (~c0_1(a2194)) | (~c3_1(a2194))))),
% 1.64/1.34 inference(monotonicity,[status(thm)],[2526])).
% 1.64/1.34 tff(2528,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c1_1(a2196)) | c2_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c0_1(a2186) | c2_1(a2186) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2194) | c0_1(a2186) | (~ndr1_0) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c3_1(a2186)) | c2_1(a2186) | (~c0_1(a2194)) | (~c3_1(a2194)))),
% 1.64/1.34 inference(transitivity,[status(thm)],[2527, 2525])).
% 1.64/1.34 tff(2529,plain,
% 1.64/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c1_1(a2196)) | c2_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c0_1(a2186) | c2_1(a2186) | (~c3_1(a2186)))),
% 1.64/1.34 inference(quant_inst,[status(thm)],[])).
% 1.64/1.34 tff(2530,plain,
% 1.64/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2194) | c0_1(a2186) | (~ndr1_0) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c3_1(a2186)) | c2_1(a2186) | (~c0_1(a2194)) | (~c3_1(a2194))),
% 1.64/1.34 inference(modus_ponens,[status(thm)],[2529, 2528])).
% 1.64/1.34 tff(2531,plain,
% 1.64/1.34 ($false),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2530, 111, 2524, 2513, 2502, 2468, 2467, 2277, 2466, 2237, 2430, 2420])).
% 1.64/1.34 tff(2532,plain,(hskp16 | c2_1(a2186) | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.64/1.34 tff(2533,plain,
% 1.64/1.34 ($false),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2532, 2419, 2410, 11, 2385])).
% 1.64/1.34 tff(2534,plain,(c1_1(a2174) | hskp16 | c2_1(a2174) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.34 tff(2535,plain,
% 1.64/1.34 (hskp16),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2534, 2402, 2384, 147])).
% 1.64/1.34 tff(2536,plain,
% 1.64/1.34 (~c3_1(a2195)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[408, 2535])).
% 1.64/1.34 tff(2537,plain,
% 1.64/1.34 (~c2_1(a2195)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[414, 2535])).
% 1.64/1.34 tff(2538,plain,
% 1.64/1.34 (~hskp26),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2319, 2385])).
% 1.64/1.34 tff(2539,plain,
% 1.64/1.34 (~hskp17),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[2418, 2402, 2384, 147])).
% 1.64/1.34 tff(2540,plain,
% 1.64/1.34 (hskp24),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[109, 2539, 2538])).
% 1.64/1.34 tff(2541,plain,
% 1.64/1.34 (~c1_1(a2195)),
% 1.64/1.34 inference(unit_resolution,[status(thm)],[420, 2535])).
% 1.64/1.34 tff(2542,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a2262) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2262) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2543,plain,
% 1.64/1.34 (((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c0_1(a2262) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.64/1.34 inference(rewrite,[status(thm)],[])).
% 1.64/1.34 tff(2544,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a2262) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262))))),
% 1.64/1.34 inference(monotonicity,[status(thm)],[2543])).
% 1.64/1.34 tff(2545,plain,
% 1.64/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2262) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[2544, 2542])).
% 1.64/1.35 tff(2546,plain,
% 1.64/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(2547,plain,
% 1.64/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2262) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[2546, 2545])).
% 1.64/1.35 tff(2548,plain,
% 1.64/1.35 (~c2_1(a2262)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2547, 111, 2330, 2277, 2328, 1552, 1551, 1550, 2237, 2231, 157])).
% 1.64/1.35 tff(2549,plain,
% 1.64/1.35 ($false),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2351, 111, 312, 2330, 2329, 2277, 2237, 2231, 174, 2548])).
% 1.64/1.35 tff(2550,plain,((~hskp24) | hskp0 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.35 tff(2551,plain,
% 1.64/1.35 ($false),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2550, 2541, 2540, 2385, 2537, 2536])).
% 1.64/1.35 tff(2552,plain,(c2_1(a2174) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.35 tff(2553,plain,
% 1.64/1.35 (c2_1(a2174)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2552, 147])).
% 1.64/1.35 tff(2554,plain,
% 1.64/1.35 (c1_1(a2262)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2024, 2369])).
% 1.64/1.35 tff(2555,plain,
% 1.64/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2174) | c0_1(a2262) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2262)) | (~c1_1(a2262)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2174) | c0_1(a2262) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2556,plain,
% 1.64/1.35 (((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2174) | c0_1(a2174) | (~c2_1(a2174))) <=> (c1_1(a2174) | c0_1(a2262) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2557,plain,
% 1.64/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2174) | c0_1(a2174) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2174) | c0_1(a2262) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2262)) | (~c1_1(a2262))))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[2556])).
% 1.64/1.35 tff(2558,plain,
% 1.64/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2174) | c0_1(a2174) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2174) | c0_1(a2262) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[2557, 2555])).
% 1.64/1.35 tff(2559,plain,
% 1.64/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2174) | c0_1(a2174) | (~c2_1(a2174)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(2560,plain,
% 1.64/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2174) | c0_1(a2262) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2262)) | (~c1_1(a2262))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 1.64/1.35 tff(2561,plain,
% 1.64/1.35 (~c2_1(a2262)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2560, 111, 2381, 2380, 2554, 2238, 2553, 2383, 147, 301, 2382])).
% 1.64/1.35 tff(2562,plain,
% 1.64/1.35 (hskp17),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2355, 2239, 11])).
% 1.64/1.35 tff(2563,plain,
% 1.64/1.35 (~c1_1(a2197)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[163, 2562])).
% 1.64/1.35 tff(2564,plain,
% 1.64/1.35 (c3_1(a2197)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[653, 2562])).
% 1.64/1.35 tff(2565,plain,
% 1.64/1.35 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | (~c0_1(a2197)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2566,plain,
% 1.64/1.35 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c3_1(a2197))) <=> (hskp16 | hskp13 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2567,plain,
% 1.64/1.35 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c3_1(a2197)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | (~c0_1(a2197))))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[2566])).
% 1.64/1.35 tff(2568,plain,
% 1.64/1.35 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c3_1(a2197)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[2567, 2565])).
