TSTP Solution File: SYN473-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN473-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 23:55:43 EDT 2022
% Result : Unsatisfiable 2.49s 1.86s
% Output : Proof 2.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN473-1 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 04:11:38 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 2.49/1.86 % SZS status Unsatisfiable
% 2.49/1.86 % SZS output start Proof
% 2.49/1.86 tff(c3_1_type, type, (
% 2.49/1.86 c3_1: $i > $o)).
% 2.49/1.86 tff(a802_type, type, (
% 2.49/1.86 a802: $i)).
% 2.49/1.86 tff(c2_1_type, type, (
% 2.49/1.86 c2_1: $i > $o)).
% 2.49/1.86 tff(a806_type, type, (
% 2.49/1.86 a806: $i)).
% 2.49/1.86 tff(c0_1_type, type, (
% 2.49/1.86 c0_1: $i > $o)).
% 2.49/1.86 tff(hskp9_type, type, (
% 2.49/1.86 hskp9: $o)).
% 2.49/1.86 tff(c1_1_type, type, (
% 2.49/1.86 c1_1: $i > $o)).
% 2.49/1.86 tff(ndr1_0_type, type, (
% 2.49/1.86 ndr1_0: $o)).
% 2.49/1.86 tff(hskp19_type, type, (
% 2.49/1.86 hskp19: $o)).
% 2.49/1.86 tff(a803_type, type, (
% 2.49/1.86 a803: $i)).
% 2.49/1.86 tff(hskp7_type, type, (
% 2.49/1.86 hskp7: $o)).
% 2.49/1.86 tff(a808_type, type, (
% 2.49/1.86 a808: $i)).
% 2.49/1.86 tff(hskp20_type, type, (
% 2.49/1.86 hskp20: $o)).
% 2.49/1.86 tff(hskp11_type, type, (
% 2.49/1.86 hskp11: $o)).
% 2.49/1.86 tff(a796_type, type, (
% 2.49/1.86 a796: $i)).
% 2.49/1.86 tff(hskp27_type, type, (
% 2.49/1.86 hskp27: $o)).
% 2.49/1.86 tff(a832_type, type, (
% 2.49/1.86 a832: $i)).
% 2.49/1.86 tff(hskp21_type, type, (
% 2.49/1.86 hskp21: $o)).
% 2.49/1.86 tff(hskp30_type, type, (
% 2.49/1.86 hskp30: $o)).
% 2.49/1.86 tff(a867_type, type, (
% 2.49/1.86 a867: $i)).
% 2.49/1.86 tff(a800_type, type, (
% 2.49/1.86 a800: $i)).
% 2.49/1.86 tff(a809_type, type, (
% 2.49/1.86 a809: $i)).
% 2.49/1.86 tff(hskp12_type, type, (
% 2.49/1.86 hskp12: $o)).
% 2.49/1.86 tff(hskp28_type, type, (
% 2.49/1.86 hskp28: $o)).
% 2.49/1.86 tff(hskp5_type, type, (
% 2.49/1.86 hskp5: $o)).
% 2.49/1.86 tff(a807_type, type, (
% 2.49/1.86 a807: $i)).
% 2.49/1.86 tff(hskp10_type, type, (
% 2.49/1.86 hskp10: $o)).
% 2.49/1.86 tff(hskp1_type, type, (
% 2.49/1.86 hskp1: $o)).
% 2.49/1.86 tff(a794_type, type, (
% 2.49/1.86 a794: $i)).
% 2.49/1.86 tff(a833_type, type, (
% 2.49/1.86 a833: $i)).
% 2.49/1.86 tff(hskp6_type, type, (
% 2.49/1.86 hskp6: $o)).
% 2.49/1.86 tff(a793_type, type, (
% 2.49/1.86 a793: $i)).
% 2.49/1.86 tff(hskp0_type, type, (
% 2.49/1.86 hskp0: $o)).
% 2.49/1.86 tff(a814_type, type, (
% 2.49/1.86 a814: $i)).
% 2.49/1.86 tff(a798_type, type, (
% 2.49/1.86 a798: $i)).
% 2.49/1.86 tff(hskp3_type, type, (
% 2.49/1.86 hskp3: $o)).
% 2.49/1.86 tff(a797_type, type, (
% 2.49/1.86 a797: $i)).
% 2.49/1.86 tff(a838_type, type, (
% 2.49/1.86 a838: $i)).
% 2.49/1.86 tff(hskp8_type, type, (
% 2.49/1.86 hskp8: $o)).
% 2.49/1.86 tff(a805_type, type, (
% 2.49/1.86 a805: $i)).
% 2.49/1.86 tff(a869_type, type, (
% 2.49/1.86 a869: $i)).
% 2.49/1.86 tff(hskp26_type, type, (
% 2.49/1.86 hskp26: $o)).
% 2.49/1.86 tff(a825_type, type, (
% 2.49/1.86 a825: $i)).
% 2.49/1.86 tff(hskp17_type, type, (
% 2.49/1.86 hskp17: $o)).
% 2.49/1.86 tff(a828_type, type, (
% 2.49/1.86 a828: $i)).
% 2.49/1.86 tff(hskp18_type, type, (
% 2.49/1.86 hskp18: $o)).
% 2.49/1.86 tff(a795_type, type, (
% 2.49/1.86 a795: $i)).
% 2.49/1.86 tff(hskp2_type, type, (
% 2.49/1.86 hskp2: $o)).
% 2.49/1.86 tff(a821_type, type, (
% 2.49/1.86 a821: $i)).
% 2.49/1.86 tff(hskp15_type, type, (
% 2.49/1.86 hskp15: $o)).
% 2.49/1.86 tff(a817_type, type, (
% 2.49/1.86 a817: $i)).
% 2.49/1.86 tff(a840_type, type, (
% 2.49/1.86 a840: $i)).
% 2.49/1.86 tff(hskp22_type, type, (
% 2.49/1.86 hskp22: $o)).
% 2.49/1.86 tff(hskp4_type, type, (
% 2.49/1.86 hskp4: $o)).
% 2.49/1.86 tff(a799_type, type, (
% 2.49/1.86 a799: $i)).
% 2.49/1.86 tff(hskp16_type, type, (
% 2.49/1.86 hskp16: $o)).
% 2.49/1.86 tff(a865_type, type, (
% 2.49/1.86 a865: $i)).
% 2.49/1.86 tff(hskp25_type, type, (
% 2.49/1.86 hskp25: $o)).
% 2.49/1.86 tff(a829_type, type, (
% 2.49/1.86 a829: $i)).
% 2.49/1.86 tff(hskp29_type, type, (
% 2.49/1.86 hskp29: $o)).
% 2.49/1.86 tff(a816_type, type, (
% 2.49/1.86 a816: $i)).
% 2.49/1.86 tff(hskp14_type, type, (
% 2.49/1.86 hskp14: $o)).
% 2.49/1.86 tff(hskp13_type, type, (
% 2.49/1.86 hskp13: $o)).
% 2.49/1.86 tff(1,plain,
% 2.49/1.86 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 2.49/1.86 inference(bind,[status(th)],[])).
% 2.49/1.86 tff(2,plain,
% 2.49/1.86 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.49/1.86 inference(quant_intro,[status(thm)],[1])).
% 2.49/1.86 tff(3,plain,
% 2.49/1.86 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(4,plain,
% 2.49/1.86 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 2.49/1.86 inference(bind,[status(th)],[])).
% 2.49/1.86 tff(5,plain,
% 2.49/1.86 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.49/1.86 inference(quant_intro,[status(thm)],[4])).
% 2.49/1.86 tff(6,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 2.49/1.86 tff(7,plain,
% 2.49/1.86 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[6, 5])).
% 2.49/1.86 tff(8,plain,
% 2.49/1.86 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.49/1.86 tff(9,plain,(
% 2.49/1.86 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.49/1.86 inference(skolemize,[status(sab)],[8])).
% 2.49/1.86 tff(10,plain,
% 2.49/1.86 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[9, 2])).
% 2.49/1.86 tff(11,assumption,(~hskp9), introduced(assumption)).
% 2.49/1.86 tff(12,plain,
% 2.49/1.86 (^[U: $i] : refl((hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.49/1.86 inference(bind,[status(th)],[])).
% 2.49/1.86 tff(13,plain,
% 2.49/1.86 (![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.49/1.86 inference(quant_intro,[status(thm)],[12])).
% 2.49/1.86 tff(14,plain,
% 2.49/1.86 (![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(15,plain,
% 2.49/1.86 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp20) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp20) <=> (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.49/1.86 inference(bind,[status(th)],[])).
% 2.49/1.86 tff(16,plain,
% 2.49/1.86 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp20) <=> ![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.49/1.86 inference(quant_intro,[status(thm)],[15])).
% 2.49/1.86 tff(17,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 2.49/1.86 tff(18,plain,
% 2.49/1.86 (![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[17, 16])).
% 2.49/1.86 tff(19,plain,
% 2.49/1.86 (![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[18, 14])).
% 2.49/1.86 tff(20,plain,(
% 2.49/1.86 ![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.49/1.86 inference(skolemize,[status(sab)],[19])).
% 2.49/1.86 tff(21,plain,
% 2.49/1.86 (![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[20, 13])).
% 2.49/1.86 tff(22,assumption,(~c3_1(a832)), introduced(assumption)).
% 2.49/1.86 tff(23,assumption,(hskp30), introduced(assumption)).
% 2.49/1.86 tff(24,plain,
% 2.49/1.86 (((~hskp30) | c3_1(a867)) <=> ((~hskp30) | c3_1(a867))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(25,axiom,((~hskp30) | c3_1(a867)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 2.49/1.86 tff(26,plain,
% 2.49/1.86 ((~hskp30) | c3_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[25, 24])).
% 2.49/1.86 tff(27,plain,
% 2.49/1.86 ((~hskp30) | c3_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[26, 24])).
% 2.49/1.86 tff(28,plain,
% 2.49/1.86 ((~hskp30) | c3_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[27, 24])).
% 2.49/1.86 tff(29,plain,
% 2.49/1.86 ((~hskp30) | c3_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[28, 24])).
% 2.49/1.86 tff(30,plain,
% 2.49/1.86 ((~hskp30) | c3_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[29, 24])).
% 2.49/1.86 tff(31,plain,
% 2.49/1.86 ((~hskp30) | c3_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[30, 24])).
% 2.49/1.86 tff(32,plain,
% 2.49/1.86 ((~hskp30) | c3_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[31, 24])).
% 2.49/1.86 tff(33,plain,
% 2.49/1.86 ((~hskp30) | c3_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[32, 24])).
% 2.49/1.86 tff(34,plain,
% 2.49/1.86 (c3_1(a867)),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[33, 23])).
% 2.49/1.86 tff(35,plain,
% 2.49/1.86 (((~hskp30) | c1_1(a867)) <=> ((~hskp30) | c1_1(a867))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(36,axiom,((~hskp30) | c1_1(a867)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 2.49/1.86 tff(37,plain,
% 2.49/1.86 ((~hskp30) | c1_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[36, 35])).
% 2.49/1.86 tff(38,plain,
% 2.49/1.86 ((~hskp30) | c1_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[37, 35])).
% 2.49/1.86 tff(39,plain,
% 2.49/1.86 ((~hskp30) | c1_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[38, 35])).
% 2.49/1.86 tff(40,plain,
% 2.49/1.86 ((~hskp30) | c1_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[39, 35])).
% 2.49/1.86 tff(41,plain,
% 2.49/1.86 ((~hskp30) | c1_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[40, 35])).
% 2.49/1.86 tff(42,plain,
% 2.49/1.86 ((~hskp30) | c1_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[41, 35])).
% 2.49/1.86 tff(43,plain,
% 2.49/1.86 ((~hskp30) | c1_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[42, 35])).
% 2.49/1.86 tff(44,plain,
% 2.49/1.86 ((~hskp30) | c1_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[43, 35])).
% 2.49/1.86 tff(45,plain,
% 2.49/1.86 (c1_1(a867)),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[44, 23])).
% 2.49/1.86 tff(46,plain,
% 2.49/1.86 (((~hskp30) | c0_1(a867)) <=> ((~hskp30) | c0_1(a867))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(47,axiom,((~hskp30) | c0_1(a867)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 2.49/1.86 tff(48,plain,
% 2.49/1.86 ((~hskp30) | c0_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[47, 46])).
% 2.49/1.86 tff(49,plain,
% 2.49/1.86 ((~hskp30) | c0_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[48, 46])).
% 2.49/1.86 tff(50,plain,
% 2.49/1.86 ((~hskp30) | c0_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[49, 46])).
% 2.49/1.86 tff(51,plain,
% 2.49/1.86 ((~hskp30) | c0_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[50, 46])).
% 2.49/1.86 tff(52,plain,
% 2.49/1.86 ((~hskp30) | c0_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[51, 46])).
% 2.49/1.86 tff(53,plain,
% 2.49/1.86 ((~hskp30) | c0_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[52, 46])).
% 2.49/1.86 tff(54,plain,
% 2.49/1.86 ((~hskp30) | c0_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[53, 46])).
% 2.49/1.86 tff(55,plain,
% 2.49/1.86 ((~hskp30) | c0_1(a867)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[54, 46])).
% 2.49/1.86 tff(56,plain,
% 2.49/1.86 (c0_1(a867)),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[55, 23])).
% 2.49/1.86 tff(57,assumption,(hskp9), introduced(assumption)).
% 2.49/1.86 tff(58,plain,
% 2.49/1.86 (((~hskp9) | c0_1(a806)) <=> ((~hskp9) | c0_1(a806))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(59,axiom,((~hskp9) | c0_1(a806)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 2.49/1.86 tff(60,plain,
% 2.49/1.86 ((~hskp9) | c0_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[59, 58])).
% 2.49/1.86 tff(61,plain,
% 2.49/1.86 ((~hskp9) | c0_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[60, 58])).
% 2.49/1.86 tff(62,plain,
% 2.49/1.86 ((~hskp9) | c0_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[61, 58])).
% 2.49/1.86 tff(63,plain,
% 2.49/1.86 ((~hskp9) | c0_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[62, 58])).
% 2.49/1.86 tff(64,plain,
% 2.49/1.86 ((~hskp9) | c0_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[63, 58])).
% 2.49/1.86 tff(65,plain,
% 2.49/1.86 ((~hskp9) | c0_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[64, 58])).
% 2.49/1.86 tff(66,plain,
% 2.49/1.86 ((~hskp9) | c0_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[65, 58])).
% 2.49/1.86 tff(67,plain,
% 2.49/1.86 ((~hskp9) | c0_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[66, 58])).
% 2.49/1.86 tff(68,plain,
% 2.49/1.86 (c0_1(a806)),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[67, 57])).
% 2.49/1.86 tff(69,assumption,(c1_1(a867)), introduced(assumption)).
% 2.49/1.86 tff(70,assumption,(c0_1(a867)), introduced(assumption)).
% 2.49/1.86 tff(71,plain,
% 2.49/1.86 (((~hskp9) | (~c3_1(a806))) <=> ((~hskp9) | (~c3_1(a806)))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(72,plain,
% 2.49/1.86 (((~c3_1(a806)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a806)))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(73,axiom,((~c3_1(a806)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 2.49/1.86 tff(74,plain,
% 2.49/1.86 ((~hskp9) | (~c3_1(a806))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[73, 72])).
% 2.49/1.86 tff(75,plain,
% 2.49/1.86 ((~hskp9) | (~c3_1(a806))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[74, 71])).
% 2.49/1.86 tff(76,plain,
% 2.49/1.86 (~c3_1(a806)),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[75, 57])).
% 2.49/1.86 tff(77,assumption,(c3_1(a867)), introduced(assumption)).
% 2.49/1.86 tff(78,plain,
% 2.49/1.86 (((~hskp9) | c1_1(a806)) <=> ((~hskp9) | c1_1(a806))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(79,axiom,((~hskp9) | c1_1(a806)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 2.49/1.86 tff(80,plain,
% 2.49/1.86 ((~hskp9) | c1_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[79, 78])).
% 2.49/1.86 tff(81,plain,
% 2.49/1.86 ((~hskp9) | c1_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[80, 78])).
% 2.49/1.86 tff(82,plain,
% 2.49/1.86 ((~hskp9) | c1_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[81, 78])).
% 2.49/1.86 tff(83,plain,
% 2.49/1.86 ((~hskp9) | c1_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[82, 78])).
% 2.49/1.86 tff(84,plain,
% 2.49/1.86 ((~hskp9) | c1_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[83, 78])).
% 2.49/1.86 tff(85,plain,
% 2.49/1.86 ((~hskp9) | c1_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[84, 78])).
% 2.49/1.86 tff(86,plain,
% 2.49/1.86 ((~hskp9) | c1_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[85, 78])).
% 2.49/1.86 tff(87,plain,
% 2.49/1.86 ((~hskp9) | c1_1(a806)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[86, 78])).
% 2.49/1.86 tff(88,plain,
% 2.49/1.86 (c1_1(a806)),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[87, 57])).
% 2.49/1.86 tff(89,assumption,(~c2_1(a806)), introduced(assumption)).
% 2.49/1.86 tff(90,plain,
% 2.49/1.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 2.49/1.86 inference(bind,[status(th)],[])).
% 2.49/1.86 tff(91,plain,
% 2.49/1.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 2.49/1.86 inference(quant_intro,[status(thm)],[90])).
% 2.49/1.86 tff(92,plain,
% 2.49/1.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(93,plain,
% 2.49/1.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(94,plain,
% 2.49/1.87 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[93])).
% 2.49/1.87 tff(95,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 2.49/1.87 tff(96,plain,
% 2.49/1.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[95, 94])).
% 2.49/1.87 tff(97,plain,
% 2.49/1.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[96, 92])).
% 2.49/1.87 tff(98,plain,(
% 2.49/1.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 2.49/1.87 inference(skolemize,[status(sab)],[97])).
% 2.49/1.87 tff(99,plain,
% 2.49/1.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[98, 91])).
% 2.49/1.87 tff(100,assumption,(~c3_1(a806)), introduced(assumption)).
% 2.49/1.87 tff(101,plain,
% 2.49/1.87 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(102,plain,
% 2.49/1.87 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[101])).
% 2.49/1.87 tff(103,plain,
% 2.49/1.87 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(104,plain,
% 2.49/1.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_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) | (~c3_1(U)) | (~c1_1(U)) | (~c0_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)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(105,plain,
% 2.49/1.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[104])).
% 2.49/1.87 tff(106,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 2.49/1.87 tff(107,plain,
% 2.49/1.87 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[106, 105])).
% 2.49/1.87 tff(108,plain,
% 2.49/1.87 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[107, 103])).
% 2.49/1.87 tff(109,plain,(
% 2.49/1.87 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.49/1.87 inference(skolemize,[status(sab)],[108])).
% 2.49/1.87 tff(110,plain,
% 2.49/1.87 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[109, 102])).
% 2.49/1.87 tff(111,assumption,(c1_1(a806)), introduced(assumption)).
% 2.49/1.87 tff(112,assumption,(~ndr1_0), introduced(assumption)).
% 2.49/1.87 tff(113,plain,
% 2.49/1.87 ((ndr1_0 | (~hskp19)) <=> (ndr1_0 | (~hskp19))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(114,plain,
% 2.49/1.87 (((~hskp19) | ndr1_0) <=> (ndr1_0 | (~hskp19))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(115,axiom,((~hskp19) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause12')).
% 2.49/1.87 tff(116,plain,
% 2.49/1.87 (ndr1_0 | (~hskp19)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[115, 114])).
% 2.49/1.87 tff(117,plain,
% 2.49/1.87 (ndr1_0 | (~hskp19)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[116, 113])).
% 2.49/1.87 tff(118,plain,
% 2.49/1.87 (~hskp19),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[117, 112])).
% 2.49/1.87 tff(119,plain,
% 2.49/1.87 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(120,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 2.49/1.87 tff(121,plain,
% 2.49/1.87 ((~hskp30) | ndr1_0),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[120, 119])).
% 2.49/1.87 tff(122,plain,
% 2.49/1.87 ((~hskp30) | ndr1_0),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[121, 119])).
% 2.49/1.87 tff(123,plain,
% 2.49/1.87 ((~hskp30) | ndr1_0),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[122, 119])).
% 2.49/1.87 tff(124,plain,
% 2.49/1.87 ((~hskp30) | ndr1_0),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[123, 119])).
% 2.49/1.87 tff(125,plain,
% 2.49/1.87 ((~hskp30) | ndr1_0),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[124, 119])).
% 2.49/1.87 tff(126,plain,
% 2.49/1.87 ((~hskp30) | ndr1_0),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[125, 119])).
% 2.49/1.87 tff(127,plain,
% 2.49/1.87 ((~hskp30) | ndr1_0),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[126, 119])).
% 2.49/1.87 tff(128,plain,
% 2.49/1.87 ((~hskp30) | ndr1_0),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[127, 119])).
% 2.49/1.87 tff(129,plain,
% 2.49/1.87 (~hskp30),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[128, 112])).
% 2.49/1.87 tff(130,plain,
% 2.49/1.87 ((ndr1_0 | (~hskp28)) <=> (ndr1_0 | (~hskp28))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(131,plain,
% 2.49/1.87 (((~hskp28) | ndr1_0) <=> (ndr1_0 | (~hskp28))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(132,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 2.49/1.87 tff(133,plain,
% 2.49/1.87 (ndr1_0 | (~hskp28)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[132, 131])).
% 2.49/1.87 tff(134,plain,
% 2.49/1.87 (ndr1_0 | (~hskp28)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[133, 130])).
% 2.49/1.87 tff(135,plain,
% 2.49/1.87 (~hskp28),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[134, 112])).
% 2.49/1.87 tff(136,plain,
% 2.49/1.87 ((hskp30 | hskp28 | hskp19) <=> (hskp30 | hskp28 | hskp19)),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(137,plain,
% 2.49/1.87 (((hskp30 | hskp28) | hskp19) <=> (hskp30 | hskp28 | hskp19)),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(138,plain,
% 2.49/1.87 ((hskp30 | hskp28) <=> (hskp30 | hskp28)),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(139,plain,
% 2.49/1.87 (((hskp30 | hskp28) | hskp19) <=> ((hskp30 | hskp28) | hskp19)),
% 2.49/1.87 inference(monotonicity,[status(thm)],[138])).
% 2.49/1.87 tff(140,plain,
% 2.49/1.87 (((hskp30 | hskp28) | hskp19) <=> (hskp30 | hskp28 | hskp19)),
% 2.49/1.87 inference(transitivity,[status(thm)],[139, 137])).
% 2.49/1.87 tff(141,axiom,((hskp30 | hskp28) | hskp19), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 2.49/1.87 tff(142,plain,
% 2.49/1.87 (hskp30 | hskp28 | hskp19),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[141, 140])).
% 2.49/1.87 tff(143,plain,
% 2.49/1.87 (hskp30 | hskp28 | hskp19),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[142, 136])).
% 2.49/1.87 tff(144,plain,
% 2.49/1.87 (hskp30 | hskp28 | hskp19),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[143, 136])).
% 2.49/1.87 tff(145,plain,
% 2.49/1.87 (hskp30 | hskp28 | hskp19),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[144, 136])).
% 2.49/1.87 tff(146,plain,
% 2.49/1.87 (hskp30 | hskp28 | hskp19),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[145, 136])).
% 2.49/1.87 tff(147,plain,
% 2.49/1.87 (hskp30 | hskp28 | hskp19),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[146, 136])).
% 2.49/1.87 tff(148,plain,
% 2.49/1.87 (hskp30 | hskp28 | hskp19),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[147, 136])).
% 2.49/1.87 tff(149,plain,
% 2.49/1.87 (hskp30 | hskp28 | hskp19),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[148, 136])).
% 2.49/1.87 tff(150,plain,
% 2.49/1.87 ($false),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[149, 135, 129, 118])).
% 2.49/1.87 tff(151,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 2.49/1.87 tff(152,plain,
% 2.49/1.87 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c2_1(a806) | (~c1_1(a806)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(153,plain,
% 2.49/1.87 ((hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806))) <=> (hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c2_1(a806) | (~c1_1(a806)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(154,plain,
% 2.49/1.87 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c2_1(a806) | (~c1_1(a806))))),
% 2.49/1.87 inference(monotonicity,[status(thm)],[153])).
% 2.49/1.87 tff(155,plain,
% 2.49/1.87 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c2_1(a806) | (~c1_1(a806)))),
% 2.49/1.87 inference(transitivity,[status(thm)],[154, 152])).
% 2.49/1.87 tff(156,plain,
% 2.49/1.87 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))),
% 2.49/1.87 inference(quant_inst,[status(thm)],[])).
% 2.49/1.87 tff(157,plain,
% 2.49/1.87 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c2_1(a806) | (~c1_1(a806))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[156, 155])).
% 2.49/1.87 tff(158,plain,
% 2.49/1.87 (hskp12 | c2_1(a806)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[157, 151, 70, 69, 77, 111, 100, 110])).
% 2.49/1.87 tff(159,plain,
% 2.49/1.87 (hskp12),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[158, 89])).
% 2.49/1.87 tff(160,plain,
% 2.49/1.87 (((~hskp12) | (~c0_1(a809))) <=> ((~hskp12) | (~c0_1(a809)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(161,plain,
% 2.49/1.87 (((~c0_1(a809)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a809)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(162,axiom,((~c0_1(a809)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 2.49/1.87 tff(163,plain,
% 2.49/1.87 ((~hskp12) | (~c0_1(a809))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[162, 161])).
% 2.49/1.87 tff(164,plain,
% 2.49/1.87 ((~hskp12) | (~c0_1(a809))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[163, 160])).
% 2.49/1.87 tff(165,plain,
% 2.49/1.87 (~c0_1(a809)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[164, 159])).
% 2.49/1.87 tff(166,assumption,(c0_1(a806)), introduced(assumption)).
% 2.49/1.87 tff(167,plain,
% 2.49/1.87 (((~hskp12) | c2_1(a809)) <=> ((~hskp12) | c2_1(a809))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(168,axiom,((~hskp12) | c2_1(a809)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 2.49/1.87 tff(169,plain,
% 2.49/1.87 ((~hskp12) | c2_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[168, 167])).
% 2.49/1.87 tff(170,plain,
% 2.49/1.87 ((~hskp12) | c2_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[169, 167])).
% 2.49/1.87 tff(171,plain,
% 2.49/1.87 ((~hskp12) | c2_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[170, 167])).
% 2.49/1.87 tff(172,plain,
% 2.49/1.87 ((~hskp12) | c2_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[171, 167])).
% 2.49/1.87 tff(173,plain,
% 2.49/1.87 ((~hskp12) | c2_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[172, 167])).
% 2.49/1.87 tff(174,plain,
% 2.49/1.87 ((~hskp12) | c2_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[173, 167])).
% 2.49/1.87 tff(175,plain,
% 2.49/1.87 ((~hskp12) | c2_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[174, 167])).
% 2.49/1.87 tff(176,plain,
% 2.49/1.87 ((~hskp12) | c2_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[175, 167])).
% 2.49/1.87 tff(177,plain,
% 2.49/1.87 (c2_1(a809)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[176, 159])).
% 2.49/1.87 tff(178,plain,
% 2.49/1.87 (((~hskp12) | c1_1(a809)) <=> ((~hskp12) | c1_1(a809))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(179,axiom,((~hskp12) | c1_1(a809)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 2.49/1.87 tff(180,plain,
% 2.49/1.87 ((~hskp12) | c1_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[179, 178])).
% 2.49/1.87 tff(181,plain,
% 2.49/1.87 ((~hskp12) | c1_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[180, 178])).
% 2.49/1.87 tff(182,plain,
% 2.49/1.87 ((~hskp12) | c1_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[181, 178])).
% 2.49/1.87 tff(183,plain,
% 2.49/1.87 ((~hskp12) | c1_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[182, 178])).
% 2.49/1.87 tff(184,plain,
% 2.49/1.87 ((~hskp12) | c1_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[183, 178])).
% 2.49/1.87 tff(185,plain,
% 2.49/1.87 ((~hskp12) | c1_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[184, 178])).
% 2.49/1.87 tff(186,plain,
% 2.49/1.87 ((~hskp12) | c1_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[185, 178])).
% 2.49/1.87 tff(187,plain,
% 2.49/1.87 ((~hskp12) | c1_1(a809)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[186, 178])).
% 2.49/1.87 tff(188,plain,
% 2.49/1.87 (c1_1(a809)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[187, 159])).
% 2.49/1.87 tff(189,plain,
% 2.49/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a809) | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a809) | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(190,plain,
% 2.49/1.87 (((~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809))) <=> (c0_1(a809) | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(191,plain,
% 2.49/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a809) | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a809)) | (~c1_1(a809))))),
% 2.49/1.87 inference(monotonicity,[status(thm)],[190])).
% 2.49/1.87 tff(192,plain,
% 2.49/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a809) | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.49/1.87 inference(transitivity,[status(thm)],[191, 189])).
% 2.49/1.87 tff(193,plain,
% 2.49/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.49/1.87 inference(quant_inst,[status(thm)],[])).
% 2.49/1.87 tff(194,plain,
% 2.49/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a809) | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a809)) | (~c1_1(a809))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[193, 192])).
% 2.49/1.87 tff(195,plain,
% 2.49/1.87 ($false),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[194, 151, 188, 177, 166, 111, 165, 100, 99, 89])).
% 2.49/1.87 tff(196,plain,(c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a806) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a867))), inference(lemma,lemma(discharge,[]))).
% 2.49/1.87 tff(197,plain,
% 2.49/1.87 (c2_1(a806)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[196, 88, 77, 76, 70, 69, 68])).
% 2.49/1.87 tff(198,plain,
% 2.49/1.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(199,plain,
% 2.49/1.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[198])).
% 2.49/1.87 tff(200,plain,
% 2.49/1.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(201,plain,
% 2.49/1.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(202,plain,
% 2.49/1.87 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[201])).
% 2.49/1.87 tff(203,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 2.49/1.87 tff(204,plain,
% 2.49/1.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[203, 202])).
% 2.49/1.87 tff(205,plain,
% 2.49/1.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[204, 200])).
% 2.49/1.87 tff(206,plain,(
% 2.49/1.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 2.49/1.87 inference(skolemize,[status(sab)],[205])).
% 2.49/1.87 tff(207,plain,
% 2.49/1.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[206, 199])).
% 2.49/1.87 tff(208,plain,
% 2.49/1.87 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(209,plain,
% 2.49/1.87 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[208])).
% 2.49/1.87 tff(210,plain,
% 2.49/1.87 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(211,plain,
% 2.49/1.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(212,plain,
% 2.49/1.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[211])).
% 2.49/1.87 tff(213,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 2.49/1.87 tff(214,plain,
% 2.49/1.87 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[213, 212])).
% 2.49/1.87 tff(215,plain,
% 2.49/1.87 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[214, 210])).
% 2.49/1.87 tff(216,plain,(
% 2.49/1.87 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.49/1.87 inference(skolemize,[status(sab)],[215])).
% 2.49/1.87 tff(217,plain,
% 2.49/1.87 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[216, 209])).
% 2.49/1.88 tff(218,plain,
% 2.49/1.88 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(219,plain,
% 2.49/1.88 ((hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806))) <=> (hskp5 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(220,plain,
% 2.49/1.88 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806))))),
% 2.49/1.88 inference(monotonicity,[status(thm)],[219])).
% 2.49/1.88 tff(221,plain,
% 2.49/1.88 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.49/1.88 inference(transitivity,[status(thm)],[220, 218])).
% 2.49/1.88 tff(222,plain,
% 2.49/1.88 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806)))),
% 2.49/1.88 inference(quant_inst,[status(thm)],[])).
% 2.49/1.88 tff(223,plain,
% 2.49/1.88 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[222, 221])).
% 2.49/1.88 tff(224,plain,
% 2.49/1.88 (hskp5),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[223, 151, 70, 69, 77, 68, 76, 217, 197])).
% 2.49/1.88 tff(225,plain,
% 2.49/1.88 (((~hskp5) | (~c0_1(a800))) <=> ((~hskp5) | (~c0_1(a800)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(226,plain,
% 2.49/1.88 (((~c0_1(a800)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a800)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(227,axiom,((~c0_1(a800)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 2.49/1.88 tff(228,plain,
% 2.49/1.88 ((~hskp5) | (~c0_1(a800))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[227, 226])).
% 2.49/1.88 tff(229,plain,
% 2.49/1.88 ((~hskp5) | (~c0_1(a800))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[228, 225])).
% 2.49/1.88 tff(230,plain,
% 2.49/1.88 (~c0_1(a800)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[229, 224])).
% 2.49/1.88 tff(231,plain,
% 2.49/1.88 (((~hskp5) | c3_1(a800)) <=> ((~hskp5) | c3_1(a800))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(232,axiom,((~hskp5) | c3_1(a800)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 2.49/1.88 tff(233,plain,
% 2.49/1.88 ((~hskp5) | c3_1(a800)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[232, 231])).
% 2.49/1.88 tff(234,plain,
% 2.49/1.88 ((~hskp5) | c3_1(a800)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[233, 231])).
% 2.49/1.88 tff(235,plain,
% 2.49/1.88 ((~hskp5) | c3_1(a800)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[234, 231])).
% 2.49/1.88 tff(236,plain,
% 2.49/1.88 ((~hskp5) | c3_1(a800)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[235, 231])).
% 2.49/1.88 tff(237,plain,
% 2.49/1.88 ((~hskp5) | c3_1(a800)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[236, 231])).
% 2.49/1.88 tff(238,plain,
% 2.49/1.88 ((~hskp5) | c3_1(a800)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[237, 231])).
% 2.49/1.88 tff(239,plain,
% 2.49/1.88 ((~hskp5) | c3_1(a800)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[238, 231])).
% 2.49/1.88 tff(240,plain,
% 2.49/1.88 ((~hskp5) | c3_1(a800)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[239, 231])).
% 2.49/1.88 tff(241,plain,
% 2.49/1.88 (c3_1(a800)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[240, 224])).
% 2.49/1.88 tff(242,plain,
% 2.49/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)) | (~c2_1(a800)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)) | (~c2_1(a800)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(243,plain,
% 2.49/1.88 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a800) | (~c3_1(a800)) | (~c2_1(a800))) <=> (c0_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)) | (~c2_1(a800)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(244,plain,
% 2.49/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a800) | (~c3_1(a800)) | (~c2_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)) | (~c2_1(a800)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806))))),
% 2.49/1.88 inference(monotonicity,[status(thm)],[243])).
% 2.49/1.88 tff(245,plain,
% 2.49/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a800) | (~c3_1(a800)) | (~c2_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)) | (~c2_1(a800)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 2.49/1.88 inference(transitivity,[status(thm)],[244, 242])).
% 2.49/1.88 tff(246,plain,
% 2.49/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a800) | (~c3_1(a800)) | (~c2_1(a800)))),
% 2.49/1.88 inference(quant_inst,[status(thm)],[])).
% 2.49/1.88 tff(247,plain,
% 2.49/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)) | (~c2_1(a800)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[246, 245])).
% 2.49/1.88 tff(248,plain,
% 2.49/1.88 (~c2_1(a800)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[247, 151, 70, 69, 77, 68, 88, 241, 230, 207, 197])).
% 2.49/1.88 tff(249,plain,
% 2.49/1.88 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(250,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[249])).
% 2.49/1.88 tff(251,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(252,plain,
% 2.49/1.88 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(253,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[252])).
% 2.49/1.88 tff(254,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 2.49/1.88 tff(255,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[254, 253])).
% 2.49/1.88 tff(256,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[255, 251])).
% 2.49/1.88 tff(257,plain,(
% 2.49/1.88 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.49/1.88 inference(skolemize,[status(sab)],[256])).
% 2.49/1.88 tff(258,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[257, 250])).
% 2.49/1.88 tff(259,plain,
% 2.49/1.88 (((~hskp5) | (~c1_1(a800))) <=> ((~hskp5) | (~c1_1(a800)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(260,plain,
% 2.49/1.88 (((~c1_1(a800)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a800)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(261,axiom,((~c1_1(a800)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 2.49/1.88 tff(262,plain,
% 2.49/1.88 ((~hskp5) | (~c1_1(a800))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[261, 260])).
% 2.49/1.88 tff(263,plain,
% 2.49/1.88 ((~hskp5) | (~c1_1(a800))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[262, 259])).
% 2.49/1.88 tff(264,plain,
% 2.49/1.88 (~c1_1(a800)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[263, 224])).
% 2.49/1.88 tff(265,plain,
% 2.49/1.88 (^[U: $i] : refl((hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(266,plain,
% 2.49/1.88 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[265])).
% 2.49/1.88 tff(267,plain,
% 2.49/1.88 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(268,plain,
% 2.49/1.88 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp10) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp10))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp10) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp10) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(269,plain,
% 2.49/1.88 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp10) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[268])).
% 2.49/1.88 tff(270,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 2.49/1.88 tff(271,plain,
% 2.49/1.88 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[270, 269])).
% 2.49/1.88 tff(272,plain,
% 2.49/1.88 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[271, 267])).
% 2.49/1.88 tff(273,plain,(
% 2.49/1.88 ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.49/1.88 inference(skolemize,[status(sab)],[272])).
% 2.49/1.88 tff(274,plain,
% 2.49/1.88 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[273, 266])).
% 2.49/1.88 tff(275,assumption,(hskp1), introduced(assumption)).
% 2.49/1.88 tff(276,plain,
% 2.49/1.88 (((~hskp1) | (~c2_1(a794))) <=> ((~hskp1) | (~c2_1(a794)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(277,plain,
% 2.49/1.88 (((~c2_1(a794)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a794)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(278,axiom,((~c2_1(a794)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 2.49/1.88 tff(279,plain,
% 2.49/1.88 ((~hskp1) | (~c2_1(a794))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[278, 277])).
% 2.49/1.88 tff(280,plain,
% 2.49/1.88 ((~hskp1) | (~c2_1(a794))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[279, 276])).
% 2.49/1.88 tff(281,plain,
% 2.49/1.88 (~c2_1(a794)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[280, 275])).
% 2.49/1.88 tff(282,plain,
% 2.49/1.88 (((~hskp1) | c3_1(a794)) <=> ((~hskp1) | c3_1(a794))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(283,axiom,((~hskp1) | c3_1(a794)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 2.49/1.88 tff(284,plain,
% 2.49/1.88 ((~hskp1) | c3_1(a794)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[283, 282])).
% 2.49/1.88 tff(285,plain,
% 2.49/1.88 ((~hskp1) | c3_1(a794)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[284, 282])).
% 2.49/1.88 tff(286,plain,
% 2.49/1.88 ((~hskp1) | c3_1(a794)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[285, 282])).
% 2.49/1.88 tff(287,plain,
% 2.49/1.88 ((~hskp1) | c3_1(a794)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[286, 282])).
% 2.49/1.88 tff(288,plain,
% 2.49/1.88 ((~hskp1) | c3_1(a794)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[287, 282])).
% 2.49/1.88 tff(289,plain,
% 2.49/1.88 ((~hskp1) | c3_1(a794)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[288, 282])).
% 2.49/1.88 tff(290,plain,
% 2.49/1.88 ((~hskp1) | c3_1(a794)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[289, 282])).
% 2.49/1.88 tff(291,plain,
% 2.49/1.88 ((~hskp1) | c3_1(a794)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[290, 282])).
% 2.49/1.88 tff(292,plain,
% 2.49/1.88 (c3_1(a794)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[291, 275])).
% 2.49/1.88 tff(293,plain,
% 2.49/1.88 (((~hskp1) | (~c0_1(a794))) <=> ((~hskp1) | (~c0_1(a794)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(294,plain,
% 2.49/1.88 (((~c0_1(a794)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a794)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(295,axiom,((~c0_1(a794)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 2.49/1.88 tff(296,plain,
% 2.49/1.88 ((~hskp1) | (~c0_1(a794))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[295, 294])).
% 2.49/1.88 tff(297,plain,
% 2.49/1.88 ((~hskp1) | (~c0_1(a794))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[296, 293])).
% 2.49/1.88 tff(298,plain,
% 2.49/1.88 (~c0_1(a794)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[297, 275])).
% 2.49/1.88 tff(299,plain,
% 2.49/1.88 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(300,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[299])).
% 2.49/1.88 tff(301,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(302,plain,
% 2.49/1.88 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(303,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[302])).
% 2.49/1.88 tff(304,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 2.49/1.88 tff(305,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[304, 303])).
% 2.49/1.88 tff(306,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[305, 301])).
% 2.49/1.88 tff(307,plain,(
% 2.49/1.88 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.49/1.88 inference(skolemize,[status(sab)],[306])).
% 2.49/1.88 tff(308,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[307, 300])).
% 2.49/1.88 tff(309,assumption,(~c2_1(a833)), introduced(assumption)).
% 2.49/1.88 tff(310,assumption,(~c3_1(a833)), introduced(assumption)).
% 2.49/1.88 tff(311,plain,
% 2.49/1.88 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(312,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[311])).
% 2.49/1.88 tff(313,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(314,plain,
% 2.49/1.88 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(315,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[314])).
% 2.49/1.88 tff(316,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 2.49/1.88 tff(317,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[316, 315])).
% 2.49/1.88 tff(318,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[317, 313])).
% 2.49/1.88 tff(319,plain,(
% 2.49/1.88 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.49/1.88 inference(skolemize,[status(sab)],[318])).
% 2.49/1.88 tff(320,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[319, 312])).
% 2.49/1.88 tff(321,assumption,(~c0_1(a833)), introduced(assumption)).
% 2.49/1.88 tff(322,assumption,(~c1_1(a832)), introduced(assumption)).
% 2.49/1.88 tff(323,plain,
% 2.49/1.88 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(324,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[323])).
% 2.49/1.88 tff(325,plain,
% 2.49/1.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(326,plain,
% 2.49/1.88 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))))),
% 2.49/1.89 inference(bind,[status(th)],[])).
% 2.49/1.89 tff(327,plain,
% 2.49/1.89 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.49/1.89 inference(quant_intro,[status(thm)],[326])).
% 2.49/1.89 tff(328,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 2.49/1.89 tff(329,plain,
% 2.49/1.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[328, 327])).
% 2.49/1.89 tff(330,plain,
% 2.49/1.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[329, 325])).
% 2.49/1.89 tff(331,plain,(
% 2.49/1.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.49/1.89 inference(skolemize,[status(sab)],[330])).
% 2.49/1.89 tff(332,plain,
% 2.49/1.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[331, 324])).
% 2.49/1.89 tff(333,assumption,(~c1_1(a833)), introduced(assumption)).
% 2.49/1.89 tff(334,plain,
% 2.49/1.89 (((~hskp20) | c1_1(a833)) <=> ((~hskp20) | c1_1(a833))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(335,axiom,((~hskp20) | c1_1(a833)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 2.49/1.89 tff(336,plain,
% 2.49/1.89 ((~hskp20) | c1_1(a833)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[335, 334])).
% 2.49/1.89 tff(337,plain,
% 2.49/1.89 ((~hskp20) | c1_1(a833)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[336, 334])).
% 2.49/1.89 tff(338,plain,
% 2.49/1.89 ((~hskp20) | c1_1(a833)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[337, 334])).
% 2.49/1.89 tff(339,plain,
% 2.49/1.89 ((~hskp20) | c1_1(a833)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[338, 334])).
% 2.49/1.89 tff(340,plain,
% 2.49/1.89 ((~hskp20) | c1_1(a833)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[339, 334])).
% 2.49/1.89 tff(341,plain,
% 2.49/1.89 ((~hskp20) | c1_1(a833)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[340, 334])).
% 2.49/1.89 tff(342,plain,
% 2.49/1.89 ((~hskp20) | c1_1(a833)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[341, 334])).
% 2.49/1.89 tff(343,plain,
% 2.49/1.89 ((~hskp20) | c1_1(a833)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[342, 334])).
% 2.49/1.89 tff(344,plain,
% 2.49/1.89 (~hskp20),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[343, 333])).
% 2.49/1.89 tff(345,assumption,(~hskp30), introduced(assumption)).
% 2.49/1.89 tff(346,assumption,(~hskp20), introduced(assumption)).
% 2.49/1.89 tff(347,plain,
% 2.49/1.89 (^[U: $i] : refl((hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 2.49/1.89 inference(bind,[status(th)],[])).
% 2.49/1.89 tff(348,plain,
% 2.49/1.89 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.49/1.89 inference(quant_intro,[status(thm)],[347])).
% 2.49/1.89 tff(349,plain,
% 2.49/1.89 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(350,plain,
% 2.49/1.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) <=> (hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20) <=> ((hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp20))), rewrite(((hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 2.49/1.89 inference(bind,[status(th)],[])).
% 2.49/1.89 tff(351,plain,
% 2.49/1.89 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.49/1.89 inference(quant_intro,[status(thm)],[350])).
% 2.49/1.89 tff(352,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 2.49/1.89 tff(353,plain,
% 2.49/1.89 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[352, 351])).
% 2.49/1.89 tff(354,plain,
% 2.49/1.89 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[353, 349])).
% 2.49/1.89 tff(355,plain,(
% 2.49/1.89 ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.49/1.89 inference(skolemize,[status(sab)],[354])).
% 2.49/1.89 tff(356,plain,
% 2.49/1.89 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[355, 348])).
% 2.49/1.89 tff(357,assumption,(~hskp28), introduced(assumption)).
% 2.49/1.89 tff(358,assumption,(~c2_1(a867)), introduced(assumption)).
% 2.49/1.89 tff(359,plain,
% 2.49/1.89 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 2.49/1.89 inference(bind,[status(th)],[])).
% 2.49/1.89 tff(360,plain,
% 2.49/1.89 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.49/1.89 inference(quant_intro,[status(thm)],[359])).
% 2.49/1.89 tff(361,plain,
% 2.49/1.89 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(362,plain,
% 2.49/1.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 2.49/1.89 inference(bind,[status(th)],[])).
% 2.49/1.89 tff(363,plain,
% 2.49/1.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.49/1.89 inference(quant_intro,[status(thm)],[362])).
% 2.49/1.89 tff(364,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 2.49/1.89 tff(365,plain,
% 2.49/1.89 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[364, 363])).
% 2.49/1.89 tff(366,plain,
% 2.49/1.89 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[365, 361])).
% 2.49/1.89 tff(367,plain,(
% 2.49/1.89 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.49/1.89 inference(skolemize,[status(sab)],[366])).
% 2.49/1.89 tff(368,plain,
% 2.49/1.89 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[367, 360])).
% 2.49/1.89 tff(369,plain,
% 2.49/1.89 (hskp19),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[149, 345, 357])).
% 2.49/1.89 tff(370,plain,
% 2.49/1.89 (((~hskp19) | c2_1(a832)) <=> ((~hskp19) | c2_1(a832))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(371,axiom,((~hskp19) | c2_1(a832)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 2.49/1.89 tff(372,plain,
% 2.49/1.89 ((~hskp19) | c2_1(a832)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[371, 370])).
% 2.49/1.89 tff(373,plain,
% 2.49/1.89 ((~hskp19) | c2_1(a832)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[372, 370])).
% 2.49/1.89 tff(374,plain,
% 2.49/1.89 ((~hskp19) | c2_1(a832)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[373, 370])).
% 2.49/1.89 tff(375,plain,
% 2.49/1.89 ((~hskp19) | c2_1(a832)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[374, 370])).
% 2.49/1.89 tff(376,plain,
% 2.49/1.89 ((~hskp19) | c2_1(a832)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[375, 370])).
% 2.49/1.89 tff(377,plain,
% 2.49/1.89 ((~hskp19) | c2_1(a832)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[376, 370])).
% 2.49/1.89 tff(378,plain,
% 2.49/1.89 ((~hskp19) | c2_1(a832)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[377, 370])).
% 2.49/1.89 tff(379,plain,
% 2.49/1.89 ((~hskp19) | c2_1(a832)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[378, 370])).
% 2.49/1.89 tff(380,plain,
% 2.49/1.89 (c2_1(a832)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[379, 369])).
% 2.49/1.89 tff(381,plain,
% 2.49/1.89 (((~hskp19) | (~c3_1(a832))) <=> ((~hskp19) | (~c3_1(a832)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(382,plain,
% 2.49/1.89 (((~c3_1(a832)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a832)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(383,axiom,((~c3_1(a832)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 2.49/1.89 tff(384,plain,
% 2.49/1.89 ((~hskp19) | (~c3_1(a832))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[383, 382])).
% 2.49/1.89 tff(385,plain,
% 2.49/1.89 ((~hskp19) | (~c3_1(a832))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[384, 381])).
% 2.49/1.89 tff(386,plain,
% 2.49/1.89 (~c3_1(a832)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[385, 369])).
% 2.49/1.89 tff(387,plain,
% 2.49/1.89 (((~hskp19) | (~c1_1(a832))) <=> ((~hskp19) | (~c1_1(a832)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(388,plain,
% 2.49/1.89 (((~c1_1(a832)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a832)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(389,axiom,((~c1_1(a832)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 2.49/1.89 tff(390,plain,
% 2.49/1.89 ((~hskp19) | (~c1_1(a832))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[389, 388])).
% 2.49/1.89 tff(391,plain,
% 2.49/1.89 ((~hskp19) | (~c1_1(a832))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[390, 387])).
% 2.49/1.89 tff(392,plain,
% 2.49/1.89 (~c1_1(a832)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[391, 369])).
% 2.49/1.89 tff(393,plain,
% 2.49/1.89 (^[U: $i] : refl((hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))),
% 2.49/1.89 inference(bind,[status(th)],[])).
% 2.49/1.89 tff(394,plain,
% 2.49/1.89 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.49/1.89 inference(quant_intro,[status(thm)],[393])).
% 2.49/1.89 tff(395,plain,
% 2.49/1.89 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(396,plain,
% 2.49/1.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp27))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp28) <=> ((hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp28))), rewrite(((hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp28) <=> (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp28) <=> (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))))),
% 2.49/1.89 inference(bind,[status(th)],[])).
% 2.49/1.89 tff(397,plain,
% 2.49/1.89 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp28) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.49/1.89 inference(quant_intro,[status(thm)],[396])).
% 2.49/1.89 tff(398,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 2.49/1.89 tff(399,plain,
% 2.49/1.89 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[398, 397])).
% 2.49/1.89 tff(400,plain,
% 2.49/1.89 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[399, 395])).
% 2.49/1.89 tff(401,plain,(
% 2.49/1.89 ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.49/1.89 inference(skolemize,[status(sab)],[400])).
% 2.49/1.89 tff(402,plain,
% 2.49/1.89 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[401, 394])).
% 2.49/1.89 tff(403,assumption,(~hskp27), introduced(assumption)).
% 2.49/1.89 tff(404,plain,
% 2.49/1.89 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp27 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(405,plain,
% 2.49/1.89 ((hskp28 | hskp27 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832)) <=> (hskp28 | hskp27 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(406,plain,
% 2.49/1.89 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832)))),
% 2.49/1.89 inference(monotonicity,[status(thm)],[405])).
% 2.49/1.89 tff(407,plain,
% 2.49/1.89 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp27 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 2.49/1.89 inference(transitivity,[status(thm)],[406, 404])).
% 2.49/1.89 tff(408,plain,
% 2.49/1.89 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832))),
% 2.49/1.89 inference(quant_inst,[status(thm)],[])).
% 2.49/1.89 tff(409,plain,
% 2.49/1.89 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp27 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[408, 407])).
% 2.49/1.89 tff(410,plain,
% 2.49/1.89 (hskp27 | c0_1(a832)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[409, 151, 357, 322, 22, 402])).
% 2.49/1.89 tff(411,plain,
% 2.49/1.89 (c0_1(a832)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[410, 403])).
% 2.49/1.89 tff(412,plain,
% 2.49/1.89 ((hskp28 | hskp27 | hskp21) <=> (hskp28 | hskp27 | hskp21)),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(413,plain,
% 2.49/1.89 (((hskp27 | hskp21) | hskp28) <=> (hskp28 | hskp27 | hskp21)),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(414,plain,
% 2.49/1.89 ((hskp27 | hskp21) <=> (hskp27 | hskp21)),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(415,plain,
% 2.49/1.89 (((hskp27 | hskp21) | hskp28) <=> ((hskp27 | hskp21) | hskp28)),
% 2.49/1.89 inference(monotonicity,[status(thm)],[414])).
% 2.49/1.89 tff(416,plain,
% 2.49/1.89 (((hskp27 | hskp21) | hskp28) <=> (hskp28 | hskp27 | hskp21)),
% 2.49/1.89 inference(transitivity,[status(thm)],[415, 413])).
% 2.49/1.89 tff(417,axiom,((hskp27 | hskp21) | hskp28), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 2.49/1.89 tff(418,plain,
% 2.49/1.89 (hskp28 | hskp27 | hskp21),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[417, 416])).
% 2.49/1.89 tff(419,plain,
% 2.49/1.89 (hskp28 | hskp27 | hskp21),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[418, 412])).
% 2.49/1.89 tff(420,plain,
% 2.49/1.89 (hskp28 | hskp27 | hskp21),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[419, 412])).
% 2.49/1.89 tff(421,plain,
% 2.49/1.89 (hskp28 | hskp27 | hskp21),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[420, 412])).
% 2.49/1.89 tff(422,plain,
% 2.49/1.89 (hskp28 | hskp27 | hskp21),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[421, 412])).
% 2.49/1.89 tff(423,plain,
% 2.49/1.89 (hskp28 | hskp27 | hskp21),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[422, 412])).
% 2.49/1.89 tff(424,plain,
% 2.49/1.89 (hskp28 | hskp27 | hskp21),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[423, 412])).
% 2.49/1.89 tff(425,plain,
% 2.49/1.89 (hskp28 | hskp27 | hskp21),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[424, 412])).
% 2.49/1.89 tff(426,plain,
% 2.49/1.89 (hskp21),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[425, 403, 357])).
% 2.49/1.89 tff(427,plain,
% 2.49/1.89 (((~hskp21) | (~c2_1(a838))) <=> ((~hskp21) | (~c2_1(a838)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(428,plain,
% 2.49/1.89 (((~c2_1(a838)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a838)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(429,axiom,((~c2_1(a838)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 2.49/1.89 tff(430,plain,
% 2.49/1.89 ((~hskp21) | (~c2_1(a838))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[429, 428])).
% 2.49/1.89 tff(431,plain,
% 2.49/1.89 ((~hskp21) | (~c2_1(a838))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[430, 427])).
% 2.49/1.89 tff(432,plain,
% 2.49/1.89 (~c2_1(a838)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[431, 426])).
% 2.49/1.89 tff(433,assumption,(c2_1(a832)), introduced(assumption)).
% 2.49/1.89 tff(434,plain,
% 2.49/1.89 (((~hskp21) | c3_1(a838)) <=> ((~hskp21) | c3_1(a838))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(435,axiom,((~hskp21) | c3_1(a838)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 2.49/1.89 tff(436,plain,
% 2.49/1.89 ((~hskp21) | c3_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[435, 434])).
% 2.49/1.89 tff(437,plain,
% 2.49/1.89 ((~hskp21) | c3_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[436, 434])).
% 2.49/1.89 tff(438,plain,
% 2.49/1.89 ((~hskp21) | c3_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[437, 434])).
% 2.49/1.89 tff(439,plain,
% 2.49/1.89 ((~hskp21) | c3_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[438, 434])).
% 2.49/1.89 tff(440,plain,
% 2.49/1.89 ((~hskp21) | c3_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[439, 434])).
% 2.49/1.89 tff(441,plain,
% 2.49/1.89 ((~hskp21) | c3_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[440, 434])).
% 2.49/1.89 tff(442,plain,
% 2.49/1.89 ((~hskp21) | c3_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[441, 434])).
% 2.49/1.89 tff(443,plain,
% 2.49/1.89 ((~hskp21) | c3_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[442, 434])).
% 2.49/1.89 tff(444,plain,
% 2.49/1.89 (c3_1(a838)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[443, 426])).
% 2.49/1.89 tff(445,plain,
% 2.49/1.89 (((~hskp21) | c0_1(a838)) <=> ((~hskp21) | c0_1(a838))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(446,axiom,((~hskp21) | c0_1(a838)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 2.49/1.89 tff(447,plain,
% 2.49/1.89 ((~hskp21) | c0_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[446, 445])).
% 2.49/1.89 tff(448,plain,
% 2.49/1.89 ((~hskp21) | c0_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[447, 445])).
% 2.49/1.89 tff(449,plain,
% 2.49/1.89 ((~hskp21) | c0_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[448, 445])).
% 2.49/1.89 tff(450,plain,
% 2.49/1.89 ((~hskp21) | c0_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[449, 445])).
% 2.49/1.89 tff(451,plain,
% 2.49/1.89 ((~hskp21) | c0_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[450, 445])).
% 2.49/1.89 tff(452,plain,
% 2.49/1.89 ((~hskp21) | c0_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[451, 445])).
% 2.49/1.89 tff(453,plain,
% 2.49/1.89 ((~hskp21) | c0_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[452, 445])).
% 2.49/1.89 tff(454,plain,
% 2.49/1.89 ((~hskp21) | c0_1(a838)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[453, 445])).
% 2.49/1.89 tff(455,plain,
% 2.49/1.89 (c0_1(a838)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[454, 426])).
% 2.49/1.89 tff(456,assumption,(c0_1(a832)), introduced(assumption)).
% 2.49/1.89 tff(457,assumption,(hskp8), introduced(assumption)).
% 2.49/1.89 tff(458,plain,
% 2.49/1.89 (((~hskp8) | (~c3_1(a805))) <=> ((~hskp8) | (~c3_1(a805)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(459,plain,
% 2.49/1.89 (((~c3_1(a805)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a805)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(460,axiom,((~c3_1(a805)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 2.49/1.89 tff(461,plain,
% 2.49/1.89 ((~hskp8) | (~c3_1(a805))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[460, 459])).
% 2.49/1.89 tff(462,plain,
% 2.49/1.89 ((~hskp8) | (~c3_1(a805))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[461, 458])).
% 2.49/1.89 tff(463,plain,
% 2.49/1.89 (~c3_1(a805)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[462, 457])).
% 2.49/1.89 tff(464,plain,
% 2.49/1.89 (((~hskp8) | (~c2_1(a805))) <=> ((~hskp8) | (~c2_1(a805)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(465,plain,
% 2.49/1.89 (((~c2_1(a805)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a805)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(466,axiom,((~c2_1(a805)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 2.49/1.89 tff(467,plain,
% 2.49/1.89 ((~hskp8) | (~c2_1(a805))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[466, 465])).
% 2.49/1.89 tff(468,plain,
% 2.49/1.89 ((~hskp8) | (~c2_1(a805))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[467, 464])).
% 2.49/1.89 tff(469,plain,
% 2.49/1.89 (~c2_1(a805)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[468, 457])).
% 2.49/1.89 tff(470,assumption,(~c2_1(a838)), introduced(assumption)).
% 2.49/1.89 tff(471,plain,
% 2.49/1.89 (((~hskp8) | c1_1(a805)) <=> ((~hskp8) | c1_1(a805))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(472,axiom,((~hskp8) | c1_1(a805)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 2.49/1.89 tff(473,plain,
% 2.49/1.89 ((~hskp8) | c1_1(a805)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[472, 471])).
% 2.49/1.89 tff(474,plain,
% 2.49/1.89 ((~hskp8) | c1_1(a805)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[473, 471])).
% 2.49/1.89 tff(475,plain,
% 2.49/1.89 ((~hskp8) | c1_1(a805)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[474, 471])).
% 2.49/1.89 tff(476,plain,
% 2.49/1.89 ((~hskp8) | c1_1(a805)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[475, 471])).
% 2.49/1.89 tff(477,plain,
% 2.49/1.89 ((~hskp8) | c1_1(a805)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[476, 471])).
% 2.49/1.89 tff(478,plain,
% 2.49/1.89 ((~hskp8) | c1_1(a805)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[477, 471])).
% 2.49/1.89 tff(479,plain,
% 2.49/1.89 ((~hskp8) | c1_1(a805)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[478, 471])).
% 2.49/1.89 tff(480,plain,
% 2.49/1.89 ((~hskp8) | c1_1(a805)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[479, 471])).
% 2.49/1.89 tff(481,plain,
% 2.49/1.89 (c1_1(a805)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[480, 457])).
% 2.49/1.89 tff(482,assumption,(c3_1(a838)), introduced(assumption)).
% 2.49/1.89 tff(483,assumption,(c0_1(a838)), introduced(assumption)).
% 2.49/1.89 tff(484,plain,
% 2.49/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c3_1(a832) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c3_1(a832) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(485,plain,
% 2.49/1.89 (((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c2_1(a838) | c3_1(a832) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(486,plain,
% 2.49/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c3_1(a832) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 2.49/1.89 inference(monotonicity,[status(thm)],[485])).
% 2.49/1.89 tff(487,plain,
% 2.49/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c3_1(a832) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.49/1.89 inference(transitivity,[status(thm)],[486, 484])).
% 2.49/1.89 tff(488,plain,
% 2.49/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 2.49/1.89 inference(quant_inst,[status(thm)],[])).
% 2.49/1.89 tff(489,plain,
% 2.49/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c3_1(a832) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a838)) | (~c0_1(a838))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[488, 487])).
% 2.49/1.89 tff(490,plain,
% 2.49/1.89 ($false),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[489, 151, 483, 482, 433, 481, 470, 22, 469, 463, 332, 456])).
% 2.49/1.89 tff(491,plain,((~hskp8) | (~c0_1(a838)) | (~c3_1(a838)) | (~c2_1(a832)) | c2_1(a838) | c3_1(a832) | (~c0_1(a832))), inference(lemma,lemma(discharge,[]))).
% 2.49/1.89 tff(492,plain,
% 2.49/1.89 (~hskp8),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[491, 455, 444, 433, 432, 22, 411])).
% 2.49/1.89 tff(493,plain,
% 2.49/1.89 ((hskp28 | hskp10 | hskp8) <=> (hskp28 | hskp10 | hskp8)),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(494,plain,
% 2.49/1.89 (((hskp28 | hskp8) | hskp10) <=> (hskp28 | hskp10 | hskp8)),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(495,axiom,((hskp28 | hskp8) | hskp10), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 2.49/1.89 tff(496,plain,
% 2.49/1.89 (hskp28 | hskp10 | hskp8),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[495, 494])).
% 2.49/1.89 tff(497,plain,
% 2.49/1.89 (hskp28 | hskp10 | hskp8),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[496, 493])).
% 2.59/1.90 tff(498,plain,
% 2.59/1.90 (hskp28 | hskp10 | hskp8),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[497, 493])).
% 2.59/1.90 tff(499,plain,
% 2.59/1.90 (hskp28 | hskp10 | hskp8),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[498, 493])).
% 2.59/1.90 tff(500,plain,
% 2.59/1.90 (hskp28 | hskp10 | hskp8),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[499, 493])).
% 2.59/1.90 tff(501,plain,
% 2.59/1.90 (hskp28 | hskp10 | hskp8),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[500, 493])).
% 2.59/1.90 tff(502,plain,
% 2.59/1.90 (hskp28 | hskp10 | hskp8),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[501, 493])).
% 2.59/1.90 tff(503,plain,
% 2.59/1.90 (hskp28 | hskp10 | hskp8),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[502, 493])).
% 2.59/1.90 tff(504,plain,
% 2.59/1.90 (hskp10),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[503, 492, 357])).
% 2.59/1.90 tff(505,plain,
% 2.59/1.90 (((~hskp10) | (~c3_1(a807))) <=> ((~hskp10) | (~c3_1(a807)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(506,plain,
% 2.59/1.90 (((~c3_1(a807)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a807)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(507,axiom,((~c3_1(a807)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 2.59/1.90 tff(508,plain,
% 2.59/1.90 ((~hskp10) | (~c3_1(a807))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[507, 506])).
% 2.59/1.90 tff(509,plain,
% 2.59/1.90 ((~hskp10) | (~c3_1(a807))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[508, 505])).
% 2.59/1.90 tff(510,plain,
% 2.59/1.90 (~c3_1(a807)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[509, 504])).
% 2.59/1.90 tff(511,plain,
% 2.59/1.90 (((~hskp10) | (~c0_1(a807))) <=> ((~hskp10) | (~c0_1(a807)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(512,plain,
% 2.59/1.90 (((~c0_1(a807)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a807)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(513,axiom,((~c0_1(a807)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 2.59/1.90 tff(514,plain,
% 2.59/1.90 ((~hskp10) | (~c0_1(a807))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[513, 512])).
% 2.59/1.90 tff(515,plain,
% 2.59/1.90 ((~hskp10) | (~c0_1(a807))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[514, 511])).
% 2.59/1.90 tff(516,plain,
% 2.59/1.90 (~c0_1(a807)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[515, 504])).
% 2.59/1.90 tff(517,plain,
% 2.59/1.90 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | c0_1(a807) | c3_1(a807) | (~ndr1_0) | c1_1(a807))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp27 | c0_1(a807) | c3_1(a807) | (~ndr1_0) | c1_1(a807))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(518,plain,
% 2.59/1.90 ((hskp28 | hskp27 | (~ndr1_0) | c1_1(a807) | c0_1(a807) | c3_1(a807)) <=> (hskp28 | hskp27 | c0_1(a807) | c3_1(a807) | (~ndr1_0) | c1_1(a807))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(519,plain,
% 2.59/1.90 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | (~ndr1_0) | c1_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | c0_1(a807) | c3_1(a807) | (~ndr1_0) | c1_1(a807)))),
% 2.59/1.90 inference(monotonicity,[status(thm)],[518])).
% 2.59/1.90 tff(520,plain,
% 2.59/1.90 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | (~ndr1_0) | c1_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp27 | c0_1(a807) | c3_1(a807) | (~ndr1_0) | c1_1(a807))),
% 2.59/1.90 inference(transitivity,[status(thm)],[519, 517])).
% 2.59/1.90 tff(521,plain,
% 2.59/1.90 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | (~ndr1_0) | c1_1(a807) | c0_1(a807) | c3_1(a807))),
% 2.59/1.90 inference(quant_inst,[status(thm)],[])).
% 2.59/1.90 tff(522,plain,
% 2.59/1.90 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp27 | c0_1(a807) | c3_1(a807) | (~ndr1_0) | c1_1(a807)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[521, 520])).
% 2.59/1.90 tff(523,plain,
% 2.59/1.90 (c1_1(a807)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[522, 151, 357, 403, 516, 510, 402])).
% 2.59/1.90 tff(524,plain,
% 2.59/1.90 (^[U: $i] : refl((hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 2.59/1.90 inference(bind,[status(th)],[])).
% 2.59/1.90 tff(525,plain,
% 2.59/1.90 (![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.90 inference(quant_intro,[status(thm)],[524])).
% 2.59/1.90 tff(526,plain,
% 2.59/1.90 (![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(527,plain,
% 2.59/1.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp3) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp3))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp3) <=> (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 2.59/1.90 inference(bind,[status(th)],[])).
% 2.59/1.90 tff(528,plain,
% 2.59/1.90 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp3) <=> ![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.90 inference(quant_intro,[status(thm)],[527])).
% 2.59/1.90 tff(529,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 2.59/1.90 tff(530,plain,
% 2.59/1.90 (![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[529, 528])).
% 2.59/1.90 tff(531,plain,
% 2.59/1.90 (![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[530, 526])).
% 2.59/1.90 tff(532,plain,(
% 2.59/1.90 ![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.90 inference(skolemize,[status(sab)],[531])).
% 2.59/1.90 tff(533,plain,
% 2.59/1.90 (![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[532, 525])).
% 2.59/1.90 tff(534,plain,
% 2.59/1.90 (((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp3 | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp3 | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(535,plain,
% 2.59/1.90 ((hskp27 | hskp3 | (~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832))) <=> (hskp27 | hskp3 | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(536,plain,
% 2.59/1.90 (((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp3 | (~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp3 | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832))))),
% 2.59/1.90 inference(monotonicity,[status(thm)],[535])).
% 2.59/1.90 tff(537,plain,
% 2.59/1.90 (((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp3 | (~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp3 | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.59/1.90 inference(transitivity,[status(thm)],[536, 534])).
% 2.59/1.90 tff(538,plain,
% 2.59/1.90 ((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp3 | (~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.59/1.90 inference(quant_inst,[status(thm)],[])).
% 2.59/1.90 tff(539,plain,
% 2.59/1.90 ((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp3 | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[538, 537])).
% 2.59/1.90 tff(540,plain,
% 2.59/1.90 (hskp27 | hskp3 | (~c0_1(a832))),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[539, 151, 433, 22, 533])).
% 2.59/1.90 tff(541,plain,
% 2.59/1.90 (hskp3),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[540, 411, 403])).
% 2.59/1.90 tff(542,plain,
% 2.59/1.90 (((~hskp3) | (~c3_1(a798))) <=> ((~hskp3) | (~c3_1(a798)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(543,plain,
% 2.59/1.90 (((~c3_1(a798)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a798)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(544,axiom,((~c3_1(a798)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 2.59/1.90 tff(545,plain,
% 2.59/1.90 ((~hskp3) | (~c3_1(a798))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[544, 543])).
% 2.59/1.90 tff(546,plain,
% 2.59/1.90 ((~hskp3) | (~c3_1(a798))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[545, 542])).
% 2.59/1.90 tff(547,plain,
% 2.59/1.90 (~c3_1(a798)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[546, 541])).
% 2.59/1.90 tff(548,plain,
% 2.59/1.90 (((~hskp10) | (~c2_1(a807))) <=> ((~hskp10) | (~c2_1(a807)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(549,plain,
% 2.59/1.90 (((~c2_1(a807)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a807)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(550,axiom,((~c2_1(a807)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 2.59/1.90 tff(551,plain,
% 2.59/1.90 ((~hskp10) | (~c2_1(a807))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[550, 549])).
% 2.59/1.90 tff(552,plain,
% 2.59/1.90 ((~hskp10) | (~c2_1(a807))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[551, 548])).
% 2.59/1.90 tff(553,plain,
% 2.59/1.90 (~c2_1(a807)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[552, 504])).
% 2.59/1.90 tff(554,plain,
% 2.59/1.90 (((~hskp3) | c2_1(a798)) <=> ((~hskp3) | c2_1(a798))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(555,axiom,((~hskp3) | c2_1(a798)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 2.59/1.90 tff(556,plain,
% 2.59/1.90 ((~hskp3) | c2_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[555, 554])).
% 2.59/1.90 tff(557,plain,
% 2.59/1.90 ((~hskp3) | c2_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[556, 554])).
% 2.59/1.90 tff(558,plain,
% 2.59/1.90 ((~hskp3) | c2_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[557, 554])).
% 2.59/1.90 tff(559,plain,
% 2.59/1.90 ((~hskp3) | c2_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[558, 554])).
% 2.59/1.90 tff(560,plain,
% 2.59/1.90 ((~hskp3) | c2_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[559, 554])).
% 2.59/1.90 tff(561,plain,
% 2.59/1.90 ((~hskp3) | c2_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[560, 554])).
% 2.59/1.90 tff(562,plain,
% 2.59/1.90 ((~hskp3) | c2_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[561, 554])).
% 2.59/1.90 tff(563,plain,
% 2.59/1.90 ((~hskp3) | c2_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[562, 554])).
% 2.59/1.90 tff(564,plain,
% 2.59/1.90 (c2_1(a798)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[563, 541])).
% 2.59/1.90 tff(565,plain,
% 2.59/1.90 (((~hskp3) | c0_1(a798)) <=> ((~hskp3) | c0_1(a798))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(566,axiom,((~hskp3) | c0_1(a798)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 2.59/1.90 tff(567,plain,
% 2.59/1.90 ((~hskp3) | c0_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[566, 565])).
% 2.59/1.90 tff(568,plain,
% 2.59/1.90 ((~hskp3) | c0_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[567, 565])).
% 2.59/1.90 tff(569,plain,
% 2.59/1.90 ((~hskp3) | c0_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[568, 565])).
% 2.59/1.90 tff(570,plain,
% 2.59/1.90 ((~hskp3) | c0_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[569, 565])).
% 2.59/1.90 tff(571,plain,
% 2.59/1.90 ((~hskp3) | c0_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[570, 565])).
% 2.59/1.90 tff(572,plain,
% 2.59/1.90 ((~hskp3) | c0_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[571, 565])).
% 2.59/1.90 tff(573,plain,
% 2.59/1.90 ((~hskp3) | c0_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[572, 565])).
% 2.59/1.90 tff(574,plain,
% 2.59/1.90 ((~hskp3) | c0_1(a798)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[573, 565])).
% 2.59/1.90 tff(575,plain,
% 2.59/1.90 (c0_1(a798)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[574, 541])).
% 2.59/1.90 tff(576,plain,
% 2.59/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c2_1(a807) | c3_1(a807) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a807)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a807) | c3_1(a807) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a807)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(577,plain,
% 2.59/1.90 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a807) | c3_1(a807) | (~c1_1(a807))) <=> (c2_1(a838) | c2_1(a807) | c3_1(a807) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a807)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(578,plain,
% 2.59/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a807) | c3_1(a807) | (~c1_1(a807)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c2_1(a807) | c3_1(a807) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a807)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 2.59/1.90 inference(monotonicity,[status(thm)],[577])).