% 1.64/1.35 tff(2569,plain,
% 1.64/1.35 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(2570,plain,
% 1.64/1.35 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | (~c0_1(a2197))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 1.64/1.35 tff(2571,plain,
% 1.64/1.35 (hskp13 | (~c0_1(a2197))),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2570, 111, 11, 2564, 2563, 1169])).
% 1.64/1.35 tff(2572,plain,
% 1.64/1.35 (~c0_1(a2197)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2571, 1170])).
% 1.64/1.35 tff(2573,plain,
% 1.64/1.35 (c3_1(a2262)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2013, 2369])).
% 1.64/1.35 tff(2574,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2575,plain,
% 1.64/1.35 ((hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197))) <=> (hskp0 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2576,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262))))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[2575])).
% 1.64/1.35 tff(2577,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[2576, 2574])).
% 1.64/1.35 tff(2578,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(2579,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[2578, 2577])).
% 1.64/1.35 tff(2580,plain,
% 1.64/1.35 ($false),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2579, 111, 2239, 2554, 2573, 2564, 2563, 174, 2572, 2561])).
% 1.64/1.35 tff(2581,plain,(hskp13 | c1_1(a2174) | c0_1(a2174) | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.64/1.35 tff(2582,plain,
% 1.64/1.35 (hskp13),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2581, 2238, 147, 11])).
% 1.64/1.35 tff(2583,plain,
% 1.64/1.35 (~c3_1(a2191)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[353, 2582])).
% 1.64/1.35 tff(2584,plain,
% 1.64/1.35 (~c1_1(a2191)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[359, 2582])).
% 1.64/1.35 tff(2585,plain,
% 1.64/1.35 (c0_1(a2191)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[370, 2582])).
% 1.64/1.35 tff(2586,plain,
% 1.64/1.35 (hskp15),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[377, 111, 2239, 2585, 2584, 2583, 333])).
% 1.64/1.35 tff(2587,plain,
% 1.64/1.35 (~c2_1(a2194)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[383, 2586])).
% 1.64/1.35 tff(2588,plain,
% 1.64/1.35 (c3_1(a2194)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[431, 2586])).
% 1.64/1.35 tff(2589,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2194) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2194)) | (~c1_1(a2194)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2194) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2194)) | (~c1_1(a2194)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2590,plain,
% 1.64/1.35 ((hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (hskp0 | c2_1(a2194) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2194)) | (~c1_1(a2194)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2591,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2194) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2194)) | (~c1_1(a2194))))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[2590])).
% 1.64/1.35 tff(2592,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2194) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2194)) | (~c1_1(a2194)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[2591, 2589])).
% 1.64/1.35 tff(2593,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(2594,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2194) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2194)) | (~c1_1(a2194))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[2593, 2592])).
% 1.64/1.35 tff(2595,plain,
% 1.64/1.35 (~c1_1(a2194)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2594, 111, 2239, 2588, 2277, 2587, 2237, 2231, 174])).
% 1.64/1.35 tff(2596,plain,
% 1.64/1.35 (c0_1(a2194)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[394, 2586])).
% 1.64/1.35 tff(2597,plain,
% 1.64/1.35 ($false),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[401, 111, 11, 2596, 2587, 55, 2595])).
% 1.64/1.35 tff(2598,plain,(c1_1(a2174) | hskp16 | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.35 tff(2599,plain,
% 1.64/1.35 (c1_1(a2174)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2598, 11, 147])).
% 1.64/1.35 tff(2600,assumption,(hskp13), introduced(assumption)).
% 1.64/1.35 tff(2601,plain,
% 1.64/1.35 (~c3_1(a2191)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[353, 2600])).
% 1.64/1.35 tff(2602,plain,
% 1.64/1.35 (~c1_1(a2191)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[359, 2600])).
% 1.64/1.35 tff(2603,plain,
% 1.64/1.35 (c0_1(a2191)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[370, 2600])).
% 1.64/1.35 tff(2604,assumption,(~hskp18), introduced(assumption)).
% 1.64/1.35 tff(2605,plain,
% 1.64/1.35 ($false),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1353, 111, 2604, 2603, 1132, 2553, 2602, 2601, 147, 1233])).
% 1.64/1.35 tff(2606,plain,((~hskp13) | hskp18 | (~c1_1(a2174)) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.35 tff(2607,plain,
% 1.64/1.35 (~hskp13),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2606, 120, 2599, 147])).
% 1.64/1.35 tff(2608,assumption,(~c1_1(a2197)), introduced(assumption)).
% 1.64/1.35 tff(2609,assumption,(c3_1(a2197)), introduced(assumption)).
% 1.64/1.35 tff(2610,plain,
% 1.64/1.35 (hskp13 | (~c0_1(a2197))),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2570, 111, 11, 2609, 2608, 1169])).
% 1.64/1.35 tff(2611,plain,
% 1.64/1.35 (~c0_1(a2197)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2610, 1170])).
% 1.64/1.35 tff(2612,assumption,(c2_1(a2197)), introduced(assumption)).
% 1.64/1.35 tff(2613,plain,
% 1.64/1.35 (hskp28),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1847, 1170, 2553, 147, 11, 2599])).
% 1.64/1.35 tff(2614,plain,
% 1.64/1.35 (c1_1(a2188)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[480, 2613])).
% 1.64/1.35 tff(2615,plain,
% 1.64/1.35 (c0_1(a2188)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[282, 2613])).
% 1.64/1.35 tff(2616,plain,
% 1.64/1.35 (~c3_1(a2188)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1548, 111, 2615, 2614, 2612, 2599, 2553, 2608, 147, 301, 2611])).
% 1.64/1.35 tff(2617,plain,
% 1.64/1.35 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.64/1.35 inference(bind,[status(th)],[])).
% 1.64/1.35 tff(2618,plain,
% 1.64/1.35 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.64/1.35 inference(quant_intro,[status(thm)],[2617])).
% 1.64/1.35 tff(2619,plain,
% 1.64/1.35 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2620,plain,
% 1.64/1.35 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.64/1.35 inference(bind,[status(th)],[])).
% 1.64/1.35 tff(2621,plain,
% 1.64/1.35 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.64/1.35 inference(quant_intro,[status(thm)],[2620])).