% 2.59/1.90 tff(579,plain,
% 2.59/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a807) | c3_1(a807) | (~c1_1(a807)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a807) | c3_1(a807) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a807)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.59/1.90 inference(transitivity,[status(thm)],[578, 576])).
% 2.59/1.90 tff(580,plain,
% 2.59/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a807) | c3_1(a807) | (~c1_1(a807)))),
% 2.59/1.90 inference(quant_inst,[status(thm)],[])).
% 2.59/1.90 tff(581,plain,
% 2.59/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a807) | c3_1(a807) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a807)) | (~c3_1(a838)) | (~c0_1(a838))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[580, 579])).
% 2.59/1.90 tff(582,plain,
% 2.59/1.90 ($false),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[581, 151, 455, 444, 575, 564, 432, 553, 510, 547, 332, 523])).
% 2.59/1.90 tff(583,plain,(hskp27 | hskp28 | (~c2_1(a832)) | c3_1(a832) | c1_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.59/1.90 tff(584,plain,
% 2.59/1.90 (hskp27),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[583, 380, 357, 386, 392])).
% 2.59/1.90 tff(585,plain,
% 2.59/1.90 (((~hskp27) | c3_1(a796)) <=> ((~hskp27) | c3_1(a796))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(586,axiom,((~hskp27) | c3_1(a796)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 2.59/1.90 tff(587,plain,
% 2.59/1.90 ((~hskp27) | c3_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[586, 585])).
% 2.59/1.90 tff(588,plain,
% 2.59/1.90 ((~hskp27) | c3_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[587, 585])).
% 2.59/1.90 tff(589,plain,
% 2.59/1.90 ((~hskp27) | c3_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[588, 585])).
% 2.59/1.90 tff(590,plain,
% 2.59/1.90 ((~hskp27) | c3_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[589, 585])).
% 2.59/1.90 tff(591,plain,
% 2.59/1.90 ((~hskp27) | c3_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[590, 585])).
% 2.59/1.90 tff(592,plain,
% 2.59/1.90 ((~hskp27) | c3_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[591, 585])).
% 2.59/1.90 tff(593,plain,
% 2.59/1.90 ((~hskp27) | c3_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[592, 585])).
% 2.59/1.90 tff(594,plain,
% 2.59/1.90 ((~hskp27) | c3_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[593, 585])).
% 2.59/1.90 tff(595,plain,
% 2.59/1.90 (c3_1(a796)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[594, 584])).
% 2.59/1.90 tff(596,plain,
% 2.59/1.90 (((~hskp27) | c2_1(a796)) <=> ((~hskp27) | c2_1(a796))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(597,axiom,((~hskp27) | c2_1(a796)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 2.59/1.90 tff(598,plain,
% 2.59/1.90 ((~hskp27) | c2_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[597, 596])).
% 2.59/1.90 tff(599,plain,
% 2.59/1.90 ((~hskp27) | c2_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[598, 596])).
% 2.59/1.90 tff(600,plain,
% 2.59/1.90 ((~hskp27) | c2_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[599, 596])).
% 2.59/1.90 tff(601,plain,
% 2.59/1.90 ((~hskp27) | c2_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[600, 596])).
% 2.59/1.90 tff(602,plain,
% 2.59/1.90 ((~hskp27) | c2_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[601, 596])).
% 2.59/1.90 tff(603,plain,
% 2.59/1.90 ((~hskp27) | c2_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[602, 596])).
% 2.59/1.90 tff(604,plain,
% 2.59/1.90 ((~hskp27) | c2_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[603, 596])).
% 2.59/1.90 tff(605,plain,
% 2.59/1.90 ((~hskp27) | c2_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[604, 596])).
% 2.59/1.90 tff(606,plain,
% 2.59/1.90 (c2_1(a796)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[605, 584])).
% 2.59/1.90 tff(607,plain,
% 2.59/1.90 (((~hskp27) | c0_1(a796)) <=> ((~hskp27) | c0_1(a796))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(608,axiom,((~hskp27) | c0_1(a796)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 2.59/1.90 tff(609,plain,
% 2.59/1.90 ((~hskp27) | c0_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[608, 607])).
% 2.59/1.90 tff(610,plain,
% 2.59/1.90 ((~hskp27) | c0_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[609, 607])).
% 2.59/1.90 tff(611,plain,
% 2.59/1.90 ((~hskp27) | c0_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[610, 607])).
% 2.59/1.90 tff(612,plain,
% 2.59/1.90 ((~hskp27) | c0_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[611, 607])).
% 2.59/1.90 tff(613,plain,
% 2.59/1.90 ((~hskp27) | c0_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[612, 607])).
% 2.59/1.90 tff(614,plain,
% 2.59/1.90 ((~hskp27) | c0_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[613, 607])).
% 2.59/1.90 tff(615,plain,
% 2.59/1.90 ((~hskp27) | c0_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[614, 607])).
% 2.59/1.90 tff(616,plain,
% 2.59/1.90 ((~hskp27) | c0_1(a796)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[615, 607])).
% 2.59/1.90 tff(617,plain,
% 2.59/1.90 (c0_1(a796)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[616, 584])).
% 2.59/1.90 tff(618,plain,
% 2.59/1.90 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(619,plain,
% 2.59/1.90 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)))),
% 2.59/1.90 inference(quant_inst,[status(thm)],[])).
% 2.59/1.90 tff(620,plain,
% 2.59/1.90 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[619, 618])).
% 2.59/1.90 tff(621,plain,
% 2.59/1.90 (hskp20),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[620, 345, 151, 617, 606, 595, 356])).
% 2.59/1.90 tff(622,plain,
% 2.59/1.90 (((~hskp20) | (~c2_1(a833))) <=> ((~hskp20) | (~c2_1(a833)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(623,plain,
% 2.59/1.90 (((~c2_1(a833)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a833)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(624,axiom,((~c2_1(a833)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 2.59/1.90 tff(625,plain,
% 2.59/1.90 ((~hskp20) | (~c2_1(a833))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[624, 623])).
% 2.59/1.90 tff(626,plain,
% 2.59/1.90 ((~hskp20) | (~c2_1(a833))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[625, 622])).
% 2.59/1.90 tff(627,plain,
% 2.59/1.90 (~c2_1(a833)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[626, 621])).
% 2.59/1.90 tff(628,plain,
% 2.59/1.90 (((~hskp20) | (~c0_1(a833))) <=> ((~hskp20) | (~c0_1(a833)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(629,plain,
% 2.59/1.90 (((~c0_1(a833)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a833)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(630,axiom,((~c0_1(a833)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 2.59/1.90 tff(631,plain,
% 2.59/1.90 ((~hskp20) | (~c0_1(a833))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[630, 629])).
% 2.59/1.90 tff(632,plain,
% 2.59/1.90 ((~hskp20) | (~c0_1(a833))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[631, 628])).
% 2.59/1.90 tff(633,plain,
% 2.59/1.90 (~c0_1(a833)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[632, 621])).
% 2.59/1.90 tff(634,plain,
% 2.59/1.90 (c1_1(a833)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[343, 621])).
% 2.59/1.90 tff(635,plain,
% 2.59/1.90 (hskp27),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[583, 433, 357, 22, 322])).
% 2.59/1.90 tff(636,plain,
% 2.59/1.90 (c0_1(a796)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[616, 635])).
% 2.59/1.90 tff(637,plain,
% 2.59/1.90 (c3_1(a796)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[594, 635])).
% 2.59/1.90 tff(638,plain,
% 2.59/1.90 (c2_1(a796)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[605, 635])).
% 2.59/1.90 tff(639,assumption,(c1_1(a833)), introduced(assumption)).
% 2.59/1.90 tff(640,assumption,(~c0_1(a838)), introduced(assumption)).
% 2.59/1.90 tff(641,plain,
% 2.59/1.90 (~hskp21),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[454, 640])).
% 2.59/1.90 tff(642,plain,
% 2.59/1.90 (^[U: $i] : refl((hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 2.59/1.90 inference(bind,[status(th)],[])).
% 2.59/1.90 tff(643,plain,
% 2.59/1.90 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.59/1.90 inference(quant_intro,[status(thm)],[642])).
% 2.59/1.90 tff(644,plain,
% 2.59/1.90 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(645,plain,
% 2.59/1.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp21) <=> ((hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21))), rewrite(((hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21) <=> (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp21) <=> (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 2.59/1.90 inference(bind,[status(th)],[])).
% 2.59/1.90 tff(646,plain,
% 2.59/1.90 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp21) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.59/1.90 inference(quant_intro,[status(thm)],[645])).
% 2.59/1.90 tff(647,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 2.59/1.90 tff(648,plain,
% 2.59/1.90 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[647, 646])).
% 2.59/1.90 tff(649,plain,
% 2.59/1.90 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[648, 644])).
% 2.59/1.90 tff(650,plain,(
% 2.59/1.90 ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.59/1.90 inference(skolemize,[status(sab)],[649])).
% 2.59/1.90 tff(651,plain,
% 2.59/1.90 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[650, 643])).
% 2.59/1.90 tff(652,plain,
% 2.59/1.90 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(653,plain,
% 2.59/1.90 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832))) <=> (hskp21 | hskp0 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(654,plain,
% 2.59/1.90 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832))))),
% 2.59/1.90 inference(monotonicity,[status(thm)],[653])).
% 2.59/1.90 tff(655,plain,
% 2.59/1.90 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)))),
% 2.59/1.90 inference(transitivity,[status(thm)],[654, 652])).
% 2.59/1.90 tff(656,plain,
% 2.59/1.90 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)))),
% 2.59/1.90 inference(quant_inst,[status(thm)],[])).
% 2.59/1.90 tff(657,plain,
% 2.59/1.90 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832))),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[656, 655])).
% 2.59/1.90 tff(658,plain,
% 2.59/1.90 (hskp21 | hskp0),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[657, 151, 433, 322, 22, 651])).
% 2.59/1.90 tff(659,plain,
% 2.59/1.90 (hskp0),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[658, 641])).
% 2.59/1.90 tff(660,plain,
% 2.59/1.90 (((~hskp0) | c2_1(a793)) <=> ((~hskp0) | c2_1(a793))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(661,axiom,((~hskp0) | c2_1(a793)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 2.59/1.90 tff(662,plain,
% 2.59/1.90 ((~hskp0) | c2_1(a793)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[661, 660])).
% 2.59/1.90 tff(663,plain,
% 2.59/1.90 ((~hskp0) | c2_1(a793)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[662, 660])).
% 2.59/1.90 tff(664,plain,
% 2.59/1.90 ((~hskp0) | c2_1(a793)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[663, 660])).
% 2.59/1.90 tff(665,plain,
% 2.59/1.90 ((~hskp0) | c2_1(a793)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[664, 660])).
% 2.59/1.90 tff(666,plain,
% 2.59/1.90 ((~hskp0) | c2_1(a793)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[665, 660])).
% 2.59/1.90 tff(667,plain,
% 2.59/1.90 ((~hskp0) | c2_1(a793)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[666, 660])).
% 2.59/1.90 tff(668,plain,
% 2.59/1.90 ((~hskp0) | c2_1(a793)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[667, 660])).
% 2.59/1.90 tff(669,plain,
% 2.59/1.90 ((~hskp0) | c2_1(a793)),
% 2.59/1.90 inference(modus_ponens,[status(thm)],[668, 660])).
% 2.59/1.90 tff(670,plain,
% 2.59/1.90 (c2_1(a793)),
% 2.59/1.90 inference(unit_resolution,[status(thm)],[669, 659])).
% 2.59/1.90 tff(671,plain,
% 2.59/1.90 (((~hskp0) | (~c1_1(a793))) <=> ((~hskp0) | (~c1_1(a793)))),
% 2.59/1.90 inference(rewrite,[status(thm)],[])).
% 2.59/1.90 tff(672,plain,
% 2.59/1.90 (((~c1_1(a793)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a793)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(673,axiom,((~c1_1(a793)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 2.59/1.91 tff(674,plain,
% 2.59/1.91 ((~hskp0) | (~c1_1(a793))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[673, 672])).
% 2.59/1.91 tff(675,plain,
% 2.59/1.91 ((~hskp0) | (~c1_1(a793))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[674, 671])).
% 2.59/1.91 tff(676,plain,
% 2.59/1.91 (~c1_1(a793)),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[675, 659])).
% 2.59/1.91 tff(677,plain,
% 2.59/1.91 (((~hskp0) | c0_1(a793)) <=> ((~hskp0) | c0_1(a793))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(678,axiom,((~hskp0) | c0_1(a793)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 2.59/1.91 tff(679,plain,
% 2.59/1.91 ((~hskp0) | c0_1(a793)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[678, 677])).
% 2.59/1.91 tff(680,plain,
% 2.59/1.91 ((~hskp0) | c0_1(a793)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[679, 677])).
% 2.59/1.91 tff(681,plain,
% 2.59/1.91 ((~hskp0) | c0_1(a793)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[680, 677])).
% 2.59/1.91 tff(682,plain,
% 2.59/1.91 ((~hskp0) | c0_1(a793)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[681, 677])).
% 2.59/1.91 tff(683,plain,
% 2.59/1.91 ((~hskp0) | c0_1(a793)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[682, 677])).
% 2.59/1.91 tff(684,plain,
% 2.59/1.91 ((~hskp0) | c0_1(a793)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[683, 677])).
% 2.59/1.91 tff(685,plain,
% 2.59/1.91 ((~hskp0) | c0_1(a793)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[684, 677])).
% 2.59/1.91 tff(686,plain,
% 2.59/1.91 ((~hskp0) | c0_1(a793)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[685, 677])).
% 2.59/1.91 tff(687,plain,
% 2.59/1.91 (c0_1(a793)),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[686, 659])).
% 2.59/1.91 tff(688,assumption,(c2_1(a796)), introduced(assumption)).
% 2.59/1.91 tff(689,assumption,(c2_1(a793)), introduced(assumption)).
% 2.59/1.91 tff(690,assumption,(c0_1(a796)), introduced(assumption)).
% 2.59/1.91 tff(691,assumption,(~c1_1(a793)), introduced(assumption)).
% 2.59/1.91 tff(692,assumption,(c0_1(a793)), introduced(assumption)).
% 2.59/1.91 tff(693,assumption,(c3_1(a796)), introduced(assumption)).
% 2.59/1.91 tff(694,plain,
% 2.59/1.91 (^[U: $i] : refl((hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))),
% 2.59/1.91 inference(bind,[status(th)],[])).
% 2.59/1.91 tff(695,plain,
% 2.59/1.91 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.59/1.91 inference(quant_intro,[status(thm)],[694])).
% 2.59/1.91 tff(696,plain,
% 2.59/1.91 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(697,plain,
% 2.59/1.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp21))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) | hskp11) <=> ((hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp11))), rewrite(((hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp11) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) | hskp11) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))))),
% 2.59/1.91 inference(bind,[status(th)],[])).
% 2.59/1.91 tff(698,plain,
% 2.59/1.91 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) | hskp11) <=> ![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.59/1.91 inference(quant_intro,[status(thm)],[697])).
% 2.59/1.91 tff(699,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 2.59/1.91 tff(700,plain,
% 2.59/1.91 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[699, 698])).
% 2.59/1.91 tff(701,plain,
% 2.59/1.91 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[700, 696])).
% 2.59/1.91 tff(702,plain,(
% 2.59/1.91 ![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.59/1.91 inference(skolemize,[status(sab)],[701])).
% 2.59/1.91 tff(703,plain,
% 2.59/1.91 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[702, 695])).
% 2.59/1.91 tff(704,assumption,(~hskp21), introduced(assumption)).
% 2.59/1.91 tff(705,assumption,(~hskp11), introduced(assumption)).
% 2.59/1.91 tff(706,plain,
% 2.59/1.91 (^[U: $i] : refl((hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 2.59/1.91 inference(bind,[status(th)],[])).
% 2.59/1.91 tff(707,plain,
% 2.59/1.91 (![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.91 inference(quant_intro,[status(thm)],[706])).
% 2.59/1.91 tff(708,plain,
% 2.59/1.91 (![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(709,plain,
% 2.59/1.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp11) <=> ((hskp26 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp26 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp11) <=> (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 2.59/1.91 inference(bind,[status(th)],[])).
% 2.59/1.91 tff(710,plain,
% 2.59/1.91 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp11) <=> ![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.91 inference(quant_intro,[status(thm)],[709])).
% 2.59/1.91 tff(711,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 2.59/1.91 tff(712,plain,
% 2.59/1.91 (![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[711, 710])).
% 2.59/1.91 tff(713,plain,
% 2.59/1.91 (![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[712, 708])).
% 2.59/1.91 tff(714,plain,(
% 2.59/1.91 ![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.91 inference(skolemize,[status(sab)],[713])).
% 2.59/1.91 tff(715,plain,
% 2.59/1.91 (![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[714, 707])).
% 2.59/1.91 tff(716,plain,
% 2.59/1.91 (((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)))) <=> ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(717,plain,
% 2.59/1.91 ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)))),
% 2.59/1.91 inference(quant_inst,[status(thm)],[])).
% 2.59/1.91 tff(718,plain,
% 2.59/1.91 ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[717, 716])).
% 2.59/1.91 tff(719,plain,
% 2.59/1.91 (hskp26 | hskp11),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[718, 151, 690, 688, 693, 715])).
% 2.59/1.91 tff(720,plain,
% 2.59/1.91 (hskp26),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[719, 705])).
% 2.59/1.91 tff(721,plain,
% 2.59/1.91 (((~hskp26) | c3_1(a869)) <=> ((~hskp26) | c3_1(a869))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(722,axiom,((~hskp26) | c3_1(a869)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 2.59/1.91 tff(723,plain,
% 2.59/1.91 ((~hskp26) | c3_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[722, 721])).
% 2.59/1.91 tff(724,plain,
% 2.59/1.91 ((~hskp26) | c3_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[723, 721])).
% 2.59/1.91 tff(725,plain,
% 2.59/1.91 ((~hskp26) | c3_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[724, 721])).
% 2.59/1.91 tff(726,plain,
% 2.59/1.91 ((~hskp26) | c3_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[725, 721])).
% 2.59/1.91 tff(727,plain,
% 2.59/1.91 ((~hskp26) | c3_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[726, 721])).
% 2.59/1.91 tff(728,plain,
% 2.59/1.91 ((~hskp26) | c3_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[727, 721])).
% 2.59/1.91 tff(729,plain,
% 2.59/1.91 ((~hskp26) | c3_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[728, 721])).
% 2.59/1.91 tff(730,plain,
% 2.59/1.91 ((~hskp26) | c3_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[729, 721])).
% 2.59/1.91 tff(731,plain,
% 2.59/1.91 (c3_1(a869)),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[730, 720])).
% 2.59/1.91 tff(732,plain,
% 2.59/1.91 (((~hskp26) | c2_1(a869)) <=> ((~hskp26) | c2_1(a869))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(733,axiom,((~hskp26) | c2_1(a869)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 2.59/1.91 tff(734,plain,
% 2.59/1.91 ((~hskp26) | c2_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[733, 732])).
% 2.59/1.91 tff(735,plain,
% 2.59/1.91 ((~hskp26) | c2_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[734, 732])).
% 2.59/1.91 tff(736,plain,
% 2.59/1.91 ((~hskp26) | c2_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[735, 732])).
% 2.59/1.91 tff(737,plain,
% 2.59/1.91 ((~hskp26) | c2_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[736, 732])).
% 2.59/1.91 tff(738,plain,
% 2.59/1.91 ((~hskp26) | c2_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[737, 732])).
% 2.59/1.91 tff(739,plain,
% 2.59/1.91 ((~hskp26) | c2_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[738, 732])).
% 2.59/1.91 tff(740,plain,
% 2.59/1.91 ((~hskp26) | c2_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[739, 732])).
% 2.59/1.91 tff(741,plain,
% 2.59/1.91 ((~hskp26) | c2_1(a869)),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[740, 732])).
% 2.59/1.91 tff(742,plain,
% 2.59/1.91 (c2_1(a869)),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[741, 720])).
% 2.59/1.91 tff(743,plain,
% 2.59/1.91 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a869)) | (~c1_1(a869)) | (~c3_1(a869)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a869)) | (~c1_1(a869)) | (~c3_1(a869)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(744,plain,
% 2.59/1.91 ((hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a869)) | (~c1_1(a869)) | (~c2_1(a869))) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a869)) | (~c1_1(a869)) | (~c3_1(a869)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(745,plain,
% 2.59/1.91 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a869)) | (~c1_1(a869)) | (~c2_1(a869)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a869)) | (~c1_1(a869)) | (~c3_1(a869))))),
% 2.59/1.91 inference(monotonicity,[status(thm)],[744])).
% 2.59/1.91 tff(746,plain,
% 2.59/1.91 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a869)) | (~c1_1(a869)) | (~c2_1(a869)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a869)) | (~c1_1(a869)) | (~c3_1(a869)))),
% 2.59/1.91 inference(transitivity,[status(thm)],[745, 743])).
% 2.59/1.91 tff(747,plain,
% 2.59/1.91 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a869)) | (~c1_1(a869)) | (~c2_1(a869)))),
% 2.59/1.91 inference(quant_inst,[status(thm)],[])).
% 2.59/1.91 tff(748,plain,
% 2.59/1.91 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a869)) | (~c1_1(a869)) | (~c3_1(a869))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[747, 746])).
% 2.59/1.91 tff(749,plain,
% 2.59/1.91 (~c1_1(a869)),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[748, 151, 704, 705, 742, 731, 703])).
% 2.59/1.91 tff(750,assumption,(c3_1(a833)), introduced(assumption)).
% 2.59/1.91 tff(751,plain,
% 2.59/1.91 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c1_1(a796)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c1_1(a796)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(752,plain,
% 2.59/1.91 ((hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c2_1(a796))) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c1_1(a796)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(753,plain,
% 2.59/1.91 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c2_1(a796)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c1_1(a796))))),
% 2.59/1.91 inference(monotonicity,[status(thm)],[752])).
% 2.59/1.91 tff(754,plain,
% 2.59/1.91 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c2_1(a796)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c1_1(a796)))),
% 2.59/1.91 inference(transitivity,[status(thm)],[753, 751])).
% 2.59/1.91 tff(755,plain,
% 2.59/1.91 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c2_1(a796)))),
% 2.59/1.91 inference(quant_inst,[status(thm)],[])).
% 2.59/1.91 tff(756,plain,
% 2.59/1.91 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c1_1(a796))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[755, 754])).
% 2.59/1.91 tff(757,plain,
% 2.59/1.91 (hskp21 | hskp11 | (~c1_1(a796))),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[756, 151, 688, 693, 703])).
% 2.59/1.91 tff(758,plain,
% 2.59/1.91 (~c1_1(a796)),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[757, 705, 704])).
% 2.59/1.91 tff(759,plain,
% 2.59/1.91 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 2.59/1.91 inference(bind,[status(th)],[])).
% 2.59/1.91 tff(760,plain,
% 2.59/1.91 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.59/1.91 inference(quant_intro,[status(thm)],[759])).
% 2.59/1.91 tff(761,plain,
% 2.59/1.91 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(762,plain,
% 2.59/1.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 2.59/1.91 inference(bind,[status(th)],[])).
% 2.59/1.91 tff(763,plain,
% 2.59/1.91 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.59/1.91 inference(quant_intro,[status(thm)],[762])).
% 2.59/1.91 tff(764,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 2.59/1.91 tff(765,plain,
% 2.59/1.91 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[764, 763])).
% 2.59/1.91 tff(766,plain,
% 2.59/1.91 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[765, 761])).
% 2.59/1.91 tff(767,plain,(
% 2.59/1.91 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.59/1.91 inference(skolemize,[status(sab)],[766])).
% 2.59/1.91 tff(768,plain,
% 2.59/1.91 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[767, 760])).
% 2.59/1.91 tff(769,plain,
% 2.59/1.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(770,plain,
% 2.59/1.91 ((hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833))) <=> (hskp8 | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(771,plain,
% 2.59/1.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.59/1.91 inference(monotonicity,[status(thm)],[770])).
% 2.59/1.91 tff(772,plain,
% 2.59/1.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.59/1.91 inference(transitivity,[status(thm)],[771, 769])).
% 2.59/1.91 tff(773,plain,
% 2.59/1.91 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.59/1.91 inference(quant_inst,[status(thm)],[])).
% 2.59/1.91 tff(774,plain,
% 2.59/1.91 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[773, 772])).
% 2.59/1.91 tff(775,plain,
% 2.59/1.91 (hskp8),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[774, 151, 688, 693, 639, 321, 768, 758, 750])).
% 2.59/1.91 tff(776,plain,
% 2.59/1.91 (~c2_1(a805)),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[468, 775])).
% 2.59/1.91 tff(777,plain,
% 2.59/1.91 (((~hskp26) | (~c0_1(a869))) <=> ((~hskp26) | (~c0_1(a869)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(778,plain,
% 2.59/1.91 (((~c0_1(a869)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a869)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(779,axiom,((~c0_1(a869)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 2.59/1.91 tff(780,plain,
% 2.59/1.91 ((~hskp26) | (~c0_1(a869))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[779, 778])).
% 2.59/1.91 tff(781,plain,
% 2.59/1.91 ((~hskp26) | (~c0_1(a869))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[780, 777])).
% 2.59/1.91 tff(782,plain,
% 2.59/1.91 (~c0_1(a869)),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[781, 720])).
% 2.59/1.91 tff(783,plain,
% 2.59/1.91 (c1_1(a805)),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[480, 775])).
% 2.59/1.91 tff(784,plain,
% 2.59/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a869) | c2_1(a805) | c1_1(a793) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a869) | (~c3_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a869) | c2_1(a805) | c1_1(a793) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a869) | (~c3_1(a869)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(785,plain,
% 2.59/1.91 (((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a869) | c0_1(a869) | (~c3_1(a869))) <=> (c0_1(a869) | c2_1(a805) | c1_1(a793) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a869) | (~c3_1(a869)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(786,plain,
% 2.59/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a869) | c0_1(a869) | (~c3_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a869) | c2_1(a805) | c1_1(a793) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a869) | (~c3_1(a869))))),
% 2.59/1.91 inference(monotonicity,[status(thm)],[785])).
% 2.59/1.91 tff(787,plain,
% 2.59/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a869) | c0_1(a869) | (~c3_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a869) | c2_1(a805) | c1_1(a793) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a869) | (~c3_1(a869)))),
% 2.59/1.91 inference(transitivity,[status(thm)],[786, 784])).
% 2.59/1.91 tff(788,plain,
% 2.59/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a869) | c0_1(a869) | (~c3_1(a869)))),
% 2.59/1.91 inference(quant_inst,[status(thm)],[])).
% 2.59/1.91 tff(789,plain,
% 2.59/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a869) | c2_1(a805) | c1_1(a793) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a869) | (~c3_1(a869))),
% 2.59/1.91 inference(modus_ponens,[status(thm)],[788, 787])).
% 2.59/1.91 tff(790,plain,
% 2.59/1.91 (~c0_1(a805)),
% 2.59/1.91 inference(unit_resolution,[status(thm)],[789, 151, 731, 783, 692, 689, 782, 776, 691, 320, 749])).
% 2.59/1.91 tff(791,plain,
% 2.59/1.91 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 2.59/1.91 inference(bind,[status(th)],[])).
% 2.59/1.91 tff(792,plain,
% 2.59/1.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.59/1.91 inference(quant_intro,[status(thm)],[791])).
% 2.59/1.91 tff(793,plain,
% 2.59/1.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.59/1.91 inference(rewrite,[status(thm)],[])).
% 2.59/1.91 tff(794,plain,
% 2.59/1.91 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 2.59/1.92 inference(bind,[status(th)],[])).
% 2.59/1.92 tff(795,plain,
% 2.59/1.92 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.59/1.92 inference(quant_intro,[status(thm)],[794])).
% 2.59/1.92 tff(796,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 2.59/1.92 tff(797,plain,
% 2.59/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.59/1.92 inference(modus_ponens,[status(thm)],[796, 795])).
% 2.59/1.92 tff(798,plain,
% 2.59/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.59/1.92 inference(modus_ponens,[status(thm)],[797, 793])).
% 2.59/1.92 tff(799,plain,(
% 2.59/1.92 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.59/1.92 inference(skolemize,[status(sab)],[798])).
% 2.59/1.92 tff(800,plain,
% 2.59/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 2.59/1.92 inference(modus_ponens,[status(thm)],[799, 792])).
% 2.59/1.92 tff(801,plain,
% 2.59/1.92 (~c3_1(a805)),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[462, 775])).
% 2.59/1.92 tff(802,plain,
% 2.59/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a805) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c0_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c0_1(a805) | (~c1_1(a805)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(803,plain,
% 2.59/1.92 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c3_1(a805) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c0_1(a805) | (~c1_1(a805)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(804,plain,
% 2.59/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a805) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c0_1(a805) | (~c1_1(a805))))),
% 2.59/1.92 inference(monotonicity,[status(thm)],[803])).
% 2.59/1.92 tff(805,plain,
% 2.59/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c0_1(a805) | (~c1_1(a805)))),
% 2.59/1.92 inference(transitivity,[status(thm)],[804, 802])).
% 2.59/1.92 tff(806,plain,
% 2.59/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 2.59/1.92 inference(quant_inst,[status(thm)],[])).
% 2.59/1.92 tff(807,plain,
% 2.59/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c0_1(a805) | (~c1_1(a805))),
% 2.59/1.92 inference(modus_ponens,[status(thm)],[806, 805])).
% 2.59/1.92 tff(808,plain,
% 2.59/1.92 ($false),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[807, 151, 690, 688, 693, 783, 801, 800, 758, 790])).
% 2.59/1.92 tff(809,plain,(hskp11 | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796)) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a793) | (~c1_1(a833)) | c0_1(a833) | (~c3_1(a833)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 2.59/1.92 tff(810,plain,
% 2.59/1.92 (~c3_1(a833)),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[809, 705, 688, 693, 704, 689, 691, 639, 321, 692, 690])).
% 2.59/1.92 tff(811,assumption,(~hskp12), introduced(assumption)).
% 2.59/1.92 tff(812,plain,
% 2.59/1.92 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c0_1(a796)) | (~c1_1(a796)) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c0_1(a796)) | (~c1_1(a796)) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(813,plain,
% 2.59/1.92 ((hskp12 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c0_1(a796)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833))) <=> (hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c0_1(a796)) | (~c1_1(a796)) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(814,plain,
% 2.59/1.92 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c0_1(a796)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c0_1(a796)) | (~c1_1(a796)) | c3_1(a833) | (~c1_1(a833))))),
% 2.59/1.92 inference(monotonicity,[status(thm)],[813])).
% 2.59/1.92 tff(815,plain,
% 2.59/1.92 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c0_1(a796)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c0_1(a796)) | (~c1_1(a796)) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.92 inference(transitivity,[status(thm)],[814, 812])).
% 2.59/1.92 tff(816,plain,
% 2.59/1.92 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c0_1(a796)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)))),
% 2.59/1.92 inference(quant_inst,[status(thm)],[])).
% 2.59/1.92 tff(817,plain,
% 2.59/1.92 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c0_1(a796)) | (~c1_1(a796)) | c3_1(a833) | (~c1_1(a833))),
% 2.59/1.92 inference(modus_ponens,[status(thm)],[816, 815])).
% 2.59/1.92 tff(818,plain,
% 2.59/1.92 (~c1_1(a796)),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[817, 151, 811, 690, 693, 639, 309, 110, 310])).
% 2.59/1.92 tff(819,plain,
% 2.59/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(820,plain,
% 2.59/1.92 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(821,plain,
% 2.59/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c3_1(a833) | (~c1_1(a833))))),
% 2.59/1.92 inference(monotonicity,[status(thm)],[820])).
% 2.59/1.92 tff(822,plain,
% 2.59/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.92 inference(transitivity,[status(thm)],[821, 819])).
% 2.59/1.92 tff(823,plain,
% 2.59/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.92 inference(quant_inst,[status(thm)],[])).
% 2.59/1.92 tff(824,plain,
% 2.59/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c3_1(a833) | (~c1_1(a833))),
% 2.59/1.92 inference(modus_ponens,[status(thm)],[823, 822])).
% 2.59/1.92 tff(825,plain,
% 2.59/1.92 ($false),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[824, 151, 690, 688, 693, 639, 321, 800, 818, 310])).
% 2.59/1.92 tff(826,plain,(c3_1(a833) | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796)) | (~c1_1(a833)) | c0_1(a833) | hskp12 | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.59/1.92 tff(827,plain,
% 2.59/1.92 (hskp12),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[826, 810, 688, 693, 639, 321, 309, 690])).
% 2.59/1.92 tff(828,plain,
% 2.59/1.92 (c2_1(a809)),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[176, 827])).
% 2.59/1.92 tff(829,plain,
% 2.59/1.92 (c1_1(a809)),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[187, 827])).
% 2.59/1.92 tff(830,plain,
% 2.59/1.92 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a809)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a809)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(831,plain,
% 2.59/1.92 ((hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a809)) | (~c1_1(a809)) | (~c2_1(a809))) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a809)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(832,plain,
% 2.59/1.92 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a809)) | (~c1_1(a809)) | (~c2_1(a809)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a809))))),
% 2.59/1.92 inference(monotonicity,[status(thm)],[831])).
% 2.59/1.92 tff(833,plain,
% 2.59/1.92 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a809)) | (~c1_1(a809)) | (~c2_1(a809)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a809)))),
% 2.59/1.92 inference(transitivity,[status(thm)],[832, 830])).
% 2.59/1.92 tff(834,plain,
% 2.59/1.92 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a809)) | (~c1_1(a809)) | (~c2_1(a809)))),
% 2.59/1.92 inference(quant_inst,[status(thm)],[])).
% 2.59/1.92 tff(835,plain,
% 2.59/1.92 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a809))),
% 2.59/1.92 inference(modus_ponens,[status(thm)],[834, 833])).
% 2.59/1.92 tff(836,plain,
% 2.59/1.92 (~c3_1(a809)),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[835, 151, 704, 705, 829, 828, 703])).
% 2.59/1.92 tff(837,plain,
% 2.59/1.92 (~c0_1(a809)),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[164, 827])).
% 2.59/1.92 tff(838,plain,
% 2.59/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c1_1(a809)) | c3_1(a809))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c1_1(a809)) | c3_1(a809))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(839,plain,
% 2.59/1.92 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809))) <=> (c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c1_1(a809)) | c3_1(a809))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(840,plain,
% 2.59/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c1_1(a809)) | c3_1(a809)))),
% 2.59/1.92 inference(monotonicity,[status(thm)],[839])).
% 2.59/1.92 tff(841,plain,
% 2.59/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c1_1(a809)) | c3_1(a809))),
% 2.59/1.92 inference(transitivity,[status(thm)],[840, 838])).
% 2.59/1.92 tff(842,plain,
% 2.59/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809)))),
% 2.59/1.92 inference(quant_inst,[status(thm)],[])).
% 2.59/1.92 tff(843,plain,
% 2.59/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c1_1(a809)) | c3_1(a809)),
% 2.59/1.92 inference(modus_ponens,[status(thm)],[842, 841])).
% 2.59/1.92 tff(844,plain,
% 2.59/1.92 ($false),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[843, 151, 690, 688, 693, 829, 837, 800, 758, 836])).
% 2.59/1.92 tff(845,plain,(hskp11 | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796)) | hskp21 | (~c1_1(a833)) | c0_1(a833) | c2_1(a833) | (~c2_1(a793)) | c1_1(a793) | (~c0_1(a793))), inference(lemma,lemma(discharge,[]))).
% 2.59/1.92 tff(846,plain,
% 2.59/1.92 (hskp11),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[845, 641, 688, 693, 690, 639, 321, 309, 689, 691, 692])).
% 2.59/1.92 tff(847,plain,
% 2.59/1.92 (((~hskp11) | (~c1_1(a808))) <=> ((~hskp11) | (~c1_1(a808)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(848,plain,
% 2.59/1.92 (((~c1_1(a808)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a808)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(849,axiom,((~c1_1(a808)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 2.59/1.92 tff(850,plain,
% 2.59/1.92 ((~hskp11) | (~c1_1(a808))),
% 2.59/1.92 inference(modus_ponens,[status(thm)],[849, 848])).
% 2.59/1.92 tff(851,plain,
% 2.59/1.92 ((~hskp11) | (~c1_1(a808))),
% 2.59/1.92 inference(modus_ponens,[status(thm)],[850, 847])).
% 2.59/1.92 tff(852,plain,
% 2.59/1.92 (~c1_1(a808)),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[851, 846])).
% 2.59/1.92 tff(853,plain,
% 2.59/1.92 (((~hskp11) | (~c2_1(a808))) <=> ((~hskp11) | (~c2_1(a808)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(854,plain,
% 2.59/1.92 (((~c2_1(a808)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a808)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(855,axiom,((~c2_1(a808)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 2.59/1.92 tff(856,plain,
% 2.59/1.92 ((~hskp11) | (~c2_1(a808))),
% 2.59/1.92 inference(modus_ponens,[status(thm)],[855, 854])).
% 2.59/1.92 tff(857,plain,
% 2.59/1.92 ((~hskp11) | (~c2_1(a808))),
% 2.59/1.92 inference(modus_ponens,[status(thm)],[856, 853])).
% 2.59/1.92 tff(858,plain,
% 2.59/1.92 (~c2_1(a808)),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[857, 846])).
% 2.59/1.92 tff(859,plain,
% 2.59/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(860,plain,
% 2.59/1.92 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(861,plain,
% 2.59/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793))))),
% 2.59/1.92 inference(monotonicity,[status(thm)],[860])).
% 2.59/1.92 tff(862,plain,
% 2.59/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 2.59/1.92 inference(transitivity,[status(thm)],[861, 859])).
% 2.59/1.92 tff(863,plain,
% 2.59/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.92 inference(quant_inst,[status(thm)],[])).
% 2.59/1.92 tff(864,plain,
% 2.59/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793))),
% 2.59/1.92 inference(modus_ponens,[status(thm)],[863, 862])).
% 2.59/1.92 tff(865,plain,
% 2.59/1.92 (c3_1(a833) | (~c3_1(a793))),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[864, 151, 690, 688, 693, 639, 689, 321, 691, 800])).
% 2.59/1.92 tff(866,plain,
% 2.59/1.92 (~c3_1(a793)),
% 2.59/1.92 inference(unit_resolution,[status(thm)],[865, 310])).
% 2.59/1.92 tff(867,plain,
% 2.59/1.92 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 2.59/1.92 inference(bind,[status(th)],[])).
% 2.59/1.92 tff(868,plain,
% 2.59/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.92 inference(quant_intro,[status(thm)],[867])).
% 2.59/1.92 tff(869,plain,
% 2.59/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.92 inference(rewrite,[status(thm)],[])).
% 2.59/1.92 tff(870,plain,
% 2.59/1.92 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 2.59/1.93 inference(bind,[status(th)],[])).
% 2.59/1.93 tff(871,plain,
% 2.59/1.93 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.93 inference(quant_intro,[status(thm)],[870])).
% 2.59/1.93 tff(872,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 2.59/1.93 tff(873,plain,
% 2.59/1.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[872, 871])).
% 2.59/1.93 tff(874,plain,
% 2.59/1.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[873, 869])).
% 2.59/1.93 tff(875,plain,(
% 2.59/1.93 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.93 inference(skolemize,[status(sab)],[874])).
% 2.59/1.93 tff(876,plain,
% 2.59/1.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[875, 868])).
% 2.59/1.93 tff(877,assumption,(~c2_1(a808)), introduced(assumption)).
% 2.59/1.93 tff(878,assumption,(~c1_1(a808)), introduced(assumption)).
% 2.59/1.93 tff(879,plain,
% 2.59/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a833) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(880,plain,
% 2.59/1.93 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833)) <=> (c0_1(a833) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(881,plain,
% 2.59/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a833) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793)))),
% 2.59/1.93 inference(monotonicity,[status(thm)],[880])).
% 2.59/1.93 tff(882,plain,
% 2.59/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793))),
% 2.59/1.93 inference(transitivity,[status(thm)],[881, 879])).
% 2.59/1.93 tff(883,plain,
% 2.59/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833))),
% 2.59/1.93 inference(quant_inst,[status(thm)],[])).
% 2.59/1.93 tff(884,plain,
% 2.59/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[883, 882])).
% 2.59/1.93 tff(885,plain,
% 2.59/1.93 ((~c3_1(a808)) | c3_1(a833) | c3_1(a793)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[884, 151, 692, 321, 309, 878, 877, 691, 876])).
% 2.59/1.93 tff(886,plain,
% 2.59/1.93 (~c3_1(a808)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[885, 310, 866])).
% 2.59/1.93 tff(887,plain,
% 2.59/1.93 (((~hskp11) | c3_1(a808)) <=> ((~hskp11) | c3_1(a808))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(888,axiom,((~hskp11) | c3_1(a808)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 2.59/1.93 tff(889,plain,
% 2.59/1.93 ((~hskp11) | c3_1(a808)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[888, 887])).
% 2.59/1.93 tff(890,plain,
% 2.59/1.93 ((~hskp11) | c3_1(a808)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[889, 887])).
% 2.59/1.93 tff(891,plain,
% 2.59/1.93 ((~hskp11) | c3_1(a808)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[890, 887])).
% 2.59/1.93 tff(892,plain,
% 2.59/1.93 ((~hskp11) | c3_1(a808)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[891, 887])).
% 2.59/1.93 tff(893,plain,
% 2.59/1.93 ((~hskp11) | c3_1(a808)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[892, 887])).
% 2.59/1.93 tff(894,plain,
% 2.59/1.93 ((~hskp11) | c3_1(a808)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[893, 887])).
% 2.59/1.93 tff(895,plain,
% 2.59/1.93 ((~hskp11) | c3_1(a808)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[894, 887])).
% 2.59/1.93 tff(896,plain,
% 2.59/1.93 ((~hskp11) | c3_1(a808)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[895, 887])).
% 2.59/1.93 tff(897,plain,
% 2.59/1.93 (~hskp11),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[896, 886])).
% 2.59/1.93 tff(898,plain,
% 2.59/1.93 (~c1_1(a796)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[757, 897, 704])).
% 2.59/1.93 tff(899,plain,
% 2.59/1.93 ($false),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[824, 151, 690, 688, 693, 639, 321, 800, 898, 310])).
% 2.59/1.93 tff(900,plain,(c3_1(a833) | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796)) | (~c1_1(a833)) | c0_1(a833) | hskp21 | (~c0_1(a793)) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~c2_1(a793))), inference(lemma,lemma(discharge,[]))).
% 2.59/1.93 tff(901,plain,
% 2.59/1.93 (c3_1(a833)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[900, 858, 688, 693, 639, 321, 641, 692, 309, 689, 852, 691, 690])).
% 2.59/1.93 tff(902,assumption,(~hskp8), introduced(assumption)).
% 2.59/1.93 tff(903,plain,
% 2.59/1.93 (hskp10),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[503, 902, 357])).
% 2.59/1.93 tff(904,plain,
% 2.59/1.93 (~c3_1(a807)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[509, 903])).
% 2.59/1.93 tff(905,plain,
% 2.59/1.93 (~c2_1(a807)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[552, 903])).
% 2.59/1.93 tff(906,plain,
% 2.59/1.93 (hskp12),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[826, 310, 688, 693, 639, 321, 309, 690])).
% 2.59/1.93 tff(907,plain,
% 2.59/1.93 (~c0_1(a809)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[164, 906])).
% 2.59/1.93 tff(908,plain,
% 2.59/1.93 (^[U: $i] : refl((hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 2.59/1.93 inference(bind,[status(th)],[])).
% 2.59/1.93 tff(909,plain,
% 2.59/1.93 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.93 inference(quant_intro,[status(thm)],[908])).
% 2.59/1.93 tff(910,plain,
% 2.59/1.93 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(911,plain,
% 2.59/1.93 (^[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)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp17) | hskp8) <=> ((hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp8))), rewrite(((hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp8) <=> (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp17) | hskp8) <=> (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 2.59/1.93 inference(bind,[status(th)],[])).
% 2.59/1.93 tff(912,plain,
% 2.59/1.93 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp17) | hskp8) <=> ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.93 inference(quant_intro,[status(thm)],[911])).
% 2.59/1.93 tff(913,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp17) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 2.59/1.93 tff(914,plain,
% 2.59/1.93 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[913, 912])).
% 2.59/1.93 tff(915,plain,
% 2.59/1.93 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[914, 910])).
% 2.59/1.93 tff(916,plain,(
% 2.59/1.93 ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.93 inference(skolemize,[status(sab)],[915])).
% 2.59/1.93 tff(917,plain,
% 2.59/1.93 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[916, 909])).
% 2.59/1.93 tff(918,plain,
% 2.59/1.93 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp8 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(919,plain,
% 2.59/1.93 ((hskp17 | hskp8 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (hskp17 | hskp8 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(920,plain,
% 2.59/1.93 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))))),
% 2.59/1.93 inference(monotonicity,[status(thm)],[919])).
% 2.59/1.93 tff(921,plain,
% 2.59/1.93 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp8 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.93 inference(transitivity,[status(thm)],[920, 918])).
% 2.59/1.93 tff(922,plain,
% 2.59/1.93 ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.93 inference(quant_inst,[status(thm)],[])).
% 2.59/1.93 tff(923,plain,
% 2.59/1.93 ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp8 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[922, 921])).
% 2.59/1.93 tff(924,plain,
% 2.59/1.93 (hskp17 | hskp8 | c3_1(a833)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[923, 151, 639, 309, 917])).
% 2.59/1.93 tff(925,plain,
% 2.59/1.93 (hskp17),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[924, 310, 902])).
% 2.59/1.93 tff(926,plain,
% 2.59/1.93 (((~hskp17) | (~c2_1(a825))) <=> ((~hskp17) | (~c2_1(a825)))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(927,plain,
% 2.59/1.93 (((~c2_1(a825)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a825)))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(928,axiom,((~c2_1(a825)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 2.59/1.93 tff(929,plain,
% 2.59/1.93 ((~hskp17) | (~c2_1(a825))),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[928, 927])).
% 2.59/1.93 tff(930,plain,
% 2.59/1.93 ((~hskp17) | (~c2_1(a825))),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[929, 926])).
% 2.59/1.93 tff(931,plain,
% 2.59/1.93 (~c2_1(a825)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[930, 925])).
% 2.59/1.93 tff(932,plain,
% 2.59/1.93 (c2_1(a809)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[176, 906])).
% 2.59/1.93 tff(933,plain,
% 2.59/1.93 (c1_1(a809)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[187, 906])).
% 2.59/1.93 tff(934,plain,
% 2.59/1.93 (((~hskp17) | c1_1(a825)) <=> ((~hskp17) | c1_1(a825))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(935,axiom,((~hskp17) | c1_1(a825)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 2.59/1.93 tff(936,plain,
% 2.59/1.93 ((~hskp17) | c1_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[935, 934])).
% 2.59/1.93 tff(937,plain,
% 2.59/1.93 ((~hskp17) | c1_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[936, 934])).
% 2.59/1.93 tff(938,plain,
% 2.59/1.93 ((~hskp17) | c1_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[937, 934])).
% 2.59/1.93 tff(939,plain,
% 2.59/1.93 ((~hskp17) | c1_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[938, 934])).
% 2.59/1.93 tff(940,plain,
% 2.59/1.93 ((~hskp17) | c1_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[939, 934])).
% 2.59/1.93 tff(941,plain,
% 2.59/1.93 ((~hskp17) | c1_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[940, 934])).
% 2.59/1.93 tff(942,plain,
% 2.59/1.93 ((~hskp17) | c1_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[941, 934])).
% 2.59/1.93 tff(943,plain,
% 2.59/1.93 ((~hskp17) | c1_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[942, 934])).
% 2.59/1.93 tff(944,plain,
% 2.59/1.93 (c1_1(a825)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[943, 925])).
% 2.59/1.93 tff(945,plain,
% 2.59/1.93 (((~hskp17) | c0_1(a825)) <=> ((~hskp17) | c0_1(a825))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(946,axiom,((~hskp17) | c0_1(a825)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 2.59/1.93 tff(947,plain,
% 2.59/1.93 ((~hskp17) | c0_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[946, 945])).
% 2.59/1.93 tff(948,plain,
% 2.59/1.93 ((~hskp17) | c0_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[947, 945])).
% 2.59/1.93 tff(949,plain,
% 2.59/1.93 ((~hskp17) | c0_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[948, 945])).
% 2.59/1.93 tff(950,plain,
% 2.59/1.93 ((~hskp17) | c0_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[949, 945])).
% 2.59/1.93 tff(951,plain,
% 2.59/1.93 ((~hskp17) | c0_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[950, 945])).
% 2.59/1.93 tff(952,plain,
% 2.59/1.93 ((~hskp17) | c0_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[951, 945])).
% 2.59/1.93 tff(953,plain,
% 2.59/1.93 ((~hskp17) | c0_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[952, 945])).
% 2.59/1.93 tff(954,plain,
% 2.59/1.93 ((~hskp17) | c0_1(a825)),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[953, 945])).
% 2.59/1.93 tff(955,plain,
% 2.59/1.93 (c0_1(a825)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[954, 925])).
% 2.59/1.93 tff(956,plain,
% 2.59/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a833) | c2_1(a825) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a825)) | (~c1_1(a825)) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a833) | c2_1(a825) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a825)) | (~c1_1(a825)) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(957,plain,
% 2.59/1.93 (((~ndr1_0) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809))) <=> (c2_1(a833) | c2_1(a825) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a825)) | (~c1_1(a825)) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(958,plain,
% 2.59/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a833) | c2_1(a825) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a825)) | (~c1_1(a825)) | c3_1(a833) | (~c1_1(a833))))),
% 2.59/1.93 inference(monotonicity,[status(thm)],[957])).
% 2.59/1.93 tff(959,plain,
% 2.59/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a833) | c2_1(a825) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a825)) | (~c1_1(a825)) | c3_1(a833) | (~c1_1(a833)))),
% 2.59/1.93 inference(transitivity,[status(thm)],[958, 956])).
% 2.59/1.93 tff(960,plain,
% 2.59/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.59/1.93 inference(quant_inst,[status(thm)],[])).
% 2.59/1.93 tff(961,plain,
% 2.59/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a833) | c2_1(a825) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a825)) | (~c1_1(a825)) | c3_1(a833) | (~c1_1(a833))),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[960, 959])).
% 2.59/1.93 tff(962,plain,
% 2.59/1.93 ($false),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[961, 151, 639, 955, 944, 933, 932, 309, 931, 907, 99, 310])).
% 2.59/1.93 tff(963,plain,(c3_1(a833) | (~c1_1(a833)) | c2_1(a833) | hskp8 | (~c2_1(a796)) | (~c3_1(a796)) | c0_1(a833) | (~c0_1(a796))), inference(lemma,lemma(discharge,[]))).
% 2.59/1.93 tff(964,plain,
% 2.59/1.93 (c3_1(a833)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[963, 902, 309, 639, 688, 693, 321, 690])).
% 2.59/1.93 tff(965,plain,
% 2.59/1.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(966,plain,
% 2.59/1.93 ((hskp8 | (~ndr1_0) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833))) <=> (hskp8 | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(967,plain,
% 2.59/1.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793))))),
% 2.59/1.93 inference(monotonicity,[status(thm)],[966])).
% 2.59/1.93 tff(968,plain,
% 2.59/1.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 2.59/1.93 inference(transitivity,[status(thm)],[967, 965])).
% 2.59/1.93 tff(969,plain,
% 2.59/1.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.59/1.93 inference(quant_inst,[status(thm)],[])).
% 2.59/1.93 tff(970,plain,
% 2.59/1.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793))),
% 2.59/1.93 inference(modus_ponens,[status(thm)],[969, 968])).
% 2.59/1.93 tff(971,plain,
% 2.59/1.93 (hskp8 | (~c3_1(a833)) | (~c3_1(a793))),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[970, 151, 639, 689, 321, 691, 768])).
% 2.59/1.93 tff(972,plain,
% 2.59/1.93 (~c3_1(a793)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[971, 964, 902])).
% 2.59/1.93 tff(973,plain,
% 2.59/1.93 (hskp11),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[809, 964, 688, 693, 641, 689, 691, 639, 321, 692, 690])).
% 2.59/1.93 tff(974,plain,
% 2.59/1.93 (~c2_1(a808)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[857, 973])).
% 2.59/1.93 tff(975,plain,
% 2.59/1.93 (~c1_1(a808)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[851, 973])).
% 2.59/1.93 tff(976,plain,
% 2.59/1.93 (c3_1(a808)),
% 2.59/1.93 inference(unit_resolution,[status(thm)],[896, 973])).
% 2.59/1.93 tff(977,assumption,(~c3_1(a838)), introduced(assumption)).
% 2.59/1.93 tff(978,plain,
% 2.59/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a838) | c3_1(a838) | c2_1(a838) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a838) | c3_1(a838) | c2_1(a838) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))),
% 2.59/1.93 inference(rewrite,[status(thm)],[])).
% 2.59/1.93 tff(979,plain,
% 2.59/1.93 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a838) | c0_1(a838) | c3_1(a838)) <=> (c0_1(a838) | c3_1(a838) | c2_1(a838) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))),
% 2.59/1.94 inference(rewrite,[status(thm)],[])).
% 2.59/1.94 tff(980,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a838) | c0_1(a838) | c3_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a838) | c3_1(a838) | c2_1(a838) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793)))),
% 2.59/1.94 inference(monotonicity,[status(thm)],[979])).
% 2.59/1.94 tff(981,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a838) | c0_1(a838) | c3_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a838) | c3_1(a838) | c2_1(a838) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))),
% 2.59/1.94 inference(transitivity,[status(thm)],[980, 978])).
% 2.59/1.94 tff(982,plain,
% 2.59/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a838) | c0_1(a838) | c3_1(a838))),
% 2.59/1.94 inference(quant_inst,[status(thm)],[])).
% 2.59/1.94 tff(983,plain,
% 2.59/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a838) | c3_1(a838) | c2_1(a838) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793)),
% 2.59/1.94 inference(modus_ponens,[status(thm)],[982, 981])).
% 2.59/1.94 tff(984,plain,
% 2.59/1.94 ($false),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[983, 151, 640, 977, 976, 692, 470, 975, 974, 691, 876, 972])).
% 2.59/1.94 tff(985,plain,(hskp8 | c0_1(a838) | c3_1(a838) | (~c0_1(a793)) | c2_1(a838) | c1_1(a793) | (~c1_1(a833)) | (~c2_1(a793)) | c0_1(a833) | (~c2_1(a796)) | (~c3_1(a796)) | (~c0_1(a796)) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.59/1.94 tff(986,plain,
% 2.59/1.94 (c3_1(a838)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[985, 902, 640, 692, 470, 691, 639, 689, 321, 688, 693, 690, 309])).
% 2.59/1.94 tff(987,plain,
% 2.59/1.94 (~c0_1(a807)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[515, 903])).
% 2.59/1.94 tff(988,plain,
% 2.59/1.94 (~c3_1(a793)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[971, 902, 750])).
% 2.59/1.94 tff(989,assumption,(~c3_1(a807)), introduced(assumption)).
% 2.59/1.94 tff(990,assumption,(~c2_1(a807)), introduced(assumption)).
% 2.59/1.94 tff(991,assumption,(~c0_1(a807)), introduced(assumption)).
% 2.59/1.94 tff(992,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 2.59/1.94 inference(rewrite,[status(thm)],[])).
% 2.59/1.94 tff(993,plain,
% 2.59/1.94 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a807) | c0_1(a807) | c3_1(a807)) <=> (c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 2.59/1.94 inference(rewrite,[status(thm)],[])).
% 2.59/1.94 tff(994,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)))),
% 2.59/1.94 inference(monotonicity,[status(thm)],[993])).
% 2.59/1.94 tff(995,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 2.59/1.94 inference(transitivity,[status(thm)],[994, 992])).
% 2.59/1.94 tff(996,plain,
% 2.59/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a807) | c0_1(a807) | c3_1(a807))),
% 2.59/1.94 inference(quant_inst,[status(thm)],[])).
% 2.59/1.94 tff(997,plain,
% 2.59/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)),
% 2.59/1.94 inference(modus_ponens,[status(thm)],[996, 995])).
% 2.59/1.94 tff(998,plain,
% 2.59/1.94 (c3_1(a793) | (~c3_1(a838)) | c1_1(a838)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[997, 151, 692, 470, 991, 990, 989, 691, 876])).
% 2.59/1.94 tff(999,plain,
% 2.59/1.94 (c1_1(a838)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[998, 988, 482])).
% 2.59/1.94 tff(1000,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))),
% 2.59/1.94 inference(rewrite,[status(thm)],[])).
% 2.59/1.94 tff(1001,plain,
% 2.59/1.94 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807)) <=> (c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))),
% 2.59/1.94 inference(rewrite,[status(thm)],[])).
% 2.59/1.94 tff(1002,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793)))),
% 2.59/1.94 inference(monotonicity,[status(thm)],[1001])).
% 2.59/1.94 tff(1003,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))),
% 2.59/1.94 inference(transitivity,[status(thm)],[1002, 1000])).
% 2.59/1.94 tff(1004,plain,
% 2.59/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807))),
% 2.59/1.94 inference(quant_inst,[status(thm)],[])).
% 2.59/1.94 tff(1005,plain,
% 2.59/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793)),
% 2.59/1.94 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 2.59/1.94 tff(1006,plain,
% 2.59/1.94 ((~c3_1(a808)) | c3_1(a793)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[1005, 151, 692, 878, 877, 991, 990, 989, 691, 876])).
% 2.59/1.94 tff(1007,plain,
% 2.59/1.94 (~c3_1(a808)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[1006, 988])).
% 2.59/1.94 tff(1008,plain,
% 2.59/1.94 (~hskp11),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[896, 1007])).
% 2.59/1.94 tff(1009,plain,
% 2.59/1.94 (~c1_1(a796)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[757, 1008, 641])).
% 2.59/1.94 tff(1010,plain,
% 2.59/1.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a838) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a838)) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a838) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a838)) | (~c1_1(a838)))),
% 2.59/1.94 inference(rewrite,[status(thm)],[])).
% 2.59/1.94 tff(1011,plain,
% 2.59/1.94 ((hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a838) | (~c3_1(a838)) | (~c1_1(a838))) <=> (hskp8 | c0_1(a838) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a838)) | (~c1_1(a838)))),
% 2.59/1.94 inference(rewrite,[status(thm)],[])).
% 2.59/1.94 tff(1012,plain,
% 2.59/1.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a838) | (~c3_1(a838)) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a838) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a838)) | (~c1_1(a838))))),
% 2.59/1.94 inference(monotonicity,[status(thm)],[1011])).
% 2.59/1.94 tff(1013,plain,
% 2.59/1.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a838) | (~c3_1(a838)) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a838) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a838)) | (~c1_1(a838)))),
% 2.59/1.94 inference(transitivity,[status(thm)],[1012, 1010])).
% 2.59/1.94 tff(1014,plain,
% 2.59/1.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a838) | (~c3_1(a838)) | (~c1_1(a838)))),
% 2.59/1.94 inference(quant_inst,[status(thm)],[])).
% 2.59/1.94 tff(1015,plain,
% 2.59/1.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a838) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a838)) | (~c1_1(a838))),
% 2.59/1.94 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 2.59/1.94 tff(1016,plain,
% 2.59/1.94 ($false),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[1015, 151, 902, 688, 693, 640, 482, 768, 1009, 999])).
% 2.59/1.94 tff(1017,plain,(hskp8 | (~c2_1(a796)) | (~c3_1(a796)) | c0_1(a838) | (~c3_1(a838)) | (~c0_1(a793)) | c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | c1_1(a808) | c2_1(a808) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.59/1.94 tff(1018,plain,
% 2.59/1.94 ($false),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[1017, 987, 986, 693, 321, 640, 692, 470, 902, 905, 904, 691, 852, 858, 901, 639, 689, 688])).
% 2.59/1.94 tff(1019,plain,(hskp8 | (~c3_1(a796)) | c0_1(a833) | c0_1(a838) | (~c0_1(a793)) | c2_1(a838) | c1_1(a793) | (~c1_1(a833)) | (~c2_1(a793)) | (~c2_1(a796)) | (~c0_1(a796)) | c2_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.59/1.94 tff(1020,plain,
% 2.59/1.94 (hskp8),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[1019, 640, 321, 637, 687, 470, 676, 639, 670, 638, 636, 309, 357])).
% 2.59/1.94 tff(1021,plain,
% 2.59/1.94 (~c3_1(a805)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[462, 1020])).
% 2.59/1.94 tff(1022,plain,
% 2.59/1.94 (hskp11),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[845, 641, 638, 637, 636, 639, 321, 309, 670, 676, 687])).
% 2.59/1.94 tff(1023,plain,
% 2.59/1.94 (~c2_1(a808)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[857, 1022])).
% 2.59/1.94 tff(1024,plain,
% 2.59/1.94 (~c2_1(a805)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[468, 1020])).
% 2.59/1.94 tff(1025,plain,
% 2.59/1.94 (~c1_1(a808)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[851, 1022])).
% 2.59/1.94 tff(1026,plain,
% 2.59/1.94 (c1_1(a805)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[480, 1020])).
% 2.59/1.94 tff(1027,plain,
% 2.59/1.94 (c3_1(a808)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[896, 1022])).
% 2.59/1.94 tff(1028,assumption,(~c3_1(a805)), introduced(assumption)).
% 2.59/1.94 tff(1029,assumption,(~c2_1(a805)), introduced(assumption)).
% 2.59/1.94 tff(1030,assumption,(c1_1(a805)), introduced(assumption)).
% 2.59/1.94 tff(1031,assumption,(c3_1(a808)), introduced(assumption)).
% 2.59/1.94 tff(1032,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a832) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a832) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.59/1.94 inference(rewrite,[status(thm)],[])).
% 2.59/1.94 tff(1033,plain,
% 2.59/1.94 (((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c3_1(a832) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.59/1.94 inference(rewrite,[status(thm)],[])).
% 2.59/1.94 tff(1034,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a832) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)) | (~c2_1(a832)) | (~c0_1(a832))))),
% 2.59/1.94 inference(monotonicity,[status(thm)],[1033])).
% 2.59/1.94 tff(1035,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a832) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.59/1.94 inference(transitivity,[status(thm)],[1034, 1032])).
% 2.59/1.94 tff(1036,plain,
% 2.59/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 2.59/1.94 inference(quant_inst,[status(thm)],[])).
% 2.59/1.94 tff(1037,plain,
% 2.59/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a832) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)) | (~c2_1(a832)) | (~c0_1(a832))),
% 2.59/1.94 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 2.59/1.94 tff(1038,plain,
% 2.59/1.94 ((~c0_1(a808)) | (~c0_1(a832))),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[1037, 151, 433, 1031, 1030, 22, 877, 1029, 1028, 332])).
% 2.59/1.94 tff(1039,plain,
% 2.59/1.94 (~c0_1(a808)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[1038, 456])).
% 2.59/1.94 tff(1040,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | (~c0_1(a832)))),
% 2.59/1.94 inference(rewrite,[status(thm)],[])).
% 2.59/1.94 tff(1041,plain,
% 2.59/1.94 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805)) <=> (c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | (~c0_1(a832)))),
% 2.59/1.94 inference(rewrite,[status(thm)],[])).
% 2.59/1.94 tff(1042,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | (~c0_1(a832))))),
% 2.59/1.94 inference(monotonicity,[status(thm)],[1041])).
% 2.59/1.94 tff(1043,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | (~c0_1(a832)))),
% 2.59/1.94 inference(transitivity,[status(thm)],[1042, 1040])).
% 2.59/1.94 tff(1044,plain,
% 2.59/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805))),
% 2.59/1.94 inference(quant_inst,[status(thm)],[])).
% 2.59/1.94 tff(1045,plain,
% 2.59/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | (~c0_1(a832))),
% 2.59/1.94 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 2.59/1.94 tff(1046,plain,
% 2.59/1.94 (c0_1(a805) | (~c0_1(a832))),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[1045, 151, 1031, 322, 22, 878, 877, 1029, 1028, 876])).
% 2.59/1.94 tff(1047,plain,
% 2.59/1.94 (c0_1(a805)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[1046, 456])).
% 2.59/1.94 tff(1048,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a832) | c1_1(a808) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a832) | c1_1(a808) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.59/1.94 inference(rewrite,[status(thm)],[])).
% 2.59/1.94 tff(1049,plain,
% 2.59/1.94 (((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (c1_1(a832) | c1_1(a808) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.59/1.94 inference(rewrite,[status(thm)],[])).
% 2.59/1.94 tff(1050,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a832) | c1_1(a808) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)) | (~c0_1(a832))))),
% 2.59/1.94 inference(monotonicity,[status(thm)],[1049])).
% 2.59/1.94 tff(1051,plain,
% 2.59/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a832) | c1_1(a808) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.59/1.94 inference(transitivity,[status(thm)],[1050, 1048])).
% 2.59/1.94 tff(1052,plain,
% 2.59/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 2.59/1.94 inference(quant_inst,[status(thm)],[])).
% 2.59/1.94 tff(1053,plain,
% 2.59/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a832) | c1_1(a808) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)) | (~c0_1(a832))),
% 2.59/1.94 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 2.59/1.94 tff(1054,plain,
% 2.59/1.94 ((~c0_1(a805)) | c0_1(a808) | (~c0_1(a832))),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[1053, 151, 433, 1031, 1030, 322, 878, 1029, 320])).
% 2.59/1.94 tff(1055,plain,
% 2.59/1.94 ($false),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[1054, 1047, 1039, 456])).
% 2.59/1.94 tff(1056,plain,((~c0_1(a832)) | (~c2_1(a832)) | (~c3_1(a808)) | (~c1_1(a805)) | c1_1(a832) | c1_1(a808) | c2_1(a805) | c3_1(a832) | c2_1(a808) | c3_1(a805)), inference(lemma,lemma(discharge,[]))).
% 2.59/1.94 tff(1057,plain,
% 2.59/1.94 (~c0_1(a832)),
% 2.59/1.94 inference(unit_resolution,[status(thm)],[1056, 1027, 433, 1026, 322, 1025, 1024, 22, 1023, 1021])).
% 2.59/1.94 tff(1058,plain,
% 2.59/1.94 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 2.59/1.94 inference(bind,[status(th)],[])).
% 2.59/1.94 tff(1059,plain,
% 2.59/1.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.95 inference(quant_intro,[status(thm)],[1058])).
% 2.59/1.95 tff(1060,plain,
% 2.59/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.95 inference(rewrite,[status(thm)],[])).
% 2.59/1.95 tff(1061,plain,
% 2.59/1.95 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 2.59/1.95 inference(bind,[status(th)],[])).
% 2.59/1.95 tff(1062,plain,
% 2.59/1.95 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.95 inference(quant_intro,[status(thm)],[1061])).
% 2.59/1.95 tff(1063,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 2.59/1.95 tff(1064,plain,
% 2.59/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.95 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 2.59/1.95 tff(1065,plain,
% 2.59/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.95 inference(modus_ponens,[status(thm)],[1064, 1060])).
% 2.59/1.95 tff(1066,plain,(
% 2.59/1.95 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.95 inference(skolemize,[status(sab)],[1065])).
% 2.59/1.95 tff(1067,plain,
% 2.59/1.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.59/1.95 inference(modus_ponens,[status(thm)],[1066, 1059])).
% 2.59/1.95 tff(1068,plain,
% 2.59/1.95 (c3_1(a833)),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[900, 1023, 638, 637, 639, 321, 641, 687, 309, 670, 1025, 676, 636])).
% 2.59/1.95 tff(1069,assumption,(~c0_1(a832)), introduced(assumption)).
% 2.59/1.95 tff(1070,plain,
% 2.59/1.95 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 2.59/1.95 inference(bind,[status(th)],[])).
% 2.59/1.95 tff(1071,plain,
% 2.59/1.95 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.59/1.95 inference(quant_intro,[status(thm)],[1070])).
% 2.59/1.95 tff(1072,plain,
% 2.59/1.95 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.59/1.95 inference(rewrite,[status(thm)],[])).
% 2.59/1.95 tff(1073,plain,
% 2.59/1.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_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)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 2.59/1.95 inference(bind,[status(th)],[])).
% 2.59/1.95 tff(1074,plain,
% 2.59/1.95 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.59/1.95 inference(quant_intro,[status(thm)],[1073])).
% 2.59/1.95 tff(1075,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 2.59/1.95 tff(1076,plain,
% 2.59/1.95 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.59/1.95 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 2.59/1.95 tff(1077,plain,
% 2.59/1.95 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.59/1.95 inference(modus_ponens,[status(thm)],[1076, 1072])).
% 2.59/1.95 tff(1078,plain,(
% 2.59/1.95 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.59/1.95 inference(skolemize,[status(sab)],[1077])).
% 2.59/1.95 tff(1079,plain,
% 2.59/1.95 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.59/1.95 inference(modus_ponens,[status(thm)],[1078, 1071])).
% 2.59/1.95 tff(1080,plain,
% 2.59/1.95 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)))),
% 2.59/1.95 inference(rewrite,[status(thm)],[])).
% 2.59/1.95 tff(1081,plain,
% 2.59/1.95 ((hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (hskp12 | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)))),
% 2.59/1.95 inference(rewrite,[status(thm)],[])).
% 2.59/1.95 tff(1082,plain,
% 2.59/1.95 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833))))),
% 2.59/1.95 inference(monotonicity,[status(thm)],[1081])).
% 2.59/1.95 tff(1083,plain,
% 2.59/1.95 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)))),
% 2.59/1.95 inference(transitivity,[status(thm)],[1082, 1080])).
% 2.59/1.95 tff(1084,plain,
% 2.59/1.95 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 2.59/1.95 inference(quant_inst,[status(thm)],[])).
% 2.59/1.95 tff(1085,plain,
% 2.59/1.95 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833))),
% 2.59/1.95 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 2.59/1.95 tff(1086,plain,
% 2.59/1.95 ($false),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[1085, 151, 811, 433, 321, 309, 22, 1079, 1069, 750])).
% 2.59/1.95 tff(1087,plain,(c0_1(a832) | hskp12 | (~c2_1(a832)) | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 2.59/1.95 tff(1088,plain,
% 2.59/1.95 (hskp12),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[1087, 1057, 433, 321, 309, 22, 1068])).
% 2.59/1.95 tff(1089,plain,
% 2.59/1.95 (~c0_1(a809)),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[164, 1088])).
% 2.59/1.95 tff(1090,plain,
% 2.59/1.95 (c2_1(a809)),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[176, 1088])).
% 2.59/1.95 tff(1091,plain,
% 2.59/1.95 (c1_1(a809)),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[187, 1088])).
% 2.59/1.95 tff(1092,plain,
% 2.59/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | c0_1(a832))),
% 2.59/1.95 inference(rewrite,[status(thm)],[])).
% 2.59/1.95 tff(1093,plain,
% 2.59/1.95 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a832) | c0_1(a832) | c3_1(a832)) <=> (c1_1(a832) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | c0_1(a832))),
% 2.59/1.95 inference(rewrite,[status(thm)],[])).
% 2.59/1.95 tff(1094,plain,
% 2.59/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | c0_1(a832)))),
% 2.59/1.95 inference(monotonicity,[status(thm)],[1093])).
% 2.59/1.95 tff(1095,plain,
% 2.59/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | c0_1(a832))),
% 2.59/1.95 inference(transitivity,[status(thm)],[1094, 1092])).
% 2.59/1.95 tff(1096,plain,
% 2.59/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a832) | c0_1(a832) | c3_1(a832))),
% 2.59/1.95 inference(quant_inst,[status(thm)],[])).
% 2.59/1.95 tff(1097,plain,
% 2.59/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | c0_1(a832)),
% 2.59/1.95 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 2.59/1.95 tff(1098,plain,
% 2.59/1.95 ($false),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[1097, 151, 433, 1091, 1090, 322, 22, 1089, 1067, 1057])).
% 2.59/1.95 tff(1099,plain,(c0_1(a838) | (~c2_1(a832)) | c1_1(a832) | c3_1(a832) | c0_1(a833) | c2_1(a833) | c2_1(a838) | (~c1_1(a833)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.59/1.95 tff(1100,plain,
% 2.59/1.95 (c0_1(a838)),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[1099, 470, 322, 22, 321, 309, 433, 639, 357])).
% 2.59/1.95 tff(1101,assumption,(~hskp0), introduced(assumption)).
% 2.59/1.95 tff(1102,plain,
% 2.59/1.95 (hskp21),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[658, 1101])).
% 2.59/1.95 tff(1103,plain,
% 2.59/1.95 (c3_1(a838)),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[443, 1102])).
% 2.59/1.95 tff(1104,plain,
% 2.59/1.95 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 2.59/1.95 inference(rewrite,[status(thm)],[])).
% 2.59/1.95 tff(1105,plain,
% 2.59/1.95 ((hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838))) <=> (hskp28 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 2.59/1.95 inference(rewrite,[status(thm)],[])).
% 2.59/1.95 tff(1106,plain,
% 2.59/1.95 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))))),
% 2.59/1.95 inference(monotonicity,[status(thm)],[1105])).
% 2.59/1.95 tff(1107,plain,
% 2.59/1.95 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 2.59/1.95 inference(transitivity,[status(thm)],[1106, 1104])).