% 1.64/1.35 tff(2622,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.64/1.35 tff(2623,plain,
% 1.64/1.35 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[2622, 2621])).
% 1.64/1.35 tff(2624,plain,
% 1.64/1.35 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[2623, 2619])).
% 1.64/1.35 tff(2625,plain,(
% 1.64/1.35 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.64/1.35 inference(skolemize,[status(sab)],[2624])).
% 1.64/1.35 tff(2626,plain,
% 1.64/1.35 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[2625, 2618])).
% 1.64/1.35 tff(2627,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2628,plain,
% 1.64/1.35 ((hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197))) <=> (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2629,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[2628])).
% 1.64/1.35 tff(2630,plain,
% 1.64/1.35 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.64/1.35 inference(transitivity,[status(thm)],[2629, 2627])).
% 1.64/1.35 tff(2631,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(2632,plain,
% 1.64/1.35 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[2631, 2630])).
% 1.64/1.35 tff(2633,plain,
% 1.64/1.35 ($false),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2632, 111, 11, 2615, 2614, 2612, 2609, 2626, 2616, 2611])).
% 1.64/1.35 tff(2634,plain,(hskp13 | hskp16 | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.35 tff(2635,plain,
% 1.64/1.35 ($false),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2634, 1553, 1542, 11, 2607, 164, 147])).
% 1.64/1.35 tff(2636,plain,((~hskp17) | hskp16 | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.35 tff(2637,plain,
% 1.64/1.35 (~hskp17),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2636, 11, 147])).
% 1.64/1.35 tff(2638,plain,
% 1.64/1.35 (hskp3),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2257, 2637, 11])).
% 1.64/1.35 tff(2639,plain,
% 1.64/1.35 (~c3_1(a2177)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1704, 2638])).
% 1.64/1.35 tff(2640,plain,
% 1.64/1.35 (~c1_1(a2177)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1596, 2638])).
% 1.64/1.35 tff(2641,plain,
% 1.64/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2177) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2177) | (~c3_1(a2186)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2642,plain,
% 1.64/1.35 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177)) <=> (c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2177) | (~c3_1(a2186)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2643,plain,
% 1.64/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2177) | (~c3_1(a2186))))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[2642])).
% 1.64/1.35 tff(2644,plain,
% 1.64/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2177) | (~c3_1(a2186)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[2643, 2641])).
% 1.64/1.35 tff(2645,plain,
% 1.64/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(2646,plain,
% 1.64/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2177) | (~c3_1(a2186))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[2645, 2644])).
% 1.64/1.35 tff(2647,plain,
% 1.64/1.35 (c2_1(a2177)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[2646, 111, 2277, 2599, 2553, 2237, 2231, 2640, 2639, 147, 157])).
% 1.64/1.35 tff(2648,plain,
% 1.64/1.35 (~c0_1(a2177)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1602, 2638])).
% 1.64/1.35 tff(2649,plain,
% 1.64/1.35 (hskp28),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[1847, 2607, 2553, 147, 11, 2599])).
% 1.64/1.35 tff(2650,plain,
% 1.64/1.35 (c1_1(a2188)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[480, 2649])).
% 1.64/1.35 tff(2651,plain,
% 1.64/1.35 (c0_1(a2188)),
% 1.64/1.35 inference(unit_resolution,[status(thm)],[282, 2649])).
% 1.64/1.35 tff(2652,plain,
% 1.64/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2177) | c1_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2177) | c1_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2653,plain,
% 1.64/1.35 (((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177))) <=> (c0_1(a2177) | c1_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)))),
% 1.64/1.35 inference(rewrite,[status(thm)],[])).
% 1.64/1.35 tff(2654,plain,
% 1.64/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2177) | c1_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177))))),
% 1.64/1.35 inference(monotonicity,[status(thm)],[2653])).
% 1.64/1.35 tff(2655,plain,
% 1.64/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2177) | c1_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)))),
% 1.64/1.35 inference(transitivity,[status(thm)],[2654, 2652])).
% 1.64/1.35 tff(2656,plain,
% 1.64/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177)))),
% 1.64/1.35 inference(quant_inst,[status(thm)],[])).
% 1.64/1.35 tff(2657,plain,
% 1.64/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2177) | c1_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177))),
% 1.64/1.35 inference(modus_ponens,[status(thm)],[2656, 2655])).
% 1.64/1.35 tff(2658,plain,
% 1.64/1.35 ((~c3_1(a2188)) | (~c2_1(a2177))),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2657, 111, 2651, 2650, 2599, 2553, 2648, 2640, 147, 301])).
% 1.64/1.36 tff(2659,plain,
% 1.64/1.36 (~c3_1(a2188)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2658, 2647])).
% 1.64/1.36 tff(2660,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | c0_1(a2186) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2186)) | (~c2_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a2186) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2661,plain,
% 1.64/1.36 ((hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186))) <=> (hskp16 | c0_1(a2186) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2662,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | c0_1(a2186) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2186)) | (~c2_1(a2186))))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[2661])).
% 1.64/1.36 tff(2663,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a2186) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.64/1.36 inference(transitivity,[status(thm)],[2662, 2660])).
% 1.64/1.36 tff(2664,plain,
% 1.64/1.36 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(2665,plain,
% 1.64/1.36 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a2186) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2186)) | (~c2_1(a2186))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 1.64/1.36 tff(2666,plain,
% 1.64/1.36 (c3_1(a2188) | (~c2_1(a2186))),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2665, 111, 11, 2651, 2650, 2277, 2237, 2626])).
% 1.64/1.36 tff(2667,plain,
% 1.64/1.36 (~c2_1(a2186)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2666, 2659])).
% 1.64/1.36 tff(2668,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2177)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2177)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2669,plain,
% 1.64/1.36 (((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177)) <=> (c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2177)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2670,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2177))))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[2669])).
% 1.64/1.36 tff(2671,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2177)))),
% 1.64/1.36 inference(transitivity,[status(thm)],[2670, 2668])).
% 1.64/1.36 tff(2672,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(2673,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2177))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[2672, 2671])).
% 1.64/1.36 tff(2674,plain,
% 1.64/1.36 (~c3_1(a2174)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2673, 111, 2599, 2648, 2640, 2639, 147, 758, 2647])).
% 1.64/1.36 tff(2675,plain,
% 1.64/1.36 (hskp16 | hskp15 | (~c1_1(a2174)) | c3_1(a2174)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[1833, 111, 147, 1827])).
% 1.64/1.36 tff(2676,plain,
% 1.64/1.36 (hskp15),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2675, 2674, 11, 2599])).
% 1.64/1.36 tff(2677,plain,
% 1.64/1.36 (~c2_1(a2194)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[383, 2676])).
% 1.64/1.36 tff(2678,plain,
% 1.64/1.36 (c3_1(a2194)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[431, 2676])).
% 1.64/1.36 tff(2679,plain,
% 1.64/1.36 (c0_1(a2194)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[394, 2676])).
% 1.64/1.36 tff(2680,plain,
% 1.64/1.36 (((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))) <=> ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp29 | hskp17 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2681,plain,
% 1.64/1.36 ((hskp29 | hskp17 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174))) <=> (hskp29 | hskp17 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2682,plain,
% 1.64/1.36 (((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174)))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[2681])).
% 1.64/1.36 tff(2683,plain,
% 1.64/1.36 (((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp29 | hskp17 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))),
% 1.64/1.36 inference(transitivity,[status(thm)],[2682, 2680])).
% 1.64/1.36 tff(2684,plain,
% 1.64/1.36 ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174)))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(2685,plain,
% 1.64/1.36 ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp29 | hskp17 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174)),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.64/1.36 tff(2686,plain,
% 1.64/1.36 (hskp29 | hskp17 | (~c1_1(a2174)) | c3_1(a2174)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2685, 111, 147, 2482])).
% 1.64/1.36 tff(2687,plain,
% 1.64/1.36 (hskp29),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2686, 2674, 2599, 2637])).
% 1.64/1.36 tff(2688,plain,
% 1.64/1.36 (c3_1(a2196)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2501, 2687])).
% 1.64/1.36 tff(2689,plain,
% 1.64/1.36 (c2_1(a2196)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2512, 2687])).
% 1.64/1.36 tff(2690,plain,
% 1.64/1.36 (c1_1(a2196)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2523, 2687])).
% 1.64/1.36 tff(2691,plain,
% 1.64/1.36 ($false),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2530, 111, 2690, 2689, 2688, 2679, 2678, 2277, 2677, 2237, 2430, 2667])).
% 1.64/1.36 tff(2692,plain,(hskp16 | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.36 tff(2693,plain,
% 1.64/1.36 (hskp16),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2692, 147])).
% 1.64/1.36 tff(2694,plain,
% 1.64/1.36 (~c2_1(a2195)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[414, 2693])).
% 1.64/1.36 tff(2695,plain,
% 1.64/1.36 (~c1_1(a2195)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[420, 2693])).
% 1.64/1.36 tff(2696,plain,
% 1.64/1.36 (~c3_1(a2195)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[408, 2693])).
% 1.64/1.36 tff(2697,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2186)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2698,plain,
% 1.64/1.36 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2186)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2699,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2186))))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[2698])).
% 1.64/1.36 tff(2700,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2186)))),
% 1.64/1.36 inference(transitivity,[status(thm)],[2699, 2697])).
% 1.64/1.36 tff(2701,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(2702,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2186))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[2701, 2700])).
% 1.64/1.36 tff(2703,plain,
% 1.64/1.36 (~c1_1(a2174)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2702, 111, 2277, 2553, 2695, 2694, 2696, 2237, 2231, 147, 157])).
% 1.64/1.36 tff(2704,plain,
% 1.64/1.36 (~hskp0),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[708, 2703])).
% 1.64/1.36 tff(2705,plain,
% 1.64/1.36 (~hskp26),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2319, 2704])).
% 1.64/1.36 tff(2706,plain,
% 1.64/1.36 (~hskp24),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2550, 2704, 2695, 2694, 2696])).
% 1.64/1.36 tff(2707,plain,
% 1.64/1.36 (hskp17),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[109, 2706, 2705])).
% 1.64/1.36 tff(2708,plain,
% 1.64/1.36 (~c1_1(a2197)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[163, 2707])).
% 1.64/1.36 tff(2709,plain,
% 1.64/1.36 (c3_1(a2197)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[653, 2707])).
% 1.64/1.36 tff(2710,plain,
% 1.64/1.36 (c2_1(a2197)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[664, 2707])).
% 1.64/1.36 tff(2711,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2712,plain,
% 1.64/1.36 ((hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2195) | c1_1(a2195) | c0_1(a2195)) <=> (hskp0 | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2713,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2195) | c1_1(a2195) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[2712])).
% 1.64/1.36 tff(2714,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2195) | c1_1(a2195) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.36 inference(transitivity,[status(thm)],[2713, 2711])).
% 1.64/1.36 tff(2715,plain,
% 1.64/1.36 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2195) | c1_1(a2195) | c0_1(a2195))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(2716,plain,
% 1.64/1.36 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[2715, 2714])).
% 1.64/1.36 tff(2717,plain,
% 1.64/1.36 (c0_1(a2195)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2716, 111, 2704, 2710, 2709, 2708, 2695, 2694, 10])).
% 1.64/1.36 tff(2718,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2174) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2174) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2195)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2719,plain,
% 1.64/1.36 (((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2174) | (~c2_1(a2174)) | (~c3_1(a2174)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174))) <=> (c1_1(a2174) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2195)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2720,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2174) | (~c2_1(a2174)) | (~c3_1(a2174)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2174) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2195))))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[2719])).
% 1.64/1.36 tff(2721,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2174) | (~c2_1(a2174)) | (~c3_1(a2174)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2174) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2195)))),
% 1.64/1.36 inference(transitivity,[status(thm)],[2720, 2718])).
% 1.64/1.36 tff(2722,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2174) | (~c2_1(a2174)) | (~c3_1(a2174)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(2723,plain,
% 1.64/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2174) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2195))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[2722, 2721])).
% 1.64/1.36 tff(2724,plain,
% 1.64/1.36 ((~c3_1(a2174)) | (~c0_1(a2195))),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2723, 111, 2703, 2553, 2694, 2696, 147, 1057])).
% 1.64/1.36 tff(2725,plain,
% 1.64/1.36 (~c3_1(a2174)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2724, 2717])).