% 2.59/1.95 tff(1108,plain,
% 2.59/1.95 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)))),
% 2.59/1.95 inference(quant_inst,[status(thm)],[])).
% 2.59/1.95 tff(1109,plain,
% 2.59/1.95 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))),
% 2.59/1.95 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 2.59/1.95 tff(1110,plain,
% 2.59/1.95 ((~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[1109, 151, 357, 470, 368])).
% 2.59/1.95 tff(1111,plain,
% 2.59/1.95 (~c1_1(a838)),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[1110, 1103, 1100])).
% 2.59/1.95 tff(1112,assumption,(hskp17), introduced(assumption)).
% 2.59/1.95 tff(1113,plain,
% 2.59/1.95 (~c2_1(a825)),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[930, 1112])).
% 2.59/1.95 tff(1114,plain,
% 2.59/1.95 (c0_1(a825)),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[954, 1112])).
% 2.59/1.95 tff(1115,plain,
% 2.59/1.95 (c1_1(a825)),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[943, 1112])).
% 2.59/1.95 tff(1116,assumption,(~c2_1(a825)), introduced(assumption)).
% 2.59/1.95 tff(1117,plain,
% 2.59/1.95 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a838) | c2_1(a825) | (~ndr1_0) | (~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | c2_1(a825) | (~ndr1_0) | (~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.59/1.95 inference(rewrite,[status(thm)],[])).
% 2.59/1.95 tff(1118,plain,
% 2.59/1.95 ((hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825))) <=> (hskp28 | c2_1(a838) | c2_1(a825) | (~ndr1_0) | (~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.59/1.95 inference(rewrite,[status(thm)],[])).
% 2.59/1.95 tff(1119,plain,
% 2.59/1.95 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a838) | c2_1(a825) | (~ndr1_0) | (~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 2.59/1.95 inference(monotonicity,[status(thm)],[1118])).
% 2.59/1.95 tff(1120,plain,
% 2.59/1.95 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | c2_1(a825) | (~ndr1_0) | (~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.59/1.95 inference(transitivity,[status(thm)],[1119, 1117])).
% 2.59/1.95 tff(1121,plain,
% 2.59/1.95 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)))),
% 2.59/1.95 inference(quant_inst,[status(thm)],[])).
% 2.59/1.95 tff(1122,plain,
% 2.59/1.95 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | c2_1(a825) | (~ndr1_0) | (~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838))),
% 2.59/1.95 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 2.59/1.95 tff(1123,plain,
% 2.59/1.95 ((~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838))),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[1122, 151, 357, 470, 1116, 368])).
% 2.59/1.95 tff(1124,plain,
% 2.59/1.95 ($false),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[1123, 1115, 1114, 483, 482])).
% 2.59/1.95 tff(1125,plain,((~hskp17) | (~c0_1(a838)) | (~c3_1(a838)) | hskp28 | c2_1(a838) | c2_1(a825)), inference(lemma,lemma(discharge,[]))).
% 2.59/1.95 tff(1126,plain,
% 2.59/1.95 ($false),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[1125, 1113, 1112, 483, 357, 470, 482])).
% 2.59/1.95 tff(1127,plain,((~hskp17) | (~c0_1(a838)) | hskp28 | c2_1(a838) | (~c3_1(a838))), inference(lemma,lemma(discharge,[]))).
% 2.59/1.95 tff(1128,plain,
% 2.59/1.95 (~hskp17),
% 2.59/1.95 inference(unit_resolution,[status(thm)],[1127, 1103, 357, 470, 1100])).
% 2.59/1.95 tff(1129,plain,
% 2.59/1.95 (^[U: $i] : refl((hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 2.59/1.95 inference(bind,[status(th)],[])).
% 2.59/1.95 tff(1130,plain,
% 2.59/1.95 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.59/1.95 inference(quant_intro,[status(thm)],[1129])).
% 2.59/1.95 tff(1131,plain,
% 2.59/1.95 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.59/1.95 inference(rewrite,[status(thm)],[])).
% 2.59/1.95 tff(1132,plain,
% 2.59/1.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0) <=> ((hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0))), rewrite(((hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 2.59/1.95 inference(bind,[status(th)],[])).
% 2.59/1.95 tff(1133,plain,
% 2.59/1.95 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.59/1.95 inference(quant_intro,[status(thm)],[1132])).
% 2.59/1.95 tff(1134,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 2.59/1.95 tff(1135,plain,
% 2.59/1.95 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.59/1.95 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 2.59/1.95 tff(1136,plain,
% 2.59/1.95 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.59/1.95 inference(modus_ponens,[status(thm)],[1135, 1131])).
% 2.59/1.95 tff(1137,plain,(
% 2.59/1.95 ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.59/1.95 inference(skolemize,[status(sab)],[1136])).
% 2.59/1.95 tff(1138,plain,
% 2.59/1.95 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.59/1.95 inference(modus_ponens,[status(thm)],[1137, 1130])).
% 2.59/1.95 tff(1139,plain,
% 2.59/1.95 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.59/1.95 inference(rewrite,[status(thm)],[])).
% 2.59/1.95 tff(1140,plain,
% 2.59/1.95 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833))) <=> (hskp17 | hskp0 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.59/1.95 inference(rewrite,[status(thm)],[])).
% 2.59/1.95 tff(1141,plain,
% 2.59/1.95 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.59/1.95 inference(monotonicity,[status(thm)],[1140])).
% 2.59/1.95 tff(1142,plain,
% 2.59/1.95 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.59/1.95 inference(transitivity,[status(thm)],[1141, 1139])).
% 2.59/1.95 tff(1143,plain,
% 2.59/1.95 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.59/1.96 inference(quant_inst,[status(thm)],[])).
% 2.59/1.96 tff(1144,plain,
% 2.59/1.96 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 2.59/1.96 tff(1145,plain,
% 2.59/1.96 (hskp17 | hskp0 | (~c3_1(a833))),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1144, 151, 639, 321, 1138])).
% 2.59/1.96 tff(1146,plain,
% 2.59/1.96 (~c3_1(a833)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1145, 1128, 1101])).
% 2.59/1.96 tff(1147,plain,
% 2.59/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1148,plain,
% 2.59/1.96 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833)) <=> (c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1149,plain,
% 2.59/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838)))),
% 2.59/1.96 inference(monotonicity,[status(thm)],[1148])).
% 2.59/1.96 tff(1150,plain,
% 2.59/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))),
% 2.59/1.96 inference(transitivity,[status(thm)],[1149, 1147])).
% 2.59/1.96 tff(1151,plain,
% 2.59/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833))),
% 2.59/1.96 inference(quant_inst,[status(thm)],[])).
% 2.59/1.96 tff(1152,plain,
% 2.59/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838)),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 2.59/1.96 tff(1153,plain,
% 2.59/1.96 ((~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1152, 151, 470, 321, 309, 322, 22, 876])).
% 2.59/1.96 tff(1154,plain,
% 2.59/1.96 (~c0_1(a832)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1153, 1146, 1103, 1111])).
% 2.59/1.96 tff(1155,plain,
% 2.59/1.96 (hskp12),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[826, 1146, 638, 637, 639, 321, 309, 636])).
% 2.59/1.96 tff(1156,plain,
% 2.59/1.96 (~c0_1(a809)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[164, 1155])).
% 2.59/1.96 tff(1157,plain,
% 2.59/1.96 (c2_1(a809)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[176, 1155])).
% 2.59/1.96 tff(1158,plain,
% 2.59/1.96 (c1_1(a809)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[187, 1155])).
% 2.59/1.96 tff(1159,plain,
% 2.59/1.96 ($false),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1097, 151, 433, 1158, 1157, 322, 22, 1156, 1067, 1154])).
% 2.59/1.96 tff(1160,plain,(hskp0 | (~c2_1(a832)) | c1_1(a832) | c3_1(a832) | c2_1(a838) | c0_1(a833) | c2_1(a833) | (~c1_1(a833)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.59/1.96 tff(1161,plain,
% 2.59/1.96 (hskp0),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1160, 470, 322, 22, 433, 321, 309, 639, 357])).
% 2.59/1.96 tff(1162,plain,
% 2.59/1.96 (c2_1(a793)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[669, 1161])).
% 2.59/1.96 tff(1163,plain,
% 2.59/1.96 (~c1_1(a793)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[675, 1161])).
% 2.59/1.96 tff(1164,plain,
% 2.59/1.96 (c0_1(a793)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[686, 1161])).
% 2.59/1.96 tff(1165,plain,
% 2.59/1.96 (hskp11),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[845, 704, 638, 637, 636, 639, 321, 309, 689, 691, 692])).
% 2.59/1.96 tff(1166,plain,
% 2.59/1.96 (~c1_1(a808)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[851, 1165])).
% 2.59/1.96 tff(1167,plain,
% 2.59/1.96 (~c2_1(a808)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[857, 1165])).
% 2.59/1.96 tff(1168,plain,
% 2.59/1.96 (c3_1(a833)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[900, 1167, 638, 637, 639, 321, 704, 692, 309, 689, 1166, 691, 636])).
% 2.59/1.96 tff(1169,plain,
% 2.59/1.96 (^[U: $i] : refl((hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 2.59/1.96 inference(bind,[status(th)],[])).
% 2.59/1.96 tff(1170,plain,
% 2.59/1.96 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.59/1.96 inference(quant_intro,[status(thm)],[1169])).
% 2.59/1.96 tff(1171,plain,
% 2.59/1.96 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1172,plain,
% 2.59/1.96 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp18) <=> ((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18))), rewrite(((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18) <=> (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp18) <=> (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 2.59/1.96 inference(bind,[status(th)],[])).
% 2.59/1.96 tff(1173,plain,
% 2.59/1.96 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp18) <=> ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.59/1.96 inference(quant_intro,[status(thm)],[1172])).
% 2.59/1.96 tff(1174,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 2.59/1.96 tff(1175,plain,
% 2.59/1.96 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1174, 1173])).
% 2.59/1.96 tff(1176,plain,
% 2.59/1.96 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1175, 1171])).
% 2.59/1.96 tff(1177,plain,(
% 2.59/1.96 ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.59/1.96 inference(skolemize,[status(sab)],[1176])).
% 2.59/1.96 tff(1178,plain,
% 2.59/1.96 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1177, 1170])).
% 2.59/1.96 tff(1179,plain,
% 2.59/1.96 (c3_1(a808)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[896, 1165])).
% 2.59/1.96 tff(1180,plain,
% 2.59/1.96 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp21 | hskp18 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp21 | hskp18 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1181,plain,
% 2.59/1.96 ((hskp21 | hskp18 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c3_1(a808))) <=> (hskp21 | hskp18 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1182,plain,
% 2.59/1.96 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp21 | hskp18 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808))))),
% 2.59/1.96 inference(monotonicity,[status(thm)],[1181])).
% 2.59/1.96 tff(1183,plain,
% 2.59/1.96 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp21 | hskp18 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)))),
% 2.59/1.96 inference(transitivity,[status(thm)],[1182, 1180])).
% 2.59/1.96 tff(1184,plain,
% 2.59/1.96 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)))),
% 2.59/1.96 inference(quant_inst,[status(thm)],[])).
% 2.59/1.96 tff(1185,plain,
% 2.59/1.96 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp21 | hskp18 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808))),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 2.59/1.96 tff(1186,plain,
% 2.59/1.96 (hskp18),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1185, 151, 704, 1179, 1166, 1167, 1178])).
% 2.59/1.96 tff(1187,plain,
% 2.59/1.96 (((~hskp18) | (~c2_1(a828))) <=> ((~hskp18) | (~c2_1(a828)))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1188,plain,
% 2.59/1.96 (((~c2_1(a828)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a828)))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1189,axiom,((~c2_1(a828)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 2.59/1.96 tff(1190,plain,
% 2.59/1.96 ((~hskp18) | (~c2_1(a828))),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 2.59/1.96 tff(1191,plain,
% 2.59/1.96 ((~hskp18) | (~c2_1(a828))),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1190, 1187])).
% 2.59/1.96 tff(1192,plain,
% 2.59/1.96 (~c2_1(a828)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1191, 1186])).
% 2.59/1.96 tff(1193,plain,
% 2.59/1.96 (((~hskp18) | (~c3_1(a828))) <=> ((~hskp18) | (~c3_1(a828)))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1194,plain,
% 2.59/1.96 (((~c3_1(a828)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a828)))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1195,axiom,((~c3_1(a828)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 2.59/1.96 tff(1196,plain,
% 2.59/1.96 ((~hskp18) | (~c3_1(a828))),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 2.59/1.96 tff(1197,plain,
% 2.59/1.96 ((~hskp18) | (~c3_1(a828))),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1196, 1193])).
% 2.59/1.96 tff(1198,plain,
% 2.59/1.96 (~c3_1(a828)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1197, 1186])).
% 2.59/1.96 tff(1199,plain,
% 2.59/1.96 (((~hskp18) | (~c1_1(a828))) <=> ((~hskp18) | (~c1_1(a828)))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1200,plain,
% 2.59/1.96 (((~c1_1(a828)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a828)))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1201,axiom,((~c1_1(a828)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 2.59/1.96 tff(1202,plain,
% 2.59/1.96 ((~hskp18) | (~c1_1(a828))),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 2.59/1.96 tff(1203,plain,
% 2.59/1.96 ((~hskp18) | (~c1_1(a828))),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1202, 1199])).
% 2.59/1.96 tff(1204,plain,
% 2.59/1.96 (~c1_1(a828)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1203, 1186])).
% 2.59/1.96 tff(1205,assumption,(~c3_1(a828)), introduced(assumption)).
% 2.59/1.96 tff(1206,assumption,(~c2_1(a828)), introduced(assumption)).
% 2.59/1.96 tff(1207,plain,
% 2.59/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a793)) | c3_1(a793))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a793)) | c3_1(a793))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1208,plain,
% 2.59/1.96 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828)) <=> (c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a793)) | c3_1(a793))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1209,plain,
% 2.59/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a793)) | c3_1(a793)))),
% 2.59/1.96 inference(monotonicity,[status(thm)],[1208])).
% 2.59/1.96 tff(1210,plain,
% 2.59/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a793)) | c3_1(a793))),
% 2.59/1.96 inference(transitivity,[status(thm)],[1209, 1207])).
% 2.59/1.96 tff(1211,plain,
% 2.59/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828))),
% 2.59/1.96 inference(quant_inst,[status(thm)],[])).
% 2.59/1.96 tff(1212,plain,
% 2.59/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a793)) | c3_1(a793)),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 2.59/1.96 tff(1213,plain,
% 2.59/1.96 (c0_1(a828) | c3_1(a793)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1212, 151, 1031, 692, 1206, 1205, 878, 877, 691, 876])).
% 2.59/1.96 tff(1214,plain,
% 2.59/1.96 (c0_1(a828)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1213, 988])).
% 2.59/1.96 tff(1215,assumption,(~c1_1(a828)), introduced(assumption)).
% 2.59/1.96 tff(1216,plain,
% 2.59/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a828)))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1217,plain,
% 2.59/1.96 (((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807)) <=> (c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a828)))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1218,plain,
% 2.59/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a828))))),
% 2.59/1.96 inference(monotonicity,[status(thm)],[1217])).
% 2.59/1.96 tff(1219,plain,
% 2.59/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a828)))),
% 2.59/1.96 inference(transitivity,[status(thm)],[1218, 1216])).
% 2.59/1.96 tff(1220,plain,
% 2.59/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807))),
% 2.59/1.96 inference(quant_inst,[status(thm)],[])).
% 2.59/1.96 tff(1221,plain,
% 2.59/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a828))),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 2.59/1.96 tff(1222,plain,
% 2.59/1.96 ($false),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1221, 151, 1031, 1215, 1205, 878, 877, 987, 905, 904, 876, 1214])).
% 2.59/1.96 tff(1223,plain,(hskp8 | (~c3_1(a808)) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~c0_1(a793)) | c2_1(a828) | c1_1(a793) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | c0_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.59/1.96 tff(1224,plain,
% 2.59/1.96 (hskp8),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1223, 1179, 1204, 1198, 1166, 1167, 692, 1192, 691, 1168, 639, 689, 321, 357])).
% 2.59/1.96 tff(1225,plain,
% 2.59/1.96 (~c3_1(a805)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[462, 1224])).
% 2.59/1.96 tff(1226,plain,
% 2.59/1.96 (~c2_1(a805)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[468, 1224])).
% 2.59/1.96 tff(1227,plain,
% 2.59/1.96 (c1_1(a805)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[480, 1224])).
% 2.59/1.96 tff(1228,plain,
% 2.59/1.96 (~c0_1(a832)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1056, 1227, 433, 1179, 322, 1166, 1226, 22, 1167, 1225])).
% 2.59/1.96 tff(1229,plain,
% 2.59/1.96 (hskp12),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1087, 1228, 433, 321, 309, 22, 1168])).
% 2.59/1.96 tff(1230,plain,
% 2.59/1.96 (~c0_1(a809)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[164, 1229])).
% 2.59/1.96 tff(1231,plain,
% 2.59/1.96 (c2_1(a809)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[176, 1229])).
% 2.59/1.96 tff(1232,plain,
% 2.59/1.96 (c1_1(a809)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[187, 1229])).
% 2.59/1.96 tff(1233,plain,
% 2.59/1.96 ($false),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1097, 151, 433, 1232, 1231, 322, 22, 1230, 1067, 1228])).
% 2.59/1.96 tff(1234,plain,(hskp21 | (~c2_1(a832)) | c1_1(a832) | c3_1(a832) | c0_1(a833) | c2_1(a833) | (~c0_1(a793)) | c1_1(a793) | (~c1_1(a833)) | (~c2_1(a793)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.59/1.96 tff(1235,plain,
% 2.59/1.96 (hskp21),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1234, 1164, 322, 22, 321, 309, 433, 1163, 639, 1162, 357])).
% 2.59/1.96 tff(1236,plain,
% 2.59/1.96 (c3_1(a838)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[443, 1235])).
% 2.59/1.96 tff(1237,plain,
% 2.59/1.96 (~c1_1(a838)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1110, 1236, 1100])).
% 2.59/1.96 tff(1238,plain,
% 2.59/1.96 (~c3_1(a793)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[971, 902, 964])).
% 2.59/1.96 tff(1239,assumption,(~c1_1(a838)), introduced(assumption)).
% 2.59/1.96 tff(1240,plain,
% 2.59/1.96 ($false),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[997, 151, 482, 692, 470, 987, 905, 904, 691, 876, 1239, 1238])).
% 2.59/1.96 tff(1241,plain,(hskp8 | (~c3_1(a838)) | (~c0_1(a793)) | c2_1(a838) | c1_1(a793) | c1_1(a838) | (~c1_1(a833)) | (~c2_1(a793)) | c0_1(a833) | c2_1(a833) | (~c2_1(a796)) | (~c3_1(a796)) | (~c0_1(a796)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.59/1.96 tff(1242,plain,
% 2.59/1.96 (hskp8),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1241, 1236, 1164, 470, 1163, 1237, 639, 1162, 321, 309, 638, 637, 636, 357])).
% 2.59/1.96 tff(1243,plain,
% 2.59/1.96 (~c2_1(a805)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[468, 1242])).
% 2.59/1.96 tff(1244,plain,
% 2.59/1.96 (c1_1(a805)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[480, 1242])).
% 2.59/1.96 tff(1245,plain,
% 2.59/1.96 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a838) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1246,plain,
% 2.59/1.96 ((hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805))) <=> (hskp28 | c2_1(a838) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.59/1.96 inference(rewrite,[status(thm)],[])).
% 2.59/1.96 tff(1247,plain,
% 2.59/1.96 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a838) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 2.59/1.96 inference(monotonicity,[status(thm)],[1246])).
% 2.59/1.96 tff(1248,plain,
% 2.59/1.96 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.59/1.96 inference(transitivity,[status(thm)],[1247, 1245])).
% 2.59/1.96 tff(1249,plain,
% 2.59/1.96 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)))),
% 2.59/1.96 inference(quant_inst,[status(thm)],[])).
% 2.59/1.96 tff(1250,plain,
% 2.59/1.96 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838))),
% 2.59/1.96 inference(modus_ponens,[status(thm)],[1249, 1248])).
% 2.59/1.96 tff(1251,plain,
% 2.59/1.96 (~c0_1(a805)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[1250, 151, 357, 1100, 1236, 1244, 470, 1243, 368])).
% 2.59/1.96 tff(1252,plain,
% 2.59/1.96 (~c3_1(a805)),
% 2.59/1.96 inference(unit_resolution,[status(thm)],[462, 1242])).
% 2.59/1.96 tff(1253,plain,
% 2.59/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c2_1(a805) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | c0_1(a805) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c2_1(a805) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | c0_1(a805) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1254,plain,
% 2.59/1.97 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a805) | c0_1(a805) | c3_1(a805)) <=> (c2_1(a838) | c2_1(a805) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | c0_1(a805) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1255,plain,
% 2.59/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a805) | c0_1(a805) | c3_1(a805))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c2_1(a805) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | c0_1(a805) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)))),
% 2.59/1.97 inference(monotonicity,[status(thm)],[1254])).
% 2.59/1.97 tff(1256,plain,
% 2.59/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a805) | c0_1(a805) | c3_1(a805))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c2_1(a805) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | c0_1(a805) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 2.59/1.97 inference(transitivity,[status(thm)],[1255, 1253])).
% 2.59/1.97 tff(1257,plain,
% 2.59/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a805) | c0_1(a805) | c3_1(a805))),
% 2.59/1.97 inference(quant_inst,[status(thm)],[])).
% 2.59/1.97 tff(1258,plain,
% 2.59/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c2_1(a805) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | c0_1(a805) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1257, 1256])).
% 2.59/1.97 tff(1259,plain,
% 2.59/1.97 (c0_1(a805) | c3_1(a793)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1258, 151, 1236, 1164, 470, 1243, 1252, 1163, 876, 1237])).
% 2.59/1.97 tff(1260,plain,
% 2.59/1.97 (c3_1(a793)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1259, 1251])).
% 2.59/1.97 tff(1261,plain,
% 2.59/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a805) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c0_1(a805) | (~c1_1(a805)) | (~c2_1(a793)) | (~c3_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c0_1(a805) | (~c1_1(a805)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1262,plain,
% 2.59/1.97 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c3_1(a805) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c0_1(a805) | (~c1_1(a805)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1263,plain,
% 2.59/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a805) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c0_1(a805) | (~c1_1(a805)) | (~c2_1(a793)) | (~c3_1(a793))))),
% 2.59/1.97 inference(monotonicity,[status(thm)],[1262])).
% 2.59/1.97 tff(1264,plain,
% 2.59/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c0_1(a805) | (~c1_1(a805)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 2.59/1.97 inference(transitivity,[status(thm)],[1263, 1261])).
% 2.59/1.97 tff(1265,plain,
% 2.59/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 2.59/1.97 inference(quant_inst,[status(thm)],[])).
% 2.59/1.97 tff(1266,plain,
% 2.59/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c0_1(a805) | (~c1_1(a805)) | (~c2_1(a793)) | (~c3_1(a793))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 2.59/1.97 tff(1267,plain,
% 2.59/1.97 ($false),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1266, 151, 636, 638, 637, 1244, 1162, 1252, 1163, 800, 1260, 1251])).
% 2.59/1.97 tff(1268,plain,(c2_1(a838) | hskp28 | (~c1_1(a833)) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~c2_1(a832))), inference(lemma,lemma(discharge,[]))).
% 2.59/1.97 tff(1269,plain,
% 2.59/1.97 (c2_1(a838)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1268, 634, 357, 633, 627, 392, 386, 380])).
% 2.59/1.97 tff(1270,plain,
% 2.59/1.97 (~hskp21),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[431, 1269])).
% 2.59/1.97 tff(1271,plain,
% 2.59/1.97 (hskp21 | hskp0),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[657, 151, 380, 392, 386, 651])).
% 2.59/1.97 tff(1272,plain,
% 2.59/1.97 (hskp0),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1271, 1270])).
% 2.59/1.97 tff(1273,plain,
% 2.59/1.97 (c2_1(a793)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[669, 1272])).
% 2.59/1.97 tff(1274,plain,
% 2.59/1.97 (c0_1(a793)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[686, 1272])).
% 2.59/1.97 tff(1275,plain,
% 2.59/1.97 (~c1_1(a793)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[675, 1272])).
% 2.59/1.97 tff(1276,plain,
% 2.59/1.97 ($false),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1234, 1275, 1274, 392, 386, 633, 627, 380, 1270, 634, 1273, 357])).
% 2.59/1.97 tff(1277,plain,(hskp30 | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.59/1.97 tff(1278,plain,
% 2.59/1.97 (hskp30),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1277, 357])).
% 2.59/1.97 tff(1279,plain,
% 2.59/1.97 (c3_1(a867)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[33, 1278])).
% 2.59/1.97 tff(1280,plain,
% 2.59/1.97 (c1_1(a867)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[44, 1278])).
% 2.59/1.97 tff(1281,plain,
% 2.59/1.97 (c0_1(a867)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[55, 1278])).
% 2.59/1.97 tff(1282,plain,
% 2.59/1.97 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)) | (~c1_1(a867)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)) | (~c1_1(a867)))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1283,plain,
% 2.59/1.97 ((hskp28 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)) | c2_1(a867) | (~c1_1(a867)) | (~c0_1(a867))) <=> (hskp28 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)) | (~c1_1(a867)))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1284,plain,
% 2.59/1.97 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)) | c2_1(a867) | (~c1_1(a867)) | (~c0_1(a867)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)) | (~c1_1(a867))))),
% 2.59/1.97 inference(monotonicity,[status(thm)],[1283])).
% 2.59/1.97 tff(1285,plain,
% 2.59/1.97 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)) | c2_1(a867) | (~c1_1(a867)) | (~c0_1(a867)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)) | (~c1_1(a867)))),
% 2.59/1.97 inference(transitivity,[status(thm)],[1284, 1282])).
% 2.59/1.97 tff(1286,plain,
% 2.59/1.97 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)) | c2_1(a867) | (~c1_1(a867)) | (~c0_1(a867)))),
% 2.59/1.97 inference(quant_inst,[status(thm)],[])).
% 2.59/1.97 tff(1287,plain,
% 2.59/1.97 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)) | (~c1_1(a867))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 2.59/1.97 tff(1288,plain,
% 2.59/1.97 ($false),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1287, 151, 357, 1281, 1280, 1279, 368, 358])).
% 2.59/1.97 tff(1289,plain,(c2_1(a867) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.59/1.97 tff(1290,plain,
% 2.59/1.97 (c2_1(a867)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1289, 357])).
% 2.59/1.97 tff(1291,plain,
% 2.59/1.97 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 2.59/1.97 inference(bind,[status(th)],[])).
% 2.59/1.97 tff(1292,plain,
% 2.59/1.97 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.59/1.97 inference(quant_intro,[status(thm)],[1291])).
% 2.59/1.97 tff(1293,plain,
% 2.59/1.97 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1294,plain,
% 2.59/1.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_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) | (~c3_1(U)) | (~c1_1(U)) | (~c2_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)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_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)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_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)) | c3_1(V)) | hskp15) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp15))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_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)) | c3_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 2.59/1.97 inference(bind,[status(th)],[])).
% 2.59/1.97 tff(1295,plain,
% 2.59/1.97 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.59/1.97 inference(quant_intro,[status(thm)],[1294])).
% 2.59/1.97 tff(1296,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 2.59/1.97 tff(1297,plain,
% 2.59/1.97 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 2.59/1.97 tff(1298,plain,
% 2.59/1.97 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1297, 1293])).
% 2.59/1.97 tff(1299,plain,(
% 2.59/1.97 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.59/1.97 inference(skolemize,[status(sab)],[1298])).
% 2.59/1.97 tff(1300,plain,
% 2.59/1.97 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1299, 1292])).
% 2.59/1.97 tff(1301,plain,
% 2.59/1.97 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 2.59/1.97 inference(bind,[status(th)],[])).
% 2.59/1.97 tff(1302,plain,
% 2.59/1.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.59/1.97 inference(quant_intro,[status(thm)],[1301])).
% 2.59/1.97 tff(1303,plain,
% 2.59/1.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1304,plain,
% 2.59/1.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp28) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 2.59/1.97 inference(bind,[status(th)],[])).
% 2.59/1.97 tff(1305,plain,
% 2.59/1.97 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.59/1.97 inference(quant_intro,[status(thm)],[1304])).
% 2.59/1.97 tff(1306,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 2.59/1.97 tff(1307,plain,
% 2.59/1.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 2.59/1.97 tff(1308,plain,
% 2.59/1.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1307, 1303])).
% 2.59/1.97 tff(1309,plain,(
% 2.59/1.97 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.59/1.97 inference(skolemize,[status(sab)],[1308])).
% 2.59/1.97 tff(1310,plain,
% 2.59/1.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1309, 1302])).
% 2.59/1.97 tff(1311,assumption,(hskp21), introduced(assumption)).
% 2.59/1.97 tff(1312,plain,
% 2.59/1.97 (~c2_1(a838)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[431, 1311])).
% 2.59/1.97 tff(1313,plain,
% 2.59/1.97 (^[U: $i] : refl((hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 2.59/1.97 inference(bind,[status(th)],[])).
% 2.59/1.97 tff(1314,plain,
% 2.59/1.97 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.97 inference(quant_intro,[status(thm)],[1313])).
% 2.59/1.97 tff(1315,plain,
% 2.59/1.97 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1316,plain,
% 2.59/1.97 (^[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)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp19) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp19))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp19) <=> (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp19) <=> (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 2.59/1.97 inference(bind,[status(th)],[])).
% 2.59/1.97 tff(1317,plain,
% 2.59/1.97 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp19) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.97 inference(quant_intro,[status(thm)],[1316])).
% 2.59/1.97 tff(1318,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 2.59/1.97 tff(1319,plain,
% 2.59/1.97 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 2.59/1.97 tff(1320,plain,
% 2.59/1.97 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1319, 1315])).
% 2.59/1.97 tff(1321,plain,(
% 2.59/1.97 ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.97 inference(skolemize,[status(sab)],[1320])).
% 2.59/1.97 tff(1322,plain,
% 2.59/1.97 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1321, 1314])).
% 2.59/1.97 tff(1323,plain,
% 2.59/1.97 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1324,plain,
% 2.59/1.97 ((hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867))) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1325,plain,
% 2.59/1.97 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867))))),
% 2.59/1.97 inference(monotonicity,[status(thm)],[1324])).
% 2.59/1.97 tff(1326,plain,
% 2.59/1.97 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 2.59/1.97 inference(transitivity,[status(thm)],[1325, 1323])).
% 2.59/1.97 tff(1327,plain,
% 2.59/1.97 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)))),
% 2.59/1.97 inference(quant_inst,[status(thm)],[])).
% 2.59/1.97 tff(1328,plain,
% 2.59/1.97 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 2.59/1.97 tff(1329,plain,
% 2.59/1.97 (hskp21 | hskp11 | (~c2_1(a867))),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1328, 151, 1280, 1279, 703])).
% 2.59/1.97 tff(1330,plain,
% 2.59/1.97 (hskp11),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1329, 704, 1290])).
% 2.59/1.97 tff(1331,plain,
% 2.59/1.97 (~c2_1(a808)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[857, 1330])).
% 2.59/1.97 tff(1332,plain,
% 2.59/1.97 (~c1_1(a808)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[851, 1330])).
% 2.59/1.97 tff(1333,plain,
% 2.59/1.97 (c3_1(a808)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[896, 1330])).
% 2.59/1.97 tff(1334,plain,
% 2.59/1.97 (hskp18),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1185, 151, 704, 1333, 1332, 1331, 1178])).
% 2.59/1.97 tff(1335,plain,
% 2.59/1.97 (~c3_1(a828)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1197, 1334])).
% 2.59/1.97 tff(1336,plain,
% 2.59/1.97 (~c2_1(a828)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1191, 1334])).
% 2.59/1.97 tff(1337,assumption,(hskp15), introduced(assumption)).
% 2.59/1.97 tff(1338,plain,
% 2.59/1.97 (((~hskp15) | (~c1_1(a817))) <=> ((~hskp15) | (~c1_1(a817)))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1339,plain,
% 2.59/1.97 (((~c1_1(a817)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a817)))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1340,axiom,((~c1_1(a817)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 2.59/1.97 tff(1341,plain,
% 2.59/1.97 ((~hskp15) | (~c1_1(a817))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1340, 1339])).
% 2.59/1.97 tff(1342,plain,
% 2.59/1.97 ((~hskp15) | (~c1_1(a817))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1341, 1338])).
% 2.59/1.97 tff(1343,plain,
% 2.59/1.97 (~c1_1(a817)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1342, 1337])).
% 2.59/1.97 tff(1344,plain,
% 2.59/1.97 (((~hskp15) | c3_1(a817)) <=> ((~hskp15) | c3_1(a817))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1345,axiom,((~hskp15) | c3_1(a817)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 2.59/1.97 tff(1346,plain,
% 2.59/1.97 ((~hskp15) | c3_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 2.59/1.97 tff(1347,plain,
% 2.59/1.97 ((~hskp15) | c3_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1346, 1344])).
% 2.59/1.97 tff(1348,plain,
% 2.59/1.97 ((~hskp15) | c3_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1347, 1344])).
% 2.59/1.97 tff(1349,plain,
% 2.59/1.97 ((~hskp15) | c3_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1348, 1344])).
% 2.59/1.97 tff(1350,plain,
% 2.59/1.97 ((~hskp15) | c3_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1349, 1344])).
% 2.59/1.97 tff(1351,plain,
% 2.59/1.97 ((~hskp15) | c3_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1350, 1344])).
% 2.59/1.97 tff(1352,plain,
% 2.59/1.97 ((~hskp15) | c3_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1351, 1344])).
% 2.59/1.97 tff(1353,plain,
% 2.59/1.97 ((~hskp15) | c3_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1352, 1344])).
% 2.59/1.97 tff(1354,plain,
% 2.59/1.97 (c3_1(a817)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1353, 1337])).
% 2.59/1.97 tff(1355,plain,
% 2.59/1.97 (((~hskp15) | c2_1(a817)) <=> ((~hskp15) | c2_1(a817))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1356,axiom,((~hskp15) | c2_1(a817)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 2.59/1.97 tff(1357,plain,
% 2.59/1.97 ((~hskp15) | c2_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 2.59/1.97 tff(1358,plain,
% 2.59/1.97 ((~hskp15) | c2_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1357, 1355])).
% 2.59/1.97 tff(1359,plain,
% 2.59/1.97 ((~hskp15) | c2_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1358, 1355])).
% 2.59/1.97 tff(1360,plain,
% 2.59/1.97 ((~hskp15) | c2_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1359, 1355])).
% 2.59/1.97 tff(1361,plain,
% 2.59/1.97 ((~hskp15) | c2_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1360, 1355])).
% 2.59/1.97 tff(1362,plain,
% 2.59/1.97 ((~hskp15) | c2_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1361, 1355])).
% 2.59/1.97 tff(1363,plain,
% 2.59/1.97 ((~hskp15) | c2_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1362, 1355])).
% 2.59/1.97 tff(1364,plain,
% 2.59/1.97 ((~hskp15) | c2_1(a817)),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1363, 1355])).
% 2.59/1.97 tff(1365,plain,
% 2.59/1.97 (c2_1(a817)),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1364, 1337])).
% 2.59/1.97 tff(1366,plain,
% 2.59/1.97 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a817) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a817)) | (~c3_1(a817)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a817) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a817)) | (~c3_1(a817)))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1367,plain,
% 2.59/1.97 ((hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817))) <=> (hskp28 | c1_1(a817) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a817)) | (~c3_1(a817)))),
% 2.59/1.97 inference(rewrite,[status(thm)],[])).
% 2.59/1.97 tff(1368,plain,
% 2.59/1.97 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a817) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a817)) | (~c3_1(a817))))),
% 2.59/1.97 inference(monotonicity,[status(thm)],[1367])).
% 2.59/1.97 tff(1369,plain,
% 2.59/1.97 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a817) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a817)) | (~c3_1(a817)))),
% 2.59/1.97 inference(transitivity,[status(thm)],[1368, 1366])).
% 2.59/1.97 tff(1370,plain,
% 2.59/1.97 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)))),
% 2.59/1.97 inference(quant_inst,[status(thm)],[])).
% 2.59/1.97 tff(1371,plain,
% 2.59/1.97 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a817) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a817)) | (~c3_1(a817))),
% 2.59/1.97 inference(modus_ponens,[status(thm)],[1370, 1369])).
% 2.59/1.97 tff(1372,plain,
% 2.59/1.97 ($false),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1371, 151, 357, 1281, 1280, 1279, 1365, 1354, 1343, 1310])).
% 2.59/1.97 tff(1373,plain,((~hskp15) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.59/1.97 tff(1374,plain,
% 2.59/1.97 (~hskp15),
% 2.59/1.97 inference(unit_resolution,[status(thm)],[1373, 357])).
% 2.59/1.97 tff(1375,assumption,(c2_1(a867)), introduced(assumption)).
% 2.59/1.97 tff(1376,assumption,(c2_1(a833)), introduced(assumption)).
% 2.59/1.97 tff(1377,plain,
% 2.59/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))),
% 2.59/1.98 inference(rewrite,[status(thm)],[])).
% 2.59/1.98 tff(1378,plain,
% 2.59/1.98 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a833) | (~c3_1(a833)) | (~c2_1(a833))) <=> (c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))),
% 2.59/1.98 inference(rewrite,[status(thm)],[])).
% 2.59/1.98 tff(1379,plain,
% 2.59/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a833) | (~c3_1(a833)) | (~c2_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833))))),
% 2.59/1.98 inference(monotonicity,[status(thm)],[1378])).
% 2.59/1.98 tff(1380,plain,
% 2.59/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a833) | (~c3_1(a833)) | (~c2_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))),
% 2.59/1.98 inference(transitivity,[status(thm)],[1379, 1377])).
% 2.59/1.98 tff(1381,plain,
% 2.59/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a833) | (~c3_1(a833)) | (~c2_1(a833)))),
% 2.59/1.98 inference(quant_inst,[status(thm)],[])).
% 2.59/1.98 tff(1382,plain,
% 2.59/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833))),
% 2.59/1.98 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 2.59/1.98 tff(1383,plain,
% 2.59/1.98 ((~c2_1(a833)) | (~c3_1(a833))),
% 2.59/1.98 inference(unit_resolution,[status(thm)],[1382, 151, 70, 69, 77, 321, 207, 1375])).
% 2.59/1.98 tff(1384,plain,
% 2.59/1.98 (~c3_1(a833)),
% 2.59/1.98 inference(unit_resolution,[status(thm)],[1383, 1376])).
% 2.59/1.98 tff(1385,assumption,(~hskp15), introduced(assumption)).
% 2.59/1.98 tff(1386,plain,
% 2.59/1.98 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | c3_1(a833))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | c3_1(a833))),
% 2.59/1.98 inference(rewrite,[status(thm)],[])).
% 2.59/1.98 tff(1387,plain,
% 2.59/1.98 ((hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a833) | c0_1(a833) | (~c2_1(a833))) <=> (hskp15 | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | c3_1(a833))),
% 2.59/1.98 inference(rewrite,[status(thm)],[])).
% 2.59/1.98 tff(1388,plain,
% 2.59/1.98 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a833) | c0_1(a833) | (~c2_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | c3_1(a833)))),
% 2.59/1.98 inference(monotonicity,[status(thm)],[1387])).
% 2.59/1.98 tff(1389,plain,
% 2.59/1.98 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a833) | c0_1(a833) | (~c2_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | c3_1(a833))),
% 2.59/1.98 inference(transitivity,[status(thm)],[1388, 1386])).
% 2.59/1.98 tff(1390,plain,
% 2.59/1.98 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a833) | c0_1(a833) | (~c2_1(a833)))),
% 2.59/1.98 inference(quant_inst,[status(thm)],[])).
% 2.59/1.98 tff(1391,plain,
% 2.59/1.98 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | c3_1(a833)),
% 2.59/1.98 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 2.59/1.98 tff(1392,plain,
% 2.59/1.98 ($false),
% 2.59/1.98 inference(unit_resolution,[status(thm)],[1391, 151, 1385, 69, 77, 321, 1376, 1300, 1384, 1375])).
% 2.59/1.98 tff(1393,plain,((~c2_1(a833)) | hskp15 | (~c1_1(a867)) | (~c3_1(a867)) | c0_1(a833) | (~c2_1(a867)) | (~c0_1(a867))), inference(lemma,lemma(discharge,[]))).
% 2.59/1.98 tff(1394,plain,
% 2.59/1.98 (~c2_1(a833)),
% 2.59/1.98 inference(unit_resolution,[status(thm)],[1393, 321, 1280, 1279, 1374, 1290, 1281])).
% 2.59/1.98 tff(1395,plain,
% 2.59/1.98 (^[U: $i] : refl((hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 2.59/1.98 inference(bind,[status(th)],[])).
% 2.59/1.98 tff(1396,plain,
% 2.59/1.98 (![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.59/1.98 inference(quant_intro,[status(thm)],[1395])).
% 2.67/1.98 tff(1397,plain,
% 2.67/1.98 (![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1398,plain,
% 2.67/1.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp2) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp2))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp2) <=> (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp2) <=> (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 2.67/1.98 inference(bind,[status(th)],[])).
% 2.67/1.98 tff(1399,plain,
% 2.67/1.98 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp2) <=> ![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.67/1.98 inference(quant_intro,[status(thm)],[1398])).
% 2.67/1.98 tff(1400,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 2.67/1.98 tff(1401,plain,
% 2.67/1.98 (![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 2.67/1.98 tff(1402,plain,
% 2.67/1.98 (![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1401, 1397])).
% 2.67/1.98 tff(1403,plain,(
% 2.67/1.98 ![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.67/1.98 inference(skolemize,[status(sab)],[1402])).
% 2.67/1.98 tff(1404,plain,
% 2.67/1.98 (![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1403, 1396])).
% 2.67/1.98 tff(1405,plain,
% 2.67/1.98 (~c1_1(a828)),
% 2.67/1.98 inference(unit_resolution,[status(thm)],[1203, 1334])).
% 2.67/1.98 tff(1406,plain,
% 2.67/1.98 (((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))) <=> ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp20 | hskp2 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1407,plain,
% 2.67/1.98 ((hskp20 | hskp2 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | c3_1(a828)) <=> (hskp20 | hskp2 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1408,plain,
% 2.67/1.98 (((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | c3_1(a828))) <=> ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0)))),
% 2.67/1.98 inference(monotonicity,[status(thm)],[1407])).
% 2.67/1.98 tff(1409,plain,
% 2.67/1.98 (((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | c3_1(a828))) <=> ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp20 | hskp2 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))),
% 2.67/1.98 inference(transitivity,[status(thm)],[1408, 1406])).
% 2.67/1.98 tff(1410,plain,
% 2.67/1.98 ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | c3_1(a828))),
% 2.67/1.98 inference(quant_inst,[status(thm)],[])).
% 2.67/1.98 tff(1411,plain,
% 2.67/1.98 ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp20 | hskp2 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0)),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 2.67/1.98 tff(1412,plain,
% 2.67/1.98 (hskp2),
% 2.67/1.98 inference(unit_resolution,[status(thm)],[1411, 151, 344, 1405, 1336, 1335, 1404])).
% 2.67/1.98 tff(1413,plain,
% 2.67/1.98 (((~hskp2) | (~c3_1(a795))) <=> ((~hskp2) | (~c3_1(a795)))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1414,plain,
% 2.67/1.98 (((~c3_1(a795)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a795)))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1415,axiom,((~c3_1(a795)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 2.67/1.98 tff(1416,plain,
% 2.67/1.98 ((~hskp2) | (~c3_1(a795))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 2.67/1.98 tff(1417,plain,
% 2.67/1.98 ((~hskp2) | (~c3_1(a795))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1416, 1413])).
% 2.67/1.98 tff(1418,plain,
% 2.67/1.98 (~c3_1(a795)),
% 2.67/1.98 inference(unit_resolution,[status(thm)],[1417, 1412])).
% 2.67/1.98 tff(1419,plain,
% 2.67/1.98 (((~hskp2) | (~c1_1(a795))) <=> ((~hskp2) | (~c1_1(a795)))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1420,plain,
% 2.67/1.98 (((~c1_1(a795)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a795)))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1421,axiom,((~c1_1(a795)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 2.67/1.98 tff(1422,plain,
% 2.67/1.98 ((~hskp2) | (~c1_1(a795))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 2.67/1.98 tff(1423,plain,
% 2.67/1.98 ((~hskp2) | (~c1_1(a795))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1422, 1419])).
% 2.67/1.98 tff(1424,plain,
% 2.67/1.98 (~c1_1(a795)),
% 2.67/1.98 inference(unit_resolution,[status(thm)],[1423, 1412])).
% 2.67/1.98 tff(1425,plain,
% 2.67/1.98 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 2.67/1.98 inference(bind,[status(th)],[])).
% 2.67/1.98 tff(1426,plain,
% 2.67/1.98 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.67/1.98 inference(quant_intro,[status(thm)],[1425])).
% 2.67/1.98 tff(1427,plain,
% 2.67/1.98 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1428,plain,
% 2.67/1.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 2.67/1.98 inference(bind,[status(th)],[])).
% 2.67/1.98 tff(1429,plain,
% 2.67/1.98 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.67/1.98 inference(quant_intro,[status(thm)],[1428])).
% 2.67/1.98 tff(1430,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 2.67/1.98 tff(1431,plain,
% 2.67/1.98 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 2.67/1.98 tff(1432,plain,
% 2.67/1.98 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1431, 1427])).
% 2.67/1.98 tff(1433,plain,(
% 2.67/1.98 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.67/1.98 inference(skolemize,[status(sab)],[1432])).
% 2.67/1.98 tff(1434,plain,
% 2.67/1.98 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1433, 1426])).
% 2.67/1.98 tff(1435,assumption,(~c2_1(a793)), introduced(assumption)).
% 2.67/1.98 tff(1436,plain,
% 2.67/1.98 (~hskp0),
% 2.67/1.98 inference(unit_resolution,[status(thm)],[669, 1435])).
% 2.67/1.98 tff(1437,assumption,(~c0_1(a793)), introduced(assumption)).
% 2.67/1.98 tff(1438,plain,
% 2.67/1.98 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1439,plain,
% 2.67/1.98 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795))) <=> (hskp21 | hskp0 | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1440,plain,
% 2.67/1.98 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795))))),
% 2.67/1.98 inference(monotonicity,[status(thm)],[1439])).
% 2.67/1.98 tff(1441,plain,
% 2.67/1.98 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)))),
% 2.67/1.98 inference(transitivity,[status(thm)],[1440, 1438])).
% 2.67/1.98 tff(1442,plain,
% 2.67/1.98 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)))),
% 2.67/1.98 inference(quant_inst,[status(thm)],[])).
% 2.67/1.98 tff(1443,plain,
% 2.67/1.98 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 2.67/1.98 tff(1444,plain,
% 2.67/1.98 (~c2_1(a795)),
% 2.67/1.98 inference(unit_resolution,[status(thm)],[1443, 151, 704, 1101, 1424, 1418, 651])).
% 2.67/1.98 tff(1445,plain,
% 2.67/1.98 (((~hskp2) | (~c0_1(a795))) <=> ((~hskp2) | (~c0_1(a795)))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1446,plain,
% 2.67/1.98 (((~c0_1(a795)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a795)))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1447,axiom,((~c0_1(a795)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 2.67/1.98 tff(1448,plain,
% 2.67/1.98 ((~hskp2) | (~c0_1(a795))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 2.67/1.98 tff(1449,plain,
% 2.67/1.98 ((~hskp2) | (~c0_1(a795))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1448, 1445])).
% 2.67/1.98 tff(1450,plain,
% 2.67/1.98 (~c0_1(a795)),
% 2.67/1.98 inference(unit_resolution,[status(thm)],[1449, 1412])).
% 2.67/1.98 tff(1451,plain,
% 2.67/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a828)))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1452,plain,
% 2.67/1.98 (((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795)) <=> (c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a828)))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1453,plain,
% 2.67/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a828))))),
% 2.67/1.98 inference(monotonicity,[status(thm)],[1452])).
% 2.67/1.98 tff(1454,plain,
% 2.67/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a828)))),
% 2.67/1.98 inference(transitivity,[status(thm)],[1453, 1451])).
% 2.67/1.98 tff(1455,plain,
% 2.67/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795))),
% 2.67/1.98 inference(quant_inst,[status(thm)],[])).
% 2.67/1.98 tff(1456,plain,
% 2.67/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a828))),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 2.67/1.98 tff(1457,plain,
% 2.67/1.98 (~c0_1(a828)),
% 2.67/1.98 inference(unit_resolution,[status(thm)],[1456, 151, 1333, 1405, 1335, 1332, 1331, 1450, 1418, 876, 1444])).
% 2.67/1.98 tff(1458,assumption,(~c2_1(a832)), introduced(assumption)).
% 2.67/1.98 tff(1459,plain,
% 2.67/1.98 (~hskp19),
% 2.67/1.98 inference(unit_resolution,[status(thm)],[379, 1458])).
% 2.67/1.98 tff(1460,plain,
% 2.67/1.98 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1461,plain,
% 2.67/1.98 ((hskp28 | hskp19 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832))) <=> (hskp28 | hskp19 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0))),
% 2.67/1.98 inference(rewrite,[status(thm)],[])).
% 2.67/1.98 tff(1462,plain,
% 2.67/1.98 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0)))),
% 2.67/1.98 inference(monotonicity,[status(thm)],[1461])).
% 2.67/1.98 tff(1463,plain,
% 2.67/1.98 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0))),
% 2.67/1.98 inference(transitivity,[status(thm)],[1462, 1460])).
% 2.67/1.98 tff(1464,plain,
% 2.67/1.98 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))),
% 2.67/1.98 inference(quant_inst,[status(thm)],[])).
% 2.67/1.98 tff(1465,plain,
% 2.67/1.98 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0)),
% 2.67/1.98 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 2.67/1.98 tff(1466,plain,
% 2.67/1.98 (hskp19 | c2_1(a832) | (~c1_1(a832))),
% 2.67/1.98 inference(unit_resolution,[status(thm)],[1465, 151, 357, 22, 1322])).
% 2.67/1.99 tff(1467,plain,
% 2.67/1.99 (~c1_1(a832)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1466, 1459, 1458])).
% 2.67/1.99 tff(1468,assumption,(hskp7), introduced(assumption)).
% 2.67/1.99 tff(1469,plain,
% 2.67/1.99 (((~hskp7) | (~c2_1(a803))) <=> ((~hskp7) | (~c2_1(a803)))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1470,plain,
% 2.67/1.99 (((~c2_1(a803)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a803)))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1471,axiom,((~c2_1(a803)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 2.67/1.99 tff(1472,plain,
% 2.67/1.99 ((~hskp7) | (~c2_1(a803))),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 2.67/1.99 tff(1473,plain,
% 2.67/1.99 ((~hskp7) | (~c2_1(a803))),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1472, 1469])).
% 2.67/1.99 tff(1474,plain,
% 2.67/1.99 (~c2_1(a803)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1473, 1468])).
% 2.67/1.99 tff(1475,plain,
% 2.67/1.99 (((~hskp7) | c3_1(a803)) <=> ((~hskp7) | c3_1(a803))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1476,axiom,((~hskp7) | c3_1(a803)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 2.67/1.99 tff(1477,plain,
% 2.67/1.99 ((~hskp7) | c3_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 2.67/1.99 tff(1478,plain,
% 2.67/1.99 ((~hskp7) | c3_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1477, 1475])).
% 2.67/1.99 tff(1479,plain,
% 2.67/1.99 ((~hskp7) | c3_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1478, 1475])).
% 2.67/1.99 tff(1480,plain,
% 2.67/1.99 ((~hskp7) | c3_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1479, 1475])).
% 2.67/1.99 tff(1481,plain,
% 2.67/1.99 ((~hskp7) | c3_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1480, 1475])).
% 2.67/1.99 tff(1482,plain,
% 2.67/1.99 ((~hskp7) | c3_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1481, 1475])).
% 2.67/1.99 tff(1483,plain,
% 2.67/1.99 ((~hskp7) | c3_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1482, 1475])).
% 2.67/1.99 tff(1484,plain,
% 2.67/1.99 ((~hskp7) | c3_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1483, 1475])).
% 2.67/1.99 tff(1485,plain,
% 2.67/1.99 (c3_1(a803)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1484, 1468])).
% 2.67/1.99 tff(1486,plain,
% 2.67/1.99 (((~hskp7) | c1_1(a803)) <=> ((~hskp7) | c1_1(a803))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1487,axiom,((~hskp7) | c1_1(a803)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 2.67/1.99 tff(1488,plain,
% 2.67/1.99 ((~hskp7) | c1_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1487, 1486])).
% 2.67/1.99 tff(1489,plain,
% 2.67/1.99 ((~hskp7) | c1_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1488, 1486])).
% 2.67/1.99 tff(1490,plain,
% 2.67/1.99 ((~hskp7) | c1_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1489, 1486])).
% 2.67/1.99 tff(1491,plain,
% 2.67/1.99 ((~hskp7) | c1_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1490, 1486])).
% 2.67/1.99 tff(1492,plain,
% 2.67/1.99 ((~hskp7) | c1_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1491, 1486])).
% 2.67/1.99 tff(1493,plain,
% 2.67/1.99 ((~hskp7) | c1_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1492, 1486])).
% 2.67/1.99 tff(1494,plain,
% 2.67/1.99 ((~hskp7) | c1_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1493, 1486])).
% 2.67/1.99 tff(1495,plain,
% 2.67/1.99 ((~hskp7) | c1_1(a803)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1494, 1486])).
% 2.67/1.99 tff(1496,plain,
% 2.67/1.99 (c1_1(a803)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1495, 1468])).
% 2.67/1.99 tff(1497,plain,
% 2.67/1.99 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | c1_1(a832) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | c1_1(a832) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1498,plain,
% 2.67/1.99 ((hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c2_1(a832) | c1_1(a832)) <=> (hskp19 | c2_1(a832) | c1_1(a832) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1499,plain,
% 2.67/1.99 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | c1_1(a832) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803))))),
% 2.67/1.99 inference(monotonicity,[status(thm)],[1498])).
% 2.67/1.99 tff(1500,plain,
% 2.67/1.99 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | c1_1(a832) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))),
% 2.67/1.99 inference(transitivity,[status(thm)],[1499, 1497])).
% 2.67/1.99 tff(1501,plain,
% 2.67/1.99 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c2_1(a832) | c1_1(a832))),
% 2.67/1.99 inference(quant_inst,[status(thm)],[])).
% 2.67/1.99 tff(1502,plain,
% 2.67/1.99 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | c1_1(a832) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803))),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 2.67/1.99 tff(1503,plain,
% 2.67/1.99 ($false),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1502, 151, 1459, 1458, 1496, 1485, 322, 22, 1474, 10])).
% 2.67/1.99 tff(1504,plain,((~hskp7) | c2_1(a832) | c1_1(a832) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.67/1.99 tff(1505,plain,
% 2.67/1.99 (~hskp7),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1504, 1458, 1467, 22])).
% 2.67/1.99 tff(1506,plain,
% 2.67/1.99 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 2.67/1.99 inference(bind,[status(th)],[])).
% 2.67/1.99 tff(1507,plain,
% 2.67/1.99 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.67/1.99 inference(quant_intro,[status(thm)],[1506])).
% 2.67/1.99 tff(1508,plain,
% 2.67/1.99 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1509,plain,
% 2.67/1.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 2.67/1.99 inference(bind,[status(th)],[])).
% 2.67/1.99 tff(1510,plain,
% 2.67/1.99 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.67/1.99 inference(quant_intro,[status(thm)],[1509])).
% 2.67/1.99 tff(1511,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 2.67/1.99 tff(1512,plain,
% 2.67/1.99 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1511, 1510])).
% 2.67/1.99 tff(1513,plain,
% 2.67/1.99 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1512, 1508])).
% 2.67/1.99 tff(1514,plain,(
% 2.67/1.99 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.67/1.99 inference(skolemize,[status(sab)],[1513])).
% 2.67/1.99 tff(1515,plain,
% 2.67/1.99 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1514, 1507])).
% 2.67/1.99 tff(1516,assumption,(hskp11), introduced(assumption)).
% 2.67/1.99 tff(1517,plain,
% 2.67/1.99 (~c1_1(a808)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[851, 1516])).
% 2.67/1.99 tff(1518,plain,
% 2.67/1.99 (c3_1(a808)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[896, 1516])).
% 2.67/1.99 tff(1519,plain,
% 2.67/1.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a808) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a808)) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a808) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a808)) | c0_1(a808))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1520,plain,
% 2.67/1.99 ((hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (hskp7 | c1_1(a808) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a808)) | c0_1(a808))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1521,plain,
% 2.67/1.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a808) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a808)) | c0_1(a808)))),
% 2.67/1.99 inference(monotonicity,[status(thm)],[1520])).
% 2.67/1.99 tff(1522,plain,
% 2.67/1.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a808) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a808)) | c0_1(a808))),
% 2.67/1.99 inference(transitivity,[status(thm)],[1521, 1519])).
% 2.67/1.99 tff(1523,plain,
% 2.67/1.99 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 2.67/1.99 inference(quant_inst,[status(thm)],[])).
% 2.67/1.99 tff(1524,plain,
% 2.67/1.99 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a808) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a808)) | c0_1(a808)),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 2.67/1.99 tff(1525,plain,
% 2.67/1.99 (hskp7 | c0_1(a808)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1524, 151, 1280, 1279, 1518, 1517, 1515, 1290])).
% 2.67/1.99 tff(1526,plain,
% 2.67/1.99 (c0_1(a808)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1525, 1505])).
% 2.67/1.99 tff(1527,plain,
% 2.67/1.99 (~c2_1(a808)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[857, 1516])).
% 2.67/1.99 tff(1528,plain,
% 2.67/1.99 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a808)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a808)))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1529,plain,
% 2.67/1.99 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808))) <=> (hskp20 | hskp9 | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a808)))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1530,plain,
% 2.67/1.99 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a808))))),
% 2.67/1.99 inference(monotonicity,[status(thm)],[1529])).
% 2.67/1.99 tff(1531,plain,
% 2.67/1.99 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a808)))),
% 2.67/1.99 inference(transitivity,[status(thm)],[1530, 1528])).
% 2.67/1.99 tff(1532,plain,
% 2.67/1.99 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)))),
% 2.67/1.99 inference(quant_inst,[status(thm)],[])).
% 2.67/1.99 tff(1533,plain,
% 2.67/1.99 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a808))),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 2.67/1.99 tff(1534,plain,
% 2.67/1.99 (hskp9 | (~c0_1(a808))),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1533, 151, 344, 1518, 1527, 21])).
% 2.67/1.99 tff(1535,plain,
% 2.67/1.99 (hskp9),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1534, 1526])).
% 2.67/1.99 tff(1536,plain,
% 2.67/1.99 (~c3_1(a806)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[75, 1535])).
% 2.67/1.99 tff(1537,plain,
% 2.67/1.99 (c1_1(a806)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[87, 1535])).
% 2.67/1.99 tff(1538,plain,
% 2.67/1.99 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1539,plain,
% 2.67/1.99 ((hskp28 | hskp19 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806))) <=> (hskp28 | hskp19 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1540,plain,
% 2.67/1.99 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806))))),
% 2.67/1.99 inference(monotonicity,[status(thm)],[1539])).
% 2.67/1.99 tff(1541,plain,
% 2.67/1.99 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))),
% 2.67/1.99 inference(transitivity,[status(thm)],[1540, 1538])).
% 2.67/1.99 tff(1542,plain,
% 2.67/1.99 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806)))),
% 2.67/1.99 inference(quant_inst,[status(thm)],[])).
% 2.67/1.99 tff(1543,plain,
% 2.67/1.99 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806))),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 2.67/1.99 tff(1544,plain,
% 2.67/1.99 (c2_1(a806)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1543, 151, 357, 1459, 1537, 1536, 1322])).
% 2.67/1.99 tff(1545,plain,
% 2.67/1.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1546,plain,
% 2.67/1.99 ((hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1547,plain,
% 2.67/1.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833))))),
% 2.67/1.99 inference(monotonicity,[status(thm)],[1546])).
% 2.67/1.99 tff(1548,plain,
% 2.67/1.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))),
% 2.67/1.99 inference(transitivity,[status(thm)],[1547, 1545])).
% 2.67/1.99 tff(1549,plain,
% 2.67/1.99 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 2.67/1.99 inference(quant_inst,[status(thm)],[])).
% 2.67/1.99 tff(1550,plain,
% 2.67/1.99 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833))),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1549, 1548])).
% 2.67/1.99 tff(1551,plain,
% 2.67/1.99 (hskp7 | (~c3_1(a833))),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1550, 151, 1280, 1279, 333, 321, 1515, 1290])).
% 2.67/1.99 tff(1552,plain,
% 2.67/1.99 (~c3_1(a833)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1551, 1505])).
% 2.67/1.99 tff(1553,assumption,(~c2_1(a795)), introduced(assumption)).
% 2.67/1.99 tff(1554,assumption,(~c0_1(a795)), introduced(assumption)).
% 2.67/1.99 tff(1555,assumption,(~c3_1(a795)), introduced(assumption)).
% 2.67/1.99 tff(1556,plain,
% 2.67/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a832)))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1557,plain,
% 2.67/1.99 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795)) <=> (c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a832)))),
% 2.67/1.99 inference(rewrite,[status(thm)],[])).
% 2.67/1.99 tff(1558,plain,
% 2.67/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a832))))),
% 2.67/1.99 inference(monotonicity,[status(thm)],[1557])).
% 2.67/1.99 tff(1559,plain,
% 2.67/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a832)))),
% 2.67/1.99 inference(transitivity,[status(thm)],[1558, 1556])).
% 2.67/1.99 tff(1560,plain,
% 2.67/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795))),
% 2.67/1.99 inference(quant_inst,[status(thm)],[])).
% 2.67/1.99 tff(1561,plain,
% 2.67/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a832))),
% 2.67/1.99 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 2.67/1.99 tff(1562,plain,
% 2.67/1.99 ($false),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1561, 151, 1518, 322, 22, 1517, 1527, 1554, 1555, 876, 456, 1553])).
% 2.67/1.99 tff(1563,plain,((~hskp11) | c1_1(a832) | c3_1(a832) | c0_1(a795) | c3_1(a795) | (~c0_1(a832)) | c2_1(a795)), inference(lemma,lemma(discharge,[]))).
% 2.67/1.99 tff(1564,plain,
% 2.67/1.99 (~c0_1(a832)),
% 2.67/1.99 inference(unit_resolution,[status(thm)],[1563, 1467, 22, 1516, 1555, 1554, 1553])).
% 2.67/1.99 tff(1565,plain,
% 2.67/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832) | c3_1(a833))),
% 2.67/2.00 inference(rewrite,[status(thm)],[])).
% 2.67/2.00 tff(1566,plain,
% 2.67/2.00 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a833) | c2_1(a833) | c0_1(a833) | c2_1(a832) | c1_1(a832) | c0_1(a832)) <=> (c2_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832) | c3_1(a833))),
% 2.67/2.00 inference(rewrite,[status(thm)],[])).
% 2.67/2.00 tff(1567,plain,
% 2.67/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a833) | c2_1(a833) | c0_1(a833) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832) | c3_1(a833)))),
% 2.67/2.00 inference(monotonicity,[status(thm)],[1566])).
% 2.67/2.00 tff(1568,plain,
% 2.67/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a833) | c2_1(a833) | c0_1(a833) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832) | c3_1(a833))),
% 2.67/2.00 inference(transitivity,[status(thm)],[1567, 1565])).
% 2.67/2.00 tff(1569,plain,
% 2.67/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a833) | c2_1(a833) | c0_1(a833) | c2_1(a832) | c1_1(a832) | c0_1(a832))),
% 2.67/2.00 inference(quant_inst,[status(thm)],[])).
% 2.67/2.00 tff(1570,plain,
% 2.67/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832) | c3_1(a833)),
% 2.67/2.00 inference(modus_ponens,[status(thm)],[1569, 1568])).
% 2.67/2.00 tff(1571,plain,
% 2.67/2.00 ($false),
% 2.67/2.00 inference(unit_resolution,[status(thm)],[1570, 151, 1458, 1537, 321, 309, 1467, 1536, 258, 1564, 1552, 1544])).
% 2.67/2.00 tff(1572,plain,(c2_1(a832) | c0_1(a833) | c2_1(a833) | hskp28 | c1_1(a833) | c3_1(a832) | (~hskp11) | c3_1(a795) | c0_1(a795) | c2_1(a795)), inference(lemma,lemma(discharge,[]))).
% 2.67/2.00 tff(1573,plain,
% 2.67/2.00 (c2_1(a832)),
% 2.67/2.00 inference(unit_resolution,[status(thm)],[1572, 1330, 309, 357, 333, 22, 321, 1418, 1450, 1444])).
% 2.67/2.00 tff(1574,plain,
% 2.67/2.00 (hskp21 | c1_1(a832) | (~c2_1(a832))),
% 2.67/2.00 inference(unit_resolution,[status(thm)],[657, 151, 1101, 22, 651])).
% 2.67/2.00 tff(1575,plain,
% 2.69/2.00 (c1_1(a832)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1574, 1573, 704])).
% 2.69/2.00 tff(1576,plain,
% 2.69/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~c1_1(a832)) | c3_1(a832) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a832)) | c3_1(a832) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1577,plain,
% 2.69/2.00 (((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a828) | c1_1(a828) | c0_1(a828)) <=> ((~c1_1(a832)) | c3_1(a832) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1578,plain,
% 2.69/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a828) | c1_1(a828) | c0_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~c1_1(a832)) | c3_1(a832) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832))))),
% 2.69/2.00 inference(monotonicity,[status(thm)],[1577])).
% 2.69/2.00 tff(1579,plain,
% 2.69/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a828) | c1_1(a828) | c0_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a832)) | c3_1(a832) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))),
% 2.69/2.00 inference(transitivity,[status(thm)],[1578, 1576])).
% 2.69/2.00 tff(1580,plain,
% 2.69/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a828) | c1_1(a828) | c0_1(a828))),
% 2.69/2.00 inference(quant_inst,[status(thm)],[])).
% 2.69/2.00 tff(1581,plain,
% 2.69/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a832)) | c3_1(a832) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832))),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1580, 1579])).
% 2.69/2.00 tff(1582,plain,
% 2.69/2.00 ((~c1_1(a832)) | c0_1(a828) | (~c2_1(a832))),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1581, 151, 22, 1405, 1336, 1335, 258])).
% 2.69/2.00 tff(1583,plain,
% 2.69/2.00 ($false),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1582, 1575, 1573, 1457])).
% 2.69/2.00 tff(1584,plain,(hskp21 | c3_1(a832) | hskp0 | c2_1(a833) | hskp28 | c1_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.69/2.00 tff(1585,plain,
% 2.69/2.00 (hskp21),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1584, 22, 1436, 309, 357, 333, 321])).
% 2.69/2.00 tff(1586,plain,
% 2.69/2.00 (c0_1(a838)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[454, 1585])).
% 2.69/2.00 tff(1587,plain,
% 2.69/2.00 (~hskp21),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[443, 977])).
% 2.69/2.00 tff(1588,plain,
% 2.69/2.00 (hskp11),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1329, 1587, 1290])).
% 2.69/2.00 tff(1589,plain,
% 2.69/2.00 (~c2_1(a808)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[857, 1588])).
% 2.69/2.00 tff(1590,plain,
% 2.69/2.00 (~c1_1(a808)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[851, 1588])).
% 2.69/2.00 tff(1591,plain,
% 2.69/2.00 (c3_1(a808)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[896, 1588])).
% 2.69/2.00 tff(1592,plain,
% 2.69/2.00 (hskp18),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1185, 151, 1587, 1591, 1590, 1589, 1178])).
% 2.69/2.00 tff(1593,plain,
% 2.69/2.00 (~c3_1(a828)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1197, 1592])).
% 2.69/2.00 tff(1594,plain,
% 2.69/2.00 (~c2_1(a828)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1191, 1592])).
% 2.69/2.00 tff(1595,plain,
% 2.69/2.00 (~c1_1(a828)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1203, 1592])).
% 2.69/2.00 tff(1596,plain,
% 2.69/2.00 (hskp2),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1411, 151, 346, 1595, 1594, 1593, 1404])).
% 2.69/2.00 tff(1597,plain,
% 2.69/2.00 (~c3_1(a795)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1417, 1596])).
% 2.69/2.00 tff(1598,plain,
% 2.69/2.00 (~c1_1(a795)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1423, 1596])).
% 2.69/2.00 tff(1599,plain,
% 2.69/2.00 (~c2_1(a795)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1443, 151, 1587, 1101, 1598, 1597, 651])).
% 2.69/2.00 tff(1600,plain,
% 2.69/2.00 (~c0_1(a795)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1449, 1596])).
% 2.69/2.00 tff(1601,plain,
% 2.69/2.00 (~c0_1(a828)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1456, 151, 1591, 1595, 1593, 1590, 1589, 1600, 1597, 876, 1599])).
% 2.69/2.00 tff(1602,plain,
% 2.69/2.00 (~c0_1(a832)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1563, 1467, 22, 1588, 1597, 1600, 1599])).
% 2.69/2.00 tff(1603,assumption,(~hskp19), introduced(assumption)).
% 2.69/2.00 tff(1604,plain,
% 2.69/2.00 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c3_1(a838) | c2_1(a838) | (~ndr1_0) | (~c1_1(a838)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c3_1(a838) | c2_1(a838) | (~ndr1_0) | (~c1_1(a838)))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1605,plain,
% 2.69/2.00 ((hskp28 | hskp19 | (~ndr1_0) | c2_1(a838) | c3_1(a838) | (~c1_1(a838))) <=> (hskp28 | hskp19 | c3_1(a838) | c2_1(a838) | (~ndr1_0) | (~c1_1(a838)))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1606,plain,
% 2.69/2.00 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a838) | c3_1(a838) | (~c1_1(a838)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c3_1(a838) | c2_1(a838) | (~ndr1_0) | (~c1_1(a838))))),
% 2.69/2.00 inference(monotonicity,[status(thm)],[1605])).
% 2.69/2.00 tff(1607,plain,
% 2.69/2.00 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a838) | c3_1(a838) | (~c1_1(a838)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c3_1(a838) | c2_1(a838) | (~ndr1_0) | (~c1_1(a838)))),
% 2.69/2.00 inference(transitivity,[status(thm)],[1606, 1604])).
% 2.69/2.00 tff(1608,plain,
% 2.69/2.00 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a838) | c3_1(a838) | (~c1_1(a838)))),
% 2.69/2.00 inference(quant_inst,[status(thm)],[])).
% 2.69/2.00 tff(1609,plain,
% 2.69/2.00 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c3_1(a838) | c2_1(a838) | (~ndr1_0) | (~c1_1(a838))),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 2.69/2.00 tff(1610,plain,
% 2.69/2.00 (hskp19 | c3_1(a838) | (~c1_1(a838))),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1609, 151, 357, 470, 1322])).
% 2.69/2.00 tff(1611,plain,
% 2.69/2.00 (~c1_1(a838)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1610, 1603, 977])).
% 2.69/2.00 tff(1612,assumption,(hskp4), introduced(assumption)).
% 2.69/2.00 tff(1613,plain,
% 2.69/2.00 (((~hskp4) | (~c1_1(a799))) <=> ((~hskp4) | (~c1_1(a799)))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1614,plain,
% 2.69/2.00 (((~c1_1(a799)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a799)))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1615,axiom,((~c1_1(a799)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 2.69/2.00 tff(1616,plain,
% 2.69/2.00 ((~hskp4) | (~c1_1(a799))),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1615, 1614])).
% 2.69/2.00 tff(1617,plain,
% 2.69/2.00 ((~hskp4) | (~c1_1(a799))),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1616, 1613])).
% 2.69/2.00 tff(1618,plain,
% 2.69/2.00 (~c1_1(a799)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1617, 1612])).
% 2.69/2.00 tff(1619,plain,
% 2.69/2.00 (((~hskp4) | c3_1(a799)) <=> ((~hskp4) | c3_1(a799))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1620,axiom,((~hskp4) | c3_1(a799)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 2.69/2.00 tff(1621,plain,
% 2.69/2.00 ((~hskp4) | c3_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 2.69/2.00 tff(1622,plain,
% 2.69/2.00 ((~hskp4) | c3_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1621, 1619])).
% 2.69/2.00 tff(1623,plain,
% 2.69/2.00 ((~hskp4) | c3_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1622, 1619])).
% 2.69/2.00 tff(1624,plain,
% 2.69/2.00 ((~hskp4) | c3_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1623, 1619])).
% 2.69/2.00 tff(1625,plain,
% 2.69/2.00 ((~hskp4) | c3_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1624, 1619])).
% 2.69/2.00 tff(1626,plain,
% 2.69/2.00 ((~hskp4) | c3_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1625, 1619])).
% 2.69/2.00 tff(1627,plain,
% 2.69/2.00 ((~hskp4) | c3_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1626, 1619])).
% 2.69/2.00 tff(1628,plain,
% 2.69/2.00 ((~hskp4) | c3_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1627, 1619])).