% 1.64/1.36 tff(2726,plain,
% 1.64/1.36 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.64/1.36 inference(bind,[status(th)],[])).
% 1.64/1.36 tff(2727,plain,
% 1.64/1.36 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.64/1.36 inference(quant_intro,[status(thm)],[2726])).
% 1.64/1.36 tff(2728,plain,
% 1.64/1.36 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2729,plain,
% 1.64/1.36 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.64/1.36 inference(bind,[status(th)],[])).
% 1.64/1.36 tff(2730,plain,
% 1.64/1.36 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.64/1.36 inference(quant_intro,[status(thm)],[2729])).
% 1.64/1.36 tff(2731,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 1.64/1.36 tff(2732,plain,
% 1.64/1.36 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[2731, 2730])).
% 1.64/1.36 tff(2733,plain,
% 1.64/1.36 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[2732, 2728])).
% 1.64/1.36 tff(2734,plain,(
% 1.64/1.36 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.64/1.36 inference(skolemize,[status(sab)],[2733])).
% 1.64/1.36 tff(2735,plain,
% 1.64/1.36 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[2734, 2727])).
% 1.64/1.36 tff(2736,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2737,plain,
% 1.64/1.36 ((hskp7 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (hskp7 | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2738,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2186))))),
% 1.64/1.36 inference(monotonicity,[status(thm)],[2737])).
% 1.64/1.36 tff(2739,plain,
% 1.64/1.36 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))),
% 1.64/1.36 inference(transitivity,[status(thm)],[2738, 2736])).
% 1.64/1.36 tff(2740,plain,
% 1.64/1.36 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.64/1.36 inference(quant_inst,[status(thm)],[])).
% 1.64/1.36 tff(2741,plain,
% 1.64/1.36 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2186))),
% 1.64/1.36 inference(modus_ponens,[status(thm)],[2740, 2739])).
% 1.64/1.36 tff(2742,plain,
% 1.64/1.36 (hskp7 | (~c2_1(a2174)) | c3_1(a2174)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2741, 111, 2277, 2237, 2231, 147, 2735])).
% 1.64/1.36 tff(2743,plain,
% 1.64/1.36 (hskp7),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[2742, 2725, 2553])).
% 1.64/1.36 tff(2744,plain,
% 1.64/1.36 (~c0_1(a2182)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[788, 2743])).
% 1.64/1.36 tff(2745,plain,
% 1.64/1.36 (c3_1(a2182)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[799, 2743])).
% 1.64/1.36 tff(2746,plain,
% 1.64/1.36 (c2_1(a2182)),
% 1.64/1.36 inference(unit_resolution,[status(thm)],[810, 2743])).
% 1.64/1.36 tff(2747,plain,
% 1.64/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.36 inference(rewrite,[status(thm)],[])).
% 1.64/1.36 tff(2748,plain,
% 1.64/1.36 (((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182))) <=> (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2749,plain,
% 1.64/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[2748])).
% 1.64/1.37 tff(2750,plain,
% 1.64/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.37 inference(transitivity,[status(thm)],[2749, 2747])).
% 1.64/1.37 tff(2751,plain,
% 1.64/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182)))),
% 1.64/1.37 inference(quant_inst,[status(thm)],[])).
% 1.64/1.37 tff(2752,plain,
% 1.64/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2751, 2750])).
% 1.64/1.37 tff(2753,plain,
% 1.64/1.37 ($false),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2752, 111, 2710, 2709, 2746, 2745, 2708, 2694, 2696, 2744, 1057, 2717])).
% 1.64/1.37 tff(2754,plain,(c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.37 tff(2755,plain,
% 1.64/1.37 (~hskp0),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[686, 2754])).
% 1.64/1.37 tff(2756,plain,
% 1.64/1.37 (hskp17),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2355, 11, 2755])).
% 1.64/1.37 tff(2757,plain,
% 1.64/1.37 (~c1_1(a2197)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[163, 2756])).
% 1.64/1.37 tff(2758,plain,
% 1.64/1.37 (c3_1(a2197)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[653, 2756])).
% 1.64/1.37 tff(2759,plain,
% 1.64/1.37 (c2_1(a2197)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[664, 2756])).
% 1.64/1.37 tff(2760,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2761,plain,
% 1.64/1.37 ((hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197))) <=> (hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2762,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197))))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[2761])).
% 1.64/1.37 tff(2763,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.64/1.37 inference(transitivity,[status(thm)],[2762, 2760])).
% 1.64/1.37 tff(2764,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197)))),
% 1.64/1.37 inference(quant_inst,[status(thm)],[])).
% 1.64/1.37 tff(2765,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2764, 2763])).
% 1.64/1.37 tff(2766,plain,
% 1.64/1.37 (hskp21 | (~c0_1(a2197))),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2765, 111, 2759, 2758, 2757, 146])).
% 1.64/1.37 tff(2767,plain,
% 1.64/1.37 (~c0_1(a2197)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2766, 136])).
% 1.64/1.37 tff(2768,plain,
% 1.64/1.37 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c1_1(a2174) | c2_1(a2174) | (~c0_1(a2174)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2174) | c2_1(a2174) | (~c0_1(a2174)) | (~ndr1_0))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2769,plain,
% 1.64/1.37 ((hskp16 | (~ndr1_0) | c2_1(a2174) | c1_1(a2174) | (~c0_1(a2174))) <=> (hskp16 | c1_1(a2174) | c2_1(a2174) | (~c0_1(a2174)) | (~ndr1_0))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2770,plain,
% 1.64/1.37 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2174) | c1_1(a2174) | (~c0_1(a2174)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c1_1(a2174) | c2_1(a2174) | (~c0_1(a2174)) | (~ndr1_0)))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[2769])).
% 1.64/1.37 tff(2771,plain,
% 1.64/1.37 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2174) | c1_1(a2174) | (~c0_1(a2174)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2174) | c2_1(a2174) | (~c0_1(a2174)) | (~ndr1_0))),
% 1.64/1.37 inference(transitivity,[status(thm)],[2770, 2768])).
% 1.64/1.37 tff(2772,plain,
% 1.64/1.37 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2174) | c1_1(a2174) | (~c0_1(a2174)))),
% 1.64/1.37 inference(quant_inst,[status(thm)],[])).
% 1.64/1.37 tff(2773,plain,
% 1.64/1.37 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2174) | c2_1(a2174) | (~c0_1(a2174)) | (~ndr1_0)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2772, 2771])).
% 1.64/1.37 tff(2774,plain,
% 1.64/1.37 (hskp16 | c1_1(a2174) | c2_1(a2174)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2773, 111, 2754, 55])).
% 1.64/1.37 tff(2775,plain,
% 1.64/1.37 (c2_1(a2174)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2774, 2238, 11])).
% 1.64/1.37 tff(2776,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2174) | c1_1(a2197) | (~c0_1(a2174)) | (~ndr1_0) | (~c2_1(a2174)) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2174) | c1_1(a2197) | (~c0_1(a2174)) | (~ndr1_0) | (~c2_1(a2174)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2777,plain,
% 1.64/1.37 ((hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2174) | (~c2_1(a2174)) | (~c0_1(a2174))) <=> (hskp21 | c1_1(a2174) | c1_1(a2197) | (~c0_1(a2174)) | (~ndr1_0) | (~c2_1(a2174)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2778,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2174) | (~c2_1(a2174)) | (~c0_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2174) | c1_1(a2197) | (~c0_1(a2174)) | (~ndr1_0) | (~c2_1(a2174)) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[2777])).
% 1.64/1.37 tff(2779,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2174) | (~c2_1(a2174)) | (~c0_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2174) | c1_1(a2197) | (~c0_1(a2174)) | (~ndr1_0) | (~c2_1(a2174)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.37 inference(transitivity,[status(thm)],[2778, 2776])).
% 1.64/1.37 tff(2780,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2174) | (~c2_1(a2174)) | (~c0_1(a2174)))),
% 1.64/1.37 inference(quant_inst,[status(thm)],[])).
% 1.64/1.37 tff(2781,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2174) | c1_1(a2197) | (~c0_1(a2174)) | (~ndr1_0) | (~c2_1(a2174)) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2780, 2779])).
% 1.64/1.37 tff(2782,plain,
% 1.64/1.37 ($false),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2781, 111, 136, 2759, 2758, 2238, 2775, 2757, 2754, 146])).
% 1.64/1.37 tff(2783,plain,(c1_1(a2174) | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.64/1.37 tff(2784,plain,
% 1.64/1.37 (c1_1(a2174)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2783, 11])).
% 1.64/1.37 tff(2785,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~c0_1(a2174)) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | (~c0_1(a2174)) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2786,plain,
% 1.64/1.37 ((hskp16 | (~ndr1_0) | (~c0_1(a2174)) | c3_1(a2174) | (~c1_1(a2174)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197))) <=> (hskp16 | (~c0_1(a2174)) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2787,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2174)) | c3_1(a2174) | (~c1_1(a2174)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~c0_1(a2174)) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[2786])).
% 1.64/1.37 tff(2788,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2174)) | c3_1(a2174) | (~c1_1(a2174)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | (~c0_1(a2174)) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.64/1.37 inference(transitivity,[status(thm)],[2787, 2785])).
% 1.64/1.37 tff(2789,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2174)) | c3_1(a2174) | (~c1_1(a2174)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.37 inference(quant_inst,[status(thm)],[])).
% 1.64/1.37 tff(2790,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | (~c0_1(a2174)) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2789, 2788])).
% 1.64/1.37 tff(2791,plain,
% 1.64/1.37 ((~c1_1(a2174)) | c3_1(a2174)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2790, 111, 11, 2759, 2758, 2754, 2626, 2767])).
% 1.64/1.37 tff(2792,plain,
% 1.64/1.37 (c3_1(a2174)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2791, 2784])).
% 1.64/1.37 tff(2793,plain,
% 1.64/1.37 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.64/1.37 inference(bind,[status(th)],[])).
% 1.64/1.37 tff(2794,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.64/1.37 inference(quant_intro,[status(thm)],[2793])).
% 1.64/1.37 tff(2795,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2796,plain,
% 1.64/1.37 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.64/1.37 inference(bind,[status(th)],[])).
% 1.64/1.37 tff(2797,plain,
% 1.64/1.37 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.64/1.37 inference(quant_intro,[status(thm)],[2796])).
% 1.64/1.37 tff(2798,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.64/1.37 tff(2799,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2798, 2797])).
% 1.64/1.37 tff(2800,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2799, 2795])).
% 1.64/1.37 tff(2801,plain,(
% 1.64/1.37 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.64/1.37 inference(skolemize,[status(sab)],[2800])).
% 1.64/1.37 tff(2802,plain,
% 1.64/1.37 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2801, 2794])).
% 1.64/1.37 tff(2803,assumption,(~c0_1(a2197)), introduced(assumption)).
% 1.64/1.37 tff(2804,assumption,(c3_1(a2174)), introduced(assumption)).
% 1.64/1.37 tff(2805,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2174) | c1_1(a2197) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2174) | c1_1(a2197) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2806,plain,
% 1.64/1.37 ((hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197))) <=> (hskp0 | c2_1(a2174) | c1_1(a2197) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2807,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2174) | c1_1(a2197) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[2806])).
% 1.64/1.37 tff(2808,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2174) | c1_1(a2197) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.64/1.37 inference(transitivity,[status(thm)],[2807, 2805])).
% 1.64/1.37 tff(2809,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))),
% 1.64/1.37 inference(quant_inst,[status(thm)],[])).
% 1.64/1.37 tff(2810,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2174) | c1_1(a2197) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2809, 2808])).
% 1.64/1.37 tff(2811,plain,
% 1.64/1.37 ($false),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2810, 111, 2755, 2609, 1132, 2384, 2608, 174, 2804, 2803])).
% 1.64/1.37 tff(2812,plain,(c2_1(a2174) | (~c3_1(a2197)) | (~c1_1(a2174)) | c1_1(a2197) | (~c3_1(a2174)) | c0_1(a2197)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.37 tff(2813,plain,
% 1.64/1.37 (c2_1(a2174)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2812, 2758, 2784, 2757, 2792, 2767])).