% 2.69/2.00 tff(1629,plain,
% 2.69/2.00 (c3_1(a799)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1628, 1612])).
% 2.69/2.00 tff(1630,plain,
% 2.69/2.00 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a799) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a799)) | (~c2_1(a799)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a799) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a799)) | (~c2_1(a799)))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1631,plain,
% 2.69/2.00 ((hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799))) <=> (hskp28 | c1_1(a799) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a799)) | (~c2_1(a799)))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1632,plain,
% 2.69/2.00 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a799) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a799)) | (~c2_1(a799))))),
% 2.69/2.00 inference(monotonicity,[status(thm)],[1631])).
% 2.69/2.00 tff(1633,plain,
% 2.69/2.00 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a799) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a799)) | (~c2_1(a799)))),
% 2.69/2.00 inference(transitivity,[status(thm)],[1632, 1630])).
% 2.69/2.00 tff(1634,plain,
% 2.69/2.00 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)))),
% 2.69/2.00 inference(quant_inst,[status(thm)],[])).
% 2.69/2.00 tff(1635,plain,
% 2.69/2.00 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a799) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a799)) | (~c2_1(a799))),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 2.69/2.00 tff(1636,plain,
% 2.69/2.00 (~c2_1(a799)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1635, 151, 357, 1281, 1280, 1279, 1629, 1618, 1310])).
% 2.69/2.00 tff(1637,plain,
% 2.69/2.00 (^[U: $i] : refl((hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 2.69/2.00 inference(bind,[status(th)],[])).
% 2.69/2.00 tff(1638,plain,
% 2.69/2.00 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.69/2.00 inference(quant_intro,[status(thm)],[1637])).
% 2.69/2.00 tff(1639,plain,
% 2.69/2.00 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1640,plain,
% 2.69/2.00 (^[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)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp1) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp1))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp1) <=> (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp1) <=> (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 2.69/2.00 inference(bind,[status(th)],[])).
% 2.69/2.00 tff(1641,plain,
% 2.69/2.00 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp1) <=> ![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.69/2.00 inference(quant_intro,[status(thm)],[1640])).
% 2.69/2.00 tff(1642,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 2.69/2.00 tff(1643,plain,
% 2.69/2.00 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 2.69/2.00 tff(1644,plain,
% 2.69/2.00 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1643, 1639])).
% 2.69/2.00 tff(1645,plain,(
% 2.69/2.00 ![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.69/2.00 inference(skolemize,[status(sab)],[1644])).
% 2.69/2.00 tff(1646,plain,
% 2.69/2.00 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1645, 1638])).
% 2.69/2.00 tff(1647,plain,
% 2.69/2.00 (((~hskp4) | c0_1(a799)) <=> ((~hskp4) | c0_1(a799))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1648,axiom,((~hskp4) | c0_1(a799)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 2.69/2.00 tff(1649,plain,
% 2.69/2.00 ((~hskp4) | c0_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1648, 1647])).
% 2.69/2.00 tff(1650,plain,
% 2.69/2.00 ((~hskp4) | c0_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1649, 1647])).
% 2.69/2.00 tff(1651,plain,
% 2.69/2.00 ((~hskp4) | c0_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1650, 1647])).
% 2.69/2.00 tff(1652,plain,
% 2.69/2.00 ((~hskp4) | c0_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1651, 1647])).
% 2.69/2.00 tff(1653,plain,
% 2.69/2.00 ((~hskp4) | c0_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1652, 1647])).
% 2.69/2.00 tff(1654,plain,
% 2.69/2.00 ((~hskp4) | c0_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1653, 1647])).
% 2.69/2.00 tff(1655,plain,
% 2.69/2.00 ((~hskp4) | c0_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1654, 1647])).
% 2.69/2.00 tff(1656,plain,
% 2.69/2.00 ((~hskp4) | c0_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1655, 1647])).
% 2.69/2.00 tff(1657,plain,
% 2.69/2.00 (c0_1(a799)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1656, 1612])).
% 2.69/2.00 tff(1658,plain,
% 2.69/2.00 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a799) | (~ndr1_0) | (~c0_1(a799)) | c2_1(a799))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a799) | (~ndr1_0) | (~c0_1(a799)) | c2_1(a799))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1659,plain,
% 2.69/2.00 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a799) | c1_1(a799) | (~c0_1(a799))) <=> (hskp20 | hskp1 | c1_1(a799) | (~ndr1_0) | (~c0_1(a799)) | c2_1(a799))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1660,plain,
% 2.69/2.00 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a799) | c1_1(a799) | (~c0_1(a799)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a799) | (~ndr1_0) | (~c0_1(a799)) | c2_1(a799)))),
% 2.69/2.00 inference(monotonicity,[status(thm)],[1659])).
% 2.69/2.00 tff(1661,plain,
% 2.69/2.00 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a799) | c1_1(a799) | (~c0_1(a799)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a799) | (~ndr1_0) | (~c0_1(a799)) | c2_1(a799))),
% 2.69/2.00 inference(transitivity,[status(thm)],[1660, 1658])).
% 2.69/2.00 tff(1662,plain,
% 2.69/2.00 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a799) | c1_1(a799) | (~c0_1(a799)))),
% 2.69/2.00 inference(quant_inst,[status(thm)],[])).
% 2.69/2.00 tff(1663,plain,
% 2.69/2.00 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a799) | (~ndr1_0) | (~c0_1(a799)) | c2_1(a799)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1662, 1661])).
% 2.69/2.00 tff(1664,plain,
% 2.69/2.00 (hskp1 | c2_1(a799)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1663, 151, 346, 1657, 1618, 1646])).
% 2.69/2.00 tff(1665,plain,
% 2.69/2.00 (hskp1),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1664, 1636])).
% 2.69/2.00 tff(1666,plain,
% 2.69/2.00 (~c2_1(a794)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[280, 1665])).
% 2.69/2.00 tff(1667,plain,
% 2.69/2.00 (c3_1(a794)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[291, 1665])).
% 2.69/2.00 tff(1668,plain,
% 2.69/2.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c3_1(a838) | c2_1(a838) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c1_1(a838))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c3_1(a838) | c2_1(a838) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c1_1(a838))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1669,plain,
% 2.69/2.00 ((hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a838) | c2_1(a838) | c1_1(a838)) <=> (hskp19 | c3_1(a838) | c2_1(a838) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c1_1(a838))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1670,plain,
% 2.69/2.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a838) | c2_1(a838) | c1_1(a838))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c3_1(a838) | c2_1(a838) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c1_1(a838)))),
% 2.69/2.00 inference(monotonicity,[status(thm)],[1669])).
% 2.69/2.00 tff(1671,plain,
% 2.69/2.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a838) | c2_1(a838) | c1_1(a838))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c3_1(a838) | c2_1(a838) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c1_1(a838))),
% 2.69/2.00 inference(transitivity,[status(thm)],[1670, 1668])).
% 2.69/2.00 tff(1672,plain,
% 2.69/2.00 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a838) | c2_1(a838) | c1_1(a838))),
% 2.69/2.00 inference(quant_inst,[status(thm)],[])).
% 2.69/2.00 tff(1673,plain,
% 2.69/2.00 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c3_1(a838) | c2_1(a838) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c1_1(a838)),
% 2.69/2.00 inference(modus_ponens,[status(thm)],[1672, 1671])).
% 2.69/2.00 tff(1674,plain,
% 2.69/2.00 (~c1_1(a794)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[1673, 151, 1603, 977, 1667, 470, 1666, 10, 1611])).
% 2.69/2.00 tff(1675,plain,
% 2.69/2.00 (~c0_1(a794)),
% 2.69/2.00 inference(unit_resolution,[status(thm)],[297, 1665])).
% 2.69/2.00 tff(1676,plain,
% 2.69/2.00 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | (~c0_1(a799)) | (~c3_1(a799)) | c2_1(a799))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~ndr1_0) | (~c0_1(a799)) | (~c3_1(a799)) | c2_1(a799))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1677,plain,
% 2.69/2.00 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a799) | (~c3_1(a799)) | (~c0_1(a799))) <=> (hskp20 | hskp9 | (~ndr1_0) | (~c0_1(a799)) | (~c3_1(a799)) | c2_1(a799))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(1678,plain,
% 2.69/2.00 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a799) | (~c3_1(a799)) | (~c0_1(a799)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | (~c0_1(a799)) | (~c3_1(a799)) | c2_1(a799)))),
% 2.69/2.01 inference(monotonicity,[status(thm)],[1677])).
% 2.69/2.01 tff(1679,plain,
% 2.69/2.01 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a799) | (~c3_1(a799)) | (~c0_1(a799)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~ndr1_0) | (~c0_1(a799)) | (~c3_1(a799)) | c2_1(a799))),
% 2.69/2.01 inference(transitivity,[status(thm)],[1678, 1676])).
% 2.69/2.01 tff(1680,plain,
% 2.69/2.01 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a799) | (~c3_1(a799)) | (~c0_1(a799)))),
% 2.69/2.01 inference(quant_inst,[status(thm)],[])).
% 2.69/2.01 tff(1681,plain,
% 2.69/2.01 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~ndr1_0) | (~c0_1(a799)) | (~c3_1(a799)) | c2_1(a799)),
% 2.69/2.01 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 2.69/2.01 tff(1682,plain,
% 2.69/2.01 (hskp9 | c2_1(a799)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1681, 151, 346, 1657, 1629, 21])).
% 2.69/2.01 tff(1683,plain,
% 2.69/2.01 (hskp9),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1682, 1636])).
% 2.69/2.01 tff(1684,plain,
% 2.69/2.01 (~c3_1(a806)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[75, 1683])).
% 2.69/2.01 tff(1685,plain,
% 2.69/2.01 (c0_1(a806)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[67, 1683])).
% 2.69/2.01 tff(1686,plain,
% 2.69/2.01 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c0_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(1687,plain,
% 2.69/2.01 ((hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a794) | c1_1(a794) | c0_1(a794)) <=> (hskp0 | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(1688,plain,
% 2.69/2.01 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a794) | c1_1(a794) | c0_1(a794))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c0_1(a806))))),
% 2.69/2.01 inference(monotonicity,[status(thm)],[1687])).
% 2.69/2.01 tff(1689,plain,
% 2.69/2.01 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a794) | c1_1(a794) | c0_1(a794))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.69/2.01 inference(transitivity,[status(thm)],[1688, 1686])).
% 2.69/2.01 tff(1690,plain,
% 2.69/2.01 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a794) | c1_1(a794) | c0_1(a794))),
% 2.69/2.01 inference(quant_inst,[status(thm)],[])).
% 2.69/2.01 tff(1691,plain,
% 2.69/2.01 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c0_1(a806))),
% 2.69/2.01 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 2.69/2.01 tff(1692,plain,
% 2.69/2.01 (~c2_1(a806)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1691, 151, 1101, 1685, 1684, 1675, 1666, 1434, 1674])).
% 2.69/2.01 tff(1693,plain,
% 2.69/2.01 (c1_1(a806)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[87, 1683])).
% 2.69/2.01 tff(1694,plain,
% 2.69/2.01 ($false),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1543, 151, 357, 1603, 1693, 1684, 1322, 1692])).
% 2.69/2.01 tff(1695,plain,((~hskp4) | hskp28 | hskp19 | hskp0 | c3_1(a838) | c2_1(a838) | hskp20), inference(lemma,lemma(discharge,[]))).
% 2.69/2.01 tff(1696,plain,
% 2.69/2.01 (~hskp4),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1695, 1459, 357, 1101, 977, 470, 346])).
% 2.69/2.01 tff(1697,plain,
% 2.69/2.01 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))),
% 2.69/2.01 inference(bind,[status(th)],[])).
% 2.69/2.01 tff(1698,plain,
% 2.69/2.01 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.69/2.01 inference(quant_intro,[status(thm)],[1697])).
% 2.69/2.01 tff(1699,plain,
% 2.69/2.01 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(1700,plain,
% 2.69/2.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))))),
% 2.69/2.01 inference(bind,[status(th)],[])).
% 2.69/2.01 tff(1701,plain,
% 2.69/2.01 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.69/2.01 inference(quant_intro,[status(thm)],[1700])).
% 2.69/2.01 tff(1702,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 2.69/2.01 tff(1703,plain,
% 2.69/2.01 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.69/2.01 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 2.69/2.01 tff(1704,plain,
% 2.69/2.01 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.69/2.01 inference(modus_ponens,[status(thm)],[1703, 1699])).
% 2.69/2.01 tff(1705,plain,(
% 2.69/2.01 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.69/2.01 inference(skolemize,[status(sab)],[1704])).
% 2.69/2.01 tff(1706,plain,
% 2.69/2.01 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.69/2.01 inference(modus_ponens,[status(thm)],[1705, 1698])).
% 2.69/2.01 tff(1707,plain,
% 2.69/2.01 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp4 | hskp3 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp4 | hskp3 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(1708,plain,
% 2.69/2.01 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832)) <=> (hskp4 | hskp3 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(1709,plain,
% 2.69/2.01 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp4 | hskp3 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832)))),
% 2.69/2.01 inference(monotonicity,[status(thm)],[1708])).
% 2.69/2.01 tff(1710,plain,
% 2.69/2.01 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp4 | hskp3 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 2.69/2.01 inference(transitivity,[status(thm)],[1709, 1707])).
% 2.69/2.01 tff(1711,plain,
% 2.69/2.01 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832))),
% 2.69/2.01 inference(quant_inst,[status(thm)],[])).
% 2.69/2.01 tff(1712,plain,
% 2.69/2.01 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp4 | hskp3 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832)),
% 2.69/2.01 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 2.69/2.01 tff(1713,plain,
% 2.69/2.01 (hskp4 | hskp3 | c1_1(a832) | c0_1(a832)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1712, 151, 22, 1706])).
% 2.69/2.01 tff(1714,plain,
% 2.69/2.01 (hskp3),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1713, 1696, 1467, 1602])).
% 2.69/2.01 tff(1715,plain,
% 2.69/2.01 (~c3_1(a798)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[546, 1714])).
% 2.69/2.01 tff(1716,plain,
% 2.69/2.01 (c2_1(a798)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[563, 1714])).
% 2.69/2.01 tff(1717,plain,
% 2.69/2.01 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c3_1(a798) | (~ndr1_0) | c1_1(a798) | (~c2_1(a798)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c3_1(a798) | (~ndr1_0) | c1_1(a798) | (~c2_1(a798)))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(1718,plain,
% 2.69/2.01 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a798) | c3_1(a798) | (~c2_1(a798))) <=> (hskp21 | hskp0 | c3_1(a798) | (~ndr1_0) | c1_1(a798) | (~c2_1(a798)))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(1719,plain,
% 2.69/2.01 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a798) | c3_1(a798) | (~c2_1(a798)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c3_1(a798) | (~ndr1_0) | c1_1(a798) | (~c2_1(a798))))),
% 2.69/2.01 inference(monotonicity,[status(thm)],[1718])).
% 2.69/2.01 tff(1720,plain,
% 2.69/2.01 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a798) | c3_1(a798) | (~c2_1(a798)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c3_1(a798) | (~ndr1_0) | c1_1(a798) | (~c2_1(a798)))),
% 2.69/2.01 inference(transitivity,[status(thm)],[1719, 1717])).
% 2.69/2.01 tff(1721,plain,
% 2.69/2.01 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a798) | c3_1(a798) | (~c2_1(a798)))),
% 2.69/2.01 inference(quant_inst,[status(thm)],[])).
% 2.69/2.01 tff(1722,plain,
% 2.69/2.01 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c3_1(a798) | (~ndr1_0) | c1_1(a798) | (~c2_1(a798))),
% 2.69/2.01 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 2.69/2.01 tff(1723,plain,
% 2.69/2.01 (c1_1(a798)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1722, 151, 1587, 1101, 1716, 1715, 651])).
% 2.69/2.01 tff(1724,plain,
% 2.69/2.01 (~c1_1(a838)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1610, 1459, 977])).
% 2.69/2.01 tff(1725,plain,
% 2.69/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a838) | c2_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | (~c0_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a838) | c2_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | (~c0_1(a838)) | c1_1(a838))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(1726,plain,
% 2.69/2.01 (((~ndr1_0) | c1_1(a838) | c3_1(a838) | (~c0_1(a838)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832)) <=> (c3_1(a838) | c2_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | (~c0_1(a838)) | c1_1(a838))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(1727,plain,
% 2.69/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a838) | c3_1(a838) | (~c0_1(a838)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a838) | c2_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | (~c0_1(a838)) | c1_1(a838)))),
% 2.69/2.01 inference(monotonicity,[status(thm)],[1726])).
% 2.69/2.01 tff(1728,plain,
% 2.69/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a838) | c3_1(a838) | (~c0_1(a838)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a838) | c2_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | (~c0_1(a838)) | c1_1(a838))),
% 2.69/2.01 inference(transitivity,[status(thm)],[1727, 1725])).
% 2.69/2.01 tff(1729,plain,
% 2.69/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a838) | c3_1(a838) | (~c0_1(a838)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832))),
% 2.69/2.01 inference(quant_inst,[status(thm)],[])).
% 2.69/2.01 tff(1730,plain,
% 2.69/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a838) | c2_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | (~c0_1(a838)) | c1_1(a838)),
% 2.69/2.01 inference(modus_ponens,[status(thm)],[1729, 1728])).
% 2.69/2.01 tff(1731,plain,
% 2.69/2.01 (~c0_1(a838)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1730, 151, 977, 1458, 1591, 22, 1590, 1589, 876, 1602, 1724])).
% 2.69/2.01 tff(1732,plain,
% 2.69/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a838) | c3_1(a838) | c2_1(a832) | c2_1(a838) | c1_1(a832) | c3_1(a798) | (~ndr1_0) | (~c1_1(a798)) | (~c2_1(a798)) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a838) | c3_1(a838) | c2_1(a832) | c2_1(a838) | c1_1(a832) | c3_1(a798) | (~ndr1_0) | (~c1_1(a798)) | (~c2_1(a798)) | c0_1(a832))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(1733,plain,
% 2.69/2.01 (((~ndr1_0) | c3_1(a798) | (~c1_1(a798)) | (~c2_1(a798)) | c3_1(a838) | c2_1(a838) | c0_1(a838) | c2_1(a832) | c1_1(a832) | c0_1(a832)) <=> (c0_1(a838) | c3_1(a838) | c2_1(a832) | c2_1(a838) | c1_1(a832) | c3_1(a798) | (~ndr1_0) | (~c1_1(a798)) | (~c2_1(a798)) | c0_1(a832))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(1734,plain,
% 2.69/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a798) | (~c1_1(a798)) | (~c2_1(a798)) | c3_1(a838) | c2_1(a838) | c0_1(a838) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a838) | c3_1(a838) | c2_1(a832) | c2_1(a838) | c1_1(a832) | c3_1(a798) | (~ndr1_0) | (~c1_1(a798)) | (~c2_1(a798)) | c0_1(a832)))),
% 2.69/2.01 inference(monotonicity,[status(thm)],[1733])).
% 2.69/2.01 tff(1735,plain,
% 2.69/2.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a798) | (~c1_1(a798)) | (~c2_1(a798)) | c3_1(a838) | c2_1(a838) | c0_1(a838) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a838) | c3_1(a838) | c2_1(a832) | c2_1(a838) | c1_1(a832) | c3_1(a798) | (~ndr1_0) | (~c1_1(a798)) | (~c2_1(a798)) | c0_1(a832))),
% 2.69/2.01 inference(transitivity,[status(thm)],[1734, 1732])).
% 2.69/2.01 tff(1736,plain,
% 2.69/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a798) | (~c1_1(a798)) | (~c2_1(a798)) | c3_1(a838) | c2_1(a838) | c0_1(a838) | c2_1(a832) | c1_1(a832) | c0_1(a832))),
% 2.69/2.01 inference(quant_inst,[status(thm)],[])).
% 2.69/2.01 tff(1737,plain,
% 2.69/2.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a838) | c3_1(a838) | c2_1(a832) | c2_1(a838) | c1_1(a832) | c3_1(a798) | (~ndr1_0) | (~c1_1(a798)) | (~c2_1(a798)) | c0_1(a832)),
% 2.69/2.01 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 2.69/2.01 tff(1738,plain,
% 2.69/2.01 ($false),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1737, 151, 1731, 977, 1458, 1716, 470, 1467, 1715, 258, 1602, 1723])).
% 2.69/2.01 tff(1739,plain,(c2_1(a832) | c3_1(a838) | c2_1(a838) | hskp0 | c3_1(a832) | hskp28 | hskp20), inference(lemma,lemma(discharge,[]))).
% 2.69/2.01 tff(1740,plain,
% 2.69/2.01 (c2_1(a832)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1739, 977, 470, 1101, 22, 357, 346])).
% 2.69/2.01 tff(1741,plain,
% 2.69/2.01 (c1_1(a832)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1574, 1740, 1587])).
% 2.69/2.01 tff(1742,plain,
% 2.69/2.01 ((~c1_1(a832)) | c0_1(a828) | (~c2_1(a832))),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1581, 151, 22, 1595, 1594, 1593, 258])).
% 2.69/2.01 tff(1743,plain,
% 2.69/2.01 ($false),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1742, 1741, 1740, 1601])).
% 2.69/2.01 tff(1744,plain,(c3_1(a838) | c3_1(a832) | hskp0 | c2_1(a838) | hskp28 | hskp20), inference(lemma,lemma(discharge,[]))).
% 2.69/2.01 tff(1745,plain,
% 2.69/2.01 (c3_1(a838)),
% 2.69/2.01 inference(unit_resolution,[status(thm)],[1744, 22, 1436, 470, 357, 344])).
% 2.69/2.01 tff(1746,plain,
% 2.69/2.01 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(1747,plain,
% 2.69/2.01 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838))) <=> (hskp20 | hskp9 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(1748,plain,
% 2.69/2.01 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838))))),
% 2.69/2.01 inference(monotonicity,[status(thm)],[1747])).
% 2.69/2.01 tff(1749,plain,
% 2.69/2.01 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.69/2.01 inference(transitivity,[status(thm)],[1748, 1746])).
% 2.69/2.01 tff(1750,plain,
% 2.69/2.01 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.69/2.01 inference(quant_inst,[status(thm)],[])).
% 2.69/2.01 tff(1751,plain,
% 2.69/2.01 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1750, 1749])).
% 2.71/2.01 tff(1752,plain,
% 2.71/2.01 (hskp9 | (~c3_1(a838)) | (~c0_1(a838))),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1751, 151, 344, 470, 21])).
% 2.71/2.01 tff(1753,plain,
% 2.71/2.01 (hskp9),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1752, 1586, 1745])).
% 2.71/2.01 tff(1754,plain,
% 2.71/2.01 (~c3_1(a806)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[75, 1753])).
% 2.71/2.01 tff(1755,plain,
% 2.71/2.01 (c0_1(a806)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[67, 1753])).
% 2.71/2.01 tff(1756,plain,
% 2.71/2.01 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a793) | c2_1(a793) | c3_1(a806) | c1_1(a793) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a793) | c2_1(a793) | c3_1(a806) | c1_1(a793) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1757,plain,
% 2.71/2.01 ((hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a793) | c1_1(a793) | c0_1(a793)) <=> (hskp0 | c0_1(a793) | c2_1(a793) | c3_1(a806) | c1_1(a793) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1758,plain,
% 2.71/2.01 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a793) | c1_1(a793) | c0_1(a793))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a793) | c2_1(a793) | c3_1(a806) | c1_1(a793) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806))))),
% 2.71/2.01 inference(monotonicity,[status(thm)],[1757])).
% 2.71/2.01 tff(1759,plain,
% 2.71/2.01 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a793) | c1_1(a793) | c0_1(a793))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a793) | c2_1(a793) | c3_1(a806) | c1_1(a793) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.71/2.01 inference(transitivity,[status(thm)],[1758, 1756])).
% 2.71/2.01 tff(1760,plain,
% 2.71/2.01 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a793) | c1_1(a793) | c0_1(a793))),
% 2.71/2.01 inference(quant_inst,[status(thm)],[])).
% 2.71/2.01 tff(1761,plain,
% 2.71/2.01 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a793) | c2_1(a793) | c3_1(a806) | c1_1(a793) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 2.71/2.01 tff(1762,plain,
% 2.71/2.01 (~c2_1(a806)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1761, 151, 1436, 1755, 1437, 1435, 1754, 691, 1434])).
% 2.71/2.01 tff(1763,plain,
% 2.71/2.01 (c1_1(a806)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[87, 1753])).
% 2.71/2.01 tff(1764,plain,
% 2.71/2.01 (hskp19 | c2_1(a806)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1543, 151, 357, 1763, 1754, 1322])).
% 2.71/2.01 tff(1765,plain,
% 2.71/2.01 (hskp19),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1764, 1762])).
% 2.71/2.01 tff(1766,plain,
% 2.71/2.01 (c2_1(a832)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[379, 1765])).
% 2.71/2.01 tff(1767,plain,
% 2.71/2.01 (~hskp17),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1127, 1586, 357, 470, 1745])).
% 2.71/2.01 tff(1768,plain,
% 2.71/2.01 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp8 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1769,plain,
% 2.71/2.01 ((hskp17 | hskp8 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806))) <=> (hskp17 | hskp8 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))),
% 2.71/2.01 inference(rewrite,[status(thm)],[])).
% 2.71/2.01 tff(1770,plain,
% 2.71/2.01 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806))))),
% 2.71/2.01 inference(monotonicity,[status(thm)],[1769])).
% 2.71/2.01 tff(1771,plain,
% 2.71/2.01 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp8 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))),
% 2.71/2.01 inference(transitivity,[status(thm)],[1770, 1768])).
% 2.71/2.01 tff(1772,plain,
% 2.71/2.01 ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806)))),
% 2.71/2.01 inference(quant_inst,[status(thm)],[])).
% 2.71/2.01 tff(1773,plain,
% 2.71/2.01 ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp8 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806))),
% 2.71/2.01 inference(modus_ponens,[status(thm)],[1772, 1771])).
% 2.71/2.01 tff(1774,plain,
% 2.71/2.01 (hskp8 | c2_1(a806)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1773, 151, 1767, 1763, 1754, 917])).
% 2.71/2.01 tff(1775,plain,
% 2.71/2.01 (hskp8),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1774, 1762])).
% 2.71/2.01 tff(1776,plain,
% 2.71/2.01 (~c0_1(a832)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[491, 1775, 1745, 1766, 470, 22, 1586])).
% 2.71/2.01 tff(1777,plain,
% 2.71/2.01 (hskp12 | c2_1(a806)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[157, 151, 1281, 1280, 1279, 1763, 1754, 110])).
% 2.71/2.01 tff(1778,plain,
% 2.71/2.01 (hskp12),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1777, 1762])).
% 2.71/2.01 tff(1779,plain,
% 2.71/2.01 (~c0_1(a809)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[164, 1778])).
% 2.71/2.01 tff(1780,plain,
% 2.71/2.01 (~c1_1(a832)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[391, 1765])).
% 2.71/2.01 tff(1781,plain,
% 2.71/2.01 (c2_1(a809)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[176, 1778])).
% 2.71/2.01 tff(1782,plain,
% 2.71/2.01 (c1_1(a809)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[187, 1778])).
% 2.71/2.01 tff(1783,plain,
% 2.71/2.01 ($false),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1097, 151, 1766, 1782, 1781, 1780, 22, 1779, 1067, 1776])).
% 2.71/2.01 tff(1784,plain,(c3_1(a832) | c2_1(a838) | hskp28 | c0_1(a793) | c2_1(a793) | c1_1(a793) | c2_1(a833) | c1_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.01 tff(1785,plain,
% 2.71/2.01 (c3_1(a832)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1784, 470, 357, 1437, 1435, 691, 309, 333, 321])).
% 2.71/2.01 tff(1786,plain,
% 2.71/2.01 (~hskp19),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[385, 1785])).
% 2.71/2.01 tff(1787,plain,
% 2.71/2.01 (~c2_1(a806)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1761, 151, 1436, 68, 1437, 1435, 76, 691, 1434])).
% 2.71/2.01 tff(1788,plain,
% 2.71/2.01 ($false),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1543, 151, 357, 1603, 88, 76, 1322, 1787])).
% 2.71/2.01 tff(1789,plain,((~hskp9) | hskp28 | hskp19 | c0_1(a793) | c2_1(a793) | c1_1(a793)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.01 tff(1790,plain,
% 2.71/2.01 (~hskp9),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1789, 1786, 357, 1437, 1435, 691])).
% 2.71/2.01 tff(1791,plain,
% 2.71/2.01 (c0_1(a838)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[454, 1311])).
% 2.71/2.01 tff(1792,plain,
% 2.71/2.01 (c3_1(a838)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[443, 1311])).
% 2.71/2.01 tff(1793,plain,
% 2.71/2.01 (hskp9 | (~c3_1(a838)) | (~c0_1(a838))),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1751, 151, 346, 470, 21])).
% 2.71/2.01 tff(1794,plain,
% 2.71/2.01 ($false),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1793, 1792, 1791, 11])).
% 2.71/2.01 tff(1795,plain,((~hskp21) | hskp9 | hskp20 | c2_1(a838)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.01 tff(1796,plain,
% 2.71/2.01 (~hskp21),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1795, 1790, 344, 470])).
% 2.71/2.01 tff(1797,plain,
% 2.71/2.01 (hskp11),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[1329, 1796, 1290])).
% 2.71/2.01 tff(1798,plain,
% 2.71/2.01 (~c2_1(a808)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[857, 1797])).
% 2.71/2.01 tff(1799,plain,
% 2.71/2.01 (c3_1(a808)),
% 2.71/2.01 inference(unit_resolution,[status(thm)],[896, 1797])).
% 2.71/2.01 tff(1800,plain,
% 2.71/2.01 (~c0_1(a808)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1533, 151, 344, 1790, 1799, 1798, 21])).
% 2.71/2.02 tff(1801,plain,
% 2.71/2.02 (~c1_1(a808)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[851, 1797])).
% 2.71/2.02 tff(1802,plain,
% 2.71/2.02 (hskp7),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1524, 151, 1280, 1279, 1799, 1801, 1515, 1290, 1800])).
% 2.71/2.02 tff(1803,plain,
% 2.71/2.02 (~c2_1(a803)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1473, 1802])).
% 2.71/2.02 tff(1804,plain,
% 2.71/2.02 (hskp18),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1185, 151, 1796, 1799, 1801, 1798, 1178])).
% 2.71/2.02 tff(1805,plain,
% 2.71/2.02 (~c3_1(a828)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1197, 1804])).
% 2.71/2.02 tff(1806,plain,
% 2.71/2.02 (~c2_1(a828)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1191, 1804])).
% 2.71/2.02 tff(1807,plain,
% 2.71/2.02 (~c1_1(a828)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1203, 1804])).
% 2.71/2.02 tff(1808,plain,
% 2.71/2.02 (c3_1(a803)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1484, 1802])).
% 2.71/2.02 tff(1809,plain,
% 2.71/2.02 (c1_1(a803)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1495, 1802])).
% 2.71/2.02 tff(1810,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1811,plain,
% 2.71/2.02 ((hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1812,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803))))),
% 2.71/2.02 inference(monotonicity,[status(thm)],[1811])).
% 2.71/2.02 tff(1813,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1812, 1810])).
% 2.71/2.02 tff(1814,plain,
% 2.71/2.02 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1815,plain,
% 2.71/2.02 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803))),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 2.71/2.02 tff(1816,plain,
% 2.71/2.02 ($false),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1815, 151, 1786, 1809, 1808, 1807, 1806, 1805, 1803, 10])).
% 2.71/2.02 tff(1817,plain,(c2_1(a838) | hskp28 | c0_1(a793) | c2_1(a793) | c1_1(a793) | c2_1(a833) | c1_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.02 tff(1818,plain,
% 2.71/2.02 (c2_1(a838)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1817, 1437, 357, 1435, 691, 309, 333, 321])).
% 2.71/2.02 tff(1819,plain,
% 2.71/2.02 (~hskp21),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[431, 1818])).
% 2.71/2.02 tff(1820,plain,
% 2.71/2.02 (hskp11),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1329, 1819, 1290])).
% 2.71/2.02 tff(1821,plain,
% 2.71/2.02 (~c2_1(a808)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[857, 1820])).
% 2.71/2.02 tff(1822,plain,
% 2.71/2.02 (c3_1(a808)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[896, 1820])).
% 2.71/2.02 tff(1823,plain,
% 2.71/2.02 (c3_1(a832)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1584, 1819, 1436, 309, 357, 333, 321])).
% 2.71/2.02 tff(1824,plain,
% 2.71/2.02 (~hskp19),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[385, 1823])).
% 2.71/2.02 tff(1825,plain,
% 2.71/2.02 (~hskp9),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1789, 1824, 357, 1437, 1435, 691])).
% 2.71/2.02 tff(1826,plain,
% 2.71/2.02 (~c0_1(a808)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1533, 151, 344, 1825, 1822, 1821, 21])).
% 2.71/2.02 tff(1827,plain,
% 2.71/2.02 (~c1_1(a808)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[851, 1820])).
% 2.71/2.02 tff(1828,plain,
% 2.71/2.02 (hskp7),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1524, 151, 1280, 1279, 1822, 1827, 1515, 1290, 1826])).
% 2.71/2.02 tff(1829,plain,
% 2.71/2.02 (~c2_1(a803)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1473, 1828])).
% 2.71/2.02 tff(1830,plain,
% 2.71/2.02 (hskp18),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1185, 151, 1819, 1822, 1827, 1821, 1178])).
% 2.71/2.02 tff(1831,plain,
% 2.71/2.02 (~c3_1(a828)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1197, 1830])).
% 2.71/2.02 tff(1832,plain,
% 2.71/2.02 (~c2_1(a828)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1191, 1830])).
% 2.71/2.02 tff(1833,plain,
% 2.71/2.02 (~c1_1(a828)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1203, 1830])).
% 2.71/2.02 tff(1834,plain,
% 2.71/2.02 (c3_1(a803)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1484, 1828])).
% 2.71/2.02 tff(1835,plain,
% 2.71/2.02 (c1_1(a803)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1495, 1828])).
% 2.71/2.02 tff(1836,plain,
% 2.71/2.02 ($false),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1815, 151, 1824, 1835, 1834, 1833, 1832, 1831, 1829, 10])).
% 2.71/2.02 tff(1837,plain,(c0_1(a793) | hskp28 | c2_1(a793) | c1_1(a793) | c2_1(a833) | c1_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.02 tff(1838,plain,
% 2.71/2.02 (c0_1(a793)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1837, 1435, 357, 691, 309, 333, 321])).
% 2.71/2.02 tff(1839,plain,
% 2.71/2.02 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a793) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a793) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1840,plain,
% 2.71/2.02 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a793) | c1_1(a793) | (~c0_1(a793))) <=> (hskp20 | hskp1 | c2_1(a793) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1841,plain,
% 2.71/2.02 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a793) | c1_1(a793) | (~c0_1(a793)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a793) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793))))),
% 2.71/2.02 inference(monotonicity,[status(thm)],[1840])).
% 2.71/2.02 tff(1842,plain,
% 2.71/2.02 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a793) | c1_1(a793) | (~c0_1(a793)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a793) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1841, 1839])).
% 2.71/2.02 tff(1843,plain,
% 2.71/2.02 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a793) | c1_1(a793) | (~c0_1(a793)))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1844,plain,
% 2.71/2.02 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a793) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793))),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 2.71/2.02 tff(1845,plain,
% 2.71/2.02 (hskp1 | c2_1(a793) | (~c0_1(a793))),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1844, 151, 344, 691, 1646])).
% 2.71/2.02 tff(1846,plain,
% 2.71/2.02 (hskp1),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1845, 1838, 1435])).
% 2.71/2.02 tff(1847,plain,
% 2.71/2.02 (~c2_1(a794)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[280, 1846])).
% 2.71/2.02 tff(1848,plain,
% 2.71/2.02 (~c0_1(a794)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[297, 1846])).
% 2.71/2.02 tff(1849,plain,
% 2.71/2.02 (c3_1(a794)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[291, 1846])).
% 2.71/2.02 tff(1850,assumption,(~c2_1(a794)), introduced(assumption)).
% 2.71/2.02 tff(1851,assumption,(c3_1(a794)), introduced(assumption)).
% 2.71/2.02 tff(1852,plain,
% 2.71/2.02 (c3_1(a832)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1584, 704, 1101, 309, 357, 333, 321])).
% 2.71/2.02 tff(1853,plain,
% 2.71/2.02 (~hskp19),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[385, 1852])).
% 2.71/2.02 tff(1854,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1855,plain,
% 2.71/2.02 ((hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1856,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794))))),
% 2.71/2.02 inference(monotonicity,[status(thm)],[1855])).
% 2.71/2.02 tff(1857,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1856, 1854])).
% 2.71/2.02 tff(1858,plain,
% 2.71/2.02 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1859,plain,
% 2.71/2.02 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794))),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1858, 1857])).
% 2.71/2.02 tff(1860,plain,
% 2.71/2.02 (~c1_1(a794)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1859, 151, 1853, 1851, 1405, 1336, 1335, 1850, 10])).
% 2.71/2.02 tff(1861,assumption,(~c0_1(a794)), introduced(assumption)).
% 2.71/2.02 tff(1862,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1863,plain,
% 2.71/2.02 ((hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1864,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867))))),
% 2.71/2.02 inference(monotonicity,[status(thm)],[1863])).
% 2.71/2.02 tff(1865,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1864, 1862])).
% 2.71/2.02 tff(1866,plain,
% 2.71/2.02 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1867,plain,
% 2.71/2.02 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867))),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 2.71/2.02 tff(1868,plain,
% 2.71/2.02 (hskp7),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1867, 151, 1280, 1279, 1851, 1861, 1515, 1290, 1860])).
% 2.71/2.02 tff(1869,plain,
% 2.71/2.02 (~c2_1(a803)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1473, 1868])).
% 2.71/2.02 tff(1870,plain,
% 2.71/2.02 (c3_1(a803)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1484, 1868])).
% 2.71/2.02 tff(1871,plain,
% 2.71/2.02 (c1_1(a803)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1495, 1868])).
% 2.71/2.02 tff(1872,plain,
% 2.71/2.02 ($false),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1815, 151, 1853, 1871, 1870, 1405, 1336, 1335, 1869, 10])).
% 2.71/2.02 tff(1873,plain,(hskp21 | (~c3_1(a794)) | c0_1(a794) | c2_1(a794) | hskp0 | c2_1(a833) | hskp28 | c1_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.02 tff(1874,plain,
% 2.71/2.02 (hskp21),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1873, 1849, 1848, 1847, 1436, 309, 357, 333, 321])).
% 2.71/2.02 tff(1875,plain,
% 2.71/2.02 (~c2_1(a838)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[431, 1874])).
% 2.71/2.02 tff(1876,plain,
% 2.71/2.02 (hskp9),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1795, 1874, 344, 1875])).
% 2.71/2.02 tff(1877,plain,
% 2.71/2.02 (~c3_1(a806)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[75, 1876])).
% 2.71/2.02 tff(1878,plain,
% 2.71/2.02 (c0_1(a806)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[67, 1876])).
% 2.71/2.02 tff(1879,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1880,plain,
% 2.71/2.02 ((hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a833) | c1_1(a833) | c0_1(a833)) <=> (hskp0 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1881,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a833) | c1_1(a833) | c0_1(a833))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806))))),
% 2.71/2.02 inference(monotonicity,[status(thm)],[1880])).
% 2.71/2.02 tff(1882,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a833) | c1_1(a833) | c0_1(a833))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1881, 1879])).
% 2.71/2.02 tff(1883,plain,
% 2.71/2.02 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a833) | c1_1(a833) | c0_1(a833))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1884,plain,
% 2.71/2.02 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806))),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1883, 1882])).
% 2.71/2.02 tff(1885,plain,
% 2.71/2.02 (~c2_1(a806)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1884, 151, 1436, 333, 1878, 321, 309, 1877, 1434])).
% 2.71/2.02 tff(1886,plain,
% 2.71/2.02 (c1_1(a806)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[87, 1876])).
% 2.71/2.02 tff(1887,plain,
% 2.71/2.02 (hskp12 | c2_1(a806)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[157, 151, 1281, 1280, 1279, 1886, 1877, 110])).
% 2.71/2.02 tff(1888,plain,
% 2.71/2.02 (hskp12),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1887, 1885])).
% 2.71/2.02 tff(1889,plain,
% 2.71/2.02 (~c0_1(a809)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[164, 1888])).
% 2.71/2.02 tff(1890,plain,
% 2.71/2.02 (c2_1(a809)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[176, 1888])).
% 2.71/2.02 tff(1891,plain,
% 2.71/2.02 (c1_1(a809)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[187, 1888])).
% 2.71/2.02 tff(1892,plain,
% 2.71/2.02 ($false),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[194, 151, 1891, 1890, 1878, 1886, 1889, 1877, 99, 1885])).
% 2.71/2.02 tff(1893,plain,(c2_1(a793) | c1_1(a833) | c0_1(a833) | c2_1(a833) | hskp28 | c1_1(a793)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.02 tff(1894,plain,
% 2.71/2.02 (c2_1(a793)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1893, 691, 321, 309, 357, 333])).
% 2.71/2.02 tff(1895,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c3_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1896,plain,
% 2.71/2.02 ((hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793))) <=> (hskp28 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1897,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c3_1(a793))))),
% 2.71/2.02 inference(monotonicity,[status(thm)],[1896])).
% 2.71/2.02 tff(1898,plain,
% 2.71/2.02 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1897, 1895])).
% 2.71/2.02 tff(1899,plain,
% 2.71/2.02 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1900,plain,
% 2.71/2.02 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c3_1(a793))),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 2.71/2.02 tff(1901,plain,
% 2.71/2.02 ((~c2_1(a793)) | (~c3_1(a793))),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1900, 151, 357, 1281, 1280, 1279, 691, 1310])).
% 2.71/2.02 tff(1902,plain,
% 2.71/2.02 (~c3_1(a793)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1901, 1894])).
% 2.71/2.02 tff(1903,plain,
% 2.71/2.02 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c1_1(a793) | (~ndr1_0) | (~c2_1(a793)) | c3_1(a793))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a793) | (~ndr1_0) | (~c2_1(a793)) | c3_1(a793))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1904,plain,
% 2.71/2.02 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793))) <=> (hskp21 | hskp0 | c1_1(a793) | (~ndr1_0) | (~c2_1(a793)) | c3_1(a793))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1905,plain,
% 2.71/2.02 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c1_1(a793) | (~ndr1_0) | (~c2_1(a793)) | c3_1(a793)))),
% 2.71/2.02 inference(monotonicity,[status(thm)],[1904])).
% 2.71/2.02 tff(1906,plain,
% 2.71/2.02 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a793) | (~ndr1_0) | (~c2_1(a793)) | c3_1(a793))),
% 2.71/2.02 inference(transitivity,[status(thm)],[1905, 1903])).
% 2.71/2.02 tff(1907,plain,
% 2.71/2.02 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)))),
% 2.71/2.02 inference(quant_inst,[status(thm)],[])).
% 2.71/2.02 tff(1908,plain,
% 2.71/2.02 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a793) | (~ndr1_0) | (~c2_1(a793)) | c3_1(a793)),
% 2.71/2.02 inference(modus_ponens,[status(thm)],[1907, 1906])).
% 2.71/2.02 tff(1909,plain,
% 2.71/2.02 (hskp21 | hskp0 | (~c2_1(a793)) | c3_1(a793)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1908, 151, 691, 651])).
% 2.71/2.02 tff(1910,plain,
% 2.71/2.02 (hskp0),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[1909, 704, 1894, 1902])).
% 2.71/2.02 tff(1911,plain,
% 2.71/2.02 (c0_1(a793)),
% 2.71/2.02 inference(unit_resolution,[status(thm)],[686, 1910])).
% 2.71/2.02 tff(1912,plain,
% 2.71/2.02 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 2.71/2.02 inference(bind,[status(th)],[])).
% 2.71/2.02 tff(1913,plain,
% 2.71/2.02 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.71/2.02 inference(quant_intro,[status(thm)],[1912])).
% 2.71/2.02 tff(1914,plain,
% 2.71/2.02 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.71/2.02 inference(rewrite,[status(thm)],[])).
% 2.71/2.02 tff(1915,plain,
% 2.71/2.02 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_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)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 2.71/2.03 inference(bind,[status(th)],[])).
% 2.71/2.03 tff(1916,plain,
% 2.71/2.03 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.71/2.03 inference(quant_intro,[status(thm)],[1915])).
% 2.71/2.03 tff(1917,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 2.71/2.03 tff(1918,plain,
% 2.71/2.03 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1917, 1916])).
% 2.71/2.03 tff(1919,plain,
% 2.71/2.03 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1918, 1914])).
% 2.71/2.03 tff(1920,plain,(
% 2.71/2.03 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.71/2.03 inference(skolemize,[status(sab)],[1919])).
% 2.71/2.03 tff(1921,plain,
% 2.71/2.03 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1920, 1913])).
% 2.71/2.03 tff(1922,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a793)) | c3_1(a793))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a793)) | c3_1(a793))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1923,plain,
% 2.71/2.03 ((hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | c1_1(a793) | (~c0_1(a793))) <=> (hskp22 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a793)) | c3_1(a793))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1924,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | c1_1(a793) | (~c0_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a793)) | c3_1(a793)))),
% 2.71/2.03 inference(monotonicity,[status(thm)],[1923])).
% 2.71/2.03 tff(1925,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | c1_1(a793) | (~c0_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a793)) | c3_1(a793))),
% 2.71/2.03 inference(transitivity,[status(thm)],[1924, 1922])).
% 2.71/2.03 tff(1926,plain,
% 2.71/2.03 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | c1_1(a793) | (~c0_1(a793)))),
% 2.71/2.03 inference(quant_inst,[status(thm)],[])).
% 2.71/2.03 tff(1927,plain,
% 2.71/2.03 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a793)) | c3_1(a793)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1926, 1925])).
% 2.71/2.03 tff(1928,plain,
% 2.71/2.03 (hskp22 | (~c0_1(a793))),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1927, 151, 1281, 1280, 1279, 691, 1921, 1902])).
% 2.71/2.03 tff(1929,plain,
% 2.71/2.03 (hskp22),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1928, 1911])).
% 2.71/2.03 tff(1930,plain,
% 2.71/2.03 (((~hskp22) | (~c0_1(a840))) <=> ((~hskp22) | (~c0_1(a840)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1931,plain,
% 2.71/2.03 (((~c0_1(a840)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a840)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1932,axiom,((~c0_1(a840)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 2.71/2.03 tff(1933,plain,
% 2.71/2.03 ((~hskp22) | (~c0_1(a840))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 2.71/2.03 tff(1934,plain,
% 2.71/2.03 ((~hskp22) | (~c0_1(a840))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1933, 1930])).
% 2.71/2.03 tff(1935,plain,
% 2.71/2.03 (~c0_1(a840)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1934, 1929])).
% 2.71/2.03 tff(1936,plain,
% 2.71/2.03 (((~hskp22) | c3_1(a840)) <=> ((~hskp22) | c3_1(a840))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1937,axiom,((~hskp22) | c3_1(a840)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 2.71/2.03 tff(1938,plain,
% 2.71/2.03 ((~hskp22) | c3_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 2.71/2.03 tff(1939,plain,
% 2.71/2.03 ((~hskp22) | c3_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1938, 1936])).
% 2.71/2.03 tff(1940,plain,
% 2.71/2.03 ((~hskp22) | c3_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1939, 1936])).
% 2.71/2.03 tff(1941,plain,
% 2.71/2.03 ((~hskp22) | c3_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1940, 1936])).
% 2.71/2.03 tff(1942,plain,
% 2.71/2.03 ((~hskp22) | c3_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1941, 1936])).
% 2.71/2.03 tff(1943,plain,
% 2.71/2.03 ((~hskp22) | c3_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1942, 1936])).
% 2.71/2.03 tff(1944,plain,
% 2.71/2.03 ((~hskp22) | c3_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1943, 1936])).
% 2.71/2.03 tff(1945,plain,
% 2.71/2.03 ((~hskp22) | c3_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1944, 1936])).
% 2.71/2.03 tff(1946,plain,
% 2.71/2.03 (c3_1(a840)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1945, 1929])).
% 2.71/2.03 tff(1947,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a840) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a840)) | (~c3_1(a840)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a840) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a840)) | (~c3_1(a840)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1948,plain,
% 2.71/2.03 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a840) | (~c3_1(a840)) | (~c2_1(a840))) <=> (c0_1(a840) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a840)) | (~c3_1(a840)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1949,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a840) | (~c3_1(a840)) | (~c2_1(a840)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a840) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a840)) | (~c3_1(a840))))),
% 2.71/2.03 inference(monotonicity,[status(thm)],[1948])).
% 2.71/2.03 tff(1950,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a840) | (~c3_1(a840)) | (~c2_1(a840)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a840) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a840)) | (~c3_1(a840)))),
% 2.71/2.03 inference(transitivity,[status(thm)],[1949, 1947])).
% 2.71/2.03 tff(1951,plain,
% 2.71/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a840) | (~c3_1(a840)) | (~c2_1(a840)))),
% 2.71/2.03 inference(quant_inst,[status(thm)],[])).
% 2.71/2.03 tff(1952,plain,
% 2.71/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a840) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a840)) | (~c3_1(a840))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 2.71/2.03 tff(1953,plain,
% 2.71/2.03 (~c2_1(a840)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1952, 151, 1281, 1280, 1279, 1946, 1935, 207, 1290])).
% 2.71/2.03 tff(1954,plain,
% 2.71/2.03 (c3_1(a833)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[884, 151, 1333, 1911, 321, 309, 1332, 1331, 691, 876, 1902])).
% 2.71/2.03 tff(1955,plain,
% 2.71/2.03 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 2.71/2.03 inference(bind,[status(th)],[])).
% 2.71/2.03 tff(1956,plain,
% 2.71/2.03 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.03 inference(quant_intro,[status(thm)],[1955])).
% 2.71/2.03 tff(1957,plain,
% 2.71/2.03 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1958,plain,
% 2.71/2.03 (^[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)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6) <=> (hskp6 | (~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)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 2.71/2.03 inference(bind,[status(th)],[])).
% 2.71/2.03 tff(1959,plain,
% 2.71/2.03 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.03 inference(quant_intro,[status(thm)],[1958])).
% 2.71/2.03 tff(1960,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)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 2.71/2.03 tff(1961,plain,
% 2.71/2.03 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1960, 1959])).
% 2.71/2.03 tff(1962,plain,
% 2.71/2.03 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1961, 1957])).
% 2.71/2.03 tff(1963,plain,(
% 2.71/2.03 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.03 inference(skolemize,[status(sab)],[1962])).
% 2.71/2.03 tff(1964,plain,
% 2.71/2.03 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1963, 1956])).
% 2.71/2.03 tff(1965,plain,
% 2.71/2.03 (((~hskp22) | c1_1(a840)) <=> ((~hskp22) | c1_1(a840))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1966,axiom,((~hskp22) | c1_1(a840)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 2.71/2.03 tff(1967,plain,
% 2.71/2.03 ((~hskp22) | c1_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1966, 1965])).
% 2.71/2.03 tff(1968,plain,
% 2.71/2.03 ((~hskp22) | c1_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1967, 1965])).
% 2.71/2.03 tff(1969,plain,
% 2.71/2.03 ((~hskp22) | c1_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1968, 1965])).
% 2.71/2.03 tff(1970,plain,
% 2.71/2.03 ((~hskp22) | c1_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1969, 1965])).
% 2.71/2.03 tff(1971,plain,
% 2.71/2.03 ((~hskp22) | c1_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1970, 1965])).
% 2.71/2.03 tff(1972,plain,
% 2.71/2.03 ((~hskp22) | c1_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1971, 1965])).
% 2.71/2.03 tff(1973,plain,
% 2.71/2.03 ((~hskp22) | c1_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1972, 1965])).
% 2.71/2.03 tff(1974,plain,
% 2.71/2.03 ((~hskp22) | c1_1(a840)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1973, 1965])).
% 2.71/2.03 tff(1975,plain,
% 2.71/2.03 (c1_1(a840)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1974, 1929])).
% 2.71/2.03 tff(1976,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | c2_1(a840) | (~c1_1(a840)) | (~c3_1(a840)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | c2_1(a840) | (~c1_1(a840)) | (~c3_1(a840)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1977,plain,
% 2.71/2.03 ((hskp6 | (~ndr1_0) | c2_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (hskp6 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | c2_1(a840) | (~c1_1(a840)) | (~c3_1(a840)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1978,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | c2_1(a840) | (~c1_1(a840)) | (~c3_1(a840))))),
% 2.71/2.03 inference(monotonicity,[status(thm)],[1977])).
% 2.71/2.03 tff(1979,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | c2_1(a840) | (~c1_1(a840)) | (~c3_1(a840)))),
% 2.71/2.03 inference(transitivity,[status(thm)],[1978, 1976])).
% 2.71/2.03 tff(1980,plain,
% 2.71/2.03 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 2.71/2.03 inference(quant_inst,[status(thm)],[])).
% 2.71/2.03 tff(1981,plain,
% 2.71/2.03 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | c2_1(a840) | (~c1_1(a840)) | (~c3_1(a840))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1980, 1979])).
% 2.71/2.03 tff(1982,plain,
% 2.71/2.03 (hskp6),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1981, 151, 1975, 1946, 333, 321, 1964, 1954, 1953])).
% 2.71/2.03 tff(1983,plain,
% 2.71/2.03 (((~hskp6) | (~c0_1(a802))) <=> ((~hskp6) | (~c0_1(a802)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1984,plain,
% 2.71/2.03 (((~c0_1(a802)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a802)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1985,axiom,((~c0_1(a802)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 2.71/2.03 tff(1986,plain,
% 2.71/2.03 ((~hskp6) | (~c0_1(a802))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1985, 1984])).
% 2.71/2.03 tff(1987,plain,
% 2.71/2.03 ((~hskp6) | (~c0_1(a802))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1986, 1983])).
% 2.71/2.03 tff(1988,plain,
% 2.71/2.03 (~c0_1(a802)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1987, 1982])).
% 2.71/2.03 tff(1989,plain,
% 2.71/2.03 (((~hskp6) | c2_1(a802)) <=> ((~hskp6) | c2_1(a802))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(1990,axiom,((~hskp6) | c2_1(a802)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 2.71/2.03 tff(1991,plain,
% 2.71/2.03 ((~hskp6) | c2_1(a802)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1990, 1989])).
% 2.71/2.03 tff(1992,plain,
% 2.71/2.03 ((~hskp6) | c2_1(a802)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1991, 1989])).
% 2.71/2.03 tff(1993,plain,
% 2.71/2.03 ((~hskp6) | c2_1(a802)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1992, 1989])).
% 2.71/2.03 tff(1994,plain,
% 2.71/2.03 ((~hskp6) | c2_1(a802)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1993, 1989])).
% 2.71/2.03 tff(1995,plain,
% 2.71/2.03 ((~hskp6) | c2_1(a802)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1994, 1989])).
% 2.71/2.03 tff(1996,plain,
% 2.71/2.03 ((~hskp6) | c2_1(a802)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1995, 1989])).
% 2.71/2.03 tff(1997,plain,
% 2.71/2.03 ((~hskp6) | c2_1(a802)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1996, 1989])).
% 2.71/2.03 tff(1998,plain,
% 2.71/2.03 ((~hskp6) | c2_1(a802)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[1997, 1989])).
% 2.71/2.03 tff(1999,plain,
% 2.71/2.03 (c2_1(a802)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[1998, 1982])).
% 2.71/2.03 tff(2000,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(2001,plain,
% 2.71/2.03 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802))) <=> (c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(2002,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802))))),
% 2.71/2.03 inference(monotonicity,[status(thm)],[2001])).
% 2.71/2.03 tff(2003,plain,
% 2.71/2.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)))),
% 2.71/2.03 inference(transitivity,[status(thm)],[2002, 2000])).
% 2.71/2.03 tff(2004,plain,
% 2.71/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))),
% 2.71/2.03 inference(quant_inst,[status(thm)],[])).
% 2.71/2.03 tff(2005,plain,
% 2.71/2.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802))),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 2.71/2.03 tff(2006,plain,
% 2.71/2.03 (~c3_1(a802)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[2005, 151, 1281, 1280, 1279, 1999, 1988, 207, 1290])).
% 2.71/2.03 tff(2007,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c0_1(a793)) | c3_1(a793))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c0_1(a793)) | c3_1(a793))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(2008,plain,
% 2.71/2.03 ((hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | (~c0_1(a793)) | (~c2_1(a793))) <=> (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c0_1(a793)) | c3_1(a793))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(2009,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | (~c0_1(a793)) | (~c2_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c0_1(a793)) | c3_1(a793)))),
% 2.71/2.03 inference(monotonicity,[status(thm)],[2008])).
% 2.71/2.03 tff(2010,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | (~c0_1(a793)) | (~c2_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c0_1(a793)) | c3_1(a793))),
% 2.71/2.03 inference(transitivity,[status(thm)],[2009, 2007])).
% 2.71/2.03 tff(2011,plain,
% 2.71/2.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | (~c0_1(a793)) | (~c2_1(a793)))),
% 2.71/2.03 inference(quant_inst,[status(thm)],[])).
% 2.71/2.03 tff(2012,plain,
% 2.71/2.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c0_1(a793)) | c3_1(a793)),
% 2.71/2.03 inference(modus_ponens,[status(thm)],[2011, 2010])).
% 2.71/2.03 tff(2013,plain,
% 2.71/2.03 (hskp5 | (~c0_1(a793))),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[2012, 151, 1281, 1280, 1279, 1894, 217, 1902])).
% 2.71/2.03 tff(2014,plain,
% 2.71/2.03 (hskp5),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[2013, 1911])).
% 2.71/2.03 tff(2015,plain,
% 2.71/2.03 (~c1_1(a800)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[263, 2014])).
% 2.71/2.03 tff(2016,plain,
% 2.71/2.03 (~c0_1(a800)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[229, 2014])).
% 2.71/2.03 tff(2017,plain,
% 2.71/2.03 (c3_1(a800)),
% 2.71/2.03 inference(unit_resolution,[status(thm)],[240, 2014])).
% 2.71/2.03 tff(2018,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(2019,plain,
% 2.71/2.03 ((hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)))),
% 2.71/2.03 inference(rewrite,[status(thm)],[])).
% 2.71/2.03 tff(2020,plain,
% 2.71/2.03 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a800))))),
% 2.71/2.04 inference(monotonicity,[status(thm)],[2019])).
% 2.71/2.04 tff(2021,plain,
% 2.71/2.04 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)))),
% 2.71/2.04 inference(transitivity,[status(thm)],[2020, 2018])).
% 2.71/2.04 tff(2022,plain,
% 2.71/2.04 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 2.71/2.04 inference(quant_inst,[status(thm)],[])).
% 2.71/2.04 tff(2023,plain,
% 2.71/2.04 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a800))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[2022, 2021])).
% 2.71/2.04 tff(2024,plain,
% 2.71/2.04 (hskp7),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[2023, 151, 1280, 1279, 2017, 2016, 2015, 1515, 1290])).
% 2.71/2.04 tff(2025,plain,
% 2.71/2.04 (~c2_1(a803)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1473, 2024])).
% 2.71/2.04 tff(2026,plain,
% 2.71/2.04 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 2.71/2.04 inference(bind,[status(th)],[])).
% 2.71/2.04 tff(2027,plain,
% 2.71/2.04 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.04 inference(quant_intro,[status(thm)],[2026])).
% 2.71/2.04 tff(2028,plain,
% 2.71/2.04 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(2029,plain,
% 2.71/2.04 (^[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) | c3_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) | c3_1(U) | (~c2_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) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_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) | c3_1(U) | (~c2_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)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 2.71/2.04 inference(bind,[status(th)],[])).
% 2.71/2.04 tff(2030,plain,
% 2.71/2.04 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.04 inference(quant_intro,[status(thm)],[2029])).
% 2.71/2.04 tff(2031,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 2.71/2.04 tff(2032,plain,
% 2.71/2.04 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 2.71/2.04 tff(2033,plain,
% 2.71/2.04 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[2032, 2028])).
% 2.71/2.04 tff(2034,plain,(
% 2.71/2.04 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.04 inference(skolemize,[status(sab)],[2033])).
% 2.71/2.04 tff(2035,plain,
% 2.71/2.04 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[2034, 2027])).
% 2.71/2.04 tff(2036,plain,
% 2.71/2.04 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a793)) | c3_1(a793))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a793)) | c3_1(a793))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(2037,plain,
% 2.71/2.04 ((hskp4 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (hskp4 | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a793)) | c3_1(a793))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(2038,plain,
% 2.71/2.04 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a793)) | c3_1(a793)))),
% 2.71/2.04 inference(monotonicity,[status(thm)],[2037])).
% 2.71/2.04 tff(2039,plain,
% 2.71/2.04 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a793)) | c3_1(a793))),
% 2.71/2.04 inference(transitivity,[status(thm)],[2038, 2036])).
% 2.71/2.04 tff(2040,plain,
% 2.71/2.04 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 2.71/2.04 inference(quant_inst,[status(thm)],[])).
% 2.71/2.04 tff(2041,plain,
% 2.71/2.04 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a793)) | c3_1(a793)),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[2040, 2039])).
% 2.71/2.04 tff(2042,plain,
% 2.71/2.04 (hskp4),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[2041, 151, 2017, 1894, 2016, 2015, 691, 2035, 1902])).
% 2.71/2.04 tff(2043,plain,
% 2.71/2.04 (~c1_1(a799)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1617, 2042])).
% 2.71/2.04 tff(2044,plain,
% 2.71/2.04 (c3_1(a799)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1628, 2042])).
% 2.71/2.04 tff(2045,plain,
% 2.71/2.04 (~c2_1(a799)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1635, 151, 357, 1281, 1280, 1279, 2044, 2043, 1310])).
% 2.71/2.04 tff(2046,plain,
% 2.71/2.04 (c0_1(a799)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1656, 2042])).
% 2.71/2.04 tff(2047,plain,
% 2.71/2.04 (hskp9 | c2_1(a799)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1681, 151, 344, 2046, 2044, 21])).
% 2.71/2.04 tff(2048,plain,
% 2.71/2.04 (hskp9),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[2047, 2045])).
% 2.71/2.04 tff(2049,plain,
% 2.71/2.04 (~c3_1(a806)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[75, 2048])).
% 2.71/2.04 tff(2050,plain,
% 2.71/2.04 (c3_1(a803)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1484, 2024])).
% 2.71/2.04 tff(2051,plain,
% 2.71/2.04 (c1_1(a803)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1495, 2024])).
% 2.71/2.04 tff(2052,plain,
% 2.71/2.04 (c1_1(a806)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[87, 2048])).
% 2.71/2.04 tff(2053,plain,
% 2.71/2.04 (c0_1(a806)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[67, 2048])).
% 2.71/2.04 tff(2054,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a806) | c2_1(a803) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a806) | c2_1(a803) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(2055,plain,
% 2.71/2.04 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a802) | c3_1(a802) | (~c2_1(a802))) <=> (c3_1(a806) | c2_1(a803) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(2056,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a806) | c2_1(a803) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806))))),
% 2.71/2.04 inference(monotonicity,[status(thm)],[2055])).
% 2.71/2.04 tff(2057,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a806) | c2_1(a803) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 2.71/2.04 inference(transitivity,[status(thm)],[2056, 2054])).
% 2.71/2.04 tff(2058,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)))),
% 2.71/2.04 inference(quant_inst,[status(thm)],[])).
% 2.71/2.04 tff(2059,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a806) | c2_1(a803) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[2058, 2057])).
% 2.71/2.04 tff(2060,plain,
% 2.71/2.04 ($false),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[2059, 151, 2053, 2052, 2051, 2050, 1999, 2049, 2025, 1988, 308, 2006])).
% 2.71/2.04 tff(2061,plain,(hskp21 | hskp28 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c1_1(a793)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.04 tff(2062,plain,
% 2.71/2.04 (hskp21),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[2061, 691, 333, 321, 309, 357])).
% 2.71/2.04 tff(2063,plain,
% 2.71/2.04 (~c2_1(a838)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[431, 2062])).
% 2.71/2.04 tff(2064,plain,
% 2.71/2.04 (hskp9),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1795, 2062, 344, 2063])).
% 2.71/2.04 tff(2065,plain,
% 2.71/2.04 (~c3_1(a806)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[75, 2064])).
% 2.71/2.04 tff(2066,plain,
% 2.71/2.04 (c1_1(a806)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[87, 2064])).
% 2.71/2.04 tff(2067,plain,
% 2.71/2.04 (c0_1(a806)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[67, 2064])).
% 2.71/2.04 tff(2068,plain,
% 2.71/2.04 (c2_1(a806)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[196, 2067, 2066, 2065, 1281, 1280, 1279])).
% 2.71/2.04 tff(2069,plain,
% 2.71/2.04 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 2.71/2.04 inference(bind,[status(th)],[])).
% 2.71/2.04 tff(2070,plain,
% 2.71/2.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.04 inference(quant_intro,[status(thm)],[2069])).
% 2.71/2.04 tff(2071,plain,
% 2.71/2.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(2072,plain,
% 2.71/2.04 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 2.71/2.04 inference(bind,[status(th)],[])).
% 2.71/2.04 tff(2073,plain,
% 2.71/2.04 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.04 inference(quant_intro,[status(thm)],[2072])).
% 2.71/2.04 tff(2074,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 2.71/2.04 tff(2075,plain,
% 2.71/2.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 2.71/2.04 tff(2076,plain,
% 2.71/2.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[2075, 2071])).
% 2.71/2.04 tff(2077,plain,(
% 2.71/2.04 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.04 inference(skolemize,[status(sab)],[2076])).
% 2.71/2.04 tff(2078,plain,
% 2.71/2.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[2077, 2070])).
% 2.71/2.04 tff(2079,plain,
% 2.71/2.04 (c3_1(a838)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[443, 2062])).
% 2.71/2.04 tff(2080,plain,
% 2.71/2.04 (c0_1(a838)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[454, 2062])).
% 2.71/2.04 tff(2081,plain,
% 2.71/2.04 (~c1_1(a838)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1109, 151, 357, 2080, 2079, 2063, 368])).
% 2.71/2.04 tff(2082,plain,
% 2.71/2.04 (hskp0 | (~c2_1(a806))),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1884, 151, 333, 2067, 321, 309, 2065, 1434])).
% 2.71/2.04 tff(2083,plain,
% 2.71/2.04 (hskp0),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[2082, 2068])).
% 2.71/2.04 tff(2084,plain,
% 2.71/2.04 (c0_1(a793)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[686, 2083])).
% 2.71/2.04 tff(2085,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a793) | (~ndr1_0) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a793) | (~ndr1_0) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(2086,plain,
% 2.71/2.04 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833)) <=> (c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a793) | (~ndr1_0) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(2087,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a793) | (~ndr1_0) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)))),
% 2.71/2.04 inference(monotonicity,[status(thm)],[2086])).
% 2.71/2.04 tff(2088,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a793) | (~ndr1_0) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 2.71/2.04 inference(transitivity,[status(thm)],[2087, 2085])).
% 2.71/2.04 tff(2089,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833))),
% 2.71/2.04 inference(quant_inst,[status(thm)],[])).
% 2.71/2.04 tff(2090,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a793) | (~ndr1_0) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 2.71/2.04 tff(2091,plain,
% 2.71/2.04 (c3_1(a833) | (~c0_1(a793)) | c1_1(a838)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[2090, 151, 2079, 2063, 321, 309, 691, 876, 1902])).
% 2.71/2.04 tff(2092,plain,
% 2.71/2.04 (c3_1(a833)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[2091, 2084, 2081])).
% 2.71/2.04 tff(2093,plain,
% 2.71/2.04 (hskp7),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1551, 2092])).
% 2.71/2.04 tff(2094,plain,
% 2.71/2.04 (~c2_1(a803)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1473, 2093])).
% 2.71/2.04 tff(2095,plain,
% 2.71/2.04 (hskp22),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1928, 2084])).
% 2.71/2.04 tff(2096,plain,
% 2.71/2.04 (~c0_1(a840)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1934, 2095])).
% 2.71/2.04 tff(2097,plain,
% 2.71/2.04 (c3_1(a803)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1484, 2093])).
% 2.71/2.04 tff(2098,plain,
% 2.71/2.04 (c3_1(a840)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1945, 2095])).
% 2.71/2.04 tff(2099,plain,
% 2.71/2.04 (c1_1(a840)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[1974, 2095])).
% 2.71/2.04 tff(2100,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a840) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c2_1(a806)) | (~c1_1(a806)) | (~c1_1(a840)) | (~c3_1(a840)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a840) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c2_1(a806)) | (~c1_1(a806)) | (~c1_1(a840)) | (~c3_1(a840)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(2101,plain,
% 2.71/2.04 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803))) <=> (c0_1(a840) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c2_1(a806)) | (~c1_1(a806)) | (~c1_1(a840)) | (~c3_1(a840)))),
% 2.71/2.04 inference(rewrite,[status(thm)],[])).
% 2.71/2.04 tff(2102,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a840) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c2_1(a806)) | (~c1_1(a806)) | (~c1_1(a840)) | (~c3_1(a840))))),
% 2.71/2.04 inference(monotonicity,[status(thm)],[2101])).
% 2.71/2.04 tff(2103,plain,
% 2.71/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a840) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c2_1(a806)) | (~c1_1(a806)) | (~c1_1(a840)) | (~c3_1(a840)))),
% 2.71/2.04 inference(transitivity,[status(thm)],[2102, 2100])).
% 2.71/2.04 tff(2104,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))),
% 2.71/2.04 inference(quant_inst,[status(thm)],[])).
% 2.71/2.04 tff(2105,plain,
% 2.71/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a840) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c2_1(a806)) | (~c1_1(a806)) | (~c1_1(a840)) | (~c3_1(a840))),
% 2.71/2.04 inference(modus_ponens,[status(thm)],[2104, 2103])).
% 2.71/2.04 tff(2106,plain,
% 2.71/2.04 (c0_1(a803)),
% 2.71/2.04 inference(unit_resolution,[status(thm)],[2105, 151, 2099, 2098, 2066, 2097, 2096, 2065, 2094, 2078, 2068])).
% 2.71/2.05 tff(2107,plain,
% 2.71/2.05 (c1_1(a803)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1495, 2093])).
% 2.71/2.05 tff(2108,plain,
% 2.71/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a833) | c0_1(a833) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a833) | c0_1(a833) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2109,plain,
% 2.71/2.05 (((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c1_1(a833) | c0_1(a833) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2110,plain,
% 2.71/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a833) | c0_1(a833) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a833)) | (~c2_1(a793)) | (~c0_1(a793))))),
% 2.71/2.05 inference(monotonicity,[status(thm)],[2109])).
% 2.71/2.05 tff(2111,plain,
% 2.71/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a833) | c0_1(a833) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 2.71/2.05 inference(transitivity,[status(thm)],[2110, 2108])).
% 2.71/2.05 tff(2112,plain,
% 2.71/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 2.71/2.05 inference(quant_inst,[status(thm)],[])).
% 2.71/2.05 tff(2113,plain,
% 2.71/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a833) | c0_1(a833) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a833)) | (~c2_1(a793)) | (~c0_1(a793))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 2.71/2.05 tff(2114,plain,
% 2.71/2.05 ($false),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2113, 151, 333, 2107, 2084, 1894, 321, 2094, 691, 320, 2092, 2106])).
% 2.71/2.05 tff(2115,plain,(c1_1(a793) | c1_1(a833) | c0_1(a833) | c2_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.71/2.05 tff(2116,plain,
% 2.71/2.05 (c1_1(a793)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2115, 309, 321, 333, 357])).
% 2.71/2.05 tff(2117,plain,
% 2.71/2.05 (~hskp0),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[675, 2116])).
% 2.71/2.05 tff(2118,plain,
% 2.71/2.05 (~c2_1(a795)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1443, 151, 704, 2117, 1424, 1418, 651])).
% 2.71/2.05 tff(2119,plain,
% 2.71/2.05 (~c0_1(a828)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1456, 151, 1333, 1405, 1335, 1332, 1331, 1450, 1418, 876, 2118])).
% 2.71/2.05 tff(2120,plain,
% 2.71/2.05 (c3_1(a832)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1584, 704, 2117, 309, 357, 333, 321])).
% 2.71/2.05 tff(2121,plain,
% 2.71/2.05 (~hskp19),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[385, 2120])).
% 2.71/2.05 tff(2122,plain,
% 2.71/2.05 (hskp9 | (~c0_1(a808))),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1533, 151, 346, 1031, 877, 21])).
% 2.71/2.05 tff(2123,plain,
% 2.71/2.05 (~c0_1(a808)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2122, 11])).
% 2.71/2.05 tff(2124,plain,
% 2.71/2.05 (hskp7 | c0_1(a808)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1524, 151, 1280, 1279, 1031, 878, 1515, 1290])).
% 2.71/2.05 tff(2125,plain,
% 2.71/2.05 (hskp7),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2124, 2123])).
% 2.71/2.05 tff(2126,plain,
% 2.71/2.05 (~c2_1(a803)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1473, 2125])).