% 1.64/1.37 tff(2814,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2197)) | c0_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2197)) | c0_1(a2197))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2815,plain,
% 1.64/1.37 ((hskp4 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197))) <=> (hskp4 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2197)) | c0_1(a2197))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2816,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2197)) | c0_1(a2197)))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[2815])).
% 1.64/1.37 tff(2817,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2197)) | c0_1(a2197))),
% 1.64/1.37 inference(transitivity,[status(thm)],[2816, 2814])).
% 1.64/1.37 tff(2818,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)))),
% 1.64/1.37 inference(quant_inst,[status(thm)],[])).
% 1.64/1.37 tff(2819,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2197)) | c0_1(a2197)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2818, 2817])).
% 1.64/1.37 tff(2820,plain,
% 1.64/1.37 (hskp4),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2819, 111, 2759, 2784, 2813, 2757, 2802, 2792, 2767])).
% 1.64/1.37 tff(2821,plain,
% 1.64/1.37 (((~hskp4) | (~c3_1(a2179))) <=> ((~hskp4) | (~c3_1(a2179)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2822,plain,
% 1.64/1.37 (((~c3_1(a2179)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a2179)))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2823,axiom,((~c3_1(a2179)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.64/1.37 tff(2824,plain,
% 1.64/1.37 ((~hskp4) | (~c3_1(a2179))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2823, 2822])).
% 1.64/1.37 tff(2825,plain,
% 1.64/1.37 ((~hskp4) | (~c3_1(a2179))),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2824, 2821])).
% 1.64/1.37 tff(2826,plain,
% 1.64/1.37 (~c3_1(a2179)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2825, 2820])).
% 1.64/1.37 tff(2827,plain,
% 1.64/1.37 (((~hskp4) | c0_1(a2179)) <=> ((~hskp4) | c0_1(a2179))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2828,axiom,((~hskp4) | c0_1(a2179)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.64/1.37 tff(2829,plain,
% 1.64/1.37 ((~hskp4) | c0_1(a2179)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2828, 2827])).
% 1.64/1.37 tff(2830,plain,
% 1.64/1.37 ((~hskp4) | c0_1(a2179)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2829, 2827])).
% 1.64/1.37 tff(2831,plain,
% 1.64/1.37 ((~hskp4) | c0_1(a2179)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2830, 2827])).
% 1.64/1.37 tff(2832,plain,
% 1.64/1.37 ((~hskp4) | c0_1(a2179)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2831, 2827])).
% 1.64/1.37 tff(2833,plain,
% 1.64/1.37 ((~hskp4) | c0_1(a2179)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2832, 2827])).
% 1.64/1.37 tff(2834,plain,
% 1.64/1.37 ((~hskp4) | c0_1(a2179)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2833, 2827])).
% 1.64/1.37 tff(2835,plain,
% 1.64/1.37 ((~hskp4) | c0_1(a2179)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2834, 2827])).
% 1.64/1.37 tff(2836,plain,
% 1.64/1.37 ((~hskp4) | c0_1(a2179)),
% 1.64/1.37 inference(modus_ponens,[status(thm)],[2835, 2827])).
% 1.64/1.37 tff(2837,plain,
% 1.64/1.37 (c0_1(a2179)),
% 1.64/1.37 inference(unit_resolution,[status(thm)],[2836, 2820])).
% 1.64/1.37 tff(2838,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | c3_1(a2179) | (~ndr1_0) | (~c1_1(a2179)) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | c3_1(a2179) | (~ndr1_0) | (~c1_1(a2179)) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2839,plain,
% 1.64/1.37 ((hskp16 | (~ndr1_0) | (~c0_1(a2179)) | c3_1(a2179) | (~c1_1(a2179)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197))) <=> (hskp16 | c3_1(a2179) | (~ndr1_0) | (~c1_1(a2179)) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.64/1.37 inference(rewrite,[status(thm)],[])).
% 1.64/1.37 tff(2840,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2179)) | c3_1(a2179) | (~c1_1(a2179)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | c3_1(a2179) | (~ndr1_0) | (~c1_1(a2179)) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.64/1.37 inference(monotonicity,[status(thm)],[2839])).
% 1.64/1.37 tff(2841,plain,
% 1.64/1.37 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2179)) | c3_1(a2179) | (~c1_1(a2179)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | c3_1(a2179) | (~ndr1_0) | (~c1_1(a2179)) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.64/1.37 inference(transitivity,[status(thm)],[2840, 2838])).
% 1.64/1.37 tff(2842,plain,
% 1.64/1.37 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2179)) | c3_1(a2179) | (~c1_1(a2179)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.38 inference(quant_inst,[status(thm)],[])).
% 1.64/1.38 tff(2843,plain,
% 1.64/1.38 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | c3_1(a2179) | (~ndr1_0) | (~c1_1(a2179)) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2842, 2841])).
% 1.64/1.38 tff(2844,plain,
% 1.64/1.38 (~c1_1(a2179)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[2843, 111, 11, 2759, 2758, 2837, 2826, 2626, 2767])).
% 1.64/1.38 tff(2845,plain,
% 1.64/1.38 (((~hskp4) | c2_1(a2179)) <=> ((~hskp4) | c2_1(a2179))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(2846,axiom,((~hskp4) | c2_1(a2179)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.64/1.38 tff(2847,plain,
% 1.64/1.38 ((~hskp4) | c2_1(a2179)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2846, 2845])).
% 1.64/1.38 tff(2848,plain,
% 1.64/1.38 ((~hskp4) | c2_1(a2179)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2847, 2845])).
% 1.64/1.38 tff(2849,plain,
% 1.64/1.38 ((~hskp4) | c2_1(a2179)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2848, 2845])).
% 1.64/1.38 tff(2850,plain,
% 1.64/1.38 ((~hskp4) | c2_1(a2179)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2849, 2845])).
% 1.64/1.38 tff(2851,plain,
% 1.64/1.38 ((~hskp4) | c2_1(a2179)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2850, 2845])).
% 1.64/1.38 tff(2852,plain,
% 1.64/1.38 ((~hskp4) | c2_1(a2179)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2851, 2845])).
% 1.64/1.38 tff(2853,plain,
% 1.64/1.38 ((~hskp4) | c2_1(a2179)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2852, 2845])).