% 2.71/2.05 tff(2127,assumption,(~c0_1(a828)), introduced(assumption)).
% 2.71/2.05 tff(2128,plain,
% 2.71/2.05 (^[U: $i] : refl((hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 2.71/2.05 inference(bind,[status(th)],[])).
% 2.71/2.05 tff(2129,plain,
% 2.71/2.05 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.71/2.05 inference(quant_intro,[status(thm)],[2128])).
% 2.71/2.05 tff(2130,plain,
% 2.71/2.05 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2131,plain,
% 2.71/2.05 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp10) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10) <=> (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp10) <=> (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 2.71/2.05 inference(bind,[status(th)],[])).
% 2.71/2.05 tff(2132,plain,
% 2.71/2.05 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp10) <=> ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.71/2.05 inference(quant_intro,[status(thm)],[2131])).
% 2.71/2.05 tff(2133,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 2.71/2.05 tff(2134,plain,
% 2.71/2.05 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 2.71/2.05 tff(2135,plain,
% 2.71/2.05 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[2134, 2130])).
% 2.71/2.05 tff(2136,plain,(
% 2.71/2.05 ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.71/2.05 inference(skolemize,[status(sab)],[2135])).
% 2.71/2.05 tff(2137,plain,
% 2.71/2.05 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[2136, 2129])).
% 2.71/2.05 tff(2138,plain,
% 2.71/2.05 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp9 | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp9 | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2139,plain,
% 2.71/2.05 ((hskp10 | hskp9 | (~ndr1_0) | c2_1(a828) | c0_1(a828) | c3_1(a828)) <=> (hskp10 | hskp9 | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2140,plain,
% 2.71/2.05 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp9 | (~ndr1_0) | c2_1(a828) | c0_1(a828) | c3_1(a828))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp9 | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828)))),
% 2.71/2.05 inference(monotonicity,[status(thm)],[2139])).
% 2.71/2.05 tff(2141,plain,
% 2.71/2.05 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp9 | (~ndr1_0) | c2_1(a828) | c0_1(a828) | c3_1(a828))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp9 | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828))),
% 2.71/2.05 inference(transitivity,[status(thm)],[2140, 2138])).
% 2.71/2.05 tff(2142,plain,
% 2.71/2.05 ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp9 | (~ndr1_0) | c2_1(a828) | c0_1(a828) | c3_1(a828))),
% 2.71/2.05 inference(quant_inst,[status(thm)],[])).
% 2.71/2.05 tff(2143,plain,
% 2.71/2.05 ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp9 | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828)),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[2142, 2141])).
% 2.71/2.05 tff(2144,plain,
% 2.71/2.05 (hskp10 | hskp9 | c0_1(a828)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2143, 151, 1206, 1205, 2137])).
% 2.71/2.05 tff(2145,plain,
% 2.71/2.05 (hskp10),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2144, 11, 2127])).
% 2.71/2.05 tff(2146,plain,
% 2.71/2.05 (~c3_1(a807)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[509, 2145])).
% 2.71/2.05 tff(2147,plain,
% 2.71/2.05 (~c2_1(a807)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[552, 2145])).
% 2.71/2.05 tff(2148,plain,
% 2.71/2.05 (c3_1(a803)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1484, 2125])).
% 2.71/2.05 tff(2149,plain,
% 2.71/2.05 (c1_1(a803)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1495, 2125])).
% 2.71/2.05 tff(2150,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a807) | c3_1(a807) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a807))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a807) | c3_1(a807) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a807))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2151,plain,
% 2.71/2.05 ((hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a807) | c2_1(a807) | c1_1(a807)) <=> (hskp19 | c2_1(a807) | c3_1(a807) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a807))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2152,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a807) | c2_1(a807) | c1_1(a807))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a807) | c3_1(a807) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a807)))),
% 2.71/2.05 inference(monotonicity,[status(thm)],[2151])).
% 2.71/2.05 tff(2153,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a807) | c2_1(a807) | c1_1(a807))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a807) | c3_1(a807) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a807))),
% 2.71/2.05 inference(transitivity,[status(thm)],[2152, 2150])).
% 2.71/2.05 tff(2154,plain,
% 2.71/2.05 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a807) | c2_1(a807) | c1_1(a807))),
% 2.71/2.05 inference(quant_inst,[status(thm)],[])).
% 2.71/2.05 tff(2155,plain,
% 2.71/2.05 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a807) | c3_1(a807) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a807)),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 2.71/2.05 tff(2156,plain,
% 2.71/2.05 (c1_1(a807)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2155, 151, 1603, 2149, 2148, 2147, 2146, 2126, 10])).
% 2.71/2.05 tff(2157,plain,
% 2.71/2.05 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c1_1(a807)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c1_1(a807)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2158,plain,
% 2.71/2.05 ((hskp28 | hskp19 | (~ndr1_0) | c2_1(a807) | c3_1(a807) | (~c1_1(a807))) <=> (hskp28 | hskp19 | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c1_1(a807)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2159,plain,
% 2.71/2.05 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a807) | c3_1(a807) | (~c1_1(a807)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c1_1(a807))))),
% 2.71/2.05 inference(monotonicity,[status(thm)],[2158])).
% 2.71/2.05 tff(2160,plain,
% 2.71/2.05 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a807) | c3_1(a807) | (~c1_1(a807)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c1_1(a807)))),
% 2.71/2.05 inference(transitivity,[status(thm)],[2159, 2157])).
% 2.71/2.05 tff(2161,plain,
% 2.71/2.05 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a807) | c3_1(a807) | (~c1_1(a807)))),
% 2.71/2.05 inference(quant_inst,[status(thm)],[])).
% 2.71/2.05 tff(2162,plain,
% 2.71/2.05 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c1_1(a807))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[2161, 2160])).
% 2.71/2.05 tff(2163,plain,
% 2.71/2.05 ($false),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2162, 151, 357, 1603, 2147, 2146, 1322, 2156])).
% 2.71/2.05 tff(2164,plain,(hskp9 | hskp28 | hskp19 | (~c3_1(a808)) | c1_1(a808) | c0_1(a828) | c2_1(a828) | c3_1(a828) | hskp20 | c2_1(a808)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.05 tff(2165,plain,
% 2.71/2.05 (hskp9),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2164, 2121, 357, 1333, 1332, 2119, 1336, 1335, 344, 1331])).
% 2.71/2.05 tff(2166,plain,
% 2.71/2.05 (c0_1(a806)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[67, 2165])).
% 2.71/2.05 tff(2167,plain,
% 2.71/2.05 (c1_1(a806)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[87, 2165])).
% 2.71/2.05 tff(2168,plain,
% 2.71/2.05 (~c3_1(a806)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[75, 2165])).
% 2.71/2.05 tff(2169,plain,
% 2.71/2.05 (c2_1(a806)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[196, 2168, 2167, 2166, 1281, 1280, 1279])).
% 2.71/2.05 tff(2170,plain,
% 2.71/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a833) | c0_1(a833) | c2_1(a833) | c2_1(a828) | c3_1(a828) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a833) | c0_1(a833) | c2_1(a833) | c2_1(a828) | c3_1(a828) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a828))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2171,plain,
% 2.71/2.05 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833)) <=> (c1_1(a833) | c0_1(a833) | c2_1(a833) | c2_1(a828) | c3_1(a828) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a828))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2172,plain,
% 2.71/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a833) | c0_1(a833) | c2_1(a833) | c2_1(a828) | c3_1(a828) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a828)))),
% 2.71/2.05 inference(monotonicity,[status(thm)],[2171])).
% 2.71/2.05 tff(2173,plain,
% 2.71/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a833) | c0_1(a833) | c2_1(a833) | c2_1(a828) | c3_1(a828) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a828))),
% 2.71/2.05 inference(transitivity,[status(thm)],[2172, 2170])).
% 2.71/2.05 tff(2174,plain,
% 2.71/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833))),
% 2.71/2.05 inference(quant_inst,[status(thm)],[])).
% 2.71/2.05 tff(2175,plain,
% 2.71/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a833) | c0_1(a833) | c2_1(a833) | c2_1(a828) | c3_1(a828) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a828)),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[2174, 2173])).
% 2.71/2.05 tff(2176,plain,
% 2.71/2.05 ($false),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2175, 151, 333, 2167, 321, 309, 1336, 1335, 2168, 258, 2119, 2169])).
% 2.71/2.05 tff(2177,plain,(hskp21 | c1_1(a833) | c0_1(a833) | c2_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.71/2.05 tff(2178,plain,
% 2.71/2.05 (hskp21),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2177, 309, 321, 333, 357])).
% 2.71/2.05 tff(2179,plain,
% 2.71/2.05 (~c2_1(a838)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[431, 2178])).
% 2.71/2.05 tff(2180,plain,
% 2.71/2.05 (hskp9),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1795, 2178, 344, 2179])).
% 2.71/2.05 tff(2181,plain,
% 2.71/2.05 (c0_1(a806)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[67, 2180])).
% 2.71/2.05 tff(2182,plain,
% 2.71/2.05 (c1_1(a806)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[87, 2180])).
% 2.71/2.05 tff(2183,plain,
% 2.71/2.05 (~c3_1(a806)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[75, 2180])).
% 2.71/2.05 tff(2184,plain,
% 2.71/2.05 (c2_1(a806)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[196, 2183, 2182, 2181, 1281, 1280, 1279])).
% 2.71/2.05 tff(2185,plain,
% 2.71/2.05 ($false),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[1884, 151, 2117, 333, 2181, 321, 309, 2183, 1434, 2184])).
% 2.71/2.05 tff(2186,plain,(c2_1(a833) | c1_1(a833) | c0_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.71/2.05 tff(2187,plain,
% 2.71/2.05 (c1_1(a833)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2186, 1394, 321, 357])).
% 2.71/2.05 tff(2188,plain,
% 2.71/2.05 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2189,plain,
% 2.71/2.05 ((hskp28 | hskp19 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (hskp28 | hskp19 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2190,plain,
% 2.71/2.05 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))))),
% 2.71/2.05 inference(monotonicity,[status(thm)],[2189])).
% 2.71/2.05 tff(2191,plain,
% 2.71/2.05 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 2.71/2.05 inference(transitivity,[status(thm)],[2190, 2188])).
% 2.71/2.05 tff(2192,plain,
% 2.71/2.05 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 2.71/2.05 inference(quant_inst,[status(thm)],[])).
% 2.71/2.05 tff(2193,plain,
% 2.71/2.05 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 2.71/2.05 tff(2194,plain,
% 2.71/2.05 (hskp19 | c3_1(a833)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2193, 151, 357, 639, 309, 1322])).
% 2.71/2.05 tff(2195,plain,
% 2.71/2.05 (c3_1(a833)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2194, 1603])).
% 2.71/2.05 tff(2196,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2197,plain,
% 2.71/2.05 ((hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (hskp19 | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.71/2.05 inference(rewrite,[status(thm)],[])).
% 2.71/2.05 tff(2198,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.71/2.05 inference(monotonicity,[status(thm)],[2197])).
% 2.71/2.05 tff(2199,plain,
% 2.71/2.05 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.71/2.05 inference(transitivity,[status(thm)],[2198, 2196])).
% 2.71/2.05 tff(2200,plain,
% 2.71/2.05 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 2.71/2.05 inference(quant_inst,[status(thm)],[])).
% 2.71/2.05 tff(2201,plain,
% 2.71/2.05 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.71/2.05 inference(modus_ponens,[status(thm)],[2200, 2199])).
% 2.71/2.05 tff(2202,plain,
% 2.71/2.05 (hskp19 | (~c3_1(a833))),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2201, 151, 639, 309, 1215, 1206, 1205, 10])).
% 2.71/2.05 tff(2203,plain,
% 2.71/2.05 ($false),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2202, 2195, 1603])).
% 2.71/2.05 tff(2204,plain,(hskp19 | (~c1_1(a833)) | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.71/2.05 tff(2205,plain,
% 2.71/2.05 (hskp19),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[2204, 1405, 1394, 2187, 1336, 1335, 357])).
% 2.71/2.05 tff(2206,plain,
% 2.71/2.05 (~c3_1(a832)),
% 2.71/2.05 inference(unit_resolution,[status(thm)],[385, 2205])).
% 2.71/2.06 tff(2207,plain,
% 2.71/2.06 (c2_1(a832)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[379, 2205])).
% 2.71/2.06 tff(2208,plain,
% 2.71/2.06 (~c1_1(a832)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[391, 2205])).
% 2.71/2.06 tff(2209,plain,
% 2.71/2.06 (hskp0),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[657, 151, 704, 2207, 2208, 2206, 651])).
% 2.71/2.06 tff(2210,plain,
% 2.71/2.06 (~c1_1(a793)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[675, 2209])).
% 2.71/2.06 tff(2211,plain,
% 2.71/2.06 (c0_1(a793)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[686, 2209])).
% 2.71/2.06 tff(2212,plain,
% 2.71/2.06 (c2_1(a793)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[669, 2209])).
% 2.71/2.06 tff(2213,plain,
% 2.71/2.06 ($false),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1234, 2212, 2211, 2187, 704, 321, 1394, 2210, 2208, 2207, 2206, 357])).
% 2.71/2.06 tff(2214,plain,(hskp21 | c0_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.71/2.06 tff(2215,plain,
% 2.71/2.06 (hskp21),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2214, 321, 357])).
% 2.71/2.06 tff(2216,plain,
% 2.71/2.06 (c3_1(a838)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[443, 2215])).
% 2.71/2.06 tff(2217,assumption,(hskp19), introduced(assumption)).
% 2.71/2.06 tff(2218,plain,
% 2.71/2.06 (c2_1(a832)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[379, 2217])).
% 2.71/2.06 tff(2219,plain,
% 2.71/2.06 (~c2_1(a838)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[431, 2215])).
% 2.71/2.06 tff(2220,plain,
% 2.71/2.06 (~c1_1(a832)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[391, 2217])).
% 2.71/2.06 tff(2221,plain,
% 2.71/2.06 (~c3_1(a832)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[385, 2217])).
% 2.71/2.06 tff(2222,plain,
% 2.71/2.06 ($false),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1268, 2221, 2220, 357, 321, 1394, 2187, 2219, 2218])).
% 2.71/2.06 tff(2223,plain,((~hskp19) | hskp28 | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.06 tff(2224,plain,
% 2.71/2.06 (~hskp19),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2223, 321, 357])).
% 2.71/2.06 tff(2225,plain,
% 2.71/2.06 (^[U: $i] : refl((hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))),
% 2.71/2.06 inference(bind,[status(th)],[])).
% 2.71/2.06 tff(2226,plain,
% 2.71/2.06 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.71/2.06 inference(quant_intro,[status(thm)],[2225])).
% 2.71/2.06 tff(2227,plain,
% 2.71/2.06 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2228,plain,
% 2.71/2.06 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19) <=> ((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp19))), rewrite(((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))))),
% 2.71/2.06 inference(bind,[status(th)],[])).
% 2.71/2.06 tff(2229,plain,
% 2.71/2.06 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.71/2.06 inference(quant_intro,[status(thm)],[2228])).
% 2.71/2.06 tff(2230,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 2.71/2.06 tff(2231,plain,
% 2.71/2.06 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 2.71/2.06 tff(2232,plain,
% 2.71/2.06 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2231, 2227])).
% 2.71/2.06 tff(2233,plain,(
% 2.71/2.06 ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.71/2.06 inference(skolemize,[status(sab)],[2232])).
% 2.71/2.06 tff(2234,plain,
% 2.71/2.06 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2233, 2226])).
% 2.71/2.06 tff(2235,plain,
% 2.71/2.06 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2236,plain,
% 2.71/2.06 ((hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867))) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2237,plain,
% 2.71/2.06 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867))))),
% 2.71/2.06 inference(monotonicity,[status(thm)],[2236])).
% 2.71/2.06 tff(2238,plain,
% 2.71/2.06 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 2.71/2.06 inference(transitivity,[status(thm)],[2237, 2235])).
% 2.71/2.06 tff(2239,plain,
% 2.71/2.06 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)))),
% 2.71/2.06 inference(quant_inst,[status(thm)],[])).
% 2.71/2.06 tff(2240,plain,
% 2.71/2.06 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2239, 2238])).
% 2.71/2.06 tff(2241,plain,
% 2.71/2.06 (hskp27 | hskp19 | (~c2_1(a867))),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2240, 151, 1280, 1279, 2234])).
% 2.71/2.06 tff(2242,plain,
% 2.71/2.06 (hskp27),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2241, 2224, 1290])).
% 2.71/2.06 tff(2243,plain,
% 2.71/2.06 (c3_1(a796)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[594, 2242])).
% 2.71/2.06 tff(2244,plain,
% 2.71/2.06 (c2_1(a796)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[605, 2242])).
% 2.71/2.06 tff(2245,plain,
% 2.71/2.06 (c0_1(a838)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[454, 2215])).
% 2.71/2.06 tff(2246,plain,
% 2.71/2.06 (~hskp17),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1127, 2245, 357, 2219, 2216])).
% 2.71/2.06 tff(2247,plain,
% 2.71/2.06 (hskp19 | c3_1(a833)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2193, 151, 357, 2187, 1394, 1322])).
% 2.71/2.06 tff(2248,plain,
% 2.71/2.06 (c3_1(a833)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2247, 2224])).
% 2.71/2.06 tff(2249,plain,
% 2.71/2.06 (hskp17 | hskp0 | (~c3_1(a833)) | (~c1_1(a833))),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1144, 151, 321, 1138])).
% 2.71/2.06 tff(2250,plain,
% 2.71/2.06 (hskp0),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2249, 2248, 2187, 2246])).
% 2.71/2.06 tff(2251,plain,
% 2.71/2.06 (c2_1(a793)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[669, 2250])).
% 2.71/2.06 tff(2252,plain,
% 2.71/2.06 (c0_1(a793)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[686, 2250])).
% 2.71/2.06 tff(2253,plain,
% 2.71/2.06 (c0_1(a796)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[616, 2242])).
% 2.71/2.06 tff(2254,plain,
% 2.71/2.06 (~c1_1(a838)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1109, 151, 357, 2245, 2216, 2219, 368])).
% 2.71/2.06 tff(2255,plain,
% 2.71/2.06 (~c1_1(a793)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[675, 2250])).
% 2.71/2.06 tff(2256,plain,
% 2.71/2.06 (hskp8),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1241, 2255, 2187, 2254, 2253, 2219, 2252, 2251, 321, 1394, 2244, 2243, 2216, 357])).
% 2.71/2.06 tff(2257,plain,
% 2.71/2.06 (~c3_1(a805)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[462, 2256])).
% 2.71/2.06 tff(2258,plain,
% 2.71/2.06 (~c2_1(a805)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[468, 2256])).
% 2.71/2.06 tff(2259,plain,
% 2.71/2.06 (c1_1(a805)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[480, 2256])).
% 2.71/2.06 tff(2260,plain,
% 2.71/2.06 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2261,plain,
% 2.71/2.06 ((hskp28 | hskp19 | (~ndr1_0) | c2_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (hskp28 | hskp19 | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2262,plain,
% 2.71/2.06 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805))))),
% 2.71/2.06 inference(monotonicity,[status(thm)],[2261])).
% 2.71/2.06 tff(2263,plain,
% 2.71/2.06 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)))),
% 2.71/2.06 inference(transitivity,[status(thm)],[2262, 2260])).
% 2.71/2.06 tff(2264,plain,
% 2.71/2.06 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 2.71/2.06 inference(quant_inst,[status(thm)],[])).
% 2.71/2.06 tff(2265,plain,
% 2.71/2.06 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2264, 2263])).
% 2.71/2.06 tff(2266,plain,
% 2.71/2.06 ($false),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2265, 151, 357, 2224, 2259, 2258, 2257, 1322])).
% 2.71/2.06 tff(2267,plain,(c0_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.71/2.06 tff(2268,plain,
% 2.71/2.06 (c0_1(a833)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2267, 357])).
% 2.71/2.06 tff(2269,plain,
% 2.71/2.06 (~hskp20),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[632, 2268])).
% 2.71/2.06 tff(2270,plain,
% 2.71/2.06 (hskp9),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1795, 1311, 2269, 1312])).
% 2.71/2.06 tff(2271,plain,
% 2.71/2.06 (c0_1(a806)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[67, 2270])).
% 2.71/2.06 tff(2272,plain,
% 2.71/2.06 (c1_1(a806)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[87, 2270])).
% 2.71/2.06 tff(2273,plain,
% 2.71/2.06 (~c3_1(a806)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[75, 2270])).
% 2.71/2.06 tff(2274,plain,
% 2.71/2.06 (c2_1(a806)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[196, 2273, 2272, 2271, 1281, 1280, 1279])).
% 2.71/2.06 tff(2275,plain,
% 2.71/2.06 (^[U: $i] : refl((hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 2.71/2.06 inference(bind,[status(th)],[])).
% 2.71/2.06 tff(2276,plain,
% 2.71/2.06 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.71/2.06 inference(quant_intro,[status(thm)],[2275])).
% 2.71/2.06 tff(2277,plain,
% 2.71/2.06 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2278,plain,
% 2.71/2.06 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp16) <=> ((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp16))), rewrite(((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 2.71/2.06 inference(bind,[status(th)],[])).
% 2.71/2.06 tff(2279,plain,
% 2.71/2.06 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp16) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.71/2.06 inference(quant_intro,[status(thm)],[2278])).
% 2.71/2.06 tff(2280,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 2.71/2.06 tff(2281,plain,
% 2.71/2.06 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2280, 2279])).
% 2.71/2.06 tff(2282,plain,
% 2.71/2.06 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2281, 2277])).
% 2.71/2.06 tff(2283,plain,(
% 2.71/2.06 ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.71/2.06 inference(skolemize,[status(sab)],[2282])).
% 2.71/2.06 tff(2284,plain,
% 2.71/2.06 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2283, 2276])).
% 2.71/2.06 tff(2285,plain,
% 2.71/2.06 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2286,plain,
% 2.71/2.06 ((hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c0_1(a867))) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2287,plain,
% 2.71/2.06 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867))))),
% 2.71/2.06 inference(monotonicity,[status(thm)],[2286])).
% 2.71/2.06 tff(2288,plain,
% 2.71/2.06 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)))),
% 2.71/2.06 inference(transitivity,[status(thm)],[2287, 2285])).
% 2.71/2.06 tff(2289,plain,
% 2.71/2.06 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c0_1(a867)))),
% 2.71/2.06 inference(quant_inst,[status(thm)],[])).
% 2.71/2.06 tff(2290,plain,
% 2.71/2.06 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2289, 2288])).
% 2.71/2.06 tff(2291,plain,
% 2.71/2.06 (hskp16 | hskp15 | (~c2_1(a867))),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2290, 151, 1281, 1279, 2284])).
% 2.71/2.06 tff(2292,plain,
% 2.71/2.06 (hskp16),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2291, 1374, 1290])).
% 2.71/2.06 tff(2293,plain,
% 2.71/2.06 (((~hskp16) | (~c2_1(a821))) <=> ((~hskp16) | (~c2_1(a821)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2294,plain,
% 2.71/2.06 (((~c2_1(a821)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a821)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2295,axiom,((~c2_1(a821)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 2.71/2.06 tff(2296,plain,
% 2.71/2.06 ((~hskp16) | (~c2_1(a821))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2295, 2294])).
% 2.71/2.06 tff(2297,plain,
% 2.71/2.06 ((~hskp16) | (~c2_1(a821))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2296, 2293])).
% 2.71/2.06 tff(2298,plain,
% 2.71/2.06 (~c2_1(a821)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2297, 2292])).
% 2.71/2.06 tff(2299,plain,
% 2.71/2.06 (((~hskp16) | (~c1_1(a821))) <=> ((~hskp16) | (~c1_1(a821)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2300,plain,
% 2.71/2.06 (((~c1_1(a821)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a821)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2301,axiom,((~c1_1(a821)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 2.71/2.06 tff(2302,plain,
% 2.71/2.06 ((~hskp16) | (~c1_1(a821))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2301, 2300])).
% 2.71/2.06 tff(2303,plain,
% 2.71/2.06 ((~hskp16) | (~c1_1(a821))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2302, 2299])).
% 2.71/2.06 tff(2304,plain,
% 2.71/2.06 (~c1_1(a821)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2303, 2292])).
% 2.71/2.06 tff(2305,plain,
% 2.71/2.06 (((~hskp16) | (~c0_1(a821))) <=> ((~hskp16) | (~c0_1(a821)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2306,plain,
% 2.71/2.06 (((~c0_1(a821)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a821)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2307,axiom,((~c0_1(a821)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 2.71/2.06 tff(2308,plain,
% 2.71/2.06 ((~hskp16) | (~c0_1(a821))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2307, 2306])).
% 2.71/2.06 tff(2309,plain,
% 2.71/2.06 ((~hskp16) | (~c0_1(a821))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2308, 2305])).
% 2.71/2.06 tff(2310,plain,
% 2.71/2.06 (~c0_1(a821)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2309, 2292])).
% 2.71/2.06 tff(2311,plain,
% 2.71/2.06 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a821) | c1_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a821) | c1_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2312,plain,
% 2.71/2.06 ((hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a821) | c1_1(a821) | c0_1(a821)) <=> (hskp0 | c0_1(a821) | c1_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2313,plain,
% 2.71/2.06 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a821) | c1_1(a821) | c0_1(a821))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a821) | c1_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806))))),
% 2.71/2.06 inference(monotonicity,[status(thm)],[2312])).
% 2.71/2.06 tff(2314,plain,
% 2.71/2.06 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a821) | c1_1(a821) | c0_1(a821))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a821) | c1_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 2.71/2.06 inference(transitivity,[status(thm)],[2313, 2311])).
% 2.71/2.06 tff(2315,plain,
% 2.71/2.06 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a821) | c1_1(a821) | c0_1(a821))),
% 2.71/2.06 inference(quant_inst,[status(thm)],[])).
% 2.71/2.06 tff(2316,plain,
% 2.71/2.06 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a821) | c1_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2315, 2314])).
% 2.71/2.06 tff(2317,plain,
% 2.71/2.06 (hskp0),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2316, 151, 2271, 2310, 2304, 2298, 2273, 1434, 2274])).
% 2.71/2.06 tff(2318,plain,
% 2.71/2.06 (~c1_1(a793)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[675, 2317])).
% 2.71/2.06 tff(2319,plain,
% 2.71/2.06 (c2_1(a793)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[669, 2317])).
% 2.71/2.06 tff(2320,plain,
% 2.71/2.06 (~c3_1(a793)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1900, 151, 357, 1281, 1280, 1279, 2319, 2318, 1310])).
% 2.71/2.06 tff(2321,plain,
% 2.71/2.06 (~c1_1(a838)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1109, 151, 357, 1791, 1792, 1312, 368])).
% 2.71/2.06 tff(2322,plain,
% 2.71/2.06 (c0_1(a793)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[686, 2317])).
% 2.71/2.06 tff(2323,plain,
% 2.71/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a821) | c2_1(a821) | c1_1(a793) | (~ndr1_0) | c3_1(a821) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a821) | c2_1(a821) | c1_1(a793) | (~ndr1_0) | c3_1(a821) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2324,plain,
% 2.71/2.06 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a821) | c0_1(a821) | c3_1(a821)) <=> (c2_1(a838) | c0_1(a821) | c2_1(a821) | c1_1(a793) | (~ndr1_0) | c3_1(a821) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2325,plain,
% 2.71/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a821) | c0_1(a821) | c3_1(a821))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a821) | c2_1(a821) | c1_1(a793) | (~ndr1_0) | c3_1(a821) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)))),
% 2.71/2.06 inference(monotonicity,[status(thm)],[2324])).
% 2.71/2.06 tff(2326,plain,
% 2.71/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a821) | c0_1(a821) | c3_1(a821))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a821) | c2_1(a821) | c1_1(a793) | (~ndr1_0) | c3_1(a821) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 2.71/2.06 inference(transitivity,[status(thm)],[2325, 2323])).
% 2.71/2.06 tff(2327,plain,
% 2.71/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a821) | c0_1(a821) | c3_1(a821))),
% 2.71/2.06 inference(quant_inst,[status(thm)],[])).
% 2.71/2.06 tff(2328,plain,
% 2.71/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a821) | c2_1(a821) | c1_1(a793) | (~ndr1_0) | c3_1(a821) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2327, 2326])).
% 2.71/2.06 tff(2329,plain,
% 2.71/2.06 (c3_1(a821) | c3_1(a793)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2328, 151, 1792, 2322, 1312, 2310, 2298, 2318, 876, 2321])).
% 2.71/2.06 tff(2330,plain,
% 2.71/2.06 (c3_1(a821)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2329, 2320])).
% 2.71/2.06 tff(2331,plain,
% 2.71/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a806)) | (~c1_1(a806)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a806)) | (~c1_1(a806)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2332,plain,
% 2.71/2.06 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a806)) | (~c1_1(a806)))),
% 2.71/2.06 inference(rewrite,[status(thm)],[])).
% 2.71/2.06 tff(2333,plain,
% 2.71/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a806)) | (~c1_1(a806))))),
% 2.71/2.06 inference(monotonicity,[status(thm)],[2332])).
% 2.71/2.06 tff(2334,plain,
% 2.71/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a806)) | (~c1_1(a806)))),
% 2.71/2.06 inference(transitivity,[status(thm)],[2333, 2331])).
% 2.71/2.06 tff(2335,plain,
% 2.71/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 2.71/2.06 inference(quant_inst,[status(thm)],[])).
% 2.71/2.06 tff(2336,plain,
% 2.71/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a806)) | (~c1_1(a806))),
% 2.71/2.06 inference(modus_ponens,[status(thm)],[2335, 2334])).
% 2.71/2.06 tff(2337,plain,
% 2.71/2.06 (~c1_1(a794)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[2336, 151, 2272, 1851, 2273, 1861, 1850, 2078, 2274])).
% 2.71/2.06 tff(2338,plain,
% 2.71/2.06 (hskp7),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1867, 151, 1280, 1279, 1851, 1861, 1515, 1290, 2337])).
% 2.71/2.06 tff(2339,plain,
% 2.71/2.06 (~c2_1(a803)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1473, 2338])).
% 2.71/2.06 tff(2340,plain,
% 2.71/2.06 (c1_1(a803)),
% 2.71/2.06 inference(unit_resolution,[status(thm)],[1495, 2338])).
% 2.71/2.06 tff(2341,plain,
% 2.71/2.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a821) | c1_1(a821) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a821)) | (~c2_1(a793)) | (~c0_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a821) | c1_1(a821) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a821)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(2342,plain,
% 2.71/2.07 (((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821))) <=> (c0_1(a821) | c1_1(a821) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a821)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(2343,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a821) | c1_1(a821) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a821)) | (~c2_1(a793)) | (~c0_1(a793))))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[2342])).
% 2.71/2.07 tff(2344,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a821) | c1_1(a821) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a821)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 2.71/2.07 inference(transitivity,[status(thm)],[2343, 2341])).
% 2.71/2.07 tff(2345,plain,
% 2.71/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)))),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(2346,plain,
% 2.71/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a821) | c1_1(a821) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a821)) | (~c2_1(a793)) | (~c0_1(a793))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[2345, 2344])).
% 2.71/2.07 tff(2347,plain,
% 2.71/2.07 (~c0_1(a803)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2346, 151, 2340, 2322, 2319, 2310, 2304, 2339, 2318, 320, 2330])).
% 2.71/2.07 tff(2348,plain,
% 2.71/2.07 (c3_1(a803)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1484, 2338])).
% 2.71/2.07 tff(2349,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a821)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a821)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(2350,plain,
% 2.71/2.07 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821))) <=> (c0_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a821)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(2351,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a821))))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[2350])).
% 2.71/2.07 tff(2352,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a821)))),
% 2.71/2.07 inference(transitivity,[status(thm)],[2351, 2349])).
% 2.71/2.07 tff(2353,plain,
% 2.71/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821)))),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(2354,plain,
% 2.71/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a821))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[2353, 2352])).
% 2.71/2.07 tff(2355,plain,
% 2.71/2.07 ($false),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2354, 151, 2272, 2340, 2348, 2310, 2298, 2273, 2078, 2274, 2330, 2347])).
% 2.71/2.07 tff(2356,plain,((~hskp21) | hskp28 | (~c3_1(a794)) | c0_1(a794) | c2_1(a794)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.07 tff(2357,plain,
% 2.71/2.07 (~hskp21),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2356, 292, 357, 298, 281])).
% 2.71/2.07 tff(2358,plain,
% 2.71/2.07 (hskp21 | hskp11 | (~c2_1(a867))),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1328, 151, 69, 77, 703])).
% 2.71/2.07 tff(2359,plain,
% 2.71/2.07 (hskp11),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2358, 704, 1375])).
% 2.71/2.07 tff(2360,plain,
% 2.71/2.07 (~c2_1(a808)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[857, 2359])).
% 2.71/2.07 tff(2361,plain,
% 2.71/2.07 (~c1_1(a808)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[851, 2359])).
% 2.71/2.07 tff(2362,plain,
% 2.71/2.07 (c3_1(a808)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[896, 2359])).
% 2.71/2.07 tff(2363,assumption,(~hskp18), introduced(assumption)).
% 2.71/2.07 tff(2364,plain,
% 2.71/2.07 ($false),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1185, 151, 704, 2363, 2362, 2361, 2360, 1178])).
% 2.71/2.07 tff(2365,plain,(hskp21 | hskp18 | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a867))), inference(lemma,lemma(discharge,[]))).
% 2.71/2.07 tff(2366,plain,
% 2.71/2.07 (hskp18),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2365, 2357, 1290, 1280, 1279])).
% 2.71/2.07 tff(2367,assumption,(hskp18), introduced(assumption)).
% 2.71/2.07 tff(2368,plain,
% 2.71/2.07 (~c3_1(a828)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1197, 2367])).
% 2.71/2.07 tff(2369,plain,
% 2.71/2.07 (~c2_1(a828)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1191, 2367])).
% 2.71/2.07 tff(2370,plain,
% 2.71/2.07 (~c1_1(a828)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1203, 2367])).
% 2.71/2.07 tff(2371,plain,
% 2.71/2.07 (~c1_1(a794)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1859, 151, 1603, 1851, 2370, 2369, 2368, 1850, 10])).
% 2.71/2.07 tff(2372,plain,
% 2.71/2.07 (hskp7),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1867, 151, 69, 77, 1851, 1861, 1515, 1375, 2371])).
% 2.71/2.07 tff(2373,plain,
% 2.71/2.07 (~c2_1(a803)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1473, 2372])).
% 2.71/2.07 tff(2374,plain,
% 2.71/2.07 (c3_1(a803)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1484, 2372])).
% 2.71/2.07 tff(2375,plain,
% 2.71/2.07 (c1_1(a803)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1495, 2372])).
% 2.71/2.07 tff(2376,plain,
% 2.71/2.07 ($false),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1815, 151, 1603, 2375, 2374, 2370, 2369, 2368, 2373, 10])).
% 2.71/2.07 tff(2377,plain,((~hskp18) | hskp19 | (~c1_1(a867)) | (~c3_1(a867)) | (~c3_1(a794)) | c0_1(a794) | (~c2_1(a867)) | c2_1(a794)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.07 tff(2378,plain,
% 2.71/2.07 (hskp19),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2377, 2366, 1280, 1279, 292, 298, 1290, 281])).
% 2.71/2.07 tff(2379,plain,
% 2.71/2.07 (~c3_1(a832)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[385, 2378])).
% 2.71/2.07 tff(2380,plain,
% 2.71/2.07 (c2_1(a832)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[379, 2378])).
% 2.71/2.07 tff(2381,plain,
% 2.71/2.07 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | c0_1(a832))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(2382,plain,
% 2.71/2.07 ((hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832))) <=> (hskp15 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | c0_1(a832))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(2383,plain,
% 2.71/2.07 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | c0_1(a832)))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[2382])).
% 2.71/2.07 tff(2384,plain,
% 2.71/2.07 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | c0_1(a832))),
% 2.71/2.07 inference(transitivity,[status(thm)],[2383, 2381])).
% 2.71/2.07 tff(2385,plain,
% 2.71/2.07 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(2386,plain,
% 2.71/2.07 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | c0_1(a832)),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[2385, 2384])).
% 2.71/2.07 tff(2387,plain,
% 2.71/2.07 (c0_1(a832)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2386, 151, 1374, 1280, 1279, 2380, 2379, 1300, 1290])).
% 2.71/2.07 tff(2388,plain,
% 2.71/2.07 (hskp11),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1329, 2357, 1290])).
% 2.71/2.07 tff(2389,plain,
% 2.71/2.07 (~c2_1(a808)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[857, 2388])).
% 2.71/2.07 tff(2390,plain,
% 2.71/2.07 (~c1_1(a808)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[851, 2388])).
% 2.71/2.07 tff(2391,plain,
% 2.71/2.07 (~c1_1(a832)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[391, 2378])).
% 2.71/2.07 tff(2392,plain,
% 2.71/2.07 (c3_1(a808)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[896, 2388])).
% 2.71/2.07 tff(2393,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a821) | c2_1(a821) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a821) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a821) | c2_1(a821) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a821) | (~c0_1(a832)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(2394,plain,
% 2.71/2.07 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a821) | c0_1(a821) | c3_1(a821)) <=> (c1_1(a832) | c3_1(a832) | c0_1(a821) | c2_1(a821) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a821) | (~c0_1(a832)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(2395,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a821) | c0_1(a821) | c3_1(a821))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a821) | c2_1(a821) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a821) | (~c0_1(a832))))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[2394])).
% 2.71/2.07 tff(2396,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a821) | c0_1(a821) | c3_1(a821))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a821) | c2_1(a821) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a821) | (~c0_1(a832)))),
% 2.71/2.07 inference(transitivity,[status(thm)],[2395, 2393])).
% 2.71/2.07 tff(2397,plain,
% 2.71/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a821) | c0_1(a821) | c3_1(a821))),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(2398,plain,
% 2.71/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a821) | c2_1(a821) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a821) | (~c0_1(a832))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[2397, 2396])).
% 2.71/2.07 tff(2399,plain,
% 2.71/2.07 (c3_1(a821) | (~c0_1(a832))),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2398, 151, 2392, 2391, 2379, 2310, 2298, 2390, 2389, 876])).
% 2.71/2.07 tff(2400,plain,
% 2.71/2.07 (c3_1(a821)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2399, 2387])).
% 2.71/2.07 tff(2401,plain,
% 2.71/2.07 (~c3_1(a828)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1197, 2366])).
% 2.71/2.07 tff(2402,plain,
% 2.71/2.07 (~c2_1(a828)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1191, 2366])).
% 2.71/2.07 tff(2403,plain,
% 2.71/2.07 (~c1_1(a828)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1203, 2366])).
% 2.71/2.07 tff(2404,plain,
% 2.71/2.07 (hskp2),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1411, 151, 2269, 2403, 2402, 2401, 1404])).
% 2.71/2.07 tff(2405,plain,
% 2.71/2.07 (~c0_1(a795)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1449, 2404])).
% 2.71/2.07 tff(2406,plain,
% 2.71/2.07 (~c3_1(a795)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1417, 2404])).
% 2.71/2.07 tff(2407,plain,
% 2.71/2.07 (c2_1(a795)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1563, 2406, 2391, 2388, 2387, 2405, 2379])).
% 2.71/2.07 tff(2408,plain,
% 2.71/2.07 (~c1_1(a795)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[1423, 2404])).
% 2.71/2.07 tff(2409,assumption,(~c1_1(a795)), introduced(assumption)).
% 2.71/2.07 tff(2410,assumption,(hskp12), introduced(assumption)).
% 2.71/2.07 tff(2411,plain,
% 2.71/2.07 (~c0_1(a809)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[164, 2410])).
% 2.71/2.07 tff(2412,plain,
% 2.71/2.07 (c1_1(a809)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[187, 2410])).
% 2.71/2.07 tff(2413,plain,
% 2.71/2.07 (c2_1(a809)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[176, 2410])).
% 2.71/2.07 tff(2414,assumption,(~c0_1(a809)), introduced(assumption)).
% 2.71/2.07 tff(2415,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(2416,plain,
% 2.71/2.07 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a795) | c0_1(a795) | c3_1(a795)) <=> (c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(2417,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832))))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[2416])).
% 2.71/2.07 tff(2418,plain,
% 2.71/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)))),
% 2.71/2.07 inference(transitivity,[status(thm)],[2417, 2415])).
% 2.71/2.07 tff(2419,plain,
% 2.71/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a795) | c0_1(a795) | c3_1(a795))),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(2420,plain,
% 2.71/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[2419, 2418])).
% 2.71/2.07 tff(2421,plain,
% 2.71/2.07 ((~c2_1(a809)) | (~c1_1(a809))),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2420, 151, 433, 322, 22, 2414, 1554, 2409, 1555, 1067])).
% 2.71/2.07 tff(2422,plain,
% 2.71/2.07 ($false),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2421, 2413, 2412])).
% 2.71/2.07 tff(2423,plain,((~hskp12) | (~c2_1(a832)) | c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.07 tff(2424,plain,
% 2.71/2.07 ($false),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2423, 2411, 2410, 322, 22, 433, 1554, 2409, 1555])).
% 2.71/2.07 tff(2425,plain,((~hskp12) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a795) | c1_1(a795) | c3_1(a795)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.07 tff(2426,plain,
% 2.71/2.07 (~hskp12),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2425, 2405, 2379, 2408, 2380, 2391, 2406])).
% 2.71/2.07 tff(2427,plain,
% 2.71/2.07 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a821)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a821)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(2428,plain,
% 2.71/2.07 ((hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821))) <=> (hskp12 | c0_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a821)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(2429,plain,
% 2.71/2.07 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a821))))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[2428])).
% 2.71/2.07 tff(2430,plain,
% 2.71/2.07 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a821)))),
% 2.71/2.07 inference(transitivity,[status(thm)],[2429, 2427])).
% 2.71/2.07 tff(2431,plain,
% 2.71/2.07 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821)))),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(2432,plain,
% 2.71/2.07 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a821))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[2431, 2430])).
% 2.71/2.07 tff(2433,plain,
% 2.71/2.07 ($false),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2432, 151, 2426, 2310, 2298, 2405, 2406, 1079, 2407, 2400])).
% 2.71/2.07 tff(2434,plain,((~hskp1) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.71/2.07 tff(2435,plain,
% 2.71/2.07 (~hskp1),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[2434, 357])).
% 2.71/2.07 tff(2436,plain,
% 2.71/2.07 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 2.71/2.07 inference(bind,[status(th)],[])).
% 2.71/2.07 tff(2437,plain,
% 2.71/2.07 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.71/2.07 inference(quant_intro,[status(thm)],[2436])).
% 2.71/2.07 tff(2438,plain,
% 2.71/2.07 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(2439,plain,
% 2.71/2.07 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 2.71/2.08 inference(bind,[status(th)],[])).
% 2.71/2.08 tff(2440,plain,
% 2.71/2.08 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.71/2.08 inference(quant_intro,[status(thm)],[2439])).
% 2.71/2.08 tff(2441,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 2.71/2.08 tff(2442,plain,
% 2.71/2.08 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2441, 2440])).
% 2.71/2.08 tff(2443,plain,
% 2.71/2.08 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2442, 2438])).
% 2.71/2.08 tff(2444,plain,(
% 2.71/2.08 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.71/2.08 inference(skolemize,[status(sab)],[2443])).
% 2.71/2.08 tff(2445,plain,
% 2.71/2.08 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2444, 2437])).
% 2.71/2.08 tff(2446,plain,
% 2.71/2.08 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a821) | c1_1(a821) | c2_1(a821) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a821) | c1_1(a821) | c2_1(a821) | (~ndr1_0))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2447,plain,
% 2.71/2.08 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a821) | c1_1(a821) | c0_1(a821)) <=> (hskp2 | hskp1 | c0_1(a821) | c1_1(a821) | c2_1(a821) | (~ndr1_0))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2448,plain,
% 2.71/2.08 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a821) | c1_1(a821) | c0_1(a821))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a821) | c1_1(a821) | c2_1(a821) | (~ndr1_0)))),
% 2.71/2.08 inference(monotonicity,[status(thm)],[2447])).
% 2.71/2.08 tff(2449,plain,
% 2.71/2.08 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a821) | c1_1(a821) | c0_1(a821))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a821) | c1_1(a821) | c2_1(a821) | (~ndr1_0))),
% 2.71/2.08 inference(transitivity,[status(thm)],[2448, 2446])).
% 2.71/2.08 tff(2450,plain,
% 2.71/2.08 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a821) | c1_1(a821) | c0_1(a821))),
% 2.71/2.08 inference(quant_inst,[status(thm)],[])).
% 2.71/2.08 tff(2451,plain,
% 2.71/2.08 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a821) | c1_1(a821) | c2_1(a821) | (~ndr1_0)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 2.71/2.08 tff(2452,plain,
% 2.71/2.08 (hskp2 | hskp1),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[2451, 151, 2310, 2304, 2298, 2445])).
% 2.71/2.08 tff(2453,plain,
% 2.71/2.08 (hskp2),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[2452, 2435])).
% 2.71/2.08 tff(2454,plain,
% 2.71/2.08 (~c3_1(a795)),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[1417, 2453])).
% 2.71/2.08 tff(2455,plain,
% 2.71/2.08 (~c0_1(a795)),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[1449, 2453])).
% 2.71/2.08 tff(2456,plain,
% 2.71/2.08 (^[U: $i] : refl((hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 2.71/2.08 inference(bind,[status(th)],[])).
% 2.71/2.08 tff(2457,plain,
% 2.71/2.08 (![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.08 inference(quant_intro,[status(thm)],[2456])).
% 2.71/2.08 tff(2458,plain,
% 2.71/2.08 (![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2459,plain,
% 2.71/2.08 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp25))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp1) <=> ((hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp1))), rewrite(((hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp1) <=> (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 2.71/2.08 inference(bind,[status(th)],[])).
% 2.71/2.08 tff(2460,plain,
% 2.71/2.08 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp1) <=> ![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.08 inference(quant_intro,[status(thm)],[2459])).
% 2.71/2.08 tff(2461,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 2.71/2.08 tff(2462,plain,
% 2.71/2.08 (![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2461, 2460])).
% 2.71/2.08 tff(2463,plain,
% 2.71/2.08 (![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2462, 2458])).
% 2.71/2.08 tff(2464,plain,(
% 2.71/2.08 ![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.08 inference(skolemize,[status(sab)],[2463])).
% 2.71/2.08 tff(2465,plain,
% 2.71/2.08 (![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2464, 2457])).
% 2.71/2.08 tff(2466,plain,
% 2.71/2.08 (((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))) <=> ((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2467,plain,
% 2.71/2.08 ((hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867))) <=> (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2468,plain,
% 2.71/2.08 (((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867))))),
% 2.71/2.08 inference(monotonicity,[status(thm)],[2467])).
% 2.71/2.08 tff(2469,plain,
% 2.71/2.08 (((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))),
% 2.71/2.08 inference(transitivity,[status(thm)],[2468, 2466])).
% 2.71/2.08 tff(2470,plain,
% 2.71/2.08 ((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)))),
% 2.71/2.08 inference(quant_inst,[status(thm)],[])).
% 2.71/2.08 tff(2471,plain,
% 2.71/2.08 ((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2470, 2469])).
% 2.71/2.08 tff(2472,plain,
% 2.71/2.08 (hskp25 | hskp1),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[2471, 151, 1281, 1280, 1279, 2465])).
% 2.71/2.08 tff(2473,plain,
% 2.71/2.08 (hskp25),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[2472, 2435])).
% 2.71/2.08 tff(2474,plain,
% 2.71/2.08 (((~hskp25) | (~c3_1(a865))) <=> ((~hskp25) | (~c3_1(a865)))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2475,plain,
% 2.71/2.08 (((~c3_1(a865)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a865)))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2476,axiom,((~c3_1(a865)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 2.71/2.08 tff(2477,plain,
% 2.71/2.08 ((~hskp25) | (~c3_1(a865))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2476, 2475])).
% 2.71/2.08 tff(2478,plain,
% 2.71/2.08 ((~hskp25) | (~c3_1(a865))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2477, 2474])).
% 2.71/2.08 tff(2479,plain,
% 2.71/2.08 (~c3_1(a865)),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[2478, 2473])).
% 2.71/2.08 tff(2480,plain,
% 2.71/2.08 (((~hskp25) | c2_1(a865)) <=> ((~hskp25) | c2_1(a865))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2481,axiom,((~hskp25) | c2_1(a865)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 2.71/2.08 tff(2482,plain,
% 2.71/2.08 ((~hskp25) | c2_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 2.71/2.08 tff(2483,plain,
% 2.71/2.08 ((~hskp25) | c2_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2482, 2480])).
% 2.71/2.08 tff(2484,plain,
% 2.71/2.08 ((~hskp25) | c2_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2483, 2480])).
% 2.71/2.08 tff(2485,plain,
% 2.71/2.08 ((~hskp25) | c2_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2484, 2480])).
% 2.71/2.08 tff(2486,plain,
% 2.71/2.08 ((~hskp25) | c2_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2485, 2480])).
% 2.71/2.08 tff(2487,plain,
% 2.71/2.08 ((~hskp25) | c2_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2486, 2480])).
% 2.71/2.08 tff(2488,plain,
% 2.71/2.08 ((~hskp25) | c2_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2487, 2480])).
% 2.71/2.08 tff(2489,plain,
% 2.71/2.08 ((~hskp25) | c2_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2488, 2480])).
% 2.71/2.08 tff(2490,plain,
% 2.71/2.08 (c2_1(a865)),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[2489, 2473])).
% 2.71/2.08 tff(2491,plain,
% 2.71/2.08 (((~hskp25) | c1_1(a865)) <=> ((~hskp25) | c1_1(a865))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2492,axiom,((~hskp25) | c1_1(a865)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 2.71/2.08 tff(2493,plain,
% 2.71/2.08 ((~hskp25) | c1_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2492, 2491])).
% 2.71/2.08 tff(2494,plain,
% 2.71/2.08 ((~hskp25) | c1_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2493, 2491])).
% 2.71/2.08 tff(2495,plain,
% 2.71/2.08 ((~hskp25) | c1_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2494, 2491])).
% 2.71/2.08 tff(2496,plain,
% 2.71/2.08 ((~hskp25) | c1_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2495, 2491])).
% 2.71/2.08 tff(2497,plain,
% 2.71/2.08 ((~hskp25) | c1_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2496, 2491])).
% 2.71/2.08 tff(2498,plain,
% 2.71/2.08 ((~hskp25) | c1_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2497, 2491])).
% 2.71/2.08 tff(2499,plain,
% 2.71/2.08 ((~hskp25) | c1_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2498, 2491])).
% 2.71/2.08 tff(2500,plain,
% 2.71/2.08 ((~hskp25) | c1_1(a865)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2499, 2491])).
% 2.71/2.08 tff(2501,plain,
% 2.71/2.08 (c1_1(a865)),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[2500, 2473])).
% 2.71/2.08 tff(2502,plain,
% 2.71/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a865) | c0_1(a821) | c1_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a865) | c0_1(a821) | c1_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c2_1(a865)) | (~c1_1(a865)))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2503,plain,
% 2.71/2.08 (((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a821) | c1_1(a821) | c0_1(a821)) <=> (c3_1(a865) | c0_1(a821) | c1_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c2_1(a865)) | (~c1_1(a865)))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2504,plain,
% 2.71/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a821) | c1_1(a821) | c0_1(a821))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a865) | c0_1(a821) | c1_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c2_1(a865)) | (~c1_1(a865))))),
% 2.71/2.08 inference(monotonicity,[status(thm)],[2503])).
% 2.71/2.08 tff(2505,plain,
% 2.71/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a821) | c1_1(a821) | c0_1(a821))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a865) | c0_1(a821) | c1_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c2_1(a865)) | (~c1_1(a865)))),
% 2.71/2.08 inference(transitivity,[status(thm)],[2504, 2502])).
% 2.71/2.08 tff(2506,plain,
% 2.71/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a821) | c1_1(a821) | c0_1(a821))),
% 2.71/2.08 inference(quant_inst,[status(thm)],[])).
% 2.71/2.08 tff(2507,plain,
% 2.71/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a865) | c0_1(a821) | c1_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c2_1(a865)) | (~c1_1(a865))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2506, 2505])).
% 2.71/2.08 tff(2508,plain,
% 2.71/2.08 (c2_1(a795)),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[2507, 151, 2501, 2490, 2479, 2310, 2304, 2298, 2455, 2454, 258])).
% 2.71/2.08 tff(2509,plain,
% 2.71/2.08 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a795)))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2510,plain,
% 2.71/2.08 ((hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795))) <=> (hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a795)))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2511,plain,
% 2.71/2.08 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a795))))),
% 2.71/2.08 inference(monotonicity,[status(thm)],[2510])).
% 2.71/2.08 tff(2512,plain,
% 2.71/2.08 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a795)))),
% 2.71/2.08 inference(transitivity,[status(thm)],[2511, 2509])).
% 2.71/2.08 tff(2513,plain,
% 2.71/2.08 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795)))),
% 2.71/2.08 inference(quant_inst,[status(thm)],[])).
% 2.71/2.08 tff(2514,plain,
% 2.71/2.08 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a795))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2513, 2512])).
% 2.71/2.08 tff(2515,plain,
% 2.71/2.08 ($false),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[2514, 151, 1374, 1280, 1279, 2455, 2454, 1300, 2508, 1290])).
% 2.71/2.08 tff(2516,plain,(hskp28), inference(lemma,lemma(discharge,[]))).
% 2.71/2.08 tff(2517,plain,
% 2.71/2.08 (((~hskp28) | c3_1(a797)) <=> ((~hskp28) | c3_1(a797))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2518,axiom,((~hskp28) | c3_1(a797)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 2.71/2.08 tff(2519,plain,
% 2.71/2.08 ((~hskp28) | c3_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2518, 2517])).
% 2.71/2.08 tff(2520,plain,
% 2.71/2.08 ((~hskp28) | c3_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2519, 2517])).
% 2.71/2.08 tff(2521,plain,
% 2.71/2.08 ((~hskp28) | c3_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2520, 2517])).
% 2.71/2.08 tff(2522,plain,
% 2.71/2.08 ((~hskp28) | c3_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2521, 2517])).
% 2.71/2.08 tff(2523,plain,
% 2.71/2.08 ((~hskp28) | c3_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2522, 2517])).
% 2.71/2.08 tff(2524,plain,
% 2.71/2.08 ((~hskp28) | c3_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2523, 2517])).
% 2.71/2.08 tff(2525,plain,
% 2.71/2.08 ((~hskp28) | c3_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2524, 2517])).
% 2.71/2.08 tff(2526,plain,
% 2.71/2.08 ((~hskp28) | c3_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2525, 2517])).
% 2.71/2.08 tff(2527,plain,
% 2.71/2.08 (c3_1(a797)),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[2526, 2516])).
% 2.71/2.08 tff(2528,plain,
% 2.71/2.08 (((~hskp28) | c2_1(a797)) <=> ((~hskp28) | c2_1(a797))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2529,axiom,((~hskp28) | c2_1(a797)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 2.71/2.08 tff(2530,plain,
% 2.71/2.08 ((~hskp28) | c2_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2529, 2528])).
% 2.71/2.08 tff(2531,plain,
% 2.71/2.08 ((~hskp28) | c2_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2530, 2528])).
% 2.71/2.08 tff(2532,plain,
% 2.71/2.08 ((~hskp28) | c2_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2531, 2528])).
% 2.71/2.08 tff(2533,plain,
% 2.71/2.08 ((~hskp28) | c2_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2532, 2528])).
% 2.71/2.08 tff(2534,plain,
% 2.71/2.08 ((~hskp28) | c2_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2533, 2528])).
% 2.71/2.08 tff(2535,plain,
% 2.71/2.08 ((~hskp28) | c2_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2534, 2528])).
% 2.71/2.08 tff(2536,plain,
% 2.71/2.08 ((~hskp28) | c2_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2535, 2528])).
% 2.71/2.08 tff(2537,plain,
% 2.71/2.08 ((~hskp28) | c2_1(a797)),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2536, 2528])).
% 2.71/2.08 tff(2538,plain,
% 2.71/2.08 (c2_1(a797)),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[2537, 2516])).
% 2.71/2.08 tff(2539,plain,
% 2.71/2.08 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2540,plain,
% 2.71/2.08 ((hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797))) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2541,plain,
% 2.71/2.08 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797))))),
% 2.71/2.08 inference(monotonicity,[status(thm)],[2540])).
% 2.71/2.08 tff(2542,plain,
% 2.71/2.08 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 2.71/2.08 inference(transitivity,[status(thm)],[2541, 2539])).
% 2.71/2.08 tff(2543,plain,
% 2.71/2.08 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))),
% 2.71/2.08 inference(quant_inst,[status(thm)],[])).
% 2.71/2.08 tff(2544,plain,
% 2.71/2.08 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2543, 2542])).
% 2.71/2.08 tff(2545,plain,
% 2.71/2.08 (hskp30 | hskp20 | (~c0_1(a797))),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[2544, 151, 2538, 2527, 356])).
% 2.71/2.08 tff(2546,plain,
% 2.71/2.08 (~c0_1(a797)),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[2545, 346, 345])).
% 2.71/2.08 tff(2547,plain,
% 2.71/2.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 2.71/2.08 inference(bind,[status(th)],[])).
% 2.71/2.08 tff(2548,plain,
% 2.71/2.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.08 inference(quant_intro,[status(thm)],[2547])).
% 2.71/2.08 tff(2549,plain,
% 2.71/2.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(2550,plain,
% 2.71/2.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 2.71/2.08 inference(bind,[status(th)],[])).
% 2.71/2.08 tff(2551,plain,
% 2.71/2.08 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.08 inference(quant_intro,[status(thm)],[2550])).
% 2.71/2.08 tff(2552,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 2.71/2.08 tff(2553,plain,
% 2.71/2.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2552, 2551])).
% 2.71/2.08 tff(2554,plain,
% 2.71/2.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2553, 2549])).
% 2.71/2.08 tff(2555,plain,(
% 2.71/2.08 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.08 inference(skolemize,[status(sab)],[2554])).
% 2.71/2.08 tff(2556,plain,
% 2.71/2.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[2555, 2548])).
% 2.71/2.08 tff(2557,plain,
% 2.71/2.08 (((~hskp28) | c1_1(a797)) <=> ((~hskp28) | c1_1(a797))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(2558,axiom,((~hskp28) | c1_1(a797)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 2.71/2.09 tff(2559,plain,
% 2.71/2.09 ((~hskp28) | c1_1(a797)),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2558, 2557])).
% 2.71/2.09 tff(2560,plain,
% 2.71/2.09 ((~hskp28) | c1_1(a797)),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2559, 2557])).
% 2.71/2.09 tff(2561,plain,
% 2.71/2.09 ((~hskp28) | c1_1(a797)),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2560, 2557])).
% 2.71/2.09 tff(2562,plain,
% 2.71/2.09 ((~hskp28) | c1_1(a797)),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2561, 2557])).
% 2.71/2.09 tff(2563,plain,
% 2.71/2.09 ((~hskp28) | c1_1(a797)),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2562, 2557])).
% 2.71/2.09 tff(2564,plain,
% 2.71/2.09 ((~hskp28) | c1_1(a797)),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2563, 2557])).
% 2.71/2.09 tff(2565,plain,
% 2.71/2.09 ((~hskp28) | c1_1(a797)),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2564, 2557])).
% 2.71/2.09 tff(2566,plain,
% 2.71/2.09 ((~hskp28) | c1_1(a797)),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2565, 2557])).
% 2.71/2.09 tff(2567,plain,
% 2.71/2.09 (c1_1(a797)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2566, 2516])).
% 2.71/2.09 tff(2568,plain,
% 2.71/2.09 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(2569,plain,
% 2.71/2.09 ((hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797))) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(2570,plain,
% 2.71/2.09 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797))))),
% 2.71/2.09 inference(monotonicity,[status(thm)],[2569])).
% 2.71/2.09 tff(2571,plain,
% 2.71/2.09 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 2.71/2.09 inference(transitivity,[status(thm)],[2570, 2568])).
% 2.71/2.09 tff(2572,plain,
% 2.71/2.09 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)))),
% 2.71/2.09 inference(quant_inst,[status(thm)],[])).
% 2.71/2.09 tff(2573,plain,
% 2.71/2.09 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797))),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2572, 2571])).
% 2.71/2.09 tff(2574,plain,
% 2.71/2.09 (hskp21 | hskp11),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2573, 151, 2567, 2538, 2527, 703])).
% 2.71/2.09 tff(2575,plain,
% 2.71/2.09 (hskp11),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2574, 704])).
% 2.71/2.09 tff(2576,plain,
% 2.71/2.09 (~c2_1(a808)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[857, 2575])).
% 2.71/2.09 tff(2577,plain,
% 2.71/2.09 (~c1_1(a808)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[851, 2575])).
% 2.71/2.09 tff(2578,plain,
% 2.71/2.09 (c3_1(a808)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[896, 2575])).
% 2.71/2.09 tff(2579,plain,
% 2.71/2.09 (hskp18),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[1185, 151, 704, 2578, 2577, 2576, 1178])).
% 2.71/2.09 tff(2580,plain,
% 2.71/2.09 (~c3_1(a828)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[1197, 2579])).
% 2.71/2.09 tff(2581,plain,
% 2.71/2.09 (~c2_1(a828)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[1191, 2579])).
% 2.71/2.09 tff(2582,plain,
% 2.71/2.09 (~c1_1(a828)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[1203, 2579])).
% 2.71/2.09 tff(2583,assumption,(hskp27), introduced(assumption)).
% 2.71/2.09 tff(2584,plain,
% 2.71/2.09 (c3_1(a796)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[594, 2583])).
% 2.71/2.09 tff(2585,plain,
% 2.71/2.09 (c2_1(a796)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[605, 2583])).
% 2.71/2.09 tff(2586,plain,
% 2.71/2.09 (c0_1(a796)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[616, 2583])).
% 2.71/2.09 tff(2587,plain,
% 2.71/2.09 ($false),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[620, 345, 151, 346, 2586, 2585, 2584, 356])).
% 2.71/2.09 tff(2588,plain,((~hskp27) | hskp30 | hskp20), inference(lemma,lemma(discharge,[]))).
% 2.71/2.09 tff(2589,plain,
% 2.71/2.09 (~hskp27),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2588, 346, 345])).
% 2.71/2.09 tff(2590,plain,
% 2.71/2.09 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(2591,plain,
% 2.71/2.09 ((hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797))) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(2592,plain,
% 2.71/2.09 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797))))),
% 2.71/2.09 inference(monotonicity,[status(thm)],[2591])).
% 2.71/2.09 tff(2593,plain,
% 2.71/2.09 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 2.71/2.09 inference(transitivity,[status(thm)],[2592, 2590])).
% 2.71/2.09 tff(2594,plain,
% 2.71/2.09 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)))),
% 2.71/2.09 inference(quant_inst,[status(thm)],[])).
% 2.71/2.09 tff(2595,plain,
% 2.71/2.09 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797))),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2594, 2593])).
% 2.71/2.09 tff(2596,plain,
% 2.71/2.09 (hskp27 | hskp19),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2595, 151, 2567, 2538, 2527, 2234])).
% 2.71/2.09 tff(2597,plain,
% 2.71/2.09 (hskp19),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2596, 2589])).
% 2.71/2.09 tff(2598,plain,
% 2.71/2.09 (~c1_1(a832)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[391, 2597])).
% 2.71/2.09 tff(2599,plain,
% 2.71/2.09 (hskp20 | hskp2),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[1411, 151, 1215, 1206, 1205, 1404])).
% 2.71/2.09 tff(2600,plain,
% 2.71/2.09 (hskp2),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2599, 346])).
% 2.71/2.09 tff(2601,plain,
% 2.71/2.09 (~c3_1(a795)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[1417, 2600])).
% 2.71/2.09 tff(2602,plain,
% 2.71/2.09 (~c1_1(a795)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[1423, 2600])).
% 2.71/2.09 tff(2603,plain,
% 2.71/2.09 (~c0_1(a795)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[1449, 2600])).
% 2.71/2.09 tff(2604,plain,
% 2.71/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a795)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a795)))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(2605,plain,
% 2.71/2.09 (((~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a795) | c0_1(a795) | c3_1(a795)) <=> (c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a795)))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(2606,plain,
% 2.71/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a795))))),
% 2.71/2.09 inference(monotonicity,[status(thm)],[2605])).
% 2.71/2.09 tff(2607,plain,
% 2.71/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a795)))),
% 2.71/2.09 inference(transitivity,[status(thm)],[2606, 2604])).
% 2.71/2.09 tff(2608,plain,
% 2.71/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a795) | c0_1(a795) | c3_1(a795))),
% 2.71/2.09 inference(quant_inst,[status(thm)],[])).
% 2.71/2.09 tff(2609,plain,
% 2.71/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a795))),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2608, 2607])).
% 2.71/2.09 tff(2610,plain,
% 2.71/2.09 (~c2_1(a795)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2609, 151, 2567, 2538, 2603, 2602, 2601, 1067, 2546])).
% 2.71/2.09 tff(2611,plain,
% 2.71/2.09 (~c3_1(a832)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[385, 2597])).
% 2.71/2.09 tff(2612,plain,
% 2.71/2.09 (~c0_1(a832)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[1563, 2611, 1516, 2603, 2601, 2610, 2598])).
% 2.71/2.09 tff(2613,plain,
% 2.71/2.09 (c2_1(a832)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[379, 2597])).
% 2.71/2.09 tff(2614,plain,
% 2.71/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | c0_1(a832))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(2615,plain,
% 2.71/2.09 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a832) | c0_1(a832) | c3_1(a832)) <=> (c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | c0_1(a832))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(2616,plain,
% 2.71/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | c0_1(a832)))),
% 2.71/2.09 inference(monotonicity,[status(thm)],[2615])).
% 2.71/2.09 tff(2617,plain,
% 2.71/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | c0_1(a832))),
% 2.71/2.09 inference(transitivity,[status(thm)],[2616, 2614])).
% 2.71/2.09 tff(2618,plain,
% 2.71/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a832) | c0_1(a832) | c3_1(a832))),
% 2.71/2.09 inference(quant_inst,[status(thm)],[])).
% 2.71/2.09 tff(2619,plain,
% 2.71/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | c0_1(a832)),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2618, 2617])).
% 2.71/2.09 tff(2620,plain,
% 2.71/2.09 ($false),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2619, 151, 2567, 2538, 2613, 2598, 2611, 1067, 2612, 2546])).
% 2.71/2.09 tff(2621,plain,(hskp20 | (~hskp11) | hskp30 | c1_1(a828) | c2_1(a828) | c3_1(a828)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.09 tff(2622,plain,
% 2.71/2.09 (hskp20),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2621, 2575, 345, 2582, 2581, 2580])).
% 2.71/2.09 tff(2623,plain,
% 2.71/2.09 (~c0_1(a833)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[632, 2622])).
% 2.71/2.09 tff(2624,plain,
% 2.71/2.09 (c1_1(a833)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[343, 2622])).
% 2.71/2.09 tff(2625,plain,
% 2.71/2.09 (~c2_1(a833)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[626, 2622])).
% 2.71/2.09 tff(2626,plain,
% 2.71/2.09 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 2.71/2.09 inference(bind,[status(th)],[])).
% 2.71/2.09 tff(2627,plain,
% 2.71/2.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.09 inference(quant_intro,[status(thm)],[2626])).
% 2.71/2.09 tff(2628,plain,
% 2.71/2.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(2629,plain,
% 2.71/2.09 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 2.71/2.09 inference(bind,[status(th)],[])).
% 2.71/2.09 tff(2630,plain,
% 2.71/2.09 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.09 inference(quant_intro,[status(thm)],[2629])).
% 2.71/2.09 tff(2631,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 2.71/2.09 tff(2632,plain,
% 2.71/2.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2631, 2630])).
% 2.71/2.09 tff(2633,plain,
% 2.71/2.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2632, 2628])).
% 2.71/2.09 tff(2634,plain,(
% 2.71/2.09 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.09 inference(skolemize,[status(sab)],[2633])).
% 2.71/2.09 tff(2635,plain,
% 2.71/2.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2634, 2627])).
% 2.71/2.09 tff(2636,plain,
% 2.71/2.09 (~c3_1(a833)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2202, 1603])).
% 2.71/2.09 tff(2637,plain,
% 2.71/2.09 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 2.71/2.09 inference(bind,[status(th)],[])).
% 2.71/2.09 tff(2638,plain,
% 2.71/2.09 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.71/2.09 inference(quant_intro,[status(thm)],[2637])).
% 2.71/2.09 tff(2639,plain,
% 2.71/2.09 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(2640,plain,
% 2.71/2.09 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | 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)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp3) <=> (hskp3 | (~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)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 2.71/2.09 inference(bind,[status(th)],[])).
% 2.71/2.09 tff(2641,plain,
% 2.71/2.09 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.71/2.09 inference(quant_intro,[status(thm)],[2640])).
% 2.71/2.09 tff(2642,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)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 2.71/2.09 tff(2643,plain,
% 2.71/2.09 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2642, 2641])).
% 2.71/2.09 tff(2644,plain,
% 2.71/2.09 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2643, 2639])).
% 2.71/2.09 tff(2645,plain,(
% 2.71/2.09 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.71/2.09 inference(skolemize,[status(sab)],[2644])).
% 2.71/2.09 tff(2646,plain,
% 2.71/2.09 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2645, 2638])).
% 2.71/2.09 tff(2647,assumption,(~hskp3), introduced(assumption)).
% 2.71/2.09 tff(2648,plain,
% 2.71/2.09 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(2649,plain,
% 2.71/2.09 ((hskp3 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)) | c3_1(a833) | c0_1(a833) | (~c1_1(a833))) <=> (hskp3 | c0_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(2650,plain,
% 2.71/2.09 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)) | c3_1(a833) | c0_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))))),
% 2.71/2.09 inference(monotonicity,[status(thm)],[2649])).
% 2.71/2.09 tff(2651,plain,
% 2.71/2.09 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)) | c3_1(a833) | c0_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 2.71/2.09 inference(transitivity,[status(thm)],[2650, 2648])).
% 2.71/2.09 tff(2652,plain,
% 2.71/2.09 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)) | c3_1(a833) | c0_1(a833) | (~c1_1(a833)))),
% 2.71/2.09 inference(quant_inst,[status(thm)],[])).
% 2.71/2.09 tff(2653,plain,
% 2.71/2.09 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[2652, 2651])).
% 2.71/2.09 tff(2654,plain,
% 2.71/2.09 ($false),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2653, 151, 2647, 639, 321, 309, 2646, 310])).
% 2.71/2.09 tff(2655,plain,(c3_1(a833) | hskp3 | (~c1_1(a833)) | c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.09 tff(2656,plain,
% 2.71/2.09 (hskp3),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2655, 2636, 309, 321, 639])).
% 2.71/2.09 tff(2657,plain,
% 2.71/2.09 (~c3_1(a798)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[546, 2656])).
% 2.71/2.09 tff(2658,plain,
% 2.71/2.09 (hskp27),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[2596, 1603])).
% 2.71/2.09 tff(2659,plain,
% 2.71/2.09 (c0_1(a796)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[616, 2658])).
% 2.71/2.09 tff(2660,plain,
% 2.71/2.09 (c2_1(a796)),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[605, 2658])).
% 2.71/2.10 tff(2661,plain,
% 2.71/2.10 (c3_1(a796)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[594, 2658])).
% 2.71/2.10 tff(2662,plain,
% 2.71/2.10 (hskp12),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[826, 2661, 309, 639, 2660, 321, 2636, 2659])).
% 2.71/2.10 tff(2663,plain,
% 2.71/2.10 (~c0_1(a809)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[164, 2662])).
% 2.71/2.10 tff(2664,plain,
% 2.71/2.10 (c2_1(a798)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[563, 2656])).
% 2.71/2.10 tff(2665,plain,
% 2.71/2.10 (c0_1(a798)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[574, 2656])).
% 2.71/2.10 tff(2666,plain,
% 2.71/2.10 (c2_1(a809)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[176, 2662])).
% 2.71/2.10 tff(2667,plain,
% 2.71/2.10 (c1_1(a809)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[187, 2662])).
% 2.71/2.10 tff(2668,plain,
% 2.71/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a809) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a809) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.71/2.10 inference(rewrite,[status(thm)],[])).
% 2.71/2.10 tff(2669,plain,
% 2.71/2.10 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (c0_1(a809) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.71/2.10 inference(rewrite,[status(thm)],[])).
% 2.71/2.10 tff(2670,plain,
% 2.71/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a809) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a809)) | (~c1_1(a809))))),
% 2.71/2.10 inference(monotonicity,[status(thm)],[2669])).
% 2.71/2.10 tff(2671,plain,
% 2.71/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a809) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.71/2.10 inference(transitivity,[status(thm)],[2670, 2668])).
% 2.71/2.10 tff(2672,plain,
% 2.71/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 2.71/2.10 inference(quant_inst,[status(thm)],[])).
% 2.71/2.10 tff(2673,plain,
% 2.71/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a809) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a809)) | (~c1_1(a809))),
% 2.71/2.10 inference(modus_ponens,[status(thm)],[2672, 2671])).
% 2.71/2.10 tff(2674,plain,
% 2.71/2.10 (c0_1(a808)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[2673, 151, 2667, 2666, 1031, 2665, 2664, 2663, 877, 2657, 2635])).
% 2.71/2.10 tff(2675,plain,
% 2.71/2.10 (hskp8),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[963, 2659, 309, 2636, 2660, 2661, 321, 639])).
% 2.71/2.10 tff(2676,plain,
% 2.71/2.10 (~c3_1(a805)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[462, 2675])).
% 2.71/2.10 tff(2677,plain,
% 2.71/2.10 (~c2_1(a805)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[468, 2675])).
% 2.71/2.10 tff(2678,plain,
% 2.71/2.10 (c1_1(a805)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[480, 2675])).
% 2.71/2.10 tff(2679,plain,
% 2.71/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a808) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a808) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)))),
% 2.71/2.10 inference(rewrite,[status(thm)],[])).
% 2.71/2.10 tff(2680,plain,
% 2.71/2.10 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c2_1(a808) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)))),
% 2.71/2.10 inference(rewrite,[status(thm)],[])).
% 2.71/2.10 tff(2681,plain,
% 2.71/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a808) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808))))),
% 2.71/2.10 inference(monotonicity,[status(thm)],[2680])).
% 2.71/2.10 tff(2682,plain,
% 2.71/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a808) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)))),
% 2.71/2.10 inference(transitivity,[status(thm)],[2681, 2679])).
% 2.71/2.10 tff(2683,plain,
% 2.71/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 2.71/2.10 inference(quant_inst,[status(thm)],[])).
% 2.71/2.10 tff(2684,plain,
% 2.71/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a808) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808))),
% 2.71/2.10 inference(modus_ponens,[status(thm)],[2683, 2682])).
% 2.71/2.10 tff(2685,plain,
% 2.71/2.10 ($false),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[2684, 151, 1031, 2678, 2665, 2664, 877, 2677, 2676, 2657, 332, 2674])).
% 2.71/2.10 tff(2686,plain,(hskp19 | (~c3_1(a808)) | c2_1(a808) | c2_1(a833) | (~c1_1(a833)) | c0_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828)), inference(lemma,lemma(discharge,[]))).
% 2.71/2.10 tff(2687,plain,
% 2.71/2.10 (hskp19),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[2686, 2578, 2576, 2625, 2624, 2623, 2582, 2581, 2580])).
% 2.71/2.10 tff(2688,plain,
% 2.71/2.10 (~c3_1(a832)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[385, 2687])).
% 2.71/2.10 tff(2689,plain,
% 2.71/2.10 (~c1_1(a832)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[391, 2687])).
% 2.71/2.10 tff(2690,plain,
% 2.71/2.10 (c2_1(a832)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[379, 2687])).
% 2.71/2.10 tff(2691,plain,
% 2.71/2.10 (hskp0),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[657, 151, 704, 2690, 2689, 2688, 651])).
% 2.71/2.10 tff(2692,plain,
% 2.71/2.10 (~c1_1(a793)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[675, 2691])).
% 2.71/2.10 tff(2693,plain,
% 2.71/2.10 (c2_1(a793)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[669, 2691])).
% 2.71/2.10 tff(2694,plain,
% 2.71/2.10 (c0_1(a793)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[686, 2691])).
% 2.71/2.10 tff(2695,plain,
% 2.71/2.10 (hskp19),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[2686, 1031, 877, 309, 639, 321, 1215, 1206, 1205])).
% 2.71/2.10 tff(2696,plain,
% 2.71/2.10 (~c3_1(a832)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[385, 2695])).
% 2.71/2.10 tff(2697,plain,
% 2.71/2.10 (c2_1(a832)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[379, 2695])).
% 2.71/2.10 tff(2698,plain,
% 2.71/2.10 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a832)) | c0_1(a832))),
% 2.71/2.10 inference(rewrite,[status(thm)],[])).
% 2.71/2.10 tff(2699,plain,
% 2.71/2.10 ((hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832))) <=> (hskp15 | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a832)) | c0_1(a832))),
% 2.71/2.10 inference(rewrite,[status(thm)],[])).
% 2.71/2.10 tff(2700,plain,
% 2.71/2.10 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a832)) | c0_1(a832)))),
% 2.71/2.10 inference(monotonicity,[status(thm)],[2699])).
% 2.71/2.10 tff(2701,plain,
% 2.71/2.10 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a832)) | c0_1(a832))),
% 2.71/2.10 inference(transitivity,[status(thm)],[2700, 2698])).
% 2.71/2.10 tff(2702,plain,
% 2.71/2.10 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))),
% 2.71/2.10 inference(quant_inst,[status(thm)],[])).
% 2.71/2.10 tff(2703,plain,
% 2.71/2.10 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a832)) | c0_1(a832)),
% 2.71/2.10 inference(modus_ponens,[status(thm)],[2702, 2701])).
% 2.71/2.10 tff(2704,plain,
% 2.71/2.10 (hskp15 | c0_1(a832)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[2703, 151, 2567, 2538, 2527, 2697, 2696, 1300])).
% 2.71/2.10 tff(2705,plain,
% 2.71/2.10 (c0_1(a832)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[2704, 1385])).
% 2.71/2.10 tff(2706,plain,
% 2.71/2.10 (~c1_1(a832)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[391, 2695])).
% 2.71/2.10 tff(2707,plain,
% 2.71/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a832)) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a832)) | c3_1(a833))),
% 2.71/2.10 inference(rewrite,[status(thm)],[])).
% 2.71/2.10 tff(2708,plain,
% 2.71/2.10 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833)) <=> (c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a832)) | c3_1(a833))),
% 2.71/2.10 inference(rewrite,[status(thm)],[])).
% 2.71/2.10 tff(2709,plain,
% 2.71/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a832)) | c3_1(a833)))),
% 2.71/2.10 inference(monotonicity,[status(thm)],[2708])).
% 2.71/2.10 tff(2710,plain,
% 2.71/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a832)) | c3_1(a833))),
% 2.71/2.10 inference(transitivity,[status(thm)],[2709, 2707])).
% 2.71/2.10 tff(2711,plain,
% 2.71/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833))),
% 2.71/2.10 inference(quant_inst,[status(thm)],[])).
% 2.71/2.10 tff(2712,plain,
% 2.71/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a832)) | c3_1(a833)),
% 2.71/2.10 inference(modus_ponens,[status(thm)],[2711, 2710])).
% 2.71/2.10 tff(2713,plain,
% 2.71/2.10 ((~c0_1(a832)) | c3_1(a833)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[2712, 151, 1031, 321, 309, 2706, 2696, 878, 877, 876])).
% 2.71/2.10 tff(2714,plain,
% 2.71/2.10 (c3_1(a833)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[2713, 2705])).
% 2.71/2.10 tff(2715,plain,
% 2.71/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a832)))),
% 2.71/2.10 inference(rewrite,[status(thm)],[])).
% 2.71/2.10 tff(2716,plain,
% 2.71/2.10 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828)) <=> (c1_1(a832) | c3_1(a832) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a832)))),
% 2.71/2.10 inference(rewrite,[status(thm)],[])).
% 2.71/2.10 tff(2717,plain,
% 2.71/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a832))))),
% 2.71/2.10 inference(monotonicity,[status(thm)],[2716])).
% 2.71/2.10 tff(2718,plain,
% 2.71/2.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a832)))),
% 2.71/2.10 inference(transitivity,[status(thm)],[2717, 2715])).
% 2.71/2.10 tff(2719,plain,
% 2.71/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828))),
% 2.71/2.10 inference(quant_inst,[status(thm)],[])).
% 2.71/2.10 tff(2720,plain,
% 2.71/2.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a832))),
% 2.71/2.10 inference(modus_ponens,[status(thm)],[2719, 2718])).
% 2.71/2.10 tff(2721,plain,
% 2.71/2.10 (c0_1(a828) | (~c0_1(a832))),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[2720, 151, 1031, 2706, 2696, 1206, 1205, 878, 877, 876])).
% 2.71/2.10 tff(2722,plain,
% 2.71/2.10 (c0_1(a828)),
% 2.71/2.10 inference(unit_resolution,[status(thm)],[2721, 2705])).
% 2.71/2.10 tff(2723,plain,
% 2.71/2.10 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 2.71/2.10 inference(bind,[status(th)],[])).
% 2.71/2.10 tff(2724,plain,
% 2.71/2.10 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.71/2.10 inference(quant_intro,[status(thm)],[2723])).
% 2.71/2.10 tff(2725,plain,
% 2.71/2.10 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.71/2.10 inference(rewrite,[status(thm)],[])).
% 2.71/2.10 tff(2726,plain,
% 2.71/2.10 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 2.71/2.10 inference(bind,[status(th)],[])).
% 2.71/2.10 tff(2727,plain,
% 2.71/2.10 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.71/2.10 inference(quant_intro,[status(thm)],[2726])).
% 2.71/2.10 tff(2728,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 2.71/2.10 tff(2729,plain,
% 2.71/2.10 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.71/2.10 inference(modus_ponens,[status(thm)],[2728, 2727])).
% 2.71/2.10 tff(2730,plain,
% 2.71/2.10 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.71/2.10 inference(modus_ponens,[status(thm)],[2729, 2725])).
% 2.71/2.10 tff(2731,plain,(
% 2.71/2.10 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.71/2.10 inference(skolemize,[status(sab)],[2730])).
% 2.71/2.10 tff(2732,plain,
% 2.71/2.10 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 2.71/2.10 inference(modus_ponens,[status(thm)],[2731, 2724])).
% 2.71/2.10 tff(2733,plain,
% 2.71/2.10 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp29 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 2.71/2.10 inference(rewrite,[status(thm)],[])).
% 2.71/2.10 tff(2734,plain,
% 2.71/2.10 ((hskp29 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (hskp29 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 2.71/2.10 inference(rewrite,[status(thm)],[])).
% 2.71/2.10 tff(2735,plain,
% 2.71/2.10 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c0_1(a828))))),
% 2.71/2.10 inference(monotonicity,[status(thm)],[2734])).
% 2.71/2.10 tff(2736,plain,
% 2.71/2.10 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp29 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 2.71/2.10 inference(transitivity,[status(thm)],[2735, 2733])).
% 2.71/2.10 tff(2737,plain,
% 2.71/2.10 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 2.71/2.11 inference(quant_inst,[status(thm)],[])).
% 2.71/2.11 tff(2738,plain,
% 2.71/2.11 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp29 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c0_1(a828))),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2737, 2736])).
% 2.71/2.11 tff(2739,plain,
% 2.71/2.11 (hskp29 | (~c0_1(a828))),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2738, 151, 1215, 1206, 1205, 2732])).
% 2.71/2.11 tff(2740,plain,
% 2.71/2.11 (hskp29),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2739, 2722])).
% 2.71/2.11 tff(2741,plain,
% 2.71/2.11 (((~hskp29) | c0_1(a829)) <=> ((~hskp29) | c0_1(a829))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2742,axiom,((~hskp29) | c0_1(a829)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 2.71/2.11 tff(2743,plain,
% 2.71/2.11 ((~hskp29) | c0_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2742, 2741])).
% 2.71/2.11 tff(2744,plain,
% 2.71/2.11 ((~hskp29) | c0_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2743, 2741])).
% 2.71/2.11 tff(2745,plain,
% 2.71/2.11 ((~hskp29) | c0_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2744, 2741])).
% 2.71/2.11 tff(2746,plain,
% 2.71/2.11 ((~hskp29) | c0_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2745, 2741])).
% 2.71/2.11 tff(2747,plain,
% 2.71/2.11 ((~hskp29) | c0_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2746, 2741])).
% 2.71/2.11 tff(2748,plain,
% 2.71/2.11 ((~hskp29) | c0_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2747, 2741])).
% 2.71/2.11 tff(2749,plain,
% 2.71/2.11 ((~hskp29) | c0_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2748, 2741])).
% 2.71/2.11 tff(2750,plain,
% 2.71/2.11 ((~hskp29) | c0_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2749, 2741])).
% 2.71/2.11 tff(2751,plain,
% 2.71/2.11 (c0_1(a829)),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2750, 2740])).
% 2.71/2.11 tff(2752,plain,
% 2.71/2.11 (((~hskp29) | c2_1(a829)) <=> ((~hskp29) | c2_1(a829))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2753,axiom,((~hskp29) | c2_1(a829)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 2.71/2.11 tff(2754,plain,
% 2.71/2.11 ((~hskp29) | c2_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2753, 2752])).
% 2.71/2.11 tff(2755,plain,
% 2.71/2.11 ((~hskp29) | c2_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2754, 2752])).
% 2.71/2.11 tff(2756,plain,
% 2.71/2.11 ((~hskp29) | c2_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2755, 2752])).
% 2.71/2.11 tff(2757,plain,
% 2.71/2.11 ((~hskp29) | c2_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2756, 2752])).
% 2.71/2.11 tff(2758,plain,
% 2.71/2.11 ((~hskp29) | c2_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2757, 2752])).
% 2.71/2.11 tff(2759,plain,
% 2.71/2.11 ((~hskp29) | c2_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2758, 2752])).
% 2.71/2.11 tff(2760,plain,
% 2.71/2.11 ((~hskp29) | c2_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2759, 2752])).
% 2.71/2.11 tff(2761,plain,
% 2.71/2.11 ((~hskp29) | c2_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2760, 2752])).
% 2.71/2.11 tff(2762,plain,
% 2.71/2.11 (c2_1(a829)),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2761, 2740])).
% 2.71/2.11 tff(2763,plain,
% 2.71/2.11 (((~hskp29) | c1_1(a829)) <=> ((~hskp29) | c1_1(a829))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2764,axiom,((~hskp29) | c1_1(a829)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 2.71/2.11 tff(2765,plain,
% 2.71/2.11 ((~hskp29) | c1_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2764, 2763])).
% 2.71/2.11 tff(2766,plain,
% 2.71/2.11 ((~hskp29) | c1_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2765, 2763])).
% 2.71/2.11 tff(2767,plain,
% 2.71/2.11 ((~hskp29) | c1_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2766, 2763])).
% 2.71/2.11 tff(2768,plain,
% 2.71/2.11 ((~hskp29) | c1_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2767, 2763])).
% 2.71/2.11 tff(2769,plain,
% 2.71/2.11 ((~hskp29) | c1_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2768, 2763])).
% 2.71/2.11 tff(2770,plain,
% 2.71/2.11 ((~hskp29) | c1_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2769, 2763])).
% 2.71/2.11 tff(2771,plain,
% 2.71/2.11 ((~hskp29) | c1_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2770, 2763])).
% 2.71/2.11 tff(2772,plain,
% 2.71/2.11 ((~hskp29) | c1_1(a829)),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2771, 2763])).
% 2.71/2.11 tff(2773,plain,
% 2.71/2.11 (c1_1(a829)),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2772, 2740])).
% 2.71/2.11 tff(2774,assumption,(~hskp16), introduced(assumption)).
% 2.71/2.11 tff(2775,assumption,(c2_1(a829)), introduced(assumption)).
% 2.71/2.11 tff(2776,assumption,(c0_1(a829)), introduced(assumption)).
% 2.71/2.11 tff(2777,plain,
% 2.71/2.11 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a829)) | (~c3_1(a829)) | (~c2_1(a829)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a829)) | (~c3_1(a829)) | (~c2_1(a829)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2778,plain,
% 2.71/2.11 ((hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a829)) | (~c2_1(a829)) | (~c0_1(a829))) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a829)) | (~c3_1(a829)) | (~c2_1(a829)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2779,plain,
% 2.71/2.11 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a829)) | (~c2_1(a829)) | (~c0_1(a829)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a829)) | (~c3_1(a829)) | (~c2_1(a829))))),
% 2.71/2.11 inference(monotonicity,[status(thm)],[2778])).
% 2.71/2.11 tff(2780,plain,
% 2.71/2.11 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a829)) | (~c2_1(a829)) | (~c0_1(a829)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a829)) | (~c3_1(a829)) | (~c2_1(a829)))),
% 2.71/2.11 inference(transitivity,[status(thm)],[2779, 2777])).
% 2.71/2.11 tff(2781,plain,
% 2.71/2.11 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a829)) | (~c2_1(a829)) | (~c0_1(a829)))),
% 2.71/2.11 inference(quant_inst,[status(thm)],[])).
% 2.71/2.11 tff(2782,plain,
% 2.71/2.11 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a829)) | (~c3_1(a829)) | (~c2_1(a829))),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2781, 2780])).
% 2.71/2.11 tff(2783,plain,
% 2.71/2.11 (hskp16 | (~c3_1(a829))),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2782, 151, 1385, 2776, 2775, 2284])).
% 2.71/2.11 tff(2784,plain,
% 2.71/2.11 (~c3_1(a829)),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2783, 2774])).
% 2.71/2.11 tff(2785,plain,
% 2.71/2.11 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2786,plain,
% 2.71/2.11 ((hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797))) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2787,plain,
% 2.71/2.11 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797))))),
% 2.71/2.11 inference(monotonicity,[status(thm)],[2786])).
% 2.71/2.11 tff(2788,plain,
% 2.71/2.11 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 2.71/2.11 inference(transitivity,[status(thm)],[2787, 2785])).
% 2.71/2.11 tff(2789,plain,
% 2.71/2.11 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))),
% 2.71/2.11 inference(quant_inst,[status(thm)],[])).
% 2.71/2.11 tff(2790,plain,
% 2.71/2.11 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797))),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2789, 2788])).
% 2.71/2.11 tff(2791,plain,
% 2.71/2.11 (hskp16 | hskp15 | (~c0_1(a797))),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2790, 151, 2538, 2527, 2284])).
% 2.71/2.11 tff(2792,plain,
% 2.71/2.11 (~c0_1(a797)),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2791, 2774, 1385])).
% 2.71/2.11 tff(2793,assumption,(c1_1(a829)), introduced(assumption)).
% 2.71/2.11 tff(2794,plain,
% 2.71/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a833)) | c3_1(a829) | (~c2_1(a829)) | (~c1_1(a829)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a833)) | c3_1(a829) | (~c2_1(a829)) | (~c1_1(a829)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2795,plain,
% 2.71/2.11 (((~ndr1_0) | c3_1(a829) | (~c1_1(a829)) | (~c2_1(a829)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a833)) | c3_1(a829) | (~c2_1(a829)) | (~c1_1(a829)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2796,plain,
% 2.71/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a829) | (~c1_1(a829)) | (~c2_1(a829)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a833)) | c3_1(a829) | (~c2_1(a829)) | (~c1_1(a829))))),
% 2.71/2.11 inference(monotonicity,[status(thm)],[2795])).
% 2.71/2.11 tff(2797,plain,
% 2.71/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a829) | (~c1_1(a829)) | (~c2_1(a829)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a833)) | c3_1(a829) | (~c2_1(a829)) | (~c1_1(a829)))),
% 2.71/2.11 inference(transitivity,[status(thm)],[2796, 2794])).
% 2.71/2.11 tff(2798,plain,
% 2.71/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a829) | (~c1_1(a829)) | (~c2_1(a829)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 2.71/2.11 inference(quant_inst,[status(thm)],[])).
% 2.71/2.11 tff(2799,plain,
% 2.71/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a833)) | c3_1(a829) | (~c2_1(a829)) | (~c1_1(a829))),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2798, 2797])).
% 2.71/2.11 tff(2800,plain,
% 2.71/2.11 ($false),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2799, 151, 2793, 2775, 2567, 2527, 321, 309, 2078, 750, 2792, 2784])).
% 2.71/2.11 tff(2801,plain,(hskp16 | (~c1_1(a829)) | (~c2_1(a829)) | c0_1(a833) | c2_1(a833) | (~c3_1(a833)) | hskp15 | (~c0_1(a829))), inference(lemma,lemma(discharge,[]))).
% 2.71/2.11 tff(2802,plain,
% 2.71/2.11 (hskp16),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2801, 2773, 2762, 321, 309, 2714, 1385, 2751])).
% 2.71/2.11 tff(2803,plain,
% 2.71/2.11 (~c2_1(a821)),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2297, 2802])).
% 2.71/2.11 tff(2804,plain,
% 2.71/2.11 (~c0_1(a821)),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2309, 2802])).
% 2.71/2.11 tff(2805,plain,
% 2.71/2.11 (c3_1(a821)),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2398, 151, 1031, 2706, 2696, 2804, 2803, 878, 877, 876, 2705])).
% 2.71/2.11 tff(2806,plain,
% 2.71/2.11 (~c1_1(a821)),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2303, 2802])).
% 2.71/2.11 tff(2807,plain,
% 2.71/2.11 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a833) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2808,plain,
% 2.71/2.11 ((hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821))) <=> (hskp6 | c2_1(a833) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2809,plain,
% 2.71/2.11 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a833) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.71/2.11 inference(monotonicity,[status(thm)],[2808])).
% 2.71/2.11 tff(2810,plain,
% 2.71/2.11 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.71/2.11 inference(transitivity,[status(thm)],[2809, 2807])).
% 2.71/2.11 tff(2811,plain,
% 2.71/2.11 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)))),
% 2.71/2.11 inference(quant_inst,[status(thm)],[])).
% 2.71/2.11 tff(2812,plain,
% 2.71/2.11 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2811, 2810])).
% 2.71/2.11 tff(2813,plain,
% 2.71/2.11 (hskp6 | (~c3_1(a821))),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2812, 151, 639, 309, 2804, 2806, 1964, 2714])).
% 2.71/2.11 tff(2814,plain,
% 2.71/2.11 (hskp6),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2813, 2805])).
% 2.71/2.11 tff(2815,plain,
% 2.71/2.11 (~c0_1(a802)),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[1987, 2814])).
% 2.71/2.11 tff(2816,plain,
% 2.71/2.11 (c2_1(a802)),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[1998, 2814])).
% 2.71/2.11 tff(2817,plain,
% 2.71/2.11 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a833) | c2_1(a833) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a833) | c2_1(a833) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a833)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2818,plain,
% 2.71/2.11 ((hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (hskp12 | c0_1(a833) | c2_1(a833) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a833)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2819,plain,
% 2.71/2.11 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a833) | c2_1(a833) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a833))))),
% 2.71/2.11 inference(monotonicity,[status(thm)],[2818])).
% 2.71/2.11 tff(2820,plain,
% 2.71/2.11 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a833) | c2_1(a833) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a833)))),
% 2.71/2.11 inference(transitivity,[status(thm)],[2819, 2817])).
% 2.71/2.11 tff(2821,plain,
% 2.71/2.11 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 2.71/2.11 inference(quant_inst,[status(thm)],[])).
% 2.71/2.11 tff(2822,plain,
% 2.71/2.11 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a833) | c2_1(a833) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a833))),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2821, 2820])).
% 2.71/2.11 tff(2823,plain,
% 2.71/2.11 (c3_1(a802)),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2822, 151, 811, 2816, 321, 309, 2815, 1079, 2714])).
% 2.71/2.11 tff(2824,plain,
% 2.71/2.11 (((~hskp6) | (~c1_1(a802))) <=> ((~hskp6) | (~c1_1(a802)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2825,plain,
% 2.71/2.11 (((~c1_1(a802)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a802)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2826,axiom,((~c1_1(a802)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 2.71/2.11 tff(2827,plain,
% 2.71/2.11 ((~hskp6) | (~c1_1(a802))),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2826, 2825])).
% 2.71/2.11 tff(2828,plain,
% 2.71/2.11 ((~hskp6) | (~c1_1(a802))),
% 2.71/2.11 inference(modus_ponens,[status(thm)],[2827, 2824])).
% 2.71/2.11 tff(2829,plain,
% 2.71/2.11 (~c1_1(a802)),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2828, 2814])).
% 2.71/2.11 tff(2830,plain,
% 2.71/2.11 ($false),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[1056, 463, 481, 1031, 322, 456, 878, 469, 22, 877, 433])).
% 2.71/2.11 tff(2831,plain,((~hskp8) | (~c3_1(a808)) | c1_1(a832) | (~c0_1(a832)) | c1_1(a808) | c3_1(a832) | c2_1(a808) | (~c2_1(a832))), inference(lemma,lemma(discharge,[]))).
% 2.71/2.11 tff(2832,plain,
% 2.71/2.11 (~hskp8),
% 2.71/2.11 inference(unit_resolution,[status(thm)],[2831, 2705, 2706, 1031, 878, 2696, 877, 2697])).
% 2.71/2.11 tff(2833,plain,
% 2.71/2.11 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | c1_1(a802) | (~ndr1_0) | (~c3_1(a802)) | (~c2_1(a802)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a802) | (~ndr1_0) | (~c3_1(a802)) | (~c2_1(a802)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2834,plain,
% 2.71/2.11 ((hskp8 | (~ndr1_0) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833))) <=> (hskp8 | c0_1(a833) | c1_1(a802) | (~ndr1_0) | (~c3_1(a802)) | (~c2_1(a802)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.71/2.11 inference(rewrite,[status(thm)],[])).
% 2.71/2.11 tff(2835,plain,
% 2.71/2.11 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | c1_1(a802) | (~ndr1_0) | (~c3_1(a802)) | (~c2_1(a802)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.71/2.11 inference(monotonicity,[status(thm)],[2834])).
% 2.71/2.11 tff(2836,plain,
% 2.71/2.11 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a802) | (~ndr1_0) | (~c3_1(a802)) | (~c2_1(a802)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.11 inference(transitivity,[status(thm)],[2835, 2833])).
% 2.81/2.11 tff(2837,plain,
% 2.81/2.11 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.11 inference(quant_inst,[status(thm)],[])).
% 2.81/2.11 tff(2838,plain,
% 2.81/2.11 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a802) | (~ndr1_0) | (~c3_1(a802)) | (~c2_1(a802)) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.81/2.11 inference(modus_ponens,[status(thm)],[2837, 2836])).
% 2.81/2.11 tff(2839,plain,
% 2.81/2.11 ($false),
% 2.81/2.11 inference(unit_resolution,[status(thm)],[2838, 151, 2832, 639, 2816, 321, 2829, 768, 2714, 2823])).
% 2.81/2.11 tff(2840,plain,(hskp15 | (~c1_1(a833)) | c0_1(a833) | hskp12 | c2_1(a833) | (~c3_1(a808)) | c1_1(a808) | c2_1(a808) | c1_1(a828) | c2_1(a828) | c3_1(a828)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.11 tff(2841,plain,
% 2.81/2.11 (hskp15),
% 2.81/2.11 inference(unit_resolution,[status(thm)],[2840, 811, 321, 639, 309, 1031, 878, 877, 1215, 1206, 1205])).
% 2.81/2.11 tff(2842,plain,
% 2.81/2.11 (~c1_1(a817)),
% 2.81/2.11 inference(unit_resolution,[status(thm)],[1342, 2841])).
% 2.81/2.11 tff(2843,plain,
% 2.81/2.11 (c3_1(a817)),
% 2.81/2.11 inference(unit_resolution,[status(thm)],[1353, 2841])).
% 2.81/2.11 tff(2844,plain,
% 2.81/2.11 (c2_1(a817)),
% 2.81/2.11 inference(unit_resolution,[status(thm)],[1364, 2841])).
% 2.81/2.11 tff(2845,plain,
% 2.81/2.11 (c3_1(a833) | c3_1(a793)),
% 2.81/2.11 inference(unit_resolution,[status(thm)],[884, 151, 1031, 692, 321, 309, 878, 877, 691, 876])).
% 2.81/2.11 tff(2846,plain,
% 2.81/2.11 (c3_1(a793)),
% 2.81/2.11 inference(unit_resolution,[status(thm)],[2845, 310])).
% 2.81/2.11 tff(2847,assumption,(~c1_1(a817)), introduced(assumption)).
% 2.81/2.11 tff(2848,assumption,(c3_1(a817)), introduced(assumption)).
% 2.81/2.11 tff(2849,assumption,(c2_1(a817)), introduced(assumption)).
% 2.81/2.11 tff(2850,plain,
% 2.81/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)) | (~c3_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)) | (~c3_1(a793)))),
% 2.81/2.11 inference(rewrite,[status(thm)],[])).
% 2.81/2.11 tff(2851,plain,
% 2.81/2.11 (((~ndr1_0) | (~c3_1(a793)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)) | (~c3_1(a793)))),
% 2.81/2.11 inference(rewrite,[status(thm)],[])).
% 2.81/2.11 tff(2852,plain,
% 2.81/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a793)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)) | (~c3_1(a793))))),
% 2.81/2.11 inference(monotonicity,[status(thm)],[2851])).
% 2.81/2.11 tff(2853,plain,
% 2.81/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a793)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)) | (~c3_1(a793)))),
% 2.81/2.12 inference(transitivity,[status(thm)],[2852, 2850])).
% 2.81/2.12 tff(2854,plain,
% 2.81/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a793)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 2.81/2.12 inference(quant_inst,[status(thm)],[])).
% 2.81/2.12 tff(2855,plain,
% 2.81/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)) | (~c3_1(a793))),
% 2.81/2.12 inference(modus_ponens,[status(thm)],[2854, 2853])).
% 2.81/2.12 tff(2856,plain,
% 2.81/2.12 ($false),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2855, 151, 639, 2849, 2848, 692, 689, 321, 2847, 800, 310, 2846])).
% 2.81/2.12 tff(2857,plain,(c3_1(a833) | (~c1_1(a833)) | (~c2_1(a817)) | (~c3_1(a817)) | (~c0_1(a793)) | (~c2_1(a793)) | c0_1(a833) | c1_1(a817) | (~c3_1(a808)) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.12 tff(2858,plain,
% 2.81/2.12 (c3_1(a833)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2857, 2844, 639, 2843, 692, 689, 321, 2842, 1031, 309, 878, 877, 691])).
% 2.81/2.12 tff(2859,plain,
% 2.81/2.12 (c0_1(a832)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[1087, 2858, 2697, 321, 309, 2696, 811])).
% 2.81/2.12 tff(2860,plain,
% 2.81/2.12 (~hskp8),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2831, 2859, 2706, 1031, 878, 2696, 877, 2697])).
% 2.81/2.12 tff(2861,plain,
% 2.81/2.12 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2862,plain,
% 2.81/2.12 ((hskp8 | (~ndr1_0) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833))) <=> (hskp8 | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2863,plain,
% 2.81/2.12 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.81/2.12 inference(monotonicity,[status(thm)],[2862])).
% 2.81/2.12 tff(2864,plain,
% 2.81/2.12 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.12 inference(transitivity,[status(thm)],[2863, 2861])).
% 2.81/2.12 tff(2865,plain,
% 2.81/2.12 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.12 inference(quant_inst,[status(thm)],[])).
% 2.81/2.12 tff(2866,plain,
% 2.81/2.12 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.81/2.12 inference(modus_ponens,[status(thm)],[2865, 2864])).
% 2.81/2.12 tff(2867,plain,
% 2.81/2.12 ($false),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2866, 151, 2860, 639, 2844, 2843, 321, 2842, 768, 2858])).
% 2.81/2.12 tff(2868,plain,(hskp12 | (~c1_1(a833)) | c0_1(a833) | (~c3_1(a808)) | c1_1(a808) | c2_1(a808) | c2_1(a833) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a793) | c1_1(a828) | c2_1(a828) | c3_1(a828)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.12 tff(2869,plain,
% 2.81/2.12 (hskp12),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2868, 2624, 2623, 2578, 2577, 2576, 2625, 2694, 2693, 2692, 2582, 2581, 2580])).
% 2.81/2.12 tff(2870,plain,
% 2.81/2.12 (~c0_1(a809)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[164, 2869])).
% 2.81/2.12 tff(2871,plain,
% 2.81/2.12 (c2_1(a809)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[176, 2869])).
% 2.81/2.12 tff(2872,plain,
% 2.81/2.12 (c1_1(a809)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[187, 2869])).
% 2.81/2.12 tff(2873,plain,
% 2.81/2.12 (c0_1(a832)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[1097, 151, 2690, 2872, 2871, 2689, 2688, 2870, 1067])).
% 2.81/2.12 tff(2874,plain,
% 2.81/2.12 ((~c0_1(a832)) | c3_1(a833)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2712, 151, 2578, 2623, 2625, 2689, 2688, 2577, 2576, 876])).
% 2.81/2.12 tff(2875,plain,
% 2.81/2.12 (c3_1(a833)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2874, 2873])).
% 2.81/2.12 tff(2876,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2877,plain,
% 2.81/2.12 (((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2878,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833))))),
% 2.81/2.12 inference(monotonicity,[status(thm)],[2877])).
% 2.81/2.12 tff(2879,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))),
% 2.81/2.12 inference(transitivity,[status(thm)],[2878, 2876])).
% 2.81/2.12 tff(2880,plain,
% 2.81/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 2.81/2.12 inference(quant_inst,[status(thm)],[])).
% 2.81/2.12 tff(2881,plain,
% 2.81/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833))),
% 2.81/2.12 inference(modus_ponens,[status(thm)],[2880, 2879])).
% 2.81/2.12 tff(2882,plain,
% 2.81/2.12 ((~c0_1(a832)) | (~c3_1(a833))),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2881, 151, 2690, 2872, 2871, 2623, 2625, 2688, 2870, 2635])).
% 2.81/2.12 tff(2883,plain,
% 2.81/2.12 ($false),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2882, 2875, 2873])).
% 2.81/2.12 tff(2884,plain,(hskp21 | hskp30), inference(lemma,lemma(discharge,[]))).
% 2.81/2.12 tff(2885,plain,
% 2.81/2.12 (hskp21),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2884, 345])).
% 2.81/2.12 tff(2886,plain,
% 2.81/2.12 (~c2_1(a838)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[431, 2885])).
% 2.81/2.12 tff(2887,plain,
% 2.81/2.12 (hskp9),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[1795, 346, 2885, 2886])).
% 2.81/2.12 tff(2888,plain,
% 2.81/2.12 (~c3_1(a806)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[75, 2887])).
% 2.81/2.12 tff(2889,plain,
% 2.81/2.12 (c1_1(a806)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[87, 2887])).
% 2.81/2.12 tff(2890,plain,
% 2.81/2.12 (c0_1(a806)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[67, 2887])).
% 2.81/2.12 tff(2891,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a833))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2892,plain,
% 2.81/2.12 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | c3_1(a833)) <=> (c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a833))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2893,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a833)))),
% 2.81/2.12 inference(monotonicity,[status(thm)],[2892])).
% 2.81/2.12 tff(2894,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a833))),
% 2.81/2.12 inference(transitivity,[status(thm)],[2893, 2891])).
% 2.81/2.12 tff(2895,plain,
% 2.81/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | c3_1(a833))),
% 2.81/2.12 inference(quant_inst,[status(thm)],[])).
% 2.81/2.12 tff(2896,plain,
% 2.81/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a833)),
% 2.81/2.12 inference(modus_ponens,[status(thm)],[2895, 2894])).
% 2.81/2.12 tff(2897,plain,
% 2.81/2.12 (c3_1(a833)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2896, 151, 2567, 2527, 2890, 2889, 321, 309, 2888, 2556, 2546])).
% 2.81/2.12 tff(2898,plain,
% 2.81/2.12 (c0_1(a832)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2619, 151, 2567, 2538, 2613, 2598, 2611, 1067, 2546])).
% 2.81/2.12 tff(2899,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2900,plain,
% 2.81/2.12 (((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2901,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833))))),
% 2.81/2.12 inference(monotonicity,[status(thm)],[2900])).
% 2.81/2.12 tff(2902,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))),
% 2.81/2.12 inference(transitivity,[status(thm)],[2901, 2899])).
% 2.81/2.12 tff(2903,plain,
% 2.81/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 2.81/2.12 inference(quant_inst,[status(thm)],[])).
% 2.81/2.12 tff(2904,plain,
% 2.81/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833))),
% 2.81/2.12 inference(modus_ponens,[status(thm)],[2903, 2902])).
% 2.81/2.12 tff(2905,plain,
% 2.81/2.12 ((~c0_1(a832)) | (~c3_1(a833))),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2904, 151, 2567, 2538, 2613, 321, 309, 2611, 2635, 2546])).
% 2.81/2.12 tff(2906,plain,
% 2.81/2.12 ($false),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2905, 2898, 2897])).
% 2.81/2.12 tff(2907,plain,(hskp20 | c0_1(a833) | c2_1(a833) | hskp30), inference(lemma,lemma(discharge,[]))).
% 2.81/2.12 tff(2908,plain,
% 2.81/2.12 (hskp30),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2907, 344, 309, 321])).
% 2.81/2.12 tff(2909,plain,
% 2.81/2.12 (c3_1(a867)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[33, 2908])).
% 2.81/2.12 tff(2910,plain,
% 2.81/2.12 (c1_1(a867)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[44, 2908])).
% 2.81/2.12 tff(2911,plain,
% 2.81/2.12 (c0_1(a867)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[55, 2908])).
% 2.81/2.12 tff(2912,plain,
% 2.81/2.12 (c2_1(a806)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[196, 88, 2909, 76, 2911, 2910, 68])).
% 2.81/2.12 tff(2913,plain,
% 2.81/2.12 (hskp0),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[1884, 151, 333, 68, 321, 309, 76, 1434, 2912])).
% 2.81/2.12 tff(2914,plain,
% 2.81/2.12 (~c1_1(a793)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[675, 2913])).
% 2.81/2.12 tff(2915,plain,
% 2.81/2.12 (hskp5),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[223, 151, 2911, 2910, 2909, 68, 76, 217, 2912])).
% 2.81/2.12 tff(2916,plain,
% 2.81/2.12 (~c1_1(a800)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[263, 2915])).
% 2.81/2.12 tff(2917,plain,
% 2.81/2.12 (~c0_1(a800)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[229, 2915])).
% 2.81/2.12 tff(2918,plain,
% 2.81/2.12 (c3_1(a800)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[240, 2915])).
% 2.81/2.12 tff(2919,plain,
% 2.81/2.12 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a800)))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2920,plain,
% 2.81/2.12 ((hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a800)))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2921,plain,
% 2.81/2.12 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a800))))),
% 2.81/2.12 inference(monotonicity,[status(thm)],[2920])).
% 2.81/2.12 tff(2922,plain,
% 2.81/2.12 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a800)))),
% 2.81/2.12 inference(transitivity,[status(thm)],[2921, 2919])).
% 2.81/2.12 tff(2923,plain,
% 2.81/2.12 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 2.81/2.12 inference(quant_inst,[status(thm)],[])).
% 2.81/2.12 tff(2924,plain,
% 2.81/2.12 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a800))),
% 2.81/2.12 inference(modus_ponens,[status(thm)],[2923, 2922])).
% 2.81/2.12 tff(2925,plain,
% 2.81/2.12 (hskp7),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2924, 151, 2567, 2538, 2527, 2918, 2917, 2916, 1515])).
% 2.81/2.12 tff(2926,plain,
% 2.81/2.12 (~c2_1(a803)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[1473, 2925])).
% 2.81/2.12 tff(2927,plain,
% 2.81/2.12 (c2_1(a793)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[669, 2913])).
% 2.81/2.12 tff(2928,plain,
% 2.81/2.12 (c0_1(a793)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[686, 2913])).
% 2.81/2.12 tff(2929,plain,
% 2.81/2.12 (c1_1(a803)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[1495, 2925])).
% 2.81/2.12 tff(2930,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a803) | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a793)) | (~c0_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a803) | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2931,plain,
% 2.81/2.12 (((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (c2_1(a803) | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2932,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a803) | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a793)) | (~c0_1(a793))))),
% 2.81/2.12 inference(monotonicity,[status(thm)],[2931])).
% 2.81/2.12 tff(2933,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a803) | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 2.81/2.12 inference(transitivity,[status(thm)],[2932, 2930])).
% 2.81/2.12 tff(2934,plain,
% 2.81/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 2.81/2.12 inference(quant_inst,[status(thm)],[])).
% 2.81/2.12 tff(2935,plain,
% 2.81/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a803) | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a793)) | (~c0_1(a793))),
% 2.81/2.12 inference(modus_ponens,[status(thm)],[2934, 2933])).
% 2.81/2.12 tff(2936,plain,
% 2.81/2.12 (~c0_1(a803)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[2935, 151, 2929, 2918, 2928, 2927, 2926, 2917, 2916, 2914, 320])).
% 2.81/2.12 tff(2937,plain,
% 2.81/2.12 (c3_1(a803)),
% 2.81/2.12 inference(unit_resolution,[status(thm)],[1484, 2925])).
% 2.81/2.12 tff(2938,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2939,plain,
% 2.81/2.12 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803))) <=> (c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)))),
% 2.81/2.12 inference(rewrite,[status(thm)],[])).
% 2.81/2.12 tff(2940,plain,
% 2.81/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806))))),
% 2.81/2.13 inference(monotonicity,[status(thm)],[2939])).
% 2.81/2.13 tff(2941,plain,
% 2.81/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)))),
% 2.81/2.13 inference(transitivity,[status(thm)],[2940, 2938])).
% 2.81/2.13 tff(2942,plain,
% 2.81/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))),
% 2.81/2.13 inference(quant_inst,[status(thm)],[])).
% 2.81/2.13 tff(2943,plain,
% 2.81/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806))),
% 2.81/2.13 inference(modus_ponens,[status(thm)],[2942, 2941])).
% 2.81/2.13 tff(2944,plain,
% 2.81/2.13 ($false),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2943, 151, 88, 2929, 2937, 76, 2926, 2078, 2912, 2936])).
% 2.81/2.13 tff(2945,plain,((~hskp9) | c1_1(a833) | c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.13 tff(2946,plain,
% 2.81/2.13 (~hskp9),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2945, 333, 321, 309])).
% 2.81/2.13 tff(2947,plain,
% 2.81/2.13 ($false),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[1795, 1312, 1311, 346, 11])).
% 2.81/2.13 tff(2948,plain,((~hskp21) | hskp20 | hskp9), inference(lemma,lemma(discharge,[]))).
% 2.81/2.13 tff(2949,plain,
% 2.81/2.13 (~hskp21),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2948, 344, 2946])).
% 2.81/2.13 tff(2950,plain,
% 2.81/2.13 (hskp11),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2574, 2949])).
% 2.81/2.13 tff(2951,plain,
% 2.81/2.13 (c3_1(a808)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[896, 2950])).
% 2.81/2.13 tff(2952,plain,
% 2.81/2.13 (~hskp7),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[1504, 322, 22, 1458])).
% 2.81/2.13 tff(2953,plain,
% 2.81/2.13 (hskp27),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2596, 1459])).
% 2.81/2.13 tff(2954,plain,
% 2.81/2.13 (c3_1(a796)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[594, 2953])).
% 2.81/2.13 tff(2955,plain,
% 2.81/2.13 (c2_1(a796)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[605, 2953])).
% 2.81/2.13 tff(2956,plain,
% 2.81/2.13 (c0_1(a796)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[616, 2953])).
% 2.81/2.13 tff(2957,plain,
% 2.81/2.13 (hskp21),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2574, 705])).
% 2.81/2.13 tff(2958,plain,
% 2.81/2.13 (~c2_1(a838)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[431, 2957])).
% 2.81/2.13 tff(2959,plain,
% 2.81/2.13 (hskp9),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[1795, 2957, 346, 2958])).
% 2.81/2.13 tff(2960,plain,
% 2.81/2.13 (c0_1(a806)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[67, 2959])).
% 2.81/2.13 tff(2961,plain,
% 2.81/2.13 (~c3_1(a806)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[75, 2959])).
% 2.81/2.13 tff(2962,plain,
% 2.81/2.13 (c1_1(a806)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[87, 2959])).
% 2.81/2.13 tff(2963,plain,
% 2.81/2.13 (c2_1(a806)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[196, 2962, 77, 2961, 70, 69, 2960])).
% 2.81/2.13 tff(2964,plain,
% 2.81/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a869) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a869)) | (~c3_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a869) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a869)) | (~c3_1(a869)))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(2965,plain,
% 2.81/2.13 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869))) <=> (c0_1(a869) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a869)) | (~c3_1(a869)))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(2966,plain,
% 2.81/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a869) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a869)) | (~c3_1(a869))))),
% 2.81/2.13 inference(monotonicity,[status(thm)],[2965])).
% 2.81/2.13 tff(2967,plain,
% 2.81/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a869) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a869)) | (~c3_1(a869)))),
% 2.81/2.13 inference(transitivity,[status(thm)],[2966, 2964])).
% 2.81/2.13 tff(2968,plain,
% 2.81/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869)))),
% 2.81/2.13 inference(quant_inst,[status(thm)],[])).
% 2.81/2.13 tff(2969,plain,
% 2.81/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a869) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a869)) | (~c3_1(a869))),
% 2.81/2.13 inference(modus_ponens,[status(thm)],[2968, 2967])).
% 2.81/2.13 tff(2970,plain,
% 2.81/2.13 ($false),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2969, 151, 70, 69, 77, 742, 731, 2960, 2962, 782, 207, 2963])).
% 2.81/2.13 tff(2971,plain,(hskp11 | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a867)) | hskp20 | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.13 tff(2972,plain,
% 2.81/2.13 (hskp11),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2971, 2956, 2910, 2909, 344, 2911, 2955, 2954])).
% 2.81/2.13 tff(2973,plain,
% 2.81/2.13 (~c1_1(a808)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[851, 2972])).
% 2.81/2.13 tff(2974,plain,
% 2.81/2.13 (c3_1(a808)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[896, 2972])).
% 2.81/2.13 tff(2975,plain,
% 2.81/2.13 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a808) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a808)) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a808) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a808)) | c0_1(a808))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(2976,plain,
% 2.81/2.13 ((hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (hskp7 | c1_1(a808) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a808)) | c0_1(a808))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(2977,plain,
% 2.81/2.13 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a808) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a808)) | c0_1(a808)))),
% 2.81/2.13 inference(monotonicity,[status(thm)],[2976])).
% 2.81/2.13 tff(2978,plain,
% 2.81/2.13 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a808) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a808)) | c0_1(a808))),
% 2.81/2.13 inference(transitivity,[status(thm)],[2977, 2975])).
% 2.81/2.13 tff(2979,plain,
% 2.81/2.13 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 2.81/2.13 inference(quant_inst,[status(thm)],[])).
% 2.81/2.13 tff(2980,plain,
% 2.81/2.13 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a808) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a808)) | c0_1(a808)),
% 2.81/2.13 inference(modus_ponens,[status(thm)],[2979, 2978])).
% 2.81/2.13 tff(2981,plain,
% 2.81/2.13 (hskp7 | c0_1(a808)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2980, 151, 2567, 2538, 2527, 2974, 2973, 1515])).
% 2.81/2.13 tff(2982,plain,
% 2.81/2.13 (c0_1(a808)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2981, 2952])).
% 2.81/2.13 tff(2983,plain,
% 2.81/2.13 (~c2_1(a808)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[857, 2972])).
% 2.81/2.13 tff(2984,plain,
% 2.81/2.13 (hskp9 | (~c0_1(a808))),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[1533, 151, 344, 2974, 2983, 21])).
% 2.81/2.13 tff(2985,plain,
% 2.81/2.13 (hskp9),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2984, 2982])).
% 2.81/2.13 tff(2986,plain,
% 2.81/2.13 (c0_1(a806)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[67, 2985])).
% 2.81/2.13 tff(2987,plain,
% 2.81/2.13 (~c3_1(a806)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[75, 2985])).
% 2.81/2.13 tff(2988,plain,
% 2.81/2.13 (c1_1(a806)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[87, 2985])).
% 2.81/2.13 tff(2989,plain,
% 2.81/2.13 (c2_1(a806)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[196, 2988, 2909, 2987, 2911, 2910, 2986])).
% 2.81/2.13 tff(2990,plain,
% 2.81/2.13 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a833)))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(2991,plain,
% 2.81/2.13 ((hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a833)))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(2992,plain,
% 2.81/2.13 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a833))))),
% 2.81/2.13 inference(monotonicity,[status(thm)],[2991])).
% 2.81/2.13 tff(2993,plain,
% 2.81/2.13 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a833)))),
% 2.81/2.13 inference(transitivity,[status(thm)],[2992, 2990])).
% 2.81/2.13 tff(2994,plain,
% 2.81/2.13 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 2.81/2.13 inference(quant_inst,[status(thm)],[])).
% 2.81/2.13 tff(2995,plain,
% 2.81/2.13 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a833))),
% 2.81/2.13 inference(modus_ponens,[status(thm)],[2994, 2993])).
% 2.81/2.13 tff(2996,plain,
% 2.81/2.13 (hskp7 | (~c3_1(a833))),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2995, 151, 2567, 2538, 2527, 333, 321, 1515])).
% 2.81/2.13 tff(2997,plain,
% 2.81/2.13 (~c3_1(a833)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2996, 2952])).
% 2.81/2.13 tff(2998,plain,
% 2.81/2.13 (~c0_1(a832)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[2712, 151, 2974, 321, 309, 322, 22, 2973, 2983, 876, 2997])).
% 2.81/2.13 tff(2999,plain,
% 2.81/2.13 ($false),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[1570, 151, 1458, 2988, 321, 309, 322, 2987, 258, 2998, 2997, 2989])).
% 2.81/2.13 tff(3000,plain,(c1_1(a832) | c2_1(a832) | c0_1(a833) | c2_1(a833) | c3_1(a832) | c1_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.13 tff(3001,plain,
% 2.81/2.13 (c1_1(a832)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[3000, 1458, 321, 309, 22, 333])).
% 2.81/2.13 tff(3002,plain,
% 2.81/2.13 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(3003,plain,
% 2.81/2.13 ((hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832))) <=> (hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(3004,plain,
% 2.81/2.13 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867))))),
% 2.81/2.13 inference(monotonicity,[status(thm)],[3003])).
% 2.81/2.13 tff(3005,plain,
% 2.81/2.13 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))),
% 2.81/2.13 inference(transitivity,[status(thm)],[3004, 3002])).
% 2.81/2.13 tff(3006,plain,
% 2.81/2.13 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)))),
% 2.81/2.13 inference(quant_inst,[status(thm)],[])).
% 2.81/2.13 tff(3007,plain,
% 2.81/2.13 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867))),
% 2.81/2.13 inference(modus_ponens,[status(thm)],[3006, 3005])).
% 2.81/2.13 tff(3008,plain,
% 2.81/2.13 (hskp12 | c2_1(a832) | (~c1_1(a832))),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[3007, 151, 2911, 2910, 2909, 22, 110])).
% 2.81/2.13 tff(3009,plain,
% 2.81/2.13 (hskp12),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[3008, 3001, 1458])).
% 2.81/2.13 tff(3010,plain,
% 2.81/2.13 (~c0_1(a809)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[164, 3009])).
% 2.81/2.13 tff(3011,plain,
% 2.81/2.13 (c2_1(a809)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[176, 3009])).
% 2.81/2.13 tff(3012,plain,
% 2.81/2.13 (c1_1(a809)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[187, 3009])).
% 2.81/2.13 tff(3013,plain,
% 2.81/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a832)))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(3014,plain,
% 2.81/2.13 (((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809))) <=> (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a832)))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(3015,plain,
% 2.81/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a832))))),
% 2.81/2.13 inference(monotonicity,[status(thm)],[3014])).
% 2.81/2.13 tff(3016,plain,
% 2.81/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a832)))),
% 2.81/2.13 inference(transitivity,[status(thm)],[3015, 3013])).
% 2.81/2.13 tff(3017,plain,
% 2.81/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.81/2.13 inference(quant_inst,[status(thm)],[])).
% 2.81/2.13 tff(3018,plain,
% 2.81/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a832))),
% 2.81/2.13 inference(modus_ponens,[status(thm)],[3017, 3016])).
% 2.81/2.13 tff(3019,plain,
% 2.81/2.13 (~c0_1(a832)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[3018, 151, 1458, 3012, 3011, 3001, 22, 3010, 99])).
% 2.81/2.13 tff(3020,plain,
% 2.81/2.13 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(3021,plain,
% 2.81/2.13 ((hskp3 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a832) | (~c1_1(a832))) <=> (hskp3 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(3022,plain,
% 2.81/2.13 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a832) | (~c1_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | c0_1(a832)))),
% 2.81/2.13 inference(monotonicity,[status(thm)],[3021])).
% 2.81/2.13 tff(3023,plain,
% 2.81/2.13 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a832) | (~c1_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 2.81/2.13 inference(transitivity,[status(thm)],[3022, 3020])).
% 2.81/2.13 tff(3024,plain,
% 2.81/2.13 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a832) | (~c1_1(a832)))),
% 2.81/2.13 inference(quant_inst,[status(thm)],[])).
% 2.81/2.13 tff(3025,plain,
% 2.81/2.13 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | c0_1(a832)),
% 2.81/2.13 inference(modus_ponens,[status(thm)],[3024, 3023])).
% 2.81/2.13 tff(3026,plain,
% 2.81/2.13 (hskp3 | (~c1_1(a832)) | c0_1(a832)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[3025, 151, 1458, 22, 2646])).
% 2.81/2.13 tff(3027,plain,
% 2.81/2.13 (hskp3),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[3026, 3019, 3001])).
% 2.81/2.13 tff(3028,plain,
% 2.81/2.13 (~c3_1(a798)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[546, 3027])).
% 2.81/2.13 tff(3029,plain,
% 2.81/2.13 (c2_1(a798)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[563, 3027])).
% 2.81/2.13 tff(3030,plain,
% 2.81/2.13 (c0_1(a798)),
% 2.81/2.13 inference(unit_resolution,[status(thm)],[574, 3027])).
% 2.81/2.13 tff(3031,plain,
% 2.81/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(3032,plain,
% 2.81/2.13 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832))) <=> (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)))),
% 2.81/2.13 inference(rewrite,[status(thm)],[])).
% 2.81/2.13 tff(3033,plain,
% 2.81/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808))))),
% 2.81/2.14 inference(monotonicity,[status(thm)],[3032])).
% 2.81/2.14 tff(3034,plain,
% 2.81/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)))),
% 2.81/2.14 inference(transitivity,[status(thm)],[3033, 3031])).
% 2.81/2.14 tff(3035,plain,
% 2.81/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))),
% 2.81/2.14 inference(quant_inst,[status(thm)],[])).
% 2.81/2.14 tff(3036,plain,
% 2.81/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808))),
% 2.81/2.14 inference(modus_ponens,[status(thm)],[3035, 3034])).
% 2.81/2.14 tff(3037,plain,
% 2.81/2.14 (~c0_1(a808)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[3036, 151, 1458, 2974, 3030, 3029, 3001, 22, 2983, 3028, 332])).
% 2.81/2.14 tff(3038,plain,
% 2.81/2.14 ($false),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[2673, 151, 3012, 3011, 2974, 3030, 3029, 3010, 2983, 3028, 2635, 3037])).
% 2.81/2.14 tff(3039,plain,(c2_1(a832) | c3_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.14 tff(3040,plain,
% 2.81/2.14 (c2_1(a832)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[3039, 333, 321, 309, 22])).
% 2.81/2.14 tff(3041,plain,
% 2.81/2.14 (~c2_1(a808)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[857, 2950])).
% 2.81/2.14 tff(3042,plain,
% 2.81/2.14 (~c1_1(a808)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[851, 2950])).
% 2.81/2.14 tff(3043,plain,
% 2.81/2.14 (~c0_1(a808)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[1533, 151, 346, 11, 1031, 877, 21])).
% 2.81/2.14 tff(3044,plain,
% 2.81/2.14 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c1_1(a832) | c3_1(a832) | c1_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a832) | c3_1(a832) | c1_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3045,plain,
% 2.81/2.14 ((hskp4 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (hskp4 | c1_1(a832) | c3_1(a832) | c1_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3046,plain,
% 2.81/2.14 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c1_1(a832) | c3_1(a832) | c1_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832))))),
% 2.81/2.14 inference(monotonicity,[status(thm)],[3045])).
% 2.81/2.14 tff(3047,plain,
% 2.81/2.14 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a832) | c3_1(a832) | c1_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)))),
% 2.81/2.14 inference(transitivity,[status(thm)],[3046, 3044])).
% 2.81/2.14 tff(3048,plain,
% 2.81/2.14 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 2.81/2.14 inference(quant_inst,[status(thm)],[])).
% 2.81/2.14 tff(3049,plain,
% 2.81/2.14 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a832) | c3_1(a832) | c1_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832))),
% 2.81/2.14 inference(modus_ponens,[status(thm)],[3048, 3047])).
% 2.81/2.14 tff(3050,plain,
% 2.81/2.14 (hskp4),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[3049, 151, 433, 1031, 322, 22, 878, 2035, 3043])).
% 2.81/2.14 tff(3051,plain,
% 2.81/2.14 (c3_1(a799)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[1628, 3050])).
% 2.81/2.14 tff(3052,plain,
% 2.81/2.14 (c0_1(a799)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[1656, 3050])).
% 2.81/2.14 tff(3053,plain,
% 2.81/2.14 (c2_1(a799)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[1681, 151, 346, 11, 3052, 3051, 21])).
% 2.81/2.14 tff(3054,plain,
% 2.81/2.14 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3055,plain,
% 2.81/2.14 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867))) <=> (hskp20 | hskp9 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3056,plain,
% 2.81/2.14 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867))))),
% 2.81/2.14 inference(monotonicity,[status(thm)],[3055])).
% 2.81/2.14 tff(3057,plain,
% 2.81/2.14 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)))),
% 2.81/2.14 inference(transitivity,[status(thm)],[3056, 3054])).
% 2.81/2.14 tff(3058,plain,
% 2.81/2.14 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)))),
% 2.81/2.14 inference(quant_inst,[status(thm)],[])).
% 2.81/2.14 tff(3059,plain,
% 2.81/2.14 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867))),
% 2.81/2.14 inference(modus_ponens,[status(thm)],[3058, 3057])).
% 2.81/2.14 tff(3060,plain,
% 2.81/2.14 (hskp9 | c2_1(a867)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[3059, 151, 346, 70, 77, 21])).
% 2.81/2.14 tff(3061,plain,
% 2.81/2.14 (c2_1(a867)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[3060, 11])).
% 2.81/2.14 tff(3062,plain,
% 2.81/2.14 (hskp7),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[1524, 151, 69, 77, 1031, 878, 1515, 3061, 3043])).
% 2.81/2.14 tff(3063,plain,
% 2.81/2.14 (~c2_1(a803)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[1473, 3062])).
% 2.81/2.14 tff(3064,plain,
% 2.81/2.14 (c3_1(a803)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[1484, 3062])).
% 2.81/2.14 tff(3065,plain,
% 2.81/2.14 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c0_1(a803)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c0_1(a803)))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3066,plain,
% 2.81/2.14 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c0_1(a803))) <=> (hskp20 | hskp9 | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c0_1(a803)))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3067,plain,
% 2.81/2.14 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c0_1(a803)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c0_1(a803))))),
% 2.81/2.14 inference(monotonicity,[status(thm)],[3066])).
% 2.81/2.14 tff(3068,plain,
% 2.81/2.14 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c0_1(a803)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c0_1(a803)))),
% 2.81/2.14 inference(transitivity,[status(thm)],[3067, 3065])).
% 2.81/2.14 tff(3069,plain,
% 2.81/2.14 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c0_1(a803)))),
% 2.81/2.14 inference(quant_inst,[status(thm)],[])).
% 2.81/2.14 tff(3070,plain,
% 2.81/2.14 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c0_1(a803))),
% 2.81/2.14 inference(modus_ponens,[status(thm)],[3069, 3068])).
% 2.81/2.14 tff(3071,plain,
% 2.81/2.14 (~c0_1(a803)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[3070, 151, 346, 11, 3064, 3063, 21])).
% 2.81/2.14 tff(3072,plain,
% 2.81/2.14 (~c1_1(a799)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[1617, 3050])).
% 2.81/2.14 tff(3073,plain,
% 2.81/2.14 (c1_1(a803)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[1495, 3062])).
% 2.81/2.14 tff(3074,plain,
% 2.81/2.14 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a799) | (~ndr1_0) | (~c3_1(a799)) | (~c2_1(a799)) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a799) | (~ndr1_0) | (~c3_1(a799)) | (~c2_1(a799)) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3075,plain,
% 2.81/2.14 ((hskp8 | (~ndr1_0) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803))) <=> (hskp8 | c1_1(a799) | (~ndr1_0) | (~c3_1(a799)) | (~c2_1(a799)) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3076,plain,
% 2.81/2.14 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a799) | (~ndr1_0) | (~c3_1(a799)) | (~c2_1(a799)) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803))))),
% 2.81/2.14 inference(monotonicity,[status(thm)],[3075])).
% 2.81/2.14 tff(3077,plain,
% 2.81/2.14 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a799) | (~ndr1_0) | (~c3_1(a799)) | (~c2_1(a799)) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)))),
% 2.81/2.14 inference(transitivity,[status(thm)],[3076, 3074])).
% 2.81/2.14 tff(3078,plain,
% 2.81/2.14 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)))),
% 2.81/2.14 inference(quant_inst,[status(thm)],[])).
% 2.81/2.14 tff(3079,plain,
% 2.81/2.14 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a799) | (~ndr1_0) | (~c3_1(a799)) | (~c2_1(a799)) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803))),
% 2.81/2.14 inference(modus_ponens,[status(thm)],[3078, 3077])).
% 2.81/2.14 tff(3080,plain,
% 2.81/2.14 (hskp8),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[3079, 151, 3073, 3064, 3051, 3072, 768, 3071, 3053])).
% 2.81/2.14 tff(3081,plain,
% 2.81/2.14 (~c3_1(a805)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[462, 3080])).
% 2.81/2.14 tff(3082,plain,
% 2.81/2.14 (~c2_1(a805)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[468, 3080])).
% 2.81/2.14 tff(3083,plain,
% 2.81/2.14 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a808) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | (~c3_1(a808)) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a808) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | (~c3_1(a808)) | c0_1(a808))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3084,plain,
% 2.81/2.14 ((hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (hskp6 | c1_1(a808) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | (~c3_1(a808)) | c0_1(a808))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3085,plain,
% 2.81/2.14 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a808) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | (~c3_1(a808)) | c0_1(a808)))),
% 2.81/2.14 inference(monotonicity,[status(thm)],[3084])).
% 2.81/2.14 tff(3086,plain,
% 2.81/2.14 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a808) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | (~c3_1(a808)) | c0_1(a808))),
% 2.81/2.14 inference(transitivity,[status(thm)],[3085, 3083])).
% 2.81/2.14 tff(3087,plain,
% 2.81/2.14 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 2.81/2.14 inference(quant_inst,[status(thm)],[])).
% 2.81/2.14 tff(3088,plain,
% 2.81/2.14 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a808) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | (~c3_1(a808)) | c0_1(a808)),
% 2.81/2.14 inference(modus_ponens,[status(thm)],[3087, 3086])).
% 2.81/2.14 tff(3089,plain,
% 2.81/2.14 (hskp6),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[3088, 151, 1031, 3073, 3064, 878, 3063, 1964, 3043])).
% 2.81/2.14 tff(3090,plain,
% 2.81/2.14 (~c0_1(a802)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[1987, 3089])).
% 2.81/2.14 tff(3091,plain,
% 2.81/2.14 (c2_1(a802)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[1998, 3089])).
% 2.81/2.14 tff(3092,plain,
% 2.81/2.14 (~c3_1(a802)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[2005, 151, 70, 69, 77, 3091, 3090, 207, 3061])).
% 2.81/2.14 tff(3093,plain,
% 2.81/2.14 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a808) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a808)) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a808) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a808)) | c0_1(a808))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3094,plain,
% 2.81/2.14 ((hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (hskp12 | c2_1(a808) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a808)) | c0_1(a808))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3095,plain,
% 2.81/2.14 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a808) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a808)) | c0_1(a808)))),
% 2.81/2.14 inference(monotonicity,[status(thm)],[3094])).
% 2.81/2.14 tff(3096,plain,
% 2.81/2.14 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a808) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a808)) | c0_1(a808))),
% 2.81/2.14 inference(transitivity,[status(thm)],[3095, 3093])).
% 2.81/2.14 tff(3097,plain,
% 2.81/2.14 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 2.81/2.14 inference(quant_inst,[status(thm)],[])).
% 2.81/2.14 tff(3098,plain,
% 2.81/2.14 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a808) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a808)) | c0_1(a808)),
% 2.81/2.14 inference(modus_ponens,[status(thm)],[3097, 3096])).
% 2.81/2.14 tff(3099,plain,
% 2.81/2.14 (hskp12),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[3098, 151, 1031, 3091, 877, 3090, 1079, 3043, 3092])).
% 2.81/2.14 tff(3100,plain,
% 2.81/2.14 (~c0_1(a809)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[164, 3099])).
% 2.81/2.14 tff(3101,plain,
% 2.81/2.14 (c1_1(a805)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[480, 3080])).
% 2.81/2.14 tff(3102,plain,
% 2.81/2.14 (c2_1(a809)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[176, 3099])).
% 2.81/2.14 tff(3103,plain,
% 2.81/2.14 (c1_1(a809)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[187, 3099])).
% 2.81/2.14 tff(3104,plain,
% 2.81/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a809) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a809) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3105,plain,
% 2.81/2.14 (((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809))) <=> (c0_1(a809) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3106,plain,
% 2.81/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a809) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a809)) | (~c1_1(a809))))),
% 2.81/2.14 inference(monotonicity,[status(thm)],[3105])).
% 2.81/2.14 tff(3107,plain,
% 2.81/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a809) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.81/2.14 inference(transitivity,[status(thm)],[3106, 3104])).
% 2.81/2.14 tff(3108,plain,
% 2.81/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.81/2.14 inference(quant_inst,[status(thm)],[])).
% 2.81/2.14 tff(3109,plain,
% 2.81/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a809) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a809)) | (~c1_1(a809))),
% 2.81/2.14 inference(modus_ponens,[status(thm)],[3108, 3107])).
% 2.81/2.14 tff(3110,plain,
% 2.81/2.14 (~c0_1(a805)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[3109, 151, 3103, 3102, 3101, 3100, 3082, 3081, 99])).
% 2.81/2.14 tff(3111,plain,
% 2.81/2.14 (~c0_1(a832)),
% 2.81/2.14 inference(unit_resolution,[status(thm)],[2831, 3080, 1031, 322, 878, 22, 877, 433])).
% 2.81/2.14 tff(3112,plain,
% 2.81/2.14 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 2.81/2.14 inference(bind,[status(th)],[])).
% 2.81/2.14 tff(3113,plain,
% 2.81/2.14 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.81/2.14 inference(quant_intro,[status(thm)],[3112])).
% 2.81/2.14 tff(3114,plain,
% 2.81/2.14 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.81/2.14 inference(rewrite,[status(thm)],[])).
% 2.81/2.14 tff(3115,plain,
% 2.81/2.14 (^[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)) | (~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)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~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)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 2.81/2.15 inference(bind,[status(th)],[])).
% 2.81/2.15 tff(3116,plain,
% 2.81/2.15 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.81/2.15 inference(quant_intro,[status(thm)],[3115])).
% 2.81/2.15 tff(3117,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 2.81/2.15 tff(3118,plain,
% 2.81/2.15 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3117, 3116])).
% 2.81/2.15 tff(3119,plain,
% 2.81/2.15 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3118, 3114])).
% 2.81/2.15 tff(3120,plain,(
% 2.81/2.15 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.81/2.15 inference(skolemize,[status(sab)],[3119])).
% 2.81/2.15 tff(3121,plain,
% 2.81/2.15 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3120, 3113])).
% 2.81/2.15 tff(3122,plain,
% 2.81/2.15 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a832) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a832) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)) | c0_1(a832))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3123,plain,
% 2.81/2.15 ((hskp14 | (~ndr1_0) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832))) <=> (hskp14 | c3_1(a832) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)) | c0_1(a832))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3124,plain,
% 2.81/2.15 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a832) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)) | c0_1(a832)))),
% 2.81/2.15 inference(monotonicity,[status(thm)],[3123])).
% 2.81/2.15 tff(3125,plain,
% 2.81/2.15 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a832) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)) | c0_1(a832))),
% 2.81/2.15 inference(transitivity,[status(thm)],[3124, 3122])).
% 2.81/2.15 tff(3126,plain,
% 2.81/2.15 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))),
% 2.81/2.15 inference(quant_inst,[status(thm)],[])).
% 2.81/2.15 tff(3127,plain,
% 2.81/2.15 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a832) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)) | c0_1(a832)),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3126, 3125])).
% 2.81/2.15 tff(3128,plain,
% 2.81/2.15 (hskp14 | c0_1(a832)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3127, 151, 433, 3073, 3064, 22, 3121, 3071])).
% 2.81/2.15 tff(3129,plain,
% 2.81/2.15 (hskp14),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3128, 3111])).
% 2.81/2.15 tff(3130,plain,
% 2.81/2.15 (((~hskp14) | (~c1_1(a816))) <=> ((~hskp14) | (~c1_1(a816)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3131,plain,
% 2.81/2.15 (((~c1_1(a816)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a816)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3132,axiom,((~c1_1(a816)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 2.81/2.15 tff(3133,plain,
% 2.81/2.15 ((~hskp14) | (~c1_1(a816))),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3132, 3131])).
% 2.81/2.15 tff(3134,plain,
% 2.81/2.15 ((~hskp14) | (~c1_1(a816))),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3133, 3130])).
% 2.81/2.15 tff(3135,plain,
% 2.81/2.15 (~c1_1(a816)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3134, 3129])).
% 2.81/2.15 tff(3136,plain,
% 2.81/2.15 (((~hskp14) | c0_1(a816)) <=> ((~hskp14) | c0_1(a816))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3137,axiom,((~hskp14) | c0_1(a816)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 2.81/2.15 tff(3138,plain,
% 2.81/2.15 ((~hskp14) | c0_1(a816)),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3137, 3136])).
% 2.81/2.15 tff(3139,plain,
% 2.81/2.15 ((~hskp14) | c0_1(a816)),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3138, 3136])).
% 2.81/2.15 tff(3140,plain,
% 2.81/2.15 ((~hskp14) | c0_1(a816)),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3139, 3136])).
% 2.81/2.15 tff(3141,plain,
% 2.81/2.15 ((~hskp14) | c0_1(a816)),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3140, 3136])).
% 2.81/2.15 tff(3142,plain,
% 2.81/2.15 ((~hskp14) | c0_1(a816)),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3141, 3136])).
% 2.81/2.15 tff(3143,plain,
% 2.81/2.15 ((~hskp14) | c0_1(a816)),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3142, 3136])).
% 2.81/2.15 tff(3144,plain,
% 2.81/2.15 ((~hskp14) | c0_1(a816)),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3143, 3136])).
% 2.81/2.15 tff(3145,plain,
% 2.81/2.15 ((~hskp14) | c0_1(a816)),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3144, 3136])).
% 2.81/2.15 tff(3146,plain,
% 2.81/2.15 (c0_1(a816)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3145, 3129])).
% 2.81/2.15 tff(3147,plain,
% 2.81/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a816) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | c3_1(a816) | (~c0_1(a816)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a816) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | c3_1(a816) | (~c0_1(a816)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3148,plain,
% 2.81/2.15 (((~ndr1_0) | c1_1(a816) | c3_1(a816) | (~c0_1(a816)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805)) <=> (c1_1(a816) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | c3_1(a816) | (~c0_1(a816)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3149,plain,
% 2.81/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a816) | c3_1(a816) | (~c0_1(a816)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a816) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | c3_1(a816) | (~c0_1(a816))))),
% 2.81/2.15 inference(monotonicity,[status(thm)],[3148])).
% 2.81/2.15 tff(3150,plain,
% 2.81/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a816) | c3_1(a816) | (~c0_1(a816)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a816) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | c3_1(a816) | (~c0_1(a816)))),
% 2.81/2.15 inference(transitivity,[status(thm)],[3149, 3147])).
% 2.81/2.15 tff(3151,plain,
% 2.81/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a816) | c3_1(a816) | (~c0_1(a816)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805))),
% 2.81/2.15 inference(quant_inst,[status(thm)],[])).
% 2.81/2.15 tff(3152,plain,
% 2.81/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a816) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | c3_1(a816) | (~c0_1(a816))),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3151, 3150])).
% 2.81/2.15 tff(3153,plain,
% 2.81/2.15 (c3_1(a816)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3152, 151, 3146, 1031, 3135, 878, 877, 3082, 3081, 876, 3110])).
% 2.81/2.15 tff(3154,plain,
% 2.81/2.15 (((~hskp14) | (~c2_1(a816))) <=> ((~hskp14) | (~c2_1(a816)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3155,plain,
% 2.81/2.15 (((~c2_1(a816)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a816)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3156,axiom,((~c2_1(a816)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 2.81/2.15 tff(3157,plain,
% 2.81/2.15 ((~hskp14) | (~c2_1(a816))),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3156, 3155])).
% 2.81/2.15 tff(3158,plain,
% 2.81/2.15 ((~hskp14) | (~c2_1(a816))),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3157, 3154])).
% 2.81/2.15 tff(3159,plain,
% 2.81/2.15 (~c2_1(a816)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3158, 3129])).
% 2.81/2.15 tff(3160,plain,
% 2.81/2.15 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3161,plain,
% 2.81/2.15 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816))) <=> (hskp20 | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3162,plain,
% 2.81/2.15 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816))))),
% 2.81/2.15 inference(monotonicity,[status(thm)],[3161])).