% 1.64/1.38 tff(2854,plain,
% 1.64/1.38 ((~hskp4) | c2_1(a2179)),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2853, 2845])).
% 1.64/1.38 tff(2855,plain,
% 1.64/1.38 (c2_1(a2179)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[2854, 2820])).
% 1.64/1.38 tff(2856,plain,
% 1.64/1.38 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2179)) | c1_1(a2179) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2179)) | c1_1(a2179) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(2857,plain,
% 1.64/1.38 ((hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2179) | (~c2_1(a2179)) | (~c0_1(a2179))) <=> (hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2179)) | c1_1(a2179) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(2858,plain,
% 1.64/1.38 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2179) | (~c2_1(a2179)) | (~c0_1(a2179)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2179)) | c1_1(a2179) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.64/1.38 inference(monotonicity,[status(thm)],[2857])).
% 1.64/1.38 tff(2859,plain,
% 1.64/1.38 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2179) | (~c2_1(a2179)) | (~c0_1(a2179)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2179)) | c1_1(a2179) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.38 inference(transitivity,[status(thm)],[2858, 2856])).
% 1.64/1.38 tff(2860,plain,
% 1.64/1.38 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2179) | (~c2_1(a2179)) | (~c0_1(a2179)))),
% 1.64/1.38 inference(quant_inst,[status(thm)],[])).
% 1.64/1.38 tff(2861,plain,
% 1.64/1.38 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2179)) | c1_1(a2179) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.64/1.38 inference(modus_ponens,[status(thm)],[2860, 2859])).
% 1.64/1.38 tff(2862,plain,
% 1.64/1.38 ($false),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[2861, 111, 136, 2759, 2758, 2837, 2855, 2757, 146, 2844])).
% 1.64/1.38 tff(2863,plain,(hskp16), inference(lemma,lemma(discharge,[]))).
% 1.64/1.38 tff(2864,plain,
% 1.64/1.38 (~c2_1(a2195)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[414, 2863])).
% 1.64/1.38 tff(2865,plain,
% 1.64/1.38 (~c1_1(a2195)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[420, 2863])).
% 1.64/1.38 tff(2866,plain,
% 1.64/1.38 (~hskp26),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[2319, 2755])).
% 1.64/1.38 tff(2867,plain,
% 1.64/1.38 (~c3_1(a2195)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[408, 2863])).
% 1.64/1.38 tff(2868,plain,
% 1.64/1.38 (~hskp24),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[2550, 2865, 2755, 2864, 2867])).
% 1.64/1.38 tff(2869,plain,
% 1.64/1.38 (hskp17),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[109, 2868, 2866])).
% 1.64/1.38 tff(2870,plain,
% 1.64/1.38 (~c1_1(a2197)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[163, 2869])).
% 1.64/1.38 tff(2871,plain,
% 1.64/1.38 (c3_1(a2197)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[653, 2869])).
% 1.64/1.38 tff(2872,plain,
% 1.64/1.38 (c2_1(a2197)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[664, 2869])).
% 1.64/1.38 tff(2873,plain,
% 1.64/1.38 (c0_1(a2195)),
% 1.64/1.38 inference(unit_resolution,[status(thm)],[2716, 111, 2755, 2872, 2871, 2870, 2865, 2864, 10])).
% 1.64/1.38 tff(2874,plain,
% 1.64/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(2875,plain,
% 1.64/1.38 (((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2186) | (~c3_1(a2186)) | (~c2_1(a2186))) <=> (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.38 inference(rewrite,[status(thm)],[])).
% 1.64/1.38 tff(2876,plain,
% 1.64/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2186) | (~c3_1(a2186)) | (~c2_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.64/1.38 inference(monotonicity,[status(thm)],[2875])).
% 1.64/1.38 tff(2877,plain,
% 1.64/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2186) | (~c3_1(a2186)) | (~c2_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.38 inference(transitivity,[status(thm)],[2876, 2874])).
% 1.64/1.38 tff(2878,plain,
% 1.64/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2186) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.64/1.39 inference(quant_inst,[status(thm)],[])).
% 1.64/1.39 tff(2879,plain,
% 1.64/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.64/1.39 inference(modus_ponens,[status(thm)],[2878, 2877])).
% 1.64/1.39 tff(2880,plain,
% 1.64/1.39 ((~c2_1(a2186)) | (~c0_1(a2195))),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2879, 111, 2872, 2871, 2277, 2870, 2864, 2867, 2237, 1057])).
% 1.64/1.39 tff(2881,plain,
% 1.64/1.39 (~c2_1(a2186)),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2880, 2873])).
% 1.64/1.39 tff(2882,plain,
% 1.64/1.39 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2197) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | c2_1(a2186) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | c2_1(a2186) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.39 inference(rewrite,[status(thm)],[])).
% 1.64/1.39 tff(2883,plain,
% 1.64/1.39 ((hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2186) | c1_1(a2186) | c0_1(a2186)) <=> (hskp0 | c1_1(a2197) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | c2_1(a2186) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.39 inference(rewrite,[status(thm)],[])).
% 1.64/1.39 tff(2884,plain,
% 1.64/1.39 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2186) | c1_1(a2186) | c0_1(a2186))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2197) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | c2_1(a2186) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.64/1.39 inference(monotonicity,[status(thm)],[2883])).
% 1.64/1.39 tff(2885,plain,
% 1.64/1.39 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2186) | c1_1(a2186) | c0_1(a2186))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | c2_1(a2186) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.64/1.39 inference(transitivity,[status(thm)],[2884, 2882])).
% 1.64/1.39 tff(2886,plain,
% 1.64/1.39 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2186) | c1_1(a2186) | c0_1(a2186))),
% 1.64/1.39 inference(quant_inst,[status(thm)],[])).
% 1.64/1.39 tff(2887,plain,
% 1.64/1.39 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | c2_1(a2186) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.64/1.39 inference(modus_ponens,[status(thm)],[2886, 2885])).
% 1.64/1.39 tff(2888,plain,
% 1.64/1.39 ($false),
% 1.64/1.39 inference(unit_resolution,[status(thm)],[2887, 111, 2755, 2872, 2871, 2870, 2237, 2231, 10, 2881])).
% 1.64/1.39 % SZS output end Proof
%------------------------------------------------------------------------------