% 2.81/2.15 tff(3163,plain,
% 2.81/2.15 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)))),
% 2.81/2.15 inference(transitivity,[status(thm)],[3162, 3160])).
% 2.81/2.15 tff(3164,plain,
% 2.81/2.15 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))),
% 2.81/2.15 inference(quant_inst,[status(thm)],[])).
% 2.81/2.15 tff(3165,plain,
% 2.81/2.15 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816))),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3164, 3163])).
% 2.81/2.15 tff(3166,plain,
% 2.81/2.15 ($false),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3165, 151, 346, 11, 3146, 3159, 21, 3153])).
% 2.81/2.15 tff(3167,plain,(c1_1(a808) | hskp20 | hskp9 | (~c3_1(a808)) | c2_1(a808) | (~c2_1(a832)) | c3_1(a832) | c1_1(a832) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a867))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.15 tff(3168,plain,
% 2.81/2.15 (c1_1(a832)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3167, 3042, 2946, 344, 3041, 3040, 22, 2951, 2911, 2910, 2909])).
% 2.81/2.15 tff(3169,plain,
% 2.81/2.15 (~hskp19),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[391, 3168])).
% 2.81/2.15 tff(3170,plain,
% 2.81/2.15 (hskp9 | c2_1(a867)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3059, 151, 344, 2911, 2909, 21])).
% 2.81/2.15 tff(3171,plain,
% 2.81/2.15 (c2_1(a867)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3170, 2946])).
% 2.81/2.15 tff(3172,plain,
% 2.81/2.15 (hskp18),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[2365, 2949, 2909, 2910, 3171])).
% 2.81/2.15 tff(3173,plain,
% 2.81/2.15 (~c3_1(a828)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[1197, 3172])).
% 2.81/2.15 tff(3174,plain,
% 2.81/2.15 (~c2_1(a828)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[1191, 3172])).
% 2.81/2.15 tff(3175,plain,
% 2.81/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a833) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a833) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3176,plain,
% 2.81/2.15 (((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833)) <=> (c1_1(a833) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3177,plain,
% 2.81/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a833) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832))))),
% 2.81/2.15 inference(monotonicity,[status(thm)],[3176])).
% 2.81/2.15 tff(3178,plain,
% 2.81/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a833) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))),
% 2.81/2.15 inference(transitivity,[status(thm)],[3177, 3175])).
% 2.81/2.15 tff(3179,plain,
% 2.81/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833))),
% 2.81/2.15 inference(quant_inst,[status(thm)],[])).
% 2.81/2.15 tff(3180,plain,
% 2.81/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a833) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832))),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3179, 3178])).
% 2.81/2.15 tff(3181,plain,
% 2.81/2.15 (c0_1(a828)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3180, 151, 333, 3040, 321, 309, 3168, 22, 3174, 3173, 258])).
% 2.81/2.15 tff(3182,plain,
% 2.81/2.15 (~c1_1(a828)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[1203, 3172])).
% 2.81/2.15 tff(3183,plain,
% 2.81/2.15 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3184,plain,
% 2.81/2.15 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828))) <=> (hskp20 | hskp1 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3185,plain,
% 2.81/2.15 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828))))),
% 2.81/2.15 inference(monotonicity,[status(thm)],[3184])).
% 2.81/2.15 tff(3186,plain,
% 2.81/2.15 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 2.81/2.15 inference(transitivity,[status(thm)],[3185, 3183])).
% 2.81/2.15 tff(3187,plain,
% 2.81/2.15 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))),
% 2.81/2.15 inference(quant_inst,[status(thm)],[])).
% 2.81/2.15 tff(3188,plain,
% 2.81/2.15 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828))),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3187, 3186])).
% 2.81/2.15 tff(3189,plain,
% 2.81/2.15 (hskp1),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3188, 151, 344, 3182, 3174, 1646, 3181])).
% 2.81/2.15 tff(3190,plain,
% 2.81/2.15 (~c2_1(a794)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[280, 3189])).
% 2.81/2.15 tff(3191,plain,
% 2.81/2.15 (c3_1(a794)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[291, 3189])).
% 2.81/2.15 tff(3192,plain,
% 2.81/2.15 (~c0_1(a794)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[297, 3189])).
% 2.81/2.15 tff(3193,plain,
% 2.81/2.15 ($false),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[2377, 3192, 3191, 2910, 2909, 3171, 3172, 3190, 3169])).
% 2.81/2.15 tff(3194,plain,(c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.15 tff(3195,plain,
% 2.81/2.15 (c1_1(a833)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3194, 22, 309, 321])).
% 2.81/2.15 tff(3196,plain,
% 2.81/2.15 (hskp3),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[2655, 310, 309, 321, 3195])).
% 2.81/2.15 tff(3197,plain,
% 2.81/2.15 (~c3_1(a798)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[546, 3196])).
% 2.81/2.15 tff(3198,plain,
% 2.81/2.15 (c3_1(a838)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[443, 2957])).
% 2.81/2.15 tff(3199,plain,
% 2.81/2.15 (c0_1(a838)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[454, 2957])).
% 2.81/2.15 tff(3200,plain,
% 2.81/2.15 (hskp3),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[2655, 310, 309, 321, 639])).
% 2.81/2.15 tff(3201,plain,
% 2.81/2.15 (~c3_1(a798)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[546, 3200])).
% 2.81/2.15 tff(3202,plain,
% 2.81/2.15 (c2_1(a798)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[563, 3200])).
% 2.81/2.15 tff(3203,plain,
% 2.81/2.15 (c0_1(a798)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[574, 3200])).
% 2.81/2.15 tff(3204,plain,
% 2.81/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c2_1(a833) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c3_1(a833) | (~c1_1(a833)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a833) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c3_1(a833) | (~c1_1(a833)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3205,plain,
% 2.81/2.15 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (c2_1(a838) | c2_1(a833) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c3_1(a833) | (~c1_1(a833)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3206,plain,
% 2.81/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c2_1(a833) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c3_1(a833) | (~c1_1(a833)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 2.81/2.15 inference(monotonicity,[status(thm)],[3205])).
% 2.81/2.15 tff(3207,plain,
% 2.81/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a833) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c3_1(a833) | (~c1_1(a833)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.81/2.15 inference(transitivity,[status(thm)],[3206, 3204])).
% 2.81/2.15 tff(3208,plain,
% 2.81/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 2.81/2.15 inference(quant_inst,[status(thm)],[])).
% 2.81/2.15 tff(3209,plain,
% 2.81/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a833) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c3_1(a833) | (~c1_1(a833)) | (~c3_1(a838)) | (~c0_1(a838))),
% 2.81/2.15 inference(modus_ponens,[status(thm)],[3208, 3207])).
% 2.81/2.15 tff(3210,plain,
% 2.81/2.15 ($false),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3209, 151, 483, 482, 639, 3203, 3202, 470, 309, 3201, 332, 310])).
% 2.81/2.15 tff(3211,plain,(c3_1(a833) | (~c0_1(a838)) | (~c3_1(a838)) | (~c1_1(a833)) | c2_1(a838) | c2_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.15 tff(3212,plain,
% 2.81/2.15 (c3_1(a833)),
% 2.81/2.15 inference(unit_resolution,[status(thm)],[3211, 3199, 3198, 3195, 2958, 309, 321])).
% 2.81/2.15 tff(3213,plain,
% 2.81/2.15 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3214,plain,
% 2.81/2.15 ((hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a832) | c2_1(a832) | c1_1(a832)) <=> (hskp19 | c2_1(a832) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.15 inference(rewrite,[status(thm)],[])).
% 2.81/2.15 tff(3215,plain,
% 2.81/2.15 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.81/2.15 inference(monotonicity,[status(thm)],[3214])).
% 2.81/2.15 tff(3216,plain,
% 2.81/2.15 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.15 inference(transitivity,[status(thm)],[3215, 3213])).
% 2.81/2.15 tff(3217,plain,
% 2.81/2.15 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a832) | c2_1(a832) | c1_1(a832))),
% 2.81/2.16 inference(quant_inst,[status(thm)],[])).
% 2.81/2.16 tff(3218,plain,
% 2.81/2.16 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.81/2.16 inference(modus_ponens,[status(thm)],[3217, 3216])).
% 2.81/2.16 tff(3219,plain,
% 2.81/2.16 (hskp19 | c2_1(a832) | c1_1(a832) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3218, 151, 309, 22, 10])).
% 2.81/2.16 tff(3220,plain,
% 2.81/2.16 (~c3_1(a833)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3219, 322, 3195, 1458, 1459])).
% 2.81/2.16 tff(3221,plain,
% 2.81/2.16 (hskp8),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[963, 310, 309, 690, 688, 693, 321, 639])).
% 2.81/2.16 tff(3222,plain,
% 2.81/2.16 (~c3_1(a805)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[462, 3221])).
% 2.81/2.16 tff(3223,plain,
% 2.81/2.16 (~c2_1(a805)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[468, 3221])).
% 2.81/2.16 tff(3224,plain,
% 2.81/2.16 (c1_1(a805)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[480, 3221])).
% 2.81/2.16 tff(3225,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3226,plain,
% 2.81/2.16 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c2_1(a838) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3227,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 2.81/2.16 inference(monotonicity,[status(thm)],[3226])).
% 2.81/2.16 tff(3228,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.81/2.16 inference(transitivity,[status(thm)],[3227, 3225])).
% 2.81/2.16 tff(3229,plain,
% 2.81/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 2.81/2.16 inference(quant_inst,[status(thm)],[])).
% 2.81/2.16 tff(3230,plain,
% 2.81/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838))),
% 2.81/2.16 inference(modus_ponens,[status(thm)],[3229, 3228])).
% 2.81/2.16 tff(3231,plain,
% 2.81/2.16 ($false),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3230, 151, 483, 482, 3224, 3203, 3202, 470, 3223, 3222, 3201, 332])).
% 2.81/2.16 tff(3232,plain,(c3_1(a833) | (~c0_1(a838)) | (~c3_1(a838)) | c2_1(a838) | c2_1(a833) | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796)) | c0_1(a833) | (~c1_1(a833))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.16 tff(3233,plain,
% 2.81/2.16 ($false),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3232, 1312, 1791, 639, 690, 309, 310, 688, 693, 321, 1792])).
% 2.81/2.16 tff(3234,plain,((~hskp21) | (~c1_1(a833)) | (~c0_1(a796)) | c2_1(a833) | c3_1(a833) | (~c2_1(a796)) | (~c3_1(a796)) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.16 tff(3235,plain,
% 2.81/2.16 (~hskp21),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3234, 3220, 2956, 309, 3195, 2955, 2954, 321])).
% 2.81/2.16 tff(3236,plain,
% 2.81/2.16 (hskp11),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[2574, 3235])).
% 2.81/2.16 tff(3237,plain,
% 2.81/2.16 (~c1_1(a808)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[851, 3236])).
% 2.81/2.16 tff(3238,plain,
% 2.81/2.16 (c3_1(a808)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[896, 3236])).
% 2.81/2.16 tff(3239,plain,
% 2.81/2.16 (c0_1(a808)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[2980, 151, 2952, 2567, 2538, 2527, 3238, 3237, 1515])).
% 2.81/2.16 tff(3240,plain,
% 2.81/2.16 (hskp3),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[2655, 3220, 309, 321, 3195])).
% 2.81/2.16 tff(3241,plain,
% 2.81/2.16 (~c3_1(a798)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[546, 3240])).
% 2.81/2.16 tff(3242,plain,
% 2.81/2.16 (~c2_1(a808)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[857, 3236])).
% 2.81/2.16 tff(3243,plain,
% 2.81/2.16 (c2_1(a798)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[563, 3240])).
% 2.81/2.16 tff(3244,plain,
% 2.81/2.16 (c0_1(a798)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[574, 3240])).
% 2.81/2.16 tff(3245,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a833) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a833) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)) | c3_1(a833) | (~c1_1(a833)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3246,plain,
% 2.81/2.16 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (c2_1(a833) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)) | c3_1(a833) | (~c1_1(a833)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3247,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a833) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)) | c3_1(a833) | (~c1_1(a833))))),
% 2.81/2.16 inference(monotonicity,[status(thm)],[3246])).
% 2.81/2.16 tff(3248,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a833) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)) | c3_1(a833) | (~c1_1(a833)))),
% 2.81/2.16 inference(transitivity,[status(thm)],[3247, 3245])).
% 2.81/2.16 tff(3249,plain,
% 2.81/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 2.81/2.16 inference(quant_inst,[status(thm)],[])).
% 2.81/2.16 tff(3250,plain,
% 2.81/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a833) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)) | c3_1(a833) | (~c1_1(a833))),
% 2.81/2.16 inference(modus_ponens,[status(thm)],[3249, 3248])).
% 2.81/2.16 tff(3251,plain,
% 2.81/2.16 ($false),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3250, 151, 3195, 3238, 3244, 3243, 309, 3242, 3241, 332, 3220, 3239])).
% 2.81/2.16 tff(3252,plain,(c1_1(a832) | c2_1(a833) | c0_1(a833) | c2_1(a832) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.16 tff(3253,plain,
% 2.81/2.16 (c1_1(a832)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3252, 1458, 321, 309, 22])).
% 2.81/2.16 tff(3254,assumption,(c1_1(a832)), introduced(assumption)).
% 2.81/2.16 tff(3255,assumption,(~c0_1(a797)), introduced(assumption)).
% 2.81/2.16 tff(3256,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3257,plain,
% 2.81/2.16 (((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797))) <=> (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3258,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832))))),
% 2.81/2.16 inference(monotonicity,[status(thm)],[3257])).
% 2.81/2.16 tff(3259,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))),
% 2.81/2.16 inference(transitivity,[status(thm)],[3258, 3256])).
% 2.81/2.16 tff(3260,plain,
% 2.81/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))),
% 2.81/2.16 inference(quant_inst,[status(thm)],[])).
% 2.81/2.16 tff(3261,plain,
% 2.81/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832))),
% 2.81/2.16 inference(modus_ponens,[status(thm)],[3260, 3259])).
% 2.81/2.16 tff(3262,plain,
% 2.81/2.16 ($false),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3261, 151, 2567, 2538, 1458, 3254, 22, 99, 456, 3255])).
% 2.81/2.16 tff(3263,plain,(c0_1(a797) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~c0_1(a832))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.16 tff(3264,plain,
% 2.81/2.16 (c0_1(a797)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3263, 456, 3254, 22, 1458])).
% 2.81/2.16 tff(3265,plain,
% 2.81/2.16 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3266,plain,
% 2.81/2.16 ((hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832))) <=> (hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3267,plain,
% 2.81/2.16 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797))))),
% 2.81/2.16 inference(monotonicity,[status(thm)],[3266])).
% 2.81/2.16 tff(3268,plain,
% 2.81/2.16 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)))),
% 2.81/2.16 inference(transitivity,[status(thm)],[3267, 3265])).
% 2.81/2.16 tff(3269,plain,
% 2.81/2.16 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)))),
% 2.81/2.16 inference(quant_inst,[status(thm)],[])).
% 2.81/2.16 tff(3270,plain,
% 2.81/2.16 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797))),
% 2.81/2.16 inference(modus_ponens,[status(thm)],[3269, 3268])).
% 2.81/2.16 tff(3271,plain,
% 2.81/2.16 (hskp12 | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a797))),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3270, 151, 2567, 2527, 22, 110])).
% 2.81/2.16 tff(3272,plain,
% 2.81/2.16 (hskp12),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3271, 3264, 1458, 3254])).
% 2.81/2.16 tff(3273,plain,
% 2.81/2.16 (~c0_1(a809)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[164, 3272])).
% 2.81/2.16 tff(3274,plain,
% 2.81/2.16 (c2_1(a809)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[176, 3272])).
% 2.81/2.16 tff(3275,plain,
% 2.81/2.16 (c1_1(a809)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[187, 3272])).
% 2.81/2.16 tff(3276,plain,
% 2.81/2.16 ($false),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3018, 151, 1458, 3275, 3274, 3254, 22, 3273, 99, 456])).
% 2.81/2.16 tff(3277,plain,((~c0_1(a832)) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.16 tff(3278,plain,
% 2.81/2.16 (~c0_1(a832)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3277, 1458, 3254, 22])).
% 2.81/2.16 tff(3279,plain,
% 2.81/2.16 (hskp3),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3026, 3278, 3254])).
% 2.81/2.16 tff(3280,assumption,(hskp3), introduced(assumption)).
% 2.81/2.16 tff(3281,plain,
% 2.81/2.16 (~c3_1(a798)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[546, 3280])).
% 2.81/2.16 tff(3282,plain,
% 2.81/2.16 (c2_1(a798)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[563, 3280])).
% 2.81/2.16 tff(3283,plain,
% 2.81/2.16 (c0_1(a798)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[574, 3280])).
% 2.81/2.16 tff(3284,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3285,plain,
% 2.81/2.16 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832))) <=> (c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3286,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 2.81/2.16 inference(monotonicity,[status(thm)],[3285])).
% 2.81/2.16 tff(3287,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.81/2.16 inference(transitivity,[status(thm)],[3286, 3284])).
% 2.81/2.16 tff(3288,plain,
% 2.81/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))),
% 2.81/2.16 inference(quant_inst,[status(thm)],[])).
% 2.81/2.16 tff(3289,plain,
% 2.81/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a838)) | (~c0_1(a838))),
% 2.81/2.16 inference(modus_ponens,[status(thm)],[3288, 3287])).
% 2.81/2.16 tff(3290,plain,
% 2.81/2.16 ($false),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3289, 151, 483, 482, 1458, 3283, 3282, 470, 3254, 22, 3281, 332])).
% 2.81/2.16 tff(3291,plain,((~hskp3) | (~c0_1(a838)) | (~c3_1(a838)) | c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.16 tff(3292,plain,
% 2.81/2.16 ($false),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3291, 1312, 1791, 1458, 3254, 3279, 1792, 22])).
% 2.81/2.16 tff(3293,plain,((~hskp21) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.16 tff(3294,plain,
% 2.81/2.16 (~hskp21),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3293, 1458, 3253, 22])).
% 2.81/2.16 tff(3295,plain,
% 2.81/2.16 (hskp11),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[2574, 3294])).
% 2.81/2.16 tff(3296,plain,
% 2.81/2.16 (c3_1(a808)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[896, 3295])).
% 2.81/2.16 tff(3297,plain,
% 2.81/2.16 (~c2_1(a808)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[857, 3295])).
% 2.81/2.16 tff(3298,plain,
% 2.81/2.16 (hskp21 | hskp18 | c1_1(a808) | (~c3_1(a808))),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[1185, 151, 877, 1178])).
% 2.81/2.16 tff(3299,plain,
% 2.81/2.16 (c1_1(a808)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3298, 704, 1031, 2363])).
% 2.81/2.16 tff(3300,plain,
% 2.81/2.16 ($false),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[851, 3299, 2575])).
% 2.81/2.16 tff(3301,plain,(hskp21 | (~c3_1(a808)) | hskp18 | c2_1(a808)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.16 tff(3302,plain,
% 2.81/2.16 (hskp18),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3301, 3296, 3294, 3297])).
% 2.81/2.16 tff(3303,plain,
% 2.81/2.16 ($false),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[2686, 2369, 2370, 639, 309, 1603, 321, 877, 1031, 2368])).
% 2.81/2.16 tff(3304,plain,((~hskp18) | (~c1_1(a833)) | c2_1(a833) | hskp19 | c0_1(a833) | c2_1(a808) | (~c3_1(a808))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.16 tff(3305,plain,
% 2.81/2.16 ($false),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3304, 3302, 3297, 309, 1459, 321, 3195, 3296])).
% 2.81/2.16 tff(3306,plain,(c2_1(a832) | c2_1(a833) | c0_1(a833) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.16 tff(3307,plain,
% 2.81/2.16 (c2_1(a832)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3306, 22, 321, 309])).
% 2.81/2.16 tff(3308,plain,
% 2.81/2.16 (hskp12),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[1087, 1069, 3307, 321, 309, 22, 750])).
% 2.81/2.16 tff(3309,plain,
% 2.81/2.16 (~c0_1(a809)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[164, 3308])).
% 2.81/2.16 tff(3310,plain,
% 2.81/2.16 (c2_1(a809)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[176, 3308])).
% 2.81/2.16 tff(3311,plain,
% 2.81/2.16 (c1_1(a809)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[187, 3308])).
% 2.81/2.16 tff(3312,plain,
% 2.81/2.16 ($false),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[1097, 151, 3307, 3311, 3310, 322, 22, 3309, 1067, 1069])).
% 2.81/2.16 tff(3313,plain,(c0_1(a832) | c1_1(a832) | c3_1(a832) | c0_1(a833) | c2_1(a833) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.16 tff(3314,plain,
% 2.81/2.16 (c0_1(a832)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3313, 3212, 22, 321, 309, 322])).
% 2.81/2.16 tff(3315,plain,
% 2.81/2.16 ($false),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[2904, 151, 2567, 2538, 3307, 321, 309, 22, 2635, 456, 750, 3255])).
% 2.81/2.16 tff(3316,plain,(c0_1(a797) | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~c0_1(a832)) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.16 tff(3317,plain,
% 2.81/2.16 (c0_1(a797)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3316, 3314, 309, 22, 321, 3212])).
% 2.81/2.16 tff(3318,plain,
% 2.81/2.16 (((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3319,plain,
% 2.81/2.16 ((hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797))) <=> (hskp26 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3320,plain,
% 2.81/2.16 (((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797))))),
% 2.81/2.16 inference(monotonicity,[status(thm)],[3319])).
% 2.81/2.16 tff(3321,plain,
% 2.81/2.16 (((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 2.81/2.16 inference(transitivity,[status(thm)],[3320, 3318])).
% 2.81/2.16 tff(3322,plain,
% 2.81/2.16 ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))),
% 2.81/2.16 inference(quant_inst,[status(thm)],[])).
% 2.81/2.16 tff(3323,plain,
% 2.81/2.16 ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797))),
% 2.81/2.16 inference(modus_ponens,[status(thm)],[3322, 3321])).
% 2.81/2.16 tff(3324,plain,
% 2.81/2.16 (hskp26 | hskp11 | (~c0_1(a797))),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3323, 151, 2538, 2527, 715])).
% 2.81/2.16 tff(3325,plain,
% 2.81/2.16 (hskp26),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3324, 3317, 705])).
% 2.81/2.16 tff(3326,plain,
% 2.81/2.16 (~c0_1(a869)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[781, 3325])).
% 2.81/2.16 tff(3327,plain,
% 2.81/2.16 (c3_1(a869)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[730, 3325])).
% 2.81/2.16 tff(3328,plain,
% 2.81/2.16 (c2_1(a869)),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[741, 3325])).
% 2.81/2.16 tff(3329,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a869) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a869)) | (~c3_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a869) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a869)) | (~c3_1(a869)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3330,plain,
% 2.81/2.16 (((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869))) <=> (c0_1(a869) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a869)) | (~c3_1(a869)))),
% 2.81/2.16 inference(rewrite,[status(thm)],[])).
% 2.81/2.16 tff(3331,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a869) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a869)) | (~c3_1(a869))))),
% 2.81/2.16 inference(monotonicity,[status(thm)],[3330])).
% 2.81/2.16 tff(3332,plain,
% 2.81/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a869) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a869)) | (~c3_1(a869)))),
% 2.81/2.16 inference(transitivity,[status(thm)],[3331, 3329])).
% 2.81/2.16 tff(3333,plain,
% 2.81/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869)))),
% 2.81/2.16 inference(quant_inst,[status(thm)],[])).
% 2.81/2.16 tff(3334,plain,
% 2.81/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a869) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a869)) | (~c3_1(a869))),
% 2.81/2.16 inference(modus_ponens,[status(thm)],[3333, 3332])).
% 2.81/2.16 tff(3335,plain,
% 2.81/2.16 ($false),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3334, 151, 2567, 2538, 2527, 3328, 3327, 3326, 207, 3317])).
% 2.81/2.16 tff(3336,plain,(hskp11 | c2_1(a833) | c3_1(a832) | c0_1(a833) | c1_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.16 tff(3337,plain,
% 2.81/2.16 (hskp11),
% 2.81/2.16 inference(unit_resolution,[status(thm)],[3336, 322, 22, 321, 309])).
% 2.81/2.16 tff(3338,plain,
% 2.81/2.16 (~c2_1(a808)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[857, 3337])).
% 2.81/2.17 tff(3339,plain,
% 2.81/2.17 (c2_1(a798)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[563, 3196])).
% 2.81/2.17 tff(3340,plain,
% 2.81/2.17 (c0_1(a798)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[574, 3196])).
% 2.81/2.17 tff(3341,plain,
% 2.81/2.17 (c3_1(a808)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[896, 3337])).
% 2.81/2.17 tff(3342,plain,
% 2.81/2.17 (~c0_1(a808)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3250, 151, 3195, 3341, 3340, 3339, 309, 3338, 3197, 332, 310])).
% 2.81/2.17 tff(3343,plain,
% 2.81/2.17 (~c1_1(a808)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[851, 3337])).
% 2.81/2.17 tff(3344,plain,
% 2.81/2.17 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a808) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a808) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c0_1(a808))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3345,plain,
% 2.81/2.17 ((hskp0 | (~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | c1_1(a808) | c0_1(a808)) <=> (hskp0 | c1_1(a808) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c0_1(a808))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3346,plain,
% 2.81/2.17 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | c1_1(a808) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a808) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c0_1(a808)))),
% 2.81/2.17 inference(monotonicity,[status(thm)],[3345])).
% 2.81/2.17 tff(3347,plain,
% 2.81/2.17 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | c1_1(a808) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a808) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c0_1(a808))),
% 2.81/2.17 inference(transitivity,[status(thm)],[3346, 3344])).
% 2.81/2.17 tff(3348,plain,
% 2.81/2.17 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | c1_1(a808) | c0_1(a808))),
% 2.81/2.17 inference(quant_inst,[status(thm)],[])).
% 2.81/2.17 tff(3349,plain,
% 2.81/2.17 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a808) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c0_1(a808)),
% 2.81/2.17 inference(modus_ponens,[status(thm)],[3348, 3347])).
% 2.81/2.17 tff(3350,plain,
% 2.81/2.17 (hskp0),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3349, 151, 3340, 3339, 3343, 3338, 3197, 1434, 3342])).
% 2.81/2.17 tff(3351,plain,
% 2.81/2.17 (~c1_1(a793)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[675, 3350])).
% 2.81/2.17 tff(3352,plain,
% 2.81/2.17 ((~c0_1(a832)) | c3_1(a833)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[2712, 151, 3341, 321, 309, 322, 22, 3343, 3338, 876])).
% 2.81/2.17 tff(3353,plain,
% 2.81/2.17 (~c0_1(a832)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3352, 310])).
% 2.81/2.17 tff(3354,plain,
% 2.81/2.17 (hskp15 | (~c2_1(a832)) | c0_1(a832)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[2703, 151, 2567, 2538, 2527, 22, 1300])).
% 2.81/2.17 tff(3355,plain,
% 2.81/2.17 (hskp15),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3354, 3353, 3307])).
% 2.81/2.17 tff(3356,plain,
% 2.81/2.17 (~c1_1(a817)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1342, 3355])).
% 2.81/2.17 tff(3357,plain,
% 2.81/2.17 (c3_1(a817)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1353, 3355])).
% 2.81/2.17 tff(3358,plain,
% 2.81/2.17 (c2_1(a817)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1364, 3355])).
% 2.81/2.17 tff(3359,plain,
% 2.81/2.17 (c0_1(a793)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[686, 3350])).
% 2.81/2.17 tff(3360,plain,
% 2.81/2.17 (c2_1(a793)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[669, 3350])).
% 2.81/2.17 tff(3361,plain,
% 2.81/2.17 ($false),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[2857, 3360, 3359, 3195, 310, 3358, 3357, 321, 3356, 3341, 309, 3343, 3338, 3351])).
% 2.81/2.17 tff(3362,plain,(c3_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a832) | c1_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.17 tff(3363,plain,
% 2.81/2.17 (c3_1(a833)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3362, 322, 309, 22, 321])).
% 2.81/2.17 tff(3364,plain,
% 2.81/2.17 (c0_1(a832)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3313, 3363, 22, 321, 309, 322])).
% 2.81/2.17 tff(3365,plain,
% 2.81/2.17 (c0_1(a797)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3316, 3364, 309, 22, 321, 3363])).
% 2.81/2.17 tff(3366,plain,
% 2.81/2.17 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3367,plain,
% 2.81/2.17 ((hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832))) <=> (hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3368,plain,
% 2.81/2.17 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832))))),
% 2.81/2.17 inference(monotonicity,[status(thm)],[3367])).
% 2.81/2.17 tff(3369,plain,
% 2.81/2.17 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.81/2.17 inference(transitivity,[status(thm)],[3368, 3366])).
% 2.81/2.17 tff(3370,plain,
% 2.81/2.17 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))),
% 2.81/2.17 inference(quant_inst,[status(thm)],[])).
% 2.81/2.17 tff(3371,plain,
% 2.81/2.17 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832))),
% 2.81/2.17 inference(modus_ponens,[status(thm)],[3370, 3369])).
% 2.81/2.17 tff(3372,plain,
% 2.81/2.17 (hskp5 | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832))),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3371, 151, 2567, 2527, 22, 217])).
% 2.81/2.17 tff(3373,plain,
% 2.81/2.17 (hskp5),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3372, 3365, 3307, 3364])).
% 2.81/2.17 tff(3374,plain,
% 2.81/2.17 (~c1_1(a800)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[263, 3373])).
% 2.81/2.17 tff(3375,plain,
% 2.81/2.17 (~c0_1(a800)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[229, 3373])).
% 2.81/2.17 tff(3376,plain,
% 2.81/2.17 (c3_1(a800)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[240, 3373])).
% 2.81/2.17 tff(3377,plain,
% 2.81/2.17 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a833) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3378,plain,
% 2.81/2.17 ((hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (hskp6 | c2_1(a833) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3379,plain,
% 2.81/2.17 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a833) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.81/2.17 inference(monotonicity,[status(thm)],[3378])).
% 2.81/2.17 tff(3380,plain,
% 2.81/2.17 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.17 inference(transitivity,[status(thm)],[3379, 3377])).
% 2.81/2.17 tff(3381,plain,
% 2.81/2.17 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 2.81/2.17 inference(quant_inst,[status(thm)],[])).
% 2.81/2.17 tff(3382,plain,
% 2.81/2.17 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.81/2.17 inference(modus_ponens,[status(thm)],[3381, 3380])).
% 2.81/2.17 tff(3383,plain,
% 2.81/2.17 (hskp6),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3382, 151, 3195, 3376, 309, 3375, 3374, 1964, 3363])).
% 2.81/2.17 tff(3384,plain,
% 2.81/2.17 (~c0_1(a802)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1987, 3383])).
% 2.81/2.17 tff(3385,plain,
% 2.81/2.17 (c2_1(a802)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1998, 3383])).
% 2.81/2.17 tff(3386,plain,
% 2.81/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c3_1(a802)) | (~c2_1(a802)))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3387,plain,
% 2.81/2.17 (((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802))) <=> (c0_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c3_1(a802)) | (~c2_1(a802)))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3388,plain,
% 2.81/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c3_1(a802)) | (~c2_1(a802))))),
% 2.81/2.17 inference(monotonicity,[status(thm)],[3387])).
% 2.81/2.17 tff(3389,plain,
% 2.81/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c3_1(a802)) | (~c2_1(a802)))),
% 2.81/2.17 inference(transitivity,[status(thm)],[3388, 3386])).
% 2.81/2.17 tff(3390,plain,
% 2.81/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))),
% 2.81/2.17 inference(quant_inst,[status(thm)],[])).
% 2.81/2.17 tff(3391,plain,
% 2.81/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c3_1(a802)) | (~c2_1(a802))),
% 2.81/2.17 inference(modus_ponens,[status(thm)],[3390, 3389])).
% 2.81/2.17 tff(3392,plain,
% 2.81/2.17 (~c3_1(a802)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3391, 151, 2567, 2538, 2527, 3385, 3384, 207, 3365])).
% 2.81/2.17 tff(3393,plain,
% 2.81/2.17 (hskp12),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[2822, 151, 3385, 321, 309, 3384, 1079, 3363, 3392])).
% 2.81/2.17 tff(3394,plain,
% 2.81/2.17 (~c0_1(a809)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[164, 3393])).
% 2.81/2.17 tff(3395,plain,
% 2.81/2.17 (c2_1(a809)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[176, 3393])).
% 2.81/2.17 tff(3396,plain,
% 2.81/2.17 (c1_1(a809)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[187, 3393])).
% 2.81/2.17 tff(3397,plain,
% 2.81/2.17 ($false),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[2881, 151, 3307, 3396, 3395, 321, 309, 22, 3394, 2635, 3364, 3363])).
% 2.81/2.17 tff(3398,plain,(c1_1(a832) | c0_1(a833) | c2_1(a833) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.17 tff(3399,plain,
% 2.81/2.17 (c1_1(a832)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3398, 22, 309, 321])).
% 2.81/2.17 tff(3400,plain,
% 2.81/2.17 (~hskp19),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[391, 3399])).
% 2.81/2.17 tff(3401,plain,
% 2.81/2.17 (hskp27),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[2596, 3400])).
% 2.81/2.17 tff(3402,plain,
% 2.81/2.17 (c3_1(a796)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[594, 3401])).
% 2.81/2.17 tff(3403,plain,
% 2.81/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3404,plain,
% 2.81/2.17 (((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3405,plain,
% 2.81/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.81/2.17 inference(monotonicity,[status(thm)],[3404])).
% 2.81/2.17 tff(3406,plain,
% 2.81/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.17 inference(transitivity,[status(thm)],[3405, 3403])).
% 2.81/2.17 tff(3407,plain,
% 2.81/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 2.81/2.17 inference(quant_inst,[status(thm)],[])).
% 2.81/2.17 tff(3408,plain,
% 2.81/2.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.81/2.17 inference(modus_ponens,[status(thm)],[3407, 3406])).
% 2.81/2.17 tff(3409,plain,
% 2.81/2.17 ((~c1_1(a832)) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3408, 151, 321, 309, 22, 2078])).
% 2.81/2.17 tff(3410,plain,
% 2.81/2.17 (~c3_1(a833)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3409, 3399, 3195, 3307])).
% 2.81/2.17 tff(3411,plain,
% 2.81/2.17 (c0_1(a796)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[616, 3401])).
% 2.81/2.17 tff(3412,plain,
% 2.81/2.17 (c2_1(a796)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[605, 3401])).
% 2.81/2.17 tff(3413,plain,
% 2.81/2.17 (~hskp21),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3234, 3412, 3411, 309, 3195, 3410, 3402, 321])).
% 2.81/2.17 tff(3414,plain,
% 2.81/2.17 (hskp11),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[2574, 3413])).
% 2.81/2.17 tff(3415,plain,
% 2.81/2.17 (c3_1(a808)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[896, 3414])).
% 2.81/2.17 tff(3416,plain,
% 2.81/2.17 (~c2_1(a808)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[857, 3414])).
% 2.81/2.17 tff(3417,plain,
% 2.81/2.17 (hskp18),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3301, 3415, 3413, 3416])).
% 2.81/2.17 tff(3418,plain,
% 2.81/2.17 ($false),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3304, 3417, 3416, 309, 3400, 321, 3195, 3415])).
% 2.81/2.17 tff(3419,plain,(c3_1(a832) | c2_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.17 tff(3420,plain,
% 2.81/2.17 (c3_1(a832)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3419, 321, 309])).
% 2.81/2.17 tff(3421,plain,
% 2.81/2.17 (~hskp19),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[385, 3420])).
% 2.81/2.17 tff(3422,plain,
% 2.81/2.17 (hskp27),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[2596, 3421])).
% 2.81/2.17 tff(3423,plain,
% 2.81/2.17 (c3_1(a796)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[594, 3422])).
% 2.81/2.17 tff(3424,plain,
% 2.81/2.17 (~hskp21),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[2948, 2946, 344])).
% 2.81/2.17 tff(3425,plain,
% 2.81/2.17 (hskp11),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[2574, 3424])).
% 2.81/2.17 tff(3426,plain,
% 2.81/2.17 (~c2_1(a808)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[857, 3425])).
% 2.81/2.17 tff(3427,plain,
% 2.81/2.17 (c3_1(a808)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[896, 3425])).
% 2.81/2.17 tff(3428,plain,
% 2.81/2.17 (~c0_1(a808)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1533, 151, 344, 2946, 3427, 3426, 21])).
% 2.81/2.17 tff(3429,plain,
% 2.81/2.17 (c2_1(a867)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3059, 151, 344, 2946, 2911, 2909, 21])).
% 2.81/2.17 tff(3430,plain,
% 2.81/2.17 (~c1_1(a808)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[851, 3425])).
% 2.81/2.17 tff(3431,plain,
% 2.81/2.17 (hskp7 | c0_1(a808)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1524, 151, 2910, 2909, 3427, 3430, 1515, 3429])).
% 2.81/2.17 tff(3432,plain,
% 2.81/2.17 (hskp7),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3431, 3428])).
% 2.81/2.17 tff(3433,plain,
% 2.81/2.17 (~c2_1(a803)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1473, 3432])).
% 2.81/2.17 tff(3434,plain,
% 2.81/2.17 (hskp18),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3301, 3427, 3424, 3426])).
% 2.81/2.17 tff(3435,plain,
% 2.81/2.17 (~c3_1(a828)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1197, 3434])).
% 2.81/2.17 tff(3436,plain,
% 2.81/2.17 (~c2_1(a828)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1191, 3434])).
% 2.81/2.17 tff(3437,plain,
% 2.81/2.17 (~c1_1(a828)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1203, 3434])).
% 2.81/2.17 tff(3438,plain,
% 2.81/2.17 (c3_1(a803)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1484, 3432])).
% 2.81/2.17 tff(3439,plain,
% 2.81/2.17 (c1_1(a803)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1495, 3432])).
% 2.81/2.17 tff(3440,plain,
% 2.81/2.17 ($false),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1815, 151, 3421, 3439, 3438, 3437, 3436, 3435, 3433, 10])).
% 2.81/2.17 tff(3441,plain,(c1_1(a833) | c2_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.17 tff(3442,plain,
% 2.81/2.17 (c1_1(a833)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3441, 321, 309])).
% 2.81/2.17 tff(3443,plain,
% 2.81/2.17 (c2_1(a796)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[605, 3422])).
% 2.81/2.17 tff(3444,plain,
% 2.81/2.17 (c0_1(a796)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[616, 3422])).
% 2.81/2.17 tff(3445,plain,
% 2.81/2.17 (hskp18),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3301, 2578, 704, 2576])).
% 2.81/2.17 tff(3446,plain,
% 2.81/2.17 ($false),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3304, 3445, 2576, 309, 3421, 321, 3442, 2578])).
% 2.81/2.17 tff(3447,plain,(hskp21 | c2_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.17 tff(3448,plain,
% 2.81/2.17 (hskp21),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3447, 321, 309])).
% 2.81/2.17 tff(3449,plain,
% 2.81/2.17 (c3_1(a833)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3234, 3448, 3444, 309, 3443, 3442, 3423, 321])).
% 2.81/2.17 tff(3450,plain,
% 2.81/2.17 (c0_1(a838)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[454, 3448])).
% 2.81/2.17 tff(3451,plain,
% 2.81/2.17 (~c2_1(a838)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[431, 3448])).
% 2.81/2.17 tff(3452,plain,
% 2.81/2.17 (c3_1(a838)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[443, 3448])).
% 2.81/2.17 tff(3453,assumption,(c0_1(a797)), introduced(assumption)).
% 2.81/2.17 tff(3454,assumption,(hskp26), introduced(assumption)).
% 2.81/2.17 tff(3455,plain,
% 2.81/2.17 (~c0_1(a869)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[781, 3454])).
% 2.81/2.17 tff(3456,plain,
% 2.81/2.17 (c3_1(a869)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[730, 3454])).
% 2.81/2.17 tff(3457,plain,
% 2.81/2.17 (c2_1(a869)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[741, 3454])).
% 2.81/2.17 tff(3458,plain,
% 2.81/2.17 ($false),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3334, 151, 2567, 2538, 2527, 3457, 3456, 3455, 207, 3453])).
% 2.81/2.17 tff(3459,plain,((~hskp26) | (~c0_1(a797))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.17 tff(3460,plain,
% 2.81/2.17 (~hskp26),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3459, 3453])).
% 2.81/2.17 tff(3461,plain,
% 2.81/2.17 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a798) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c0_1(a798)) | (~c2_1(a798)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a798) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c0_1(a798)) | (~c2_1(a798)))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3462,plain,
% 2.81/2.17 ((hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a798) | (~c0_1(a798)) | (~c2_1(a798))) <=> (hskp5 | c3_1(a798) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c0_1(a798)) | (~c2_1(a798)))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3463,plain,
% 2.81/2.17 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a798) | (~c0_1(a798)) | (~c2_1(a798)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a798) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c0_1(a798)) | (~c2_1(a798))))),
% 2.81/2.17 inference(monotonicity,[status(thm)],[3462])).
% 2.81/2.17 tff(3464,plain,
% 2.81/2.17 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a798) | (~c0_1(a798)) | (~c2_1(a798)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a798) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c0_1(a798)) | (~c2_1(a798)))),
% 2.81/2.17 inference(transitivity,[status(thm)],[3463, 3461])).
% 2.81/2.17 tff(3465,plain,
% 2.81/2.17 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a798) | (~c0_1(a798)) | (~c2_1(a798)))),
% 2.81/2.17 inference(quant_inst,[status(thm)],[])).
% 2.81/2.17 tff(3466,plain,
% 2.81/2.17 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a798) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c0_1(a798)) | (~c2_1(a798))),
% 2.81/2.17 inference(modus_ponens,[status(thm)],[3465, 3464])).
% 2.81/2.17 tff(3467,plain,
% 2.81/2.17 (hskp5),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3466, 151, 2567, 2527, 3283, 3282, 3281, 217, 3453])).
% 2.81/2.17 tff(3468,plain,
% 2.81/2.17 (~c1_1(a800)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[263, 3467])).
% 2.81/2.17 tff(3469,plain,
% 2.81/2.17 (~c0_1(a800)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[229, 3467])).
% 2.81/2.17 tff(3470,plain,
% 2.81/2.17 (c3_1(a800)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[240, 3467])).
% 2.81/2.17 tff(3471,plain,
% 2.81/2.17 (hskp6),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3382, 151, 3442, 3470, 309, 3469, 3468, 1964, 3449])).
% 2.81/2.17 tff(3472,plain,
% 2.81/2.17 (~c0_1(a802)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1987, 3471])).
% 2.81/2.17 tff(3473,plain,
% 2.81/2.17 (c2_1(a802)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[1998, 3471])).
% 2.81/2.17 tff(3474,plain,
% 2.81/2.17 (~c3_1(a802)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[3391, 151, 2567, 2538, 2527, 3473, 3472, 207, 3453])).
% 2.81/2.17 tff(3475,plain,
% 2.81/2.17 (hskp12),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[2822, 151, 3473, 321, 309, 3472, 1079, 3449, 3474])).
% 2.81/2.17 tff(3476,plain,
% 2.81/2.17 (~c0_1(a809)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[164, 3475])).
% 2.81/2.17 tff(3477,plain,
% 2.81/2.17 (c2_1(a809)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[176, 3475])).
% 2.81/2.17 tff(3478,plain,
% 2.81/2.17 (c1_1(a809)),
% 2.81/2.17 inference(unit_resolution,[status(thm)],[187, 3475])).
% 2.81/2.17 tff(3479,plain,
% 2.81/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c0_1(a809) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c0_1(a809) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a833)))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3480,plain,
% 2.81/2.17 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | c0_1(a809) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a833)))),
% 2.81/2.17 inference(rewrite,[status(thm)],[])).
% 2.81/2.17 tff(3481,plain,
% 2.81/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c0_1(a809) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a833))))),
% 2.81/2.17 inference(monotonicity,[status(thm)],[3480])).
% 2.81/2.17 tff(3482,plain,
% 2.81/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c0_1(a809) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a833)))),
% 2.81/2.18 inference(transitivity,[status(thm)],[3481, 3479])).
% 2.81/2.18 tff(3483,plain,
% 2.81/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 2.81/2.18 inference(quant_inst,[status(thm)],[])).
% 2.81/2.18 tff(3484,plain,
% 2.81/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c0_1(a809) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a833))),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3483, 3482])).
% 2.81/2.18 tff(3485,plain,
% 2.81/2.18 ($false),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[3484, 151, 3478, 3477, 3283, 3282, 321, 309, 3476, 3281, 2635, 3449])).
% 2.81/2.18 tff(3486,plain,((~hskp3) | c0_1(a833) | c2_1(a833) | (~c0_1(a797))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.18 tff(3487,plain,
% 2.81/2.18 (~hskp3),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[3486, 3453, 309, 321])).
% 2.81/2.18 tff(3488,plain,
% 2.81/2.18 ((hskp26 | hskp9 | hskp3) <=> (hskp26 | hskp9 | hskp3)),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3489,plain,
% 2.81/2.18 (((hskp9 | hskp3) | hskp26) <=> (hskp26 | hskp9 | hskp3)),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3490,plain,
% 2.81/2.18 ((hskp9 | hskp3) <=> (hskp9 | hskp3)),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3491,plain,
% 2.81/2.18 (((hskp9 | hskp3) | hskp26) <=> ((hskp9 | hskp3) | hskp26)),
% 2.81/2.18 inference(monotonicity,[status(thm)],[3490])).
% 2.81/2.18 tff(3492,plain,
% 2.81/2.18 (((hskp9 | hskp3) | hskp26) <=> (hskp26 | hskp9 | hskp3)),
% 2.81/2.18 inference(transitivity,[status(thm)],[3491, 3489])).
% 2.81/2.18 tff(3493,axiom,((hskp9 | hskp3) | hskp26), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 2.81/2.18 tff(3494,plain,
% 2.81/2.18 (hskp26 | hskp9 | hskp3),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3493, 3492])).
% 2.81/2.18 tff(3495,plain,
% 2.81/2.18 (hskp26 | hskp9 | hskp3),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3494, 3488])).
% 2.81/2.18 tff(3496,plain,
% 2.81/2.18 (hskp26 | hskp9 | hskp3),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3495, 3488])).
% 2.81/2.18 tff(3497,plain,
% 2.81/2.18 (hskp26 | hskp9 | hskp3),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3496, 3488])).
% 2.81/2.18 tff(3498,plain,
% 2.81/2.18 (hskp26 | hskp9 | hskp3),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3497, 3488])).
% 2.81/2.18 tff(3499,plain,
% 2.81/2.18 (hskp26 | hskp9 | hskp3),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3498, 3488])).
% 2.81/2.18 tff(3500,plain,
% 2.81/2.18 (hskp26 | hskp9 | hskp3),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3499, 3488])).
% 2.81/2.18 tff(3501,plain,
% 2.81/2.18 (hskp26 | hskp9 | hskp3),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3500, 3488])).
% 2.81/2.18 tff(3502,plain,
% 2.81/2.18 (hskp9),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[3501, 3487, 3460])).
% 2.81/2.18 tff(3503,plain,
% 2.81/2.18 (~c3_1(a806)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[75, 3502])).
% 2.81/2.18 tff(3504,plain,
% 2.81/2.18 (c1_1(a806)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[87, 3502])).
% 2.81/2.18 tff(3505,plain,
% 2.81/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3506,plain,
% 2.81/2.18 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3507,plain,
% 2.81/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.81/2.18 inference(monotonicity,[status(thm)],[3506])).
% 2.81/2.18 tff(3508,plain,
% 2.81/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.18 inference(transitivity,[status(thm)],[3507, 3505])).
% 2.81/2.18 tff(3509,plain,
% 2.81/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 2.81/2.18 inference(quant_inst,[status(thm)],[])).
% 2.81/2.18 tff(3510,plain,
% 2.81/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3509, 3508])).
% 2.81/2.18 tff(3511,plain,
% 2.81/2.18 (~c2_1(a806)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[3510, 151, 3442, 3504, 321, 309, 3503, 2078, 3449])).
% 2.81/2.18 tff(3512,plain,
% 2.81/2.18 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c2_1(a806) | (~c1_1(a806)))),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3513,plain,
% 2.81/2.18 ((hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806))) <=> (hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c2_1(a806) | (~c1_1(a806)))),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3514,plain,
% 2.81/2.18 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c2_1(a806) | (~c1_1(a806))))),
% 2.81/2.18 inference(monotonicity,[status(thm)],[3513])).
% 2.81/2.18 tff(3515,plain,
% 2.81/2.18 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c2_1(a806) | (~c1_1(a806)))),
% 2.81/2.18 inference(transitivity,[status(thm)],[3514, 3512])).
% 2.81/2.18 tff(3516,plain,
% 2.81/2.18 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))),
% 2.81/2.18 inference(quant_inst,[status(thm)],[])).
% 2.81/2.18 tff(3517,plain,
% 2.81/2.18 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c2_1(a806) | (~c1_1(a806))),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3516, 3515])).
% 2.81/2.18 tff(3518,plain,
% 2.81/2.18 (hskp12),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[3517, 151, 2567, 2527, 3504, 3503, 110, 3511, 3453])).
% 2.81/2.18 tff(3519,plain,
% 2.81/2.18 (~c0_1(a809)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[164, 3518])).
% 2.81/2.18 tff(3520,plain,
% 2.81/2.18 (c0_1(a806)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[67, 3502])).
% 2.81/2.18 tff(3521,plain,
% 2.81/2.18 (c2_1(a809)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[176, 3518])).
% 2.81/2.18 tff(3522,plain,
% 2.81/2.18 (c1_1(a809)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[187, 3518])).
% 2.81/2.18 tff(3523,plain,
% 2.81/2.18 ($false),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[194, 151, 3522, 3521, 3520, 3504, 3519, 3503, 99, 3511])).
% 2.81/2.18 tff(3524,plain,((~c0_1(a797)) | c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.18 tff(3525,plain,
% 2.81/2.18 (~c0_1(a797)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[3524, 321, 309])).
% 2.81/2.18 tff(3526,assumption,(hskp6), introduced(assumption)).
% 2.81/2.18 tff(3527,plain,
% 2.81/2.18 (~c1_1(a802)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[2828, 3526])).
% 2.81/2.18 tff(3528,plain,
% 2.81/2.18 (~c0_1(a802)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[1987, 3526])).
% 2.81/2.18 tff(3529,plain,
% 2.81/2.18 (c2_1(a802)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[1998, 3526])).
% 2.81/2.18 tff(3530,plain,
% 2.81/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a802) | c1_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c3_1(a802) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a802) | c1_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c3_1(a802) | (~c2_1(a802)))),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3531,plain,
% 2.81/2.18 (((~ndr1_0) | c1_1(a802) | c3_1(a802) | (~c2_1(a802)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a802) | c0_1(a802) | c3_1(a802)) <=> (c0_1(a802) | c1_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c3_1(a802) | (~c2_1(a802)))),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3532,plain,
% 2.81/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a802) | c3_1(a802) | (~c2_1(a802)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a802) | c0_1(a802) | c3_1(a802))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a802) | c1_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c3_1(a802) | (~c2_1(a802))))),
% 2.81/2.18 inference(monotonicity,[status(thm)],[3531])).
% 2.81/2.18 tff(3533,plain,
% 2.81/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a802) | c3_1(a802) | (~c2_1(a802)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a802) | c0_1(a802) | c3_1(a802))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a802) | c1_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c3_1(a802) | (~c2_1(a802)))),
% 2.81/2.18 inference(transitivity,[status(thm)],[3532, 3530])).
% 2.81/2.18 tff(3534,plain,
% 2.81/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a802) | c3_1(a802) | (~c2_1(a802)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a802) | c0_1(a802) | c3_1(a802))),
% 2.81/2.18 inference(quant_inst,[status(thm)],[])).
% 2.81/2.18 tff(3535,plain,
% 2.81/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a802) | c1_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c3_1(a802) | (~c2_1(a802))),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 2.81/2.18 tff(3536,plain,
% 2.81/2.18 (c3_1(a802)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[3535, 151, 2567, 2538, 3529, 3528, 3527, 1067, 3255])).
% 2.81/2.18 tff(3537,plain,
% 2.81/2.18 (hskp8),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[2838, 151, 639, 3529, 321, 3527, 768, 750, 3536])).
% 2.81/2.18 tff(3538,plain,
% 2.81/2.18 (~c3_1(a805)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[462, 3537])).
% 2.81/2.18 tff(3539,plain,
% 2.81/2.18 (~c2_1(a805)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[468, 3537])).
% 2.81/2.18 tff(3540,plain,
% 2.81/2.18 (c1_1(a805)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[480, 3537])).
% 2.81/2.18 tff(3541,plain,
% 2.81/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a805)) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a805)) | (~c1_1(a805)))),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3542,plain,
% 2.81/2.18 (((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797))) <=> (c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a805)) | (~c1_1(a805)))),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3543,plain,
% 2.81/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a805)) | (~c1_1(a805))))),
% 2.81/2.18 inference(monotonicity,[status(thm)],[3542])).
% 2.81/2.18 tff(3544,plain,
% 2.81/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a805)) | (~c1_1(a805)))),
% 2.81/2.18 inference(transitivity,[status(thm)],[3543, 3541])).
% 2.81/2.18 tff(3545,plain,
% 2.81/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))),
% 2.81/2.18 inference(quant_inst,[status(thm)],[])).
% 2.81/2.18 tff(3546,plain,
% 2.81/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a805)) | (~c1_1(a805))),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3545, 3544])).
% 2.81/2.18 tff(3547,plain,
% 2.81/2.18 (~c0_1(a805)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[3546, 151, 2567, 2538, 3540, 3539, 3538, 99, 3255])).
% 2.81/2.18 tff(3548,plain,
% 2.81/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a805) | c1_1(a802) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | c1_1(a802) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | (~c1_1(a805)))),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3549,plain,
% 2.81/2.18 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c3_1(a805) | c1_1(a802) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | (~c1_1(a805)))),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3550,plain,
% 2.81/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a805) | c1_1(a802) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | (~c1_1(a805))))),
% 2.81/2.18 inference(monotonicity,[status(thm)],[3549])).
% 2.81/2.18 tff(3551,plain,
% 2.81/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | c1_1(a802) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | (~c1_1(a805)))),
% 2.81/2.18 inference(transitivity,[status(thm)],[3550, 3548])).
% 2.81/2.18 tff(3552,plain,
% 2.81/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 2.81/2.18 inference(quant_inst,[status(thm)],[])).
% 2.81/2.18 tff(3553,plain,
% 2.81/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | c1_1(a802) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | (~c1_1(a805))),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3552, 3551])).
% 2.81/2.18 tff(3554,plain,
% 2.81/2.18 ($false),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[3553, 151, 690, 688, 693, 3540, 3529, 3538, 3527, 800, 3536, 3547])).
% 2.81/2.18 tff(3555,plain,((~hskp6) | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796)) | c0_1(a797) | (~c1_1(a833)) | c0_1(a833) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.18 tff(3556,plain,
% 2.81/2.18 (~hskp6),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[3555, 3525, 3443, 3423, 3444, 3442, 321, 3449])).
% 2.81/2.18 tff(3557,plain,
% 2.81/2.18 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a833) | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3558,plain,
% 2.81/2.18 ((hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a832) | c0_1(a832) | (~c3_1(a832))) <=> (hskp6 | c2_1(a833) | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3559,plain,
% 2.81/2.18 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a832) | c0_1(a832) | (~c3_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a833) | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.81/2.18 inference(monotonicity,[status(thm)],[3558])).
% 2.81/2.18 tff(3560,plain,
% 2.81/2.18 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a832) | c0_1(a832) | (~c3_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.18 inference(transitivity,[status(thm)],[3559, 3557])).
% 2.81/2.18 tff(3561,plain,
% 2.81/2.18 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a832) | c0_1(a832) | (~c3_1(a832)))),
% 2.81/2.18 inference(quant_inst,[status(thm)],[])).
% 2.81/2.18 tff(3562,plain,
% 2.81/2.18 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.81/2.18 inference(modus_ponens,[status(thm)],[3561, 3560])).
% 2.81/2.18 tff(3563,plain,
% 2.81/2.18 (c0_1(a832)),
% 2.81/2.18 inference(unit_resolution,[status(thm)],[3562, 151, 3556, 3442, 309, 322, 3420, 1964, 3449])).
% 2.81/2.18 tff(3564,plain,
% 2.81/2.18 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 2.81/2.18 inference(bind,[status(th)],[])).
% 2.81/2.18 tff(3565,plain,
% 2.81/2.18 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.81/2.18 inference(quant_intro,[status(thm)],[3564])).
% 2.81/2.18 tff(3566,plain,
% 2.81/2.18 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.81/2.18 inference(rewrite,[status(thm)],[])).
% 2.81/2.18 tff(3567,plain,
% 2.81/2.18 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 2.81/2.19 inference(bind,[status(th)],[])).
% 2.81/2.19 tff(3568,plain,
% 2.81/2.19 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.81/2.19 inference(quant_intro,[status(thm)],[3567])).
% 2.81/2.19 tff(3569,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 2.81/2.19 tff(3570,plain,
% 2.81/2.19 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3569, 3568])).
% 2.81/2.19 tff(3571,plain,
% 2.81/2.19 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3570, 3566])).
% 2.81/2.19 tff(3572,plain,(
% 2.81/2.19 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.81/2.19 inference(skolemize,[status(sab)],[3571])).
% 2.81/2.19 tff(3573,plain,
% 2.81/2.19 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3572, 3565])).
% 2.81/2.19 tff(3574,assumption,(c3_1(a832)), introduced(assumption)).
% 2.81/2.19 tff(3575,assumption,(~hskp13), introduced(assumption)).
% 2.81/2.19 tff(3576,plain,
% 2.81/2.19 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3577,plain,
% 2.81/2.19 ((hskp13 | (~ndr1_0) | c1_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797))) <=> (hskp13 | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3578,plain,
% 2.81/2.19 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832))))),
% 2.81/2.19 inference(monotonicity,[status(thm)],[3577])).
% 2.81/2.19 tff(3579,plain,
% 2.81/2.19 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))),
% 2.81/2.19 inference(transitivity,[status(thm)],[3578, 3576])).
% 2.81/2.19 tff(3580,plain,
% 2.81/2.19 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)))),
% 2.81/2.19 inference(quant_inst,[status(thm)],[])).
% 2.81/2.19 tff(3581,plain,
% 2.81/2.19 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832))),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3580, 3579])).
% 2.81/2.19 tff(3582,plain,
% 2.81/2.19 ($false),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3581, 151, 3575, 2567, 2538, 322, 3574, 3573, 456, 3255])).
% 2.81/2.19 tff(3583,plain,(c0_1(a797) | hskp13 | c1_1(a832) | (~c3_1(a832)) | (~c0_1(a832))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.19 tff(3584,plain,
% 2.81/2.19 (hskp13),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3583, 3563, 3525, 3420, 322])).
% 2.81/2.19 tff(3585,plain,
% 2.81/2.19 (((~hskp13) | (~c3_1(a814))) <=> ((~hskp13) | (~c3_1(a814)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3586,plain,
% 2.81/2.19 (((~c3_1(a814)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a814)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3587,axiom,((~c3_1(a814)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 2.81/2.19 tff(3588,plain,
% 2.81/2.19 ((~hskp13) | (~c3_1(a814))),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3587, 3586])).
% 2.81/2.19 tff(3589,plain,
% 2.81/2.19 ((~hskp13) | (~c3_1(a814))),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3588, 3585])).
% 2.81/2.19 tff(3590,plain,
% 2.81/2.19 (~c3_1(a814)),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3589, 3584])).
% 2.81/2.19 tff(3591,plain,
% 2.81/2.19 (((~hskp13) | (~c0_1(a814))) <=> ((~hskp13) | (~c0_1(a814)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3592,plain,
% 2.81/2.19 (((~c0_1(a814)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a814)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3593,axiom,((~c0_1(a814)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 2.81/2.19 tff(3594,plain,
% 2.81/2.19 ((~hskp13) | (~c0_1(a814))),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3593, 3592])).
% 2.81/2.19 tff(3595,plain,
% 2.81/2.19 ((~hskp13) | (~c0_1(a814))),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3594, 3591])).
% 2.81/2.19 tff(3596,plain,
% 2.81/2.19 (~c0_1(a814)),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3595, 3584])).
% 2.81/2.19 tff(3597,plain,
% 2.81/2.19 (((~hskp13) | c1_1(a814)) <=> ((~hskp13) | c1_1(a814))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3598,axiom,((~hskp13) | c1_1(a814)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 2.81/2.19 tff(3599,plain,
% 2.81/2.19 ((~hskp13) | c1_1(a814)),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3598, 3597])).
% 2.81/2.19 tff(3600,plain,
% 2.81/2.19 ((~hskp13) | c1_1(a814)),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3599, 3597])).
% 2.81/2.19 tff(3601,plain,
% 2.81/2.19 ((~hskp13) | c1_1(a814)),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3600, 3597])).
% 2.81/2.19 tff(3602,plain,
% 2.81/2.19 ((~hskp13) | c1_1(a814)),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3601, 3597])).
% 2.81/2.19 tff(3603,plain,
% 2.81/2.19 ((~hskp13) | c1_1(a814)),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3602, 3597])).
% 2.81/2.19 tff(3604,plain,
% 2.81/2.19 ((~hskp13) | c1_1(a814)),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3603, 3597])).
% 2.81/2.19 tff(3605,plain,
% 2.81/2.19 ((~hskp13) | c1_1(a814)),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3604, 3597])).
% 2.81/2.19 tff(3606,plain,
% 2.81/2.19 ((~hskp13) | c1_1(a814)),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3605, 3597])).
% 2.81/2.19 tff(3607,plain,
% 2.81/2.19 (c1_1(a814)),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3606, 3584])).
% 2.81/2.19 tff(3608,assumption,(hskp13), introduced(assumption)).
% 2.81/2.19 tff(3609,plain,
% 2.81/2.19 (~c3_1(a814)),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3589, 3608])).
% 2.81/2.19 tff(3610,plain,
% 2.81/2.19 (c1_1(a814)),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3606, 3608])).
% 2.81/2.19 tff(3611,plain,
% 2.81/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3612,plain,
% 2.81/2.19 (((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3613,plain,
% 2.81/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.81/2.19 inference(monotonicity,[status(thm)],[3612])).
% 2.81/2.19 tff(3614,plain,
% 2.81/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.81/2.19 inference(transitivity,[status(thm)],[3613, 3611])).
% 2.81/2.19 tff(3615,plain,
% 2.81/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 2.81/2.19 inference(quant_inst,[status(thm)],[])).
% 2.81/2.19 tff(3616,plain,
% 2.81/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3615, 3614])).
% 2.81/2.19 tff(3617,plain,
% 2.81/2.19 (~c2_1(a814)),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3616, 151, 3442, 3610, 321, 309, 3609, 2078, 3449])).
% 2.81/2.19 tff(3618,plain,
% 2.81/2.19 (~c0_1(a814)),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3595, 3608])).
% 2.81/2.19 tff(3619,plain,
% 2.81/2.19 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a814) | c3_1(a814) | (~ndr1_0) | c2_1(a814) | (~c1_1(a814)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a814) | c3_1(a814) | (~ndr1_0) | c2_1(a814) | (~c1_1(a814)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3620,plain,
% 2.81/2.19 ((hskp3 | (~ndr1_0) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)) | c3_1(a814) | c0_1(a814) | (~c1_1(a814))) <=> (hskp3 | c0_1(a814) | c3_1(a814) | (~ndr1_0) | c2_1(a814) | (~c1_1(a814)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3621,plain,
% 2.81/2.19 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)) | c3_1(a814) | c0_1(a814) | (~c1_1(a814)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a814) | c3_1(a814) | (~ndr1_0) | c2_1(a814) | (~c1_1(a814))))),
% 2.81/2.19 inference(monotonicity,[status(thm)],[3620])).
% 2.81/2.19 tff(3622,plain,
% 2.81/2.19 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)) | c3_1(a814) | c0_1(a814) | (~c1_1(a814)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a814) | c3_1(a814) | (~ndr1_0) | c2_1(a814) | (~c1_1(a814)))),
% 2.81/2.19 inference(transitivity,[status(thm)],[3621, 3619])).
% 2.81/2.19 tff(3623,plain,
% 2.81/2.19 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)) | c3_1(a814) | c0_1(a814) | (~c1_1(a814)))),
% 2.81/2.19 inference(quant_inst,[status(thm)],[])).
% 2.81/2.19 tff(3624,plain,
% 2.81/2.19 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a814) | c3_1(a814) | (~ndr1_0) | c2_1(a814) | (~c1_1(a814))),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3623, 3622])).
% 2.81/2.19 tff(3625,plain,
% 2.81/2.19 (hskp3),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3624, 151, 3610, 3618, 3609, 2646, 3617])).
% 2.81/2.19 tff(3626,plain,
% 2.81/2.19 (~c3_1(a798)),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[546, 3625])).
% 2.81/2.19 tff(3627,plain,
% 2.81/2.19 (c2_1(a798)),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[563, 3625])).
% 2.81/2.19 tff(3628,plain,
% 2.81/2.19 (c0_1(a798)),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[574, 3625])).
% 2.81/2.19 tff(3629,plain,
% 2.81/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a832) | (~c3_1(a832)) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | (~c3_1(a832)) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c0_1(a832)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3630,plain,
% 2.81/2.19 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814))) <=> (c2_1(a832) | (~c3_1(a832)) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c0_1(a832)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3631,plain,
% 2.81/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a832) | (~c3_1(a832)) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c0_1(a832))))),
% 2.81/2.19 inference(monotonicity,[status(thm)],[3630])).
% 2.81/2.19 tff(3632,plain,
% 2.81/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | (~c3_1(a832)) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c0_1(a832)))),
% 2.81/2.19 inference(transitivity,[status(thm)],[3631, 3629])).
% 2.81/2.19 tff(3633,plain,
% 2.81/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)))),
% 2.81/2.19 inference(quant_inst,[status(thm)],[])).
% 2.81/2.19 tff(3634,plain,
% 2.81/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | (~c3_1(a832)) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c0_1(a832))),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3633, 3632])).
% 2.81/2.19 tff(3635,plain,
% 2.81/2.19 ($false),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3634, 151, 1458, 3610, 3628, 3627, 3420, 3609, 3626, 332, 456, 3617])).
% 2.81/2.19 tff(3636,plain,((~hskp13) | c2_1(a832) | (~c0_1(a832)) | c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.19 tff(3637,plain,
% 2.81/2.19 (c2_1(a832)),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3636, 3584, 3563, 321, 309])).
% 2.81/2.19 tff(3638,plain,
% 2.81/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a832) | (~c3_1(a832)) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a814)) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a832) | (~c3_1(a832)) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a814)) | (~c2_1(a832)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3639,plain,
% 2.81/2.19 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a832) | (~c3_1(a832)) | (~c2_1(a832)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814))) <=> (c1_1(a832) | (~c3_1(a832)) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a814)) | (~c2_1(a832)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3640,plain,
% 2.81/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a832) | (~c3_1(a832)) | (~c2_1(a832)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a832) | (~c3_1(a832)) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a814)) | (~c2_1(a832))))),
% 2.81/2.19 inference(monotonicity,[status(thm)],[3639])).
% 2.81/2.19 tff(3641,plain,
% 2.81/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a832) | (~c3_1(a832)) | (~c2_1(a832)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a832) | (~c3_1(a832)) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a814)) | (~c2_1(a832)))),
% 2.81/2.19 inference(transitivity,[status(thm)],[3640, 3638])).
% 2.81/2.19 tff(3642,plain,
% 2.81/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a832) | (~c3_1(a832)) | (~c2_1(a832)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814)))),
% 2.81/2.19 inference(quant_inst,[status(thm)],[])).
% 2.81/2.19 tff(3643,plain,
% 2.81/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a832) | (~c3_1(a832)) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a814)) | (~c2_1(a832))),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3642, 3641])).
% 2.81/2.19 tff(3644,plain,
% 2.81/2.19 ($false),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3643, 151, 3444, 3443, 3423, 3637, 3607, 322, 3420, 3596, 3590, 800])).
% 2.81/2.19 tff(3645,plain,(c1_1(a832) | c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.81/2.19 tff(3646,plain,
% 2.81/2.19 (c1_1(a832)),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3645, 321, 309])).
% 2.81/2.19 tff(3647,plain,
% 2.81/2.19 (~hskp19),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[385, 3574])).
% 2.81/2.19 tff(3648,plain,
% 2.81/2.19 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3649,plain,
% 2.81/2.19 ((hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3650,plain,
% 2.81/2.19 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0)))),
% 2.81/2.19 inference(monotonicity,[status(thm)],[3649])).
% 2.81/2.19 tff(3651,plain,
% 2.81/2.19 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))),
% 2.81/2.19 inference(transitivity,[status(thm)],[3650, 3648])).
% 2.81/2.19 tff(3652,plain,
% 2.81/2.19 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 2.81/2.19 inference(quant_inst,[status(thm)],[])).
% 2.81/2.19 tff(3653,plain,
% 2.81/2.19 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0)),
% 2.81/2.19 inference(modus_ponens,[status(thm)],[3652, 3651])).
% 2.81/2.19 tff(3654,plain,
% 2.81/2.19 ($false),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3653, 151, 3647, 1458, 3254, 3574, 2370, 2369, 2368, 10])).
% 2.81/2.19 tff(3655,plain,((~hskp18) | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832))), inference(lemma,lemma(discharge,[]))).
% 2.81/2.19 tff(3656,plain,
% 2.81/2.19 (~hskp18),
% 2.81/2.19 inference(unit_resolution,[status(thm)],[3655, 1458, 3646, 3420])).
% 2.81/2.19 tff(3657,plain,
% 2.81/2.19 (^[U: $i] : refl((hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 2.81/2.19 inference(bind,[status(th)],[])).
% 2.81/2.19 tff(3658,plain,
% 2.81/2.19 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.81/2.19 inference(quant_intro,[status(thm)],[3657])).
% 2.81/2.19 tff(3659,plain,
% 2.81/2.19 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.81/2.19 inference(rewrite,[status(thm)],[])).
% 2.81/2.19 tff(3660,plain,
% 2.81/2.19 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp18) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp18) <=> (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 2.89/2.20 inference(bind,[status(th)],[])).
% 2.89/2.20 tff(3661,plain,
% 2.89/2.20 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp18) <=> ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.89/2.20 inference(quant_intro,[status(thm)],[3660])).
% 2.89/2.20 tff(3662,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 2.89/2.20 tff(3663,plain,
% 2.89/2.20 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.89/2.20 inference(modus_ponens,[status(thm)],[3662, 3661])).
% 2.89/2.20 tff(3664,plain,
% 2.89/2.20 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.89/2.20 inference(modus_ponens,[status(thm)],[3663, 3659])).
% 2.89/2.20 tff(3665,plain,(
% 2.89/2.20 ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.89/2.20 inference(skolemize,[status(sab)],[3664])).
% 2.89/2.20 tff(3666,plain,
% 2.89/2.20 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.89/2.20 inference(modus_ponens,[status(thm)],[3665, 3658])).
% 2.89/2.20 tff(3667,plain,
% 2.89/2.20 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3668,plain,
% 2.89/2.20 ((hskp18 | hskp14 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833))) <=> (hskp18 | hskp14 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3669,plain,
% 2.89/2.20 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.89/2.20 inference(monotonicity,[status(thm)],[3668])).
% 2.89/2.20 tff(3670,plain,
% 2.89/2.20 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.20 inference(transitivity,[status(thm)],[3669, 3667])).
% 2.89/2.20 tff(3671,plain,
% 2.89/2.20 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.20 inference(quant_inst,[status(thm)],[])).
% 2.89/2.20 tff(3672,plain,
% 2.89/2.20 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.89/2.20 inference(modus_ponens,[status(thm)],[3671, 3670])).
% 2.89/2.20 tff(3673,plain,
% 2.89/2.20 (hskp18 | hskp14 | (~c3_1(a833)) | (~c1_1(a833))),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3672, 151, 321, 3666])).
% 2.89/2.20 tff(3674,plain,
% 2.89/2.20 (hskp14),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3673, 3656, 3442, 3449])).
% 2.89/2.20 tff(3675,assumption,(hskp14), introduced(assumption)).
% 2.89/2.20 tff(3676,plain,
% 2.89/2.20 (~c1_1(a816)),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3134, 3675])).
% 2.89/2.20 tff(3677,plain,
% 2.89/2.20 (~c2_1(a816)),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3158, 3675])).
% 2.89/2.20 tff(3678,assumption,(~c3_1(a816)), introduced(assumption)).
% 2.89/2.20 tff(3679,assumption,(~c2_1(a816)), introduced(assumption)).
% 2.89/2.20 tff(3680,assumption,(~c1_1(a816)), introduced(assumption)).
% 2.89/2.20 tff(3681,plain,
% 2.89/2.20 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3682,plain,
% 2.89/2.20 ((hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a816) | c2_1(a816) | c1_1(a816)) <=> (hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3683,plain,
% 2.89/2.20 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a816) | c2_1(a816) | c1_1(a816))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816)))),
% 2.89/2.20 inference(monotonicity,[status(thm)],[3682])).
% 2.89/2.20 tff(3684,plain,
% 2.89/2.20 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a816) | c2_1(a816) | c1_1(a816))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816))),
% 2.89/2.20 inference(transitivity,[status(thm)],[3683, 3681])).
% 2.89/2.20 tff(3685,plain,
% 2.89/2.20 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a816) | c2_1(a816) | c1_1(a816))),
% 2.89/2.20 inference(quant_inst,[status(thm)],[])).
% 2.89/2.20 tff(3686,plain,
% 2.89/2.20 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816)),
% 2.89/2.20 inference(modus_ponens,[status(thm)],[3685, 3684])).
% 2.89/2.20 tff(3687,plain,
% 2.89/2.20 ($false),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3686, 151, 3647, 1458, 3254, 3574, 3680, 3679, 10, 3678])).
% 2.89/2.20 tff(3688,plain,(c3_1(a816) | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.20 tff(3689,plain,
% 2.89/2.20 (c3_1(a816)),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3688, 3677, 3254, 3574, 3676, 1458])).
% 2.89/2.20 tff(3690,plain,
% 2.89/2.20 (c0_1(a816)),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3145, 3675])).
% 2.89/2.20 tff(3691,plain,
% 2.89/2.20 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | c1_1(a816) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | c1_1(a816) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a816)) | (~c0_1(a816)))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3692,plain,
% 2.89/2.20 ((hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797))) <=> (hskp13 | c1_1(a816) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a816)) | (~c0_1(a816)))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3693,plain,
% 2.89/2.20 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | c1_1(a816) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a816)) | (~c0_1(a816))))),
% 2.89/2.20 inference(monotonicity,[status(thm)],[3692])).
% 2.89/2.20 tff(3694,plain,
% 2.89/2.20 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | c1_1(a816) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a816)) | (~c0_1(a816)))),
% 2.89/2.20 inference(transitivity,[status(thm)],[3693, 3691])).
% 2.89/2.20 tff(3695,plain,
% 2.89/2.20 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)))),
% 2.89/2.20 inference(quant_inst,[status(thm)],[])).
% 2.89/2.20 tff(3696,plain,
% 2.89/2.20 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | c1_1(a816) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a816)) | (~c0_1(a816))),
% 2.89/2.20 inference(modus_ponens,[status(thm)],[3695, 3694])).
% 2.89/2.20 tff(3697,plain,
% 2.89/2.20 ($false),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3696, 151, 3575, 2567, 2538, 3690, 3676, 3573, 3255, 3689])).
% 2.89/2.20 tff(3698,plain,((~hskp14) | hskp13 | c0_1(a797) | (~c1_1(a832)) | (~c3_1(a832)) | c2_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.20 tff(3699,plain,
% 2.89/2.20 (hskp13),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3698, 3674, 3525, 3646, 3420, 1458])).
% 2.89/2.20 tff(3700,plain,
% 2.89/2.20 (~c0_1(a832)),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3636, 3699, 1458, 321, 309])).
% 2.89/2.20 tff(3701,plain,
% 2.89/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3702,plain,
% 2.89/2.20 (((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a832) | c0_1(a832) | (~c3_1(a832))) <=> (c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3703,plain,
% 2.89/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a832) | c0_1(a832) | (~c3_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.89/2.20 inference(monotonicity,[status(thm)],[3702])).
% 2.89/2.20 tff(3704,plain,
% 2.89/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a832) | c0_1(a832) | (~c3_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.20 inference(transitivity,[status(thm)],[3703, 3701])).
% 2.89/2.20 tff(3705,plain,
% 2.89/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a832) | c0_1(a832) | (~c3_1(a832)))),
% 2.89/2.20 inference(quant_inst,[status(thm)],[])).
% 2.89/2.20 tff(3706,plain,
% 2.89/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.89/2.20 inference(modus_ponens,[status(thm)],[3705, 3704])).
% 2.89/2.20 tff(3707,plain,
% 2.89/2.20 (~c2_1(a814)),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3706, 151, 639, 1458, 3610, 321, 3574, 3609, 2078, 1069, 750])).
% 2.89/2.20 tff(3708,plain,
% 2.89/2.20 (hskp3),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3624, 151, 3610, 3618, 3609, 2646, 3707])).
% 2.89/2.20 tff(3709,plain,
% 2.89/2.20 (~c3_1(a798)),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[546, 3708])).
% 2.89/2.20 tff(3710,plain,
% 2.89/2.20 (c2_1(a798)),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[563, 3708])).
% 2.89/2.20 tff(3711,plain,
% 2.89/2.20 (c0_1(a798)),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[574, 3708])).
% 2.89/2.20 tff(3712,plain,
% 2.89/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3713,plain,
% 2.89/2.20 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814))) <=> (c2_1(a838) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3714,plain,
% 2.89/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 2.89/2.20 inference(monotonicity,[status(thm)],[3713])).
% 2.89/2.20 tff(3715,plain,
% 2.89/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 2.89/2.20 inference(transitivity,[status(thm)],[3714, 3712])).
% 2.89/2.20 tff(3716,plain,
% 2.89/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)))),
% 2.89/2.20 inference(quant_inst,[status(thm)],[])).
% 2.89/2.20 tff(3717,plain,
% 2.89/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c3_1(a838)) | (~c0_1(a838))),
% 2.89/2.20 inference(modus_ponens,[status(thm)],[3716, 3715])).
% 2.89/2.20 tff(3718,plain,
% 2.89/2.20 ($false),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3717, 151, 483, 482, 3610, 3711, 3710, 470, 3609, 3709, 332, 3707])).
% 2.89/2.20 tff(3719,plain,((~hskp13) | (~c0_1(a838)) | (~c3_1(a838)) | c2_1(a838) | (~c1_1(a833)) | c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c0_1(a832) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 2.89/2.20 tff(3720,plain,
% 2.89/2.20 ($false),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3719, 3700, 3699, 3452, 3451, 3442, 1458, 321, 3420, 3450, 3449])).
% 2.89/2.20 tff(3721,plain,(c2_1(a832) | c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.20 tff(3722,plain,
% 2.89/2.20 (c2_1(a832)),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3721, 321, 309])).
% 2.89/2.20 tff(3723,plain,
% 2.89/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~c1_1(a832)) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~c1_1(a832)) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3724,plain,
% 2.89/2.20 (((~ndr1_0) | (~c3_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c2_1(a832)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797))) <=> ((~c1_1(a832)) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3725,plain,
% 2.89/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c2_1(a832)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~c1_1(a832)) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832))))),
% 2.89/2.20 inference(monotonicity,[status(thm)],[3724])).
% 2.89/2.20 tff(3726,plain,
% 2.89/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c2_1(a832)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~c1_1(a832)) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.89/2.20 inference(transitivity,[status(thm)],[3725, 3723])).
% 2.89/2.20 tff(3727,plain,
% 2.89/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c2_1(a832)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797)))),
% 2.89/2.20 inference(quant_inst,[status(thm)],[])).
% 2.89/2.20 tff(3728,plain,
% 2.89/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~c1_1(a832)) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832))),
% 2.89/2.20 inference(modus_ponens,[status(thm)],[3727, 3726])).
% 2.89/2.20 tff(3729,plain,
% 2.89/2.20 ((~c2_1(a832)) | (~c0_1(a832))),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3728, 151, 2538, 2527, 3646, 3420, 207, 3525])).
% 2.89/2.20 tff(3730,plain,
% 2.89/2.20 (~c0_1(a832)),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3729, 3722])).
% 2.89/2.20 tff(3731,plain,
% 2.89/2.20 ($false),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[2201, 151, 1603, 639, 309, 2370, 2369, 2368, 10, 750])).
% 2.89/2.20 tff(3732,plain,((~hskp18) | hskp19 | (~c1_1(a833)) | c2_1(a833) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 2.89/2.20 tff(3733,plain,
% 2.89/2.20 (~hskp18),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3732, 3421, 3442, 309, 3449])).
% 2.89/2.20 tff(3734,plain,
% 2.89/2.20 (hskp14),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3673, 3733, 3442, 3449])).
% 2.89/2.20 tff(3735,plain,
% 2.89/2.20 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~c1_1(a832)) | c1_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | (~c1_1(a832)) | c1_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c2_1(a832)) | c0_1(a832))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3736,plain,
% 2.89/2.20 ((hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a832) | (~c1_1(a832)) | (~c2_1(a832))) <=> (hskp13 | (~c1_1(a832)) | c1_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c2_1(a832)) | c0_1(a832))),
% 2.89/2.20 inference(rewrite,[status(thm)],[])).
% 2.89/2.20 tff(3737,plain,
% 2.89/2.20 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a832) | (~c1_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~c1_1(a832)) | c1_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c2_1(a832)) | c0_1(a832)))),
% 2.89/2.20 inference(monotonicity,[status(thm)],[3736])).
% 2.89/2.20 tff(3738,plain,
% 2.89/2.20 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a832) | (~c1_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | (~c1_1(a832)) | c1_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c2_1(a832)) | c0_1(a832))),
% 2.89/2.20 inference(transitivity,[status(thm)],[3737, 3735])).
% 2.89/2.20 tff(3739,plain,
% 2.89/2.20 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a832) | (~c1_1(a832)) | (~c2_1(a832)))),
% 2.89/2.20 inference(quant_inst,[status(thm)],[])).
% 2.89/2.20 tff(3740,plain,
% 2.89/2.20 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | (~c1_1(a832)) | c1_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c2_1(a832)) | c0_1(a832)),
% 2.89/2.20 inference(modus_ponens,[status(thm)],[3739, 3738])).
% 2.89/2.20 tff(3741,plain,
% 2.89/2.20 (~c3_1(a816)),
% 2.89/2.20 inference(unit_resolution,[status(thm)],[3740, 151, 3575, 433, 3690, 3254, 3676, 3573, 1069])).
% 2.89/2.20 tff(3742,plain,
% 2.89/2.20 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a833) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a833) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3743,plain,
% 2.89/2.21 ((hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a816) | c2_1(a816) | c1_1(a816)) <=> (hskp19 | c2_1(a833) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3744,plain,
% 2.89/2.21 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a816) | c2_1(a816) | c1_1(a816))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a833) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.89/2.21 inference(monotonicity,[status(thm)],[3743])).
% 2.89/2.21 tff(3745,plain,
% 2.89/2.21 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a816) | c2_1(a816) | c1_1(a816))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a833) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.21 inference(transitivity,[status(thm)],[3744, 3742])).
% 2.89/2.21 tff(3746,plain,
% 2.89/2.21 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a816) | c2_1(a816) | c1_1(a816))),
% 2.89/2.21 inference(quant_inst,[status(thm)],[])).
% 2.89/2.21 tff(3747,plain,
% 2.89/2.21 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a833) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.89/2.21 inference(modus_ponens,[status(thm)],[3746, 3745])).
% 2.89/2.21 tff(3748,plain,
% 2.89/2.21 ($false),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3747, 151, 1603, 639, 309, 3676, 3677, 10, 750, 3741])).
% 2.89/2.21 tff(3749,plain,((~hskp14) | hskp19 | (~c1_1(a833)) | c2_1(a833) | (~c3_1(a833)) | hskp13 | (~c2_1(a832)) | (~c1_1(a832)) | c0_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.21 tff(3750,plain,
% 2.89/2.21 (hskp13),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3749, 3734, 3442, 309, 3449, 3421, 3722, 3646, 3730])).
% 2.89/2.21 tff(3751,plain,
% 2.89/2.21 (~c3_1(a814)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3589, 3750])).
% 2.89/2.21 tff(3752,plain,
% 2.89/2.21 (c1_1(a814)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3606, 3750])).
% 2.89/2.21 tff(3753,plain,
% 2.89/2.21 (~c2_1(a814)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3616, 151, 3442, 3752, 321, 309, 3751, 2078, 3449])).
% 2.89/2.21 tff(3754,plain,
% 2.89/2.21 (~c0_1(a814)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3595, 3750])).
% 2.89/2.21 tff(3755,plain,
% 2.89/2.21 (hskp3),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3624, 151, 3752, 3754, 3751, 2646, 3753])).
% 2.89/2.21 tff(3756,plain,
% 2.89/2.21 (~c3_1(a798)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[546, 3755])).
% 2.89/2.21 tff(3757,plain,
% 2.89/2.21 (c2_1(a798)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[563, 3755])).
% 2.89/2.21 tff(3758,plain,
% 2.89/2.21 (c0_1(a798)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[574, 3755])).
% 2.89/2.21 tff(3759,plain,
% 2.89/2.21 ($false),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3717, 151, 3450, 3452, 3752, 3758, 3757, 3451, 3751, 3756, 332, 3753])).
% 2.89/2.21 tff(3760,plain,(c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.21 tff(3761,plain,
% 2.89/2.21 (c0_1(a833)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3760, 309])).
% 2.89/2.21 tff(3762,plain,
% 2.89/2.21 (~hskp20),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[632, 3761])).
% 2.89/2.21 tff(3763,plain,
% 2.89/2.21 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3764,plain,
% 2.89/2.21 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833))) <=> (hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3765,plain,
% 2.89/2.21 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0)))),
% 2.89/2.21 inference(monotonicity,[status(thm)],[3764])).
% 2.89/2.21 tff(3766,plain,
% 2.89/2.21 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0))),
% 2.89/2.21 inference(transitivity,[status(thm)],[3765, 3763])).
% 2.89/2.21 tff(3767,plain,
% 2.89/2.21 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)))),
% 2.89/2.21 inference(quant_inst,[status(thm)],[])).
% 2.89/2.21 tff(3768,plain,
% 2.89/2.21 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0)),
% 2.89/2.21 inference(modus_ponens,[status(thm)],[3767, 3766])).
% 2.89/2.21 tff(3769,plain,
% 2.89/2.21 (hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833))),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3768, 151, 309, 1646])).
% 2.89/2.21 tff(3770,plain,
% 2.89/2.21 (hskp1),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3769, 333, 3761, 3762])).
% 2.89/2.21 tff(3771,plain,
% 2.89/2.21 (~c2_1(a794)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[280, 3770])).
% 2.89/2.21 tff(3772,plain,
% 2.89/2.21 (c3_1(a794)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[291, 3770])).
% 2.89/2.21 tff(3773,plain,
% 2.89/2.21 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3774,plain,
% 2.89/2.21 ((hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833) | c2_1(a833) | c1_1(a833)) <=> (hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3775,plain,
% 2.89/2.21 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833) | c2_1(a833) | c1_1(a833))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833)))),
% 2.89/2.21 inference(monotonicity,[status(thm)],[3774])).
% 2.89/2.21 tff(3776,plain,
% 2.89/2.21 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833) | c2_1(a833) | c1_1(a833))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833))),
% 2.89/2.21 inference(transitivity,[status(thm)],[3775, 3773])).
% 2.89/2.21 tff(3777,plain,
% 2.89/2.21 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833) | c2_1(a833) | c1_1(a833))),
% 2.89/2.21 inference(quant_inst,[status(thm)],[])).
% 2.89/2.21 tff(3778,plain,
% 2.89/2.21 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833)),
% 2.89/2.21 inference(modus_ponens,[status(thm)],[3777, 3776])).
% 2.89/2.21 tff(3779,plain,
% 2.89/2.21 (hskp19 | (~c1_1(a794))),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3778, 151, 333, 3772, 309, 3771, 10, 310])).
% 2.89/2.21 tff(3780,plain,
% 2.89/2.21 (~c1_1(a794)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3779, 1459])).
% 2.89/2.21 tff(3781,plain,
% 2.89/2.21 (~c0_1(a794)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[297, 3770])).
% 2.89/2.21 tff(3782,plain,
% 2.89/2.21 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3783,plain,
% 2.89/2.21 ((hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3784,plain,
% 2.89/2.21 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797))))),
% 2.89/2.21 inference(monotonicity,[status(thm)],[3783])).
% 2.89/2.21 tff(3785,plain,
% 2.89/2.21 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 2.89/2.21 inference(transitivity,[status(thm)],[3784, 3782])).
% 2.89/2.21 tff(3786,plain,
% 2.89/2.21 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 2.89/2.21 inference(quant_inst,[status(thm)],[])).
% 2.89/2.21 tff(3787,plain,
% 2.89/2.21 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797))),
% 2.89/2.21 inference(modus_ponens,[status(thm)],[3786, 3785])).
% 2.89/2.21 tff(3788,plain,
% 2.89/2.21 (hskp7),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3787, 151, 2567, 2538, 2527, 3772, 3781, 1515, 3780])).
% 2.89/2.21 tff(3789,plain,
% 2.89/2.21 (hskp30),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[2588, 2953, 3762])).
% 2.89/2.21 tff(3790,plain,
% 2.89/2.21 (c3_1(a867)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[33, 3789])).
% 2.89/2.21 tff(3791,plain,
% 2.89/2.21 (c0_1(a867)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[55, 3789])).
% 2.89/2.21 tff(3792,plain,
% 2.89/2.21 (c1_1(a867)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[44, 3789])).
% 2.89/2.21 tff(3793,plain,
% 2.89/2.21 (hskp11),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[2971, 3792, 3762, 2955, 2956, 3791, 3790, 2954])).
% 2.89/2.21 tff(3794,plain,
% 2.89/2.21 (~c2_1(a808)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[857, 3793])).
% 2.89/2.21 tff(3795,plain,
% 2.89/2.21 (~c1_1(a808)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[851, 3793])).
% 2.89/2.21 tff(3796,plain,
% 2.89/2.21 (c3_1(a808)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[896, 3793])).
% 2.89/2.21 tff(3797,plain,
% 2.89/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a833) | c2_1(a832) | (~c0_1(a833)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | c2_1(a832) | (~c0_1(a833)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | c3_1(a833))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3798,plain,
% 2.89/2.21 (((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832)) <=> (c1_1(a833) | c2_1(a832) | (~c0_1(a833)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | c3_1(a833))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3799,plain,
% 2.89/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a833) | c2_1(a832) | (~c0_1(a833)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | c3_1(a833)))),
% 2.89/2.21 inference(monotonicity,[status(thm)],[3798])).
% 2.89/2.21 tff(3800,plain,
% 2.89/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | c2_1(a832) | (~c0_1(a833)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | c3_1(a833))),
% 2.89/2.21 inference(transitivity,[status(thm)],[3799, 3797])).
% 2.89/2.21 tff(3801,plain,
% 2.89/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832))),
% 2.89/2.21 inference(quant_inst,[status(thm)],[])).
% 2.89/2.21 tff(3802,plain,
% 2.89/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | c2_1(a832) | (~c0_1(a833)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | c3_1(a833)),
% 2.89/2.21 inference(modus_ponens,[status(thm)],[3801, 3800])).
% 2.89/2.21 tff(3803,plain,
% 2.89/2.21 (c0_1(a832)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3802, 151, 333, 1458, 3796, 3761, 22, 3795, 3794, 876, 310])).
% 2.89/2.21 tff(3804,plain,
% 2.89/2.21 (~c1_1(a832)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3277, 3803, 22, 1458])).
% 2.89/2.21 tff(3805,plain,
% 2.89/2.21 ($false),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[1504, 3804, 3788, 22, 1458])).
% 2.89/2.21 tff(3806,plain,(c2_1(a832) | c3_1(a832) | c1_1(a833) | c3_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.21 tff(3807,plain,
% 2.89/2.21 (c2_1(a832)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3806, 22, 333, 310, 309])).
% 2.89/2.21 tff(3808,plain,
% 2.89/2.21 (((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | c1_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833))) <=> ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp20 | hskp2 | c1_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3809,plain,
% 2.89/2.21 ((hskp20 | hskp2 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | c3_1(a833)) <=> (hskp20 | hskp2 | c1_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3810,plain,
% 2.89/2.21 (((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | c3_1(a833))) <=> ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | c1_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833)))),
% 2.89/2.21 inference(monotonicity,[status(thm)],[3809])).
% 2.89/2.21 tff(3811,plain,
% 2.89/2.21 (((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | c3_1(a833))) <=> ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp20 | hskp2 | c1_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833))),
% 2.89/2.21 inference(transitivity,[status(thm)],[3810, 3808])).
% 2.89/2.21 tff(3812,plain,
% 2.89/2.21 ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | c3_1(a833))),
% 2.89/2.21 inference(quant_inst,[status(thm)],[])).
% 2.89/2.21 tff(3813,plain,
% 2.89/2.21 ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp20 | hskp2 | c1_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833)),
% 2.89/2.21 inference(modus_ponens,[status(thm)],[3812, 3811])).
% 2.89/2.21 tff(3814,plain,
% 2.89/2.21 (hskp20 | hskp2 | c1_1(a833) | c3_1(a833)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3813, 151, 309, 1404])).
% 2.89/2.21 tff(3815,plain,
% 2.89/2.21 (hskp2),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[3814, 310, 333, 3762])).
% 2.89/2.21 tff(3816,plain,
% 2.89/2.21 (~c1_1(a795)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[1423, 3815])).
% 2.89/2.21 tff(3817,plain,
% 2.89/2.21 (~c3_1(a795)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[1417, 3815])).
% 2.89/2.21 tff(3818,plain,
% 2.89/2.21 (~c0_1(a795)),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[1449, 3815])).
% 2.89/2.21 tff(3819,plain,
% 2.89/2.21 (~hskp12),
% 2.89/2.21 inference(unit_resolution,[status(thm)],[2425, 322, 1554, 2409, 22, 433, 1555])).
% 2.89/2.21 tff(3820,plain,
% 2.89/2.21 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a795)))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3821,plain,
% 2.89/2.21 ((hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (hskp12 | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a795)))),
% 2.89/2.21 inference(rewrite,[status(thm)],[])).
% 2.89/2.21 tff(3822,plain,
% 2.89/2.21 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a795))))),
% 2.89/2.21 inference(monotonicity,[status(thm)],[3821])).
% 2.89/2.21 tff(3823,plain,
% 2.89/2.21 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a795)))),
% 2.89/2.21 inference(transitivity,[status(thm)],[3822, 3820])).
% 2.89/2.21 tff(3824,plain,
% 2.89/2.21 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 2.89/2.21 inference(quant_inst,[status(thm)],[])).
% 2.89/2.21 tff(3825,plain,
% 2.89/2.21 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a795))),
% 2.89/2.21 inference(modus_ponens,[status(thm)],[3824, 3823])).
% 2.89/2.22 tff(3826,plain,
% 2.89/2.22 (hskp12 | (~c2_1(a795))),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3825, 151, 1851, 1554, 1555, 1861, 1850, 1079])).
% 2.89/2.22 tff(3827,plain,
% 2.89/2.22 (~c2_1(a795)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3826, 3819])).
% 2.89/2.22 tff(3828,assumption,(c0_1(a833)), introduced(assumption)).
% 2.89/2.22 tff(3829,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | c2_1(a795) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | c2_1(a795) | c3_1(a833))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3830,plain,
% 2.89/2.22 (((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a794) | c1_1(a794) | (~c3_1(a794)) | c2_1(a795) | c0_1(a795) | c3_1(a795)) <=> (c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | c2_1(a795) | c3_1(a833))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3831,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a794) | c1_1(a794) | (~c3_1(a794)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | c2_1(a795) | c3_1(a833)))),
% 2.89/2.22 inference(monotonicity,[status(thm)],[3830])).
% 2.89/2.22 tff(3832,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a794) | c1_1(a794) | (~c3_1(a794)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | c2_1(a795) | c3_1(a833))),
% 2.89/2.22 inference(transitivity,[status(thm)],[3831, 3829])).
% 2.89/2.22 tff(3833,plain,
% 2.89/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a794) | c1_1(a794) | (~c3_1(a794)) | c2_1(a795) | c0_1(a795) | c3_1(a795))),
% 2.89/2.22 inference(quant_inst,[status(thm)],[])).
% 2.89/2.22 tff(3834,plain,
% 2.89/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | c2_1(a795) | c3_1(a833)),
% 2.89/2.22 inference(modus_ponens,[status(thm)],[3833, 3832])).
% 2.89/2.22 tff(3835,plain,
% 2.89/2.22 (c1_1(a794)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3834, 151, 333, 1851, 3828, 1554, 1555, 1850, 876, 3827, 310])).
% 2.89/2.22 tff(3836,plain,
% 2.89/2.22 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a832)) | c0_1(a832))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3837,plain,
% 2.89/2.22 ((hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (hskp12 | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a832)) | c0_1(a832))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3838,plain,
% 2.89/2.22 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a832)) | c0_1(a832)))),
% 2.89/2.22 inference(monotonicity,[status(thm)],[3837])).
% 2.89/2.22 tff(3839,plain,
% 2.89/2.22 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a832)) | c0_1(a832))),
% 2.89/2.22 inference(transitivity,[status(thm)],[3838, 3836])).
% 2.89/2.22 tff(3840,plain,
% 2.89/2.22 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 2.89/2.22 inference(quant_inst,[status(thm)],[])).
% 2.89/2.22 tff(3841,plain,
% 2.89/2.22 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a832)) | c0_1(a832)),
% 2.89/2.22 inference(modus_ponens,[status(thm)],[3840, 3839])).
% 2.89/2.22 tff(3842,plain,
% 2.89/2.22 ($false),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3841, 151, 811, 433, 1851, 22, 1861, 1850, 1079, 1069])).
% 2.89/2.22 tff(3843,plain,(c0_1(a832) | hskp12 | (~c2_1(a832)) | (~c3_1(a794)) | c3_1(a832) | c0_1(a794) | c2_1(a794)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.22 tff(3844,plain,
% 2.89/2.22 (c0_1(a832)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3843, 3819, 433, 1851, 22, 1861, 1850])).
% 2.89/2.22 tff(3845,plain,
% 2.89/2.22 (~hskp11),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[1563, 3844, 22, 1554, 3827, 1555, 322])).
% 2.89/2.22 tff(3846,plain,
% 2.89/2.22 (hskp21),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[2574, 3845])).
% 2.89/2.22 tff(3847,plain,
% 2.89/2.22 (~c2_1(a838)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[431, 3846])).
% 2.89/2.22 tff(3848,plain,
% 2.89/2.22 (c3_1(a838)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[443, 3846])).
% 2.89/2.22 tff(3849,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a833) | c2_1(a838) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | c2_1(a838) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3850,plain,
% 2.89/2.22 (((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a795) | c0_1(a795) | c3_1(a795)) <=> (c1_1(a833) | c2_1(a838) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3851,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a833) | c2_1(a838) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838)))),
% 2.89/2.22 inference(monotonicity,[status(thm)],[3850])).
% 2.89/2.22 tff(3852,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | c2_1(a838) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))),
% 2.89/2.22 inference(transitivity,[status(thm)],[3851, 3849])).
% 2.89/2.22 tff(3853,plain,
% 2.89/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a795) | c0_1(a795) | c3_1(a795))),
% 2.89/2.22 inference(quant_inst,[status(thm)],[])).
% 2.89/2.22 tff(3854,plain,
% 2.89/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | c2_1(a838) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838)),
% 2.89/2.22 inference(modus_ponens,[status(thm)],[3853, 3852])).
% 2.89/2.22 tff(3855,plain,
% 2.89/2.22 (c1_1(a838)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3854, 151, 3848, 333, 3847, 3828, 1554, 1555, 876, 3827, 310])).
% 2.89/2.22 tff(3856,plain,
% 2.89/2.22 (~hskp20),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[632, 3828])).
% 2.89/2.22 tff(3857,plain,
% 2.89/2.22 (hskp9),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[2948, 3846, 3856])).
% 2.89/2.22 tff(3858,plain,
% 2.89/2.22 (~c3_1(a806)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[75, 3857])).
% 2.89/2.22 tff(3859,plain,
% 2.89/2.22 (c1_1(a806)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[87, 3857])).
% 2.89/2.22 tff(3860,plain,
% 2.89/2.22 (c0_1(a838)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[454, 3846])).
% 2.89/2.22 tff(3861,plain,
% 2.89/2.22 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3862,plain,
% 2.89/2.22 ((hskp12 | (~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806))) <=> (hskp12 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3863,plain,
% 2.89/2.22 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))))),
% 2.89/2.22 inference(monotonicity,[status(thm)],[3862])).
% 2.89/2.22 tff(3864,plain,
% 2.89/2.22 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 2.89/2.22 inference(transitivity,[status(thm)],[3863, 3861])).
% 2.89/2.22 tff(3865,plain,
% 2.89/2.22 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))),
% 2.89/2.22 inference(quant_inst,[status(thm)],[])).
% 2.89/2.22 tff(3866,plain,
% 2.89/2.22 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))),
% 2.89/2.22 inference(modus_ponens,[status(thm)],[3865, 3864])).
% 2.89/2.22 tff(3867,plain,
% 2.89/2.22 (c2_1(a806)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3866, 151, 3819, 3860, 3848, 3859, 3858, 110, 3855])).
% 2.89/2.22 tff(3868,plain,
% 2.89/2.22 ($false),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[2336, 151, 3859, 1851, 3858, 1861, 1850, 2078, 3867, 3835])).
% 2.89/2.22 tff(3869,plain,(c1_1(a832) | (~c3_1(a794)) | c0_1(a794) | c2_1(a794) | c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c3_1(a833) | c3_1(a832) | (~c2_1(a832)) | c1_1(a795)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.22 tff(3870,plain,
% 2.89/2.22 (c1_1(a832)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3869, 22, 3781, 3771, 333, 3761, 3818, 3817, 310, 3772, 3807, 3816])).
% 2.89/2.22 tff(3871,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a832)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a832)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a832)))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3872,plain,
% 2.89/2.22 (((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> ((~c1_1(a832)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a832)))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3873,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a832)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a832))))),
% 2.89/2.22 inference(monotonicity,[status(thm)],[3872])).
% 2.89/2.22 tff(3874,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a832)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a832)))),
% 2.89/2.22 inference(transitivity,[status(thm)],[3873, 3871])).
% 2.89/2.22 tff(3875,plain,
% 2.89/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 2.89/2.22 inference(quant_inst,[status(thm)],[])).
% 2.89/2.22 tff(3876,plain,
% 2.89/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a832)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a832))),
% 2.89/2.22 inference(modus_ponens,[status(thm)],[3875, 3874])).
% 2.89/2.22 tff(3877,plain,
% 2.89/2.22 ((~c1_1(a832)) | (~c1_1(a794)) | (~c2_1(a832))),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3876, 151, 3772, 22, 3781, 3771, 2078])).
% 2.89/2.22 tff(3878,plain,
% 2.89/2.22 (~c1_1(a794)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3877, 3870, 3807])).
% 2.89/2.22 tff(3879,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~c1_1(a832)) | c3_1(a832) | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | c2_1(a795) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a832)) | c3_1(a832) | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | c2_1(a795) | (~c2_1(a832)))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3880,plain,
% 2.89/2.22 (((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a794) | c1_1(a794) | c0_1(a794)) <=> ((~c1_1(a832)) | c3_1(a832) | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | c2_1(a795) | (~c2_1(a832)))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3881,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a794) | c1_1(a794) | c0_1(a794))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~c1_1(a832)) | c3_1(a832) | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | c2_1(a795) | (~c2_1(a832))))),
% 2.89/2.22 inference(monotonicity,[status(thm)],[3880])).
% 2.89/2.22 tff(3882,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a794) | c1_1(a794) | c0_1(a794))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a832)) | c3_1(a832) | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | c2_1(a795) | (~c2_1(a832)))),
% 2.89/2.22 inference(transitivity,[status(thm)],[3881, 3879])).
% 2.89/2.22 tff(3883,plain,
% 2.89/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a794) | c1_1(a794) | c0_1(a794))),
% 2.89/2.22 inference(quant_inst,[status(thm)],[])).
% 2.89/2.22 tff(3884,plain,
% 2.89/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a832)) | c3_1(a832) | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | c2_1(a795) | (~c2_1(a832))),
% 2.89/2.22 inference(modus_ponens,[status(thm)],[3883, 3882])).
% 2.89/2.22 tff(3885,plain,
% 2.89/2.22 ((~c1_1(a832)) | c1_1(a794) | c2_1(a795) | (~c2_1(a832))),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3884, 151, 22, 3818, 3817, 3781, 3771, 258])).
% 2.89/2.22 tff(3886,plain,
% 2.89/2.22 (c2_1(a795)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3885, 3870, 3807, 3878])).
% 2.89/2.22 tff(3887,plain,
% 2.89/2.22 (hskp12 | (~c2_1(a795))),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3825, 151, 3772, 3818, 3817, 3781, 3771, 1079])).
% 2.89/2.22 tff(3888,plain,
% 2.89/2.22 (hskp12),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3887, 3886])).
% 2.89/2.22 tff(3889,plain,
% 2.89/2.22 (~c0_1(a809)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[164, 3888])).
% 2.89/2.22 tff(3890,plain,
% 2.89/2.22 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a795)))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3891,plain,
% 2.89/2.22 ((hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795))) <=> (hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a795)))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3892,plain,
% 2.89/2.22 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a795))))),
% 2.89/2.22 inference(monotonicity,[status(thm)],[3891])).
% 2.89/2.22 tff(3893,plain,
% 2.89/2.22 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a795)))),
% 2.89/2.22 inference(transitivity,[status(thm)],[3892, 3890])).
% 2.89/2.22 tff(3894,plain,
% 2.89/2.22 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795)))),
% 2.89/2.22 inference(quant_inst,[status(thm)],[])).
% 2.89/2.22 tff(3895,plain,
% 2.89/2.22 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a795))),
% 2.89/2.22 inference(modus_ponens,[status(thm)],[3894, 3893])).
% 2.89/2.22 tff(3896,plain,
% 2.89/2.22 (hskp15 | (~c2_1(a795))),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3895, 151, 2567, 2538, 2527, 3818, 3817, 1300])).
% 2.89/2.22 tff(3897,plain,
% 2.89/2.22 (hskp15),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[3896, 3886])).
% 2.89/2.22 tff(3898,plain,
% 2.89/2.22 (~c1_1(a817)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[1342, 3897])).
% 2.89/2.22 tff(3899,plain,
% 2.89/2.22 (c1_1(a809)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[187, 3888])).
% 2.89/2.22 tff(3900,plain,
% 2.89/2.22 (c3_1(a817)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[1353, 3897])).
% 2.89/2.22 tff(3901,plain,
% 2.89/2.22 (c2_1(a817)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[1364, 3897])).
% 2.89/2.22 tff(3902,plain,
% 2.89/2.22 (~hskp19),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[391, 3870])).
% 2.89/2.22 tff(3903,plain,
% 2.89/2.22 (hskp27),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[2596, 3902])).
% 2.89/2.22 tff(3904,plain,
% 2.89/2.22 (c3_1(a796)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[594, 3903])).
% 2.89/2.22 tff(3905,plain,
% 2.89/2.22 (c2_1(a796)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[605, 3903])).
% 2.89/2.22 tff(3906,plain,
% 2.89/2.22 (c0_1(a796)),
% 2.89/2.22 inference(unit_resolution,[status(thm)],[616, 3903])).
% 2.89/2.22 tff(3907,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a817) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a809)) | c3_1(a809) | (~c2_1(a817)) | (~c3_1(a817)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a817) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a809)) | c3_1(a809) | (~c2_1(a817)) | (~c3_1(a817)))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3908,plain,
% 2.89/2.22 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809))) <=> (c1_1(a817) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a809)) | c3_1(a809) | (~c2_1(a817)) | (~c3_1(a817)))),
% 2.89/2.22 inference(rewrite,[status(thm)],[])).
% 2.89/2.22 tff(3909,plain,
% 2.89/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a817) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a809)) | c3_1(a809) | (~c2_1(a817)) | (~c3_1(a817))))),
% 2.89/2.23 inference(monotonicity,[status(thm)],[3908])).
% 2.89/2.23 tff(3910,plain,
% 2.89/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a817) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a809)) | c3_1(a809) | (~c2_1(a817)) | (~c3_1(a817)))),
% 2.89/2.23 inference(transitivity,[status(thm)],[3909, 3907])).
% 2.89/2.23 tff(3911,plain,
% 2.89/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809)))),
% 2.89/2.23 inference(quant_inst,[status(thm)],[])).
% 2.89/2.23 tff(3912,plain,
% 2.89/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a817) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a809)) | c3_1(a809) | (~c2_1(a817)) | (~c3_1(a817))),
% 2.89/2.23 inference(modus_ponens,[status(thm)],[3911, 3910])).
% 2.89/2.23 tff(3913,plain,
% 2.89/2.23 (c3_1(a809)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3912, 151, 3906, 3905, 3904, 3901, 3900, 3899, 3898, 3889, 800])).
% 2.89/2.23 tff(3914,plain,
% 2.89/2.23 (c2_1(a809)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[176, 3888])).
% 2.89/2.23 tff(3915,plain,
% 2.89/2.23 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | c3_1(a833))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp29 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | c3_1(a833))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(3916,plain,
% 2.89/2.23 ((hskp29 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | c1_1(a833)) <=> (hskp29 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | c3_1(a833))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(3917,plain,
% 2.89/2.23 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | c1_1(a833))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | c3_1(a833)))),
% 2.89/2.23 inference(monotonicity,[status(thm)],[3916])).
% 2.89/2.23 tff(3918,plain,
% 2.89/2.23 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | c1_1(a833))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp29 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | c3_1(a833))),
% 2.89/2.23 inference(transitivity,[status(thm)],[3917, 3915])).
% 2.89/2.23 tff(3919,plain,
% 2.89/2.23 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | c1_1(a833))),
% 2.89/2.23 inference(quant_inst,[status(thm)],[])).
% 2.89/2.23 tff(3920,plain,
% 2.89/2.23 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp29 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | c3_1(a833)),
% 2.89/2.23 inference(modus_ponens,[status(thm)],[3919, 3918])).
% 2.89/2.23 tff(3921,plain,
% 2.89/2.23 (hskp29),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3920, 151, 333, 3761, 309, 2732, 310])).
% 2.89/2.23 tff(3922,plain,
% 2.89/2.23 (c2_1(a829)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[2761, 3921])).
% 2.89/2.23 tff(3923,plain,
% 2.89/2.23 (c1_1(a829)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[2772, 3921])).
% 2.89/2.23 tff(3924,plain,
% 2.89/2.23 (c0_1(a829)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[2750, 3921])).
% 2.89/2.23 tff(3925,plain,
% 2.89/2.23 (hskp30),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[2588, 3903, 3762])).
% 2.89/2.23 tff(3926,plain,
% 2.89/2.23 (c3_1(a867)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[33, 3925])).
% 2.89/2.23 tff(3927,plain,
% 2.89/2.23 (c1_1(a867)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[44, 3925])).
% 2.89/2.23 tff(3928,plain,
% 2.89/2.23 (c0_1(a867)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[55, 3925])).
% 2.89/2.23 tff(3929,plain,
% 2.89/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a809) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a809)) | (~c3_1(a809)) | (~c0_1(a829)) | (~c2_1(a829)) | (~c1_1(a829)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a809) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a809)) | (~c3_1(a809)) | (~c0_1(a829)) | (~c2_1(a829)) | (~c1_1(a829)))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(3930,plain,
% 2.89/2.23 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a829)) | (~c0_1(a829)) | (~c2_1(a829)) | c0_1(a809) | (~c3_1(a809)) | (~c2_1(a809))) <=> (c0_1(a809) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a809)) | (~c3_1(a809)) | (~c0_1(a829)) | (~c2_1(a829)) | (~c1_1(a829)))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(3931,plain,
% 2.89/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a829)) | (~c0_1(a829)) | (~c2_1(a829)) | c0_1(a809) | (~c3_1(a809)) | (~c2_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a809) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a809)) | (~c3_1(a809)) | (~c0_1(a829)) | (~c2_1(a829)) | (~c1_1(a829))))),
% 2.89/2.23 inference(monotonicity,[status(thm)],[3930])).
% 2.89/2.23 tff(3932,plain,
% 2.89/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a829)) | (~c0_1(a829)) | (~c2_1(a829)) | c0_1(a809) | (~c3_1(a809)) | (~c2_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a809) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a809)) | (~c3_1(a809)) | (~c0_1(a829)) | (~c2_1(a829)) | (~c1_1(a829)))),
% 2.89/2.23 inference(transitivity,[status(thm)],[3931, 3929])).
% 2.89/2.23 tff(3933,plain,
% 2.89/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a829)) | (~c0_1(a829)) | (~c2_1(a829)) | c0_1(a809) | (~c3_1(a809)) | (~c2_1(a809)))),
% 2.89/2.23 inference(quant_inst,[status(thm)],[])).
% 2.89/2.23 tff(3934,plain,
% 2.89/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a809) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a809)) | (~c3_1(a809)) | (~c0_1(a829)) | (~c2_1(a829)) | (~c1_1(a829))),
% 2.89/2.23 inference(modus_ponens,[status(thm)],[3933, 3932])).
% 2.89/2.23 tff(3935,plain,
% 2.89/2.23 ($false),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3934, 151, 3928, 3927, 3926, 3924, 3923, 3922, 3914, 3889, 207, 3913])).
% 2.89/2.23 tff(3936,plain,(c3_1(a832) | c1_1(a833) | c3_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.23 tff(3937,plain,
% 2.89/2.23 (c3_1(a832)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3936, 310, 333, 309])).
% 2.89/2.23 tff(3938,plain,
% 2.89/2.23 (~hskp19),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[385, 3937])).
% 2.89/2.23 tff(3939,plain,
% 2.89/2.23 (~c1_1(a794)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3779, 3938])).
% 2.89/2.23 tff(3940,plain,
% 2.89/2.23 (hskp7),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3787, 151, 2567, 2538, 2527, 3772, 3781, 1515, 3939])).
% 2.89/2.23 tff(3941,plain,
% 2.89/2.23 (~c2_1(a803)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[1473, 3940])).
% 2.89/2.23 tff(3942,plain,
% 2.89/2.23 (c3_1(a803)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[1484, 3940])).
% 2.89/2.23 tff(3943,plain,
% 2.89/2.23 (c1_1(a803)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[1495, 3940])).
% 2.89/2.23 tff(3944,plain,
% 2.89/2.23 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(3945,plain,
% 2.89/2.23 ((hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833) | c2_1(a833) | c1_1(a833)) <=> (hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(3946,plain,
% 2.89/2.23 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833) | c2_1(a833) | c1_1(a833))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833)))),
% 2.89/2.23 inference(monotonicity,[status(thm)],[3945])).
% 2.89/2.23 tff(3947,plain,
% 2.89/2.23 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833) | c2_1(a833) | c1_1(a833))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833))),
% 2.89/2.23 inference(transitivity,[status(thm)],[3946, 3944])).
% 2.89/2.23 tff(3948,plain,
% 2.89/2.23 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833) | c2_1(a833) | c1_1(a833))),
% 2.89/2.23 inference(quant_inst,[status(thm)],[])).
% 2.89/2.23 tff(3949,plain,
% 2.89/2.23 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833)),
% 2.89/2.23 inference(modus_ponens,[status(thm)],[3948, 3947])).
% 2.89/2.23 tff(3950,plain,
% 2.89/2.23 ($false),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3949, 151, 3938, 333, 3943, 3942, 309, 3941, 10, 310])).
% 2.89/2.23 tff(3951,plain,(c3_1(a833) | c1_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.23 tff(3952,plain,
% 2.89/2.23 (c3_1(a833)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3951, 333, 309])).
% 2.89/2.23 tff(3953,plain,
% 2.89/2.23 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | (~c3_1(a833)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | (~c3_1(a833)))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(3954,plain,
% 2.89/2.23 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c0_1(a833))) <=> (hskp20 | hskp9 | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | (~c3_1(a833)))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(3955,plain,
% 2.89/2.23 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c0_1(a833)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | (~c3_1(a833))))),
% 2.89/2.23 inference(monotonicity,[status(thm)],[3954])).
% 2.89/2.23 tff(3956,plain,
% 2.89/2.23 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c0_1(a833)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | (~c3_1(a833)))),
% 2.89/2.23 inference(transitivity,[status(thm)],[3955, 3953])).
% 2.89/2.23 tff(3957,plain,
% 2.89/2.23 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c0_1(a833)))),
% 2.89/2.23 inference(quant_inst,[status(thm)],[])).
% 2.89/2.23 tff(3958,plain,
% 2.89/2.23 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | (~c3_1(a833))),
% 2.89/2.23 inference(modus_ponens,[status(thm)],[3957, 3956])).
% 2.89/2.23 tff(3959,plain,
% 2.89/2.23 (hskp20 | hskp9 | (~c0_1(a833)) | (~c3_1(a833))),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3958, 151, 309, 21])).
% 2.89/2.23 tff(3960,plain,
% 2.89/2.23 (hskp9),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3959, 3952, 3762, 3761])).
% 2.89/2.23 tff(3961,plain,
% 2.89/2.23 (c0_1(a806)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[67, 3960])).
% 2.89/2.23 tff(3962,plain,
% 2.89/2.23 (c1_1(a806)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[87, 3960])).
% 2.89/2.23 tff(3963,plain,
% 2.89/2.23 (~c3_1(a806)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[75, 3960])).
% 2.89/2.23 tff(3964,plain,
% 2.89/2.23 (hskp30),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[2588, 2953, 346])).
% 2.89/2.23 tff(3965,plain,
% 2.89/2.23 (c1_1(a867)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[44, 3964])).
% 2.89/2.23 tff(3966,plain,
% 2.89/2.23 (c0_1(a867)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[55, 3964])).
% 2.89/2.23 tff(3967,plain,
% 2.89/2.23 (c3_1(a867)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[33, 3964])).
% 2.89/2.23 tff(3968,plain,
% 2.89/2.23 (c2_1(a806)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[196, 3967, 111, 100, 3966, 3965, 166])).
% 2.89/2.23 tff(3969,plain,
% 2.89/2.23 ((~c1_1(a794)) | (~c2_1(a806))),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[2336, 151, 111, 1851, 100, 1861, 1850, 2078])).
% 2.89/2.23 tff(3970,plain,
% 2.89/2.23 (~c1_1(a794)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3969, 3968])).
% 2.89/2.23 tff(3971,plain,
% 2.89/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a832) | c3_1(a832) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a832) | c3_1(a832) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(3972,plain,
% 2.89/2.23 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a832) | c2_1(a832) | c0_1(a832) | c2_1(a794) | c1_1(a794) | c0_1(a794)) <=> (c2_1(a832) | c3_1(a832) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(3973,plain,
% 2.89/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a832) | c2_1(a832) | c0_1(a832) | c2_1(a794) | c1_1(a794) | c0_1(a794))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a832) | c3_1(a832) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832)))),
% 2.89/2.23 inference(monotonicity,[status(thm)],[3972])).
% 2.89/2.23 tff(3974,plain,
% 2.89/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a832) | c2_1(a832) | c0_1(a832) | c2_1(a794) | c1_1(a794) | c0_1(a794))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a832) | c3_1(a832) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832))),
% 2.89/2.23 inference(transitivity,[status(thm)],[3973, 3971])).
% 2.89/2.23 tff(3975,plain,
% 2.89/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a832) | c2_1(a832) | c0_1(a832) | c2_1(a794) | c1_1(a794) | c0_1(a794))),
% 2.89/2.23 inference(quant_inst,[status(thm)],[])).
% 2.89/2.23 tff(3976,plain,
% 2.89/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a832) | c3_1(a832) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832)),
% 2.89/2.23 inference(modus_ponens,[status(thm)],[3975, 3974])).
% 2.89/2.23 tff(3977,plain,
% 2.89/2.23 (c2_1(a832) | c1_1(a794) | (~c2_1(a806)) | c0_1(a832)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3976, 151, 111, 22, 100, 1861, 1850, 258])).
% 2.89/2.23 tff(3978,plain,
% 2.89/2.23 (c0_1(a832)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3977, 3968, 1458, 3970])).
% 2.89/2.23 tff(3979,plain,
% 2.89/2.23 (~c1_1(a832)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3277, 3978, 22, 1458])).
% 2.89/2.23 tff(3980,plain,
% 2.89/2.23 (~hskp7),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[1504, 3979, 22, 1458])).
% 2.89/2.23 tff(3981,plain,
% 2.89/2.23 ($false),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3787, 151, 3980, 2567, 2538, 2527, 1851, 1861, 1515, 3970])).
% 2.89/2.23 tff(3982,plain,(c2_1(a832) | (~c3_1(a794)) | c0_1(a794) | c3_1(a832) | (~c1_1(a806)) | c3_1(a806) | c2_1(a794) | (~c0_1(a806)) | hskp20), inference(lemma,lemma(discharge,[]))).
% 2.89/2.23 tff(3983,plain,
% 2.89/2.23 (c2_1(a832)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3982, 22, 1861, 1851, 111, 100, 1850, 166, 346])).
% 2.89/2.23 tff(3984,plain,
% 2.89/2.23 (hskp12),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3843, 1069, 433, 1851, 22, 1861, 1850])).
% 2.89/2.23 tff(3985,plain,
% 2.89/2.23 (~c0_1(a809)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[164, 3984])).
% 2.89/2.23 tff(3986,plain,
% 2.89/2.23 (c2_1(a809)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[176, 3984])).
% 2.89/2.23 tff(3987,plain,
% 2.89/2.23 (c1_1(a809)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[187, 3984])).
% 2.89/2.23 tff(3988,plain,
% 2.89/2.23 ($false),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[1097, 151, 433, 3987, 3986, 322, 22, 3985, 1067, 1069])).
% 2.89/2.23 tff(3989,plain,(c0_1(a832) | (~c2_1(a832)) | c1_1(a832) | c3_1(a832) | (~c3_1(a794)) | c0_1(a794) | c2_1(a794)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.23 tff(3990,plain,
% 2.89/2.23 (c0_1(a832)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3989, 322, 433, 22, 1851, 1861, 1850])).
% 2.89/2.23 tff(3991,plain,
% 2.89/2.23 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(3992,plain,
% 2.89/2.23 ((hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832))) <=> (hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(3993,plain,
% 2.89/2.23 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | (~c0_1(a832))))),
% 2.89/2.23 inference(monotonicity,[status(thm)],[3992])).
% 2.89/2.23 tff(3994,plain,
% 2.89/2.23 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.89/2.23 inference(transitivity,[status(thm)],[3993, 3991])).
% 2.89/2.23 tff(3995,plain,
% 2.89/2.23 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))),
% 2.89/2.23 inference(quant_inst,[status(thm)],[])).
% 2.89/2.23 tff(3996,plain,
% 2.89/2.23 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | (~c0_1(a832))),
% 2.89/2.23 inference(modus_ponens,[status(thm)],[3995, 3994])).
% 2.89/2.23 tff(3997,plain,
% 2.89/2.23 (hskp5),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3996, 151, 56, 45, 34, 433, 22, 217, 3990])).
% 2.89/2.23 tff(3998,plain,
% 2.89/2.23 (~c1_1(a800)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[263, 3997])).
% 2.89/2.23 tff(3999,plain,
% 2.89/2.23 (~c0_1(a800)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[229, 3997])).
% 2.89/2.23 tff(4000,plain,
% 2.89/2.23 (c2_1(a806)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[196, 34, 111, 100, 56, 45, 166])).
% 2.89/2.23 tff(4001,plain,
% 2.89/2.23 (~c1_1(a794)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3969, 4000])).
% 2.89/2.23 tff(4002,plain,
% 2.89/2.23 (hskp7),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[3787, 151, 2567, 2538, 2527, 1851, 1861, 1515, 4001])).
% 2.89/2.23 tff(4003,plain,
% 2.89/2.23 (~c2_1(a803)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[1473, 4002])).
% 2.89/2.23 tff(4004,plain,
% 2.89/2.23 (c3_1(a800)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[240, 3997])).
% 2.89/2.23 tff(4005,plain,
% 2.89/2.23 (c1_1(a803)),
% 2.89/2.23 inference(unit_resolution,[status(thm)],[1495, 4002])).
% 2.89/2.23 tff(4006,plain,
% 2.89/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a832) | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a832) | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(4007,plain,
% 2.89/2.23 (((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (c1_1(a832) | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.89/2.23 inference(rewrite,[status(thm)],[])).
% 2.89/2.23 tff(4008,plain,
% 2.89/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a832) | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a832)) | (~c0_1(a832))))),
% 2.89/2.24 inference(monotonicity,[status(thm)],[4007])).
% 2.89/2.24 tff(4009,plain,
% 2.89/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a832) | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.89/2.24 inference(transitivity,[status(thm)],[4008, 4006])).
% 2.89/2.24 tff(4010,plain,
% 2.89/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 2.89/2.24 inference(quant_inst,[status(thm)],[])).
% 2.89/2.24 tff(4011,plain,
% 2.89/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a832) | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a832)) | (~c0_1(a832))),
% 2.89/2.24 inference(modus_ponens,[status(thm)],[4010, 4009])).
% 2.89/2.24 tff(4012,plain,
% 2.89/2.24 (~c0_1(a803)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4011, 151, 433, 4005, 4004, 322, 4003, 3999, 3998, 320, 3990])).
% 2.89/2.24 tff(4013,plain,
% 2.89/2.24 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a832)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4014,plain,
% 2.89/2.24 ((hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c1_1(a832) | (~c0_1(a832))) <=> (hskp22 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a832)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4015,plain,
% 2.89/2.24 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c1_1(a832) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a832))))),
% 2.89/2.24 inference(monotonicity,[status(thm)],[4014])).
% 2.89/2.24 tff(4016,plain,
% 2.89/2.24 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c1_1(a832) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a832)))),
% 2.89/2.24 inference(transitivity,[status(thm)],[4015, 4013])).
% 2.89/2.24 tff(4017,plain,
% 2.89/2.24 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c1_1(a832) | (~c0_1(a832)))),
% 2.89/2.24 inference(quant_inst,[status(thm)],[])).
% 2.89/2.24 tff(4018,plain,
% 2.89/2.24 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a832))),
% 2.89/2.24 inference(modus_ponens,[status(thm)],[4017, 4016])).
% 2.89/2.24 tff(4019,plain,
% 2.89/2.24 (hskp22),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4018, 151, 56, 45, 34, 322, 22, 1921, 3990])).
% 2.89/2.24 tff(4020,plain,
% 2.89/2.24 (~c0_1(a840)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[1934, 4019])).
% 2.89/2.24 tff(4021,plain,
% 2.89/2.24 (c3_1(a803)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[1484, 4002])).
% 2.89/2.24 tff(4022,plain,
% 2.89/2.24 (c3_1(a840)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[1945, 4019])).
% 2.89/2.24 tff(4023,plain,
% 2.89/2.24 (c1_1(a840)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[1974, 4019])).
% 2.89/2.24 tff(4024,plain,
% 2.89/2.24 ($false),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[2105, 151, 4023, 4022, 111, 4021, 4020, 100, 4003, 2078, 4000, 4012])).
% 2.89/2.24 tff(4025,plain,((~hskp30) | (~c1_1(a806)) | c3_1(a806) | (~c2_1(a832)) | c1_1(a832) | (~c3_1(a794)) | c0_1(a794) | c3_1(a832) | c2_1(a794) | (~c0_1(a806))), inference(lemma,lemma(discharge,[]))).
% 2.89/2.24 tff(4026,plain,
% 2.89/2.24 (~hskp30),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4025, 322, 100, 3983, 111, 1851, 1861, 22, 1850, 166])).
% 2.89/2.24 tff(4027,plain,
% 2.89/2.24 (~c0_1(a797)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[2545, 4026, 346])).
% 2.89/2.24 tff(4028,plain,
% 2.89/2.24 (c0_1(a832)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[3989, 322, 3983, 22, 1851, 1861, 1850])).
% 2.89/2.24 tff(4029,plain,
% 2.89/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4030,plain,
% 2.89/2.24 (((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4031,plain,
% 2.89/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832))))),
% 2.89/2.24 inference(monotonicity,[status(thm)],[4030])).
% 2.89/2.24 tff(4032,plain,
% 2.89/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))),
% 2.89/2.24 inference(transitivity,[status(thm)],[4031, 4029])).
% 2.89/2.24 tff(4033,plain,
% 2.89/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 2.89/2.24 inference(quant_inst,[status(thm)],[])).
% 2.89/2.24 tff(4034,plain,
% 2.89/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832))),
% 2.89/2.24 inference(modus_ponens,[status(thm)],[4033, 4032])).
% 2.89/2.24 tff(4035,plain,
% 2.89/2.24 ($false),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4034, 151, 2567, 2538, 3983, 1851, 22, 1861, 1850, 2635, 4028, 4027])).
% 2.89/2.24 tff(4036,plain,(c1_1(a832) | (~c3_1(a794)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | hskp20 | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806))), inference(lemma,lemma(discharge,[]))).
% 2.89/2.24 tff(4037,plain,
% 2.89/2.24 (c1_1(a832)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4036, 22, 1851, 1861, 1850, 346, 100, 111, 166])).
% 2.89/2.24 tff(4038,plain,
% 2.89/2.24 ((~c1_1(a832)) | (~c1_1(a794)) | (~c2_1(a832))),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[3876, 151, 1851, 22, 1861, 1850, 2078])).
% 2.89/2.24 tff(4039,plain,
% 2.89/2.24 (~c1_1(a794)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4038, 4037, 3983])).
% 2.89/2.24 tff(4040,plain,
% 2.89/2.24 (~hskp19),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[391, 4037])).
% 2.89/2.24 tff(4041,plain,
% 2.89/2.24 (hskp27),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[2596, 4040])).
% 2.89/2.24 tff(4042,plain,
% 2.89/2.24 (hskp30),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[2588, 4041, 346])).
% 2.89/2.24 tff(4043,plain,
% 2.89/2.24 (c1_1(a867)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[44, 4042])).
% 2.89/2.24 tff(4044,plain,
% 2.89/2.24 (c0_1(a867)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[55, 4042])).
% 2.89/2.24 tff(4045,plain,
% 2.89/2.24 (c3_1(a867)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[33, 4042])).
% 2.89/2.24 tff(4046,plain,
% 2.89/2.24 (c2_1(a806)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[196, 4045, 111, 100, 4044, 4043, 166])).
% 2.89/2.24 tff(4047,plain,
% 2.89/2.24 (hskp0 | c1_1(a794) | (~c2_1(a806))),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[1691, 151, 166, 100, 1861, 1850, 1434])).
% 2.89/2.24 tff(4048,plain,
% 2.89/2.24 (hskp0),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4047, 4046, 4039])).
% 2.89/2.24 tff(4049,plain,
% 2.89/2.24 (~c1_1(a793)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[675, 4048])).
% 2.89/2.24 tff(4050,plain,
% 2.89/2.24 (hskp5),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[223, 151, 4044, 4043, 4045, 166, 100, 217, 4046])).
% 2.89/2.24 tff(4051,plain,
% 2.89/2.24 (~c1_1(a800)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[263, 4050])).
% 2.89/2.24 tff(4052,plain,
% 2.89/2.24 (~c0_1(a800)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[229, 4050])).
% 2.89/2.24 tff(4053,plain,
% 2.89/2.24 (hskp7),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[3787, 151, 2567, 2538, 2527, 1851, 1861, 1515, 4039])).
% 2.89/2.24 tff(4054,plain,
% 2.89/2.24 (~c2_1(a803)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[1473, 4053])).
% 2.89/2.24 tff(4055,plain,
% 2.89/2.24 (c2_1(a793)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[669, 4048])).
% 2.89/2.24 tff(4056,plain,
% 2.89/2.24 (c0_1(a793)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[686, 4048])).
% 2.89/2.24 tff(4057,plain,
% 2.89/2.24 (c3_1(a800)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[240, 4050])).
% 2.89/2.24 tff(4058,plain,
% 2.89/2.24 (c1_1(a803)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[1495, 4053])).
% 2.89/2.24 tff(4059,plain,
% 2.89/2.24 (~c0_1(a803)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[2935, 151, 4058, 4057, 4056, 4055, 4054, 4052, 4051, 4049, 320])).
% 2.89/2.24 tff(4060,plain,
% 2.89/2.24 (c3_1(a803)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[1484, 4053])).
% 2.89/2.24 tff(4061,plain,
% 2.89/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a832)) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a832)) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4062,plain,
% 2.89/2.24 (((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803))) <=> ((~c1_1(a832)) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4063,plain,
% 2.89/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a832)) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832))))),
% 2.89/2.24 inference(monotonicity,[status(thm)],[4062])).
% 2.89/2.24 tff(4064,plain,
% 2.89/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a832)) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)))),
% 2.89/2.24 inference(transitivity,[status(thm)],[4063, 4061])).
% 2.89/2.24 tff(4065,plain,
% 2.89/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))),
% 2.89/2.24 inference(quant_inst,[status(thm)],[])).
% 2.89/2.24 tff(4066,plain,
% 2.89/2.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a832)) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832))),
% 2.89/2.24 inference(modus_ponens,[status(thm)],[4065, 4064])).
% 2.89/2.24 tff(4067,plain,
% 2.89/2.24 ($false),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4066, 151, 3983, 4058, 4060, 4037, 22, 4054, 2078, 4059])).
% 2.89/2.24 tff(4068,plain,(c3_1(a832) | (~c0_1(a806)) | c3_1(a806) | (~c3_1(a794)) | c0_1(a794) | c2_1(a794) | (~c1_1(a806)) | hskp20), inference(lemma,lemma(discharge,[]))).
% 2.89/2.24 tff(4069,plain,
% 2.89/2.24 (c3_1(a832)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4068, 3961, 3963, 3772, 3781, 3771, 3962, 3762])).
% 2.89/2.24 tff(4070,plain,
% 2.89/2.24 (~hskp19),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[385, 4069])).
% 2.89/2.24 tff(4071,plain,
% 2.89/2.24 (hskp27),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[2596, 4070])).
% 2.89/2.24 tff(4072,plain,
% 2.89/2.24 (hskp30),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[2588, 4071, 3762])).
% 2.89/2.24 tff(4073,plain,
% 2.89/2.24 (c1_1(a867)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[44, 4072])).
% 2.89/2.24 tff(4074,plain,
% 2.89/2.24 (c0_1(a867)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[55, 4072])).
% 2.89/2.24 tff(4075,plain,
% 2.89/2.24 (c3_1(a867)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[33, 4072])).
% 2.89/2.24 tff(4076,plain,
% 2.89/2.24 (c2_1(a806)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[196, 4075, 3962, 3963, 4074, 4073, 3961])).
% 2.89/2.24 tff(4077,plain,
% 2.89/2.24 ((~c1_1(a794)) | (~c2_1(a806))),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[2336, 151, 3962, 3772, 3963, 3781, 3771, 2078])).
% 2.89/2.24 tff(4078,plain,
% 2.89/2.24 (~c1_1(a794)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4077, 4076])).
% 2.89/2.24 tff(4079,plain,
% 2.89/2.24 (hskp0 | c1_1(a794) | (~c2_1(a806))),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[1691, 151, 3961, 3963, 3781, 3771, 1434])).
% 2.89/2.24 tff(4080,plain,
% 2.89/2.24 (hskp0),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4079, 4076, 4078])).
% 2.89/2.24 tff(4081,plain,
% 2.89/2.24 (~c1_1(a793)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[675, 4080])).
% 2.89/2.24 tff(4082,plain,
% 2.89/2.24 (hskp5),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[223, 151, 4074, 4073, 4075, 3961, 3963, 217, 4076])).
% 2.89/2.24 tff(4083,plain,
% 2.89/2.24 (~c1_1(a800)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[263, 4082])).
% 2.89/2.24 tff(4084,plain,
% 2.89/2.24 (~c0_1(a800)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[229, 4082])).
% 2.89/2.24 tff(4085,plain,
% 2.89/2.24 (hskp7),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[3787, 151, 2567, 2538, 2527, 3772, 3781, 1515, 4078])).
% 2.89/2.24 tff(4086,plain,
% 2.89/2.24 (~c2_1(a803)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[1473, 4085])).
% 2.89/2.24 tff(4087,plain,
% 2.89/2.24 (c2_1(a793)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[669, 4080])).
% 2.89/2.24 tff(4088,plain,
% 2.89/2.24 (c0_1(a793)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[686, 4080])).
% 2.89/2.24 tff(4089,plain,
% 2.89/2.24 (c3_1(a800)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[240, 4082])).
% 2.89/2.24 tff(4090,plain,
% 2.89/2.24 (c1_1(a803)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[1495, 4085])).
% 2.89/2.24 tff(4091,plain,
% 2.89/2.24 (~c0_1(a803)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[2935, 151, 4090, 4089, 4088, 4087, 4086, 4084, 4083, 4081, 320])).
% 2.89/2.24 tff(4092,plain,
% 2.89/2.24 (c3_1(a803)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[1484, 4085])).
% 2.89/2.24 tff(4093,plain,
% 2.89/2.24 ($false),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[2943, 151, 3962, 4090, 4092, 3963, 4086, 2078, 4076, 4091])).
% 2.89/2.24 tff(4094,plain,(c1_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.24 tff(4095,plain,
% 2.89/2.24 (c1_1(a833)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4094, 309])).
% 2.89/2.24 tff(4096,plain,
% 2.89/2.24 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 2.89/2.24 inference(bind,[status(th)],[])).
% 2.89/2.24 tff(4097,plain,
% 2.89/2.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.89/2.24 inference(quant_intro,[status(thm)],[4096])).
% 2.89/2.24 tff(4098,plain,
% 2.89/2.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4099,plain,
% 2.89/2.24 (^[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) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 2.89/2.24 inference(bind,[status(th)],[])).
% 2.89/2.24 tff(4100,plain,
% 2.89/2.24 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.89/2.24 inference(quant_intro,[status(thm)],[4099])).
% 2.89/2.24 tff(4101,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 2.89/2.24 tff(4102,plain,
% 2.89/2.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.89/2.24 inference(modus_ponens,[status(thm)],[4101, 4100])).
% 2.89/2.24 tff(4103,plain,
% 2.89/2.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.89/2.24 inference(modus_ponens,[status(thm)],[4102, 4098])).
% 2.89/2.24 tff(4104,plain,(
% 2.89/2.24 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.89/2.24 inference(skolemize,[status(sab)],[4103])).
% 2.89/2.24 tff(4105,plain,
% 2.89/2.24 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.89/2.24 inference(modus_ponens,[status(thm)],[4104, 4097])).
% 2.89/2.24 tff(4106,plain,
% 2.89/2.24 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~c0_1(a833)) | c2_1(a833) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | (~c0_1(a833)) | c2_1(a833) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a833)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4107,plain,
% 2.89/2.24 ((hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (hskp9 | (~c0_1(a833)) | c2_1(a833) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a833)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4108,plain,
% 2.89/2.24 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~c0_1(a833)) | c2_1(a833) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a833))))),
% 2.89/2.24 inference(monotonicity,[status(thm)],[4107])).
% 2.89/2.24 tff(4109,plain,
% 2.89/2.24 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | (~c0_1(a833)) | c2_1(a833) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a833)))),
% 2.89/2.24 inference(transitivity,[status(thm)],[4108, 4106])).
% 2.89/2.24 tff(4110,plain,
% 2.89/2.24 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 2.89/2.24 inference(quant_inst,[status(thm)],[])).
% 2.89/2.24 tff(4111,plain,
% 2.89/2.24 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | (~c0_1(a833)) | c2_1(a833) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a833))),
% 2.89/2.24 inference(modus_ponens,[status(thm)],[4110, 4109])).
% 2.89/2.24 tff(4112,plain,
% 2.89/2.24 (hskp9),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4111, 151, 4095, 292, 3761, 309, 298, 281, 4105])).
% 2.89/2.24 tff(4113,plain,
% 2.89/2.24 (c1_1(a806)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[87, 4112])).
% 2.89/2.24 tff(4114,plain,
% 2.89/2.24 (c0_1(a806)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[67, 4112])).
% 2.89/2.24 tff(4115,plain,
% 2.89/2.24 (~c3_1(a806)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[75, 4112])).
% 2.89/2.24 tff(4116,plain,
% 2.89/2.24 ($false),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4068, 4115, 4114, 22, 298, 292, 281, 4113, 3762])).
% 2.89/2.24 tff(4117,plain,((~hskp1) | c3_1(a832) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.24 tff(4118,plain,
% 2.89/2.24 (~hskp1),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4117, 22, 309])).
% 2.89/2.24 tff(4119,assumption,(~hskp1), introduced(assumption)).
% 2.89/2.24 tff(4120,plain,
% 2.89/2.24 (^[U: $i] : refl((hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 2.89/2.24 inference(bind,[status(th)],[])).
% 2.89/2.24 tff(4121,plain,
% 2.89/2.24 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.89/2.24 inference(quant_intro,[status(thm)],[4120])).
% 2.89/2.24 tff(4122,plain,
% 2.89/2.24 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4123,plain,
% 2.89/2.24 (^[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) | hskp1) <=> ((hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp1))), rewrite(((hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp1) <=> (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1) <=> (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 2.89/2.24 inference(bind,[status(th)],[])).
% 2.89/2.24 tff(4124,plain,
% 2.89/2.24 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.89/2.24 inference(quant_intro,[status(thm)],[4123])).
% 2.89/2.24 tff(4125,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 2.89/2.24 tff(4126,plain,
% 2.89/2.24 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.89/2.24 inference(modus_ponens,[status(thm)],[4125, 4124])).
% 2.89/2.24 tff(4127,plain,
% 2.89/2.24 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.89/2.24 inference(modus_ponens,[status(thm)],[4126, 4122])).
% 2.89/2.24 tff(4128,plain,(
% 2.89/2.24 ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.89/2.24 inference(skolemize,[status(sab)],[4127])).
% 2.89/2.24 tff(4129,plain,
% 2.89/2.24 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.89/2.24 inference(modus_ponens,[status(thm)],[4128, 4121])).
% 2.89/2.24 tff(4130,plain,
% 2.89/2.24 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp13 | hskp1 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp13 | hskp1 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4131,plain,
% 2.89/2.24 ((hskp13 | hskp1 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (hskp13 | hskp1 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4132,plain,
% 2.89/2.24 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp13 | hskp1 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))))),
% 2.89/2.24 inference(monotonicity,[status(thm)],[4131])).
% 2.89/2.24 tff(4133,plain,
% 2.89/2.24 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp13 | hskp1 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 2.89/2.24 inference(transitivity,[status(thm)],[4132, 4130])).
% 2.89/2.24 tff(4134,plain,
% 2.89/2.24 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 2.89/2.24 inference(quant_inst,[status(thm)],[])).
% 2.89/2.24 tff(4135,plain,
% 2.89/2.24 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp13 | hskp1 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))),
% 2.89/2.24 inference(modus_ponens,[status(thm)],[4134, 4133])).
% 2.89/2.24 tff(4136,plain,
% 2.89/2.24 (hskp13 | hskp1 | c3_1(a833) | (~c1_1(a833))),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4135, 151, 309, 4129])).
% 2.89/2.24 tff(4137,plain,
% 2.89/2.24 (hskp13),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[4136, 4119, 4095, 310])).
% 2.89/2.24 tff(4138,plain,
% 2.89/2.24 (~c0_1(a814)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[3595, 4137])).
% 2.89/2.24 tff(4139,plain,
% 2.89/2.24 (c1_1(a814)),
% 2.89/2.24 inference(unit_resolution,[status(thm)],[3606, 4137])).
% 2.89/2.24 tff(4140,plain,
% 2.89/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c0_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c0_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c3_1(a833) | (~c1_1(a833)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4141,plain,
% 2.89/2.24 (((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a814) | (~c2_1(a814)) | (~c1_1(a814))) <=> ((~c0_1(a833)) | c2_1(a833) | c0_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c3_1(a833) | (~c1_1(a833)))),
% 2.89/2.24 inference(rewrite,[status(thm)],[])).
% 2.89/2.24 tff(4142,plain,
% 2.89/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a814) | (~c2_1(a814)) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c0_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c3_1(a833) | (~c1_1(a833))))),
% 2.89/2.24 inference(monotonicity,[status(thm)],[4141])).
% 2.89/2.24 tff(4143,plain,
% 2.89/2.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a814) | (~c2_1(a814)) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c0_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c3_1(a833) | (~c1_1(a833)))),
% 2.89/2.25 inference(transitivity,[status(thm)],[4142, 4140])).
% 2.89/2.25 tff(4144,plain,
% 2.89/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a814) | (~c2_1(a814)) | (~c1_1(a814)))),
% 2.89/2.25 inference(quant_inst,[status(thm)],[])).
% 2.89/2.25 tff(4145,plain,
% 2.89/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c0_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c3_1(a833) | (~c1_1(a833))),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4144, 4143])).
% 2.89/2.25 tff(4146,plain,
% 2.89/2.25 (~c2_1(a814)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4145, 151, 4095, 4139, 3761, 309, 4138, 99, 310])).
% 2.89/2.25 tff(4147,assumption,(c0_1(a808)), introduced(assumption)).
% 2.89/2.25 tff(4148,plain,
% 2.89/2.25 (hskp9),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[2122, 4147])).
% 2.89/2.25 tff(4149,plain,
% 2.89/2.25 (c1_1(a806)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[87, 4148])).
% 2.89/2.25 tff(4150,plain,
% 2.89/2.25 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c0_1(a808)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c0_1(a808)))),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4151,plain,
% 2.89/2.25 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c0_1(a808))) <=> (hskp20 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c0_1(a808)))),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4152,plain,
% 2.89/2.25 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c0_1(a808)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c0_1(a808))))),
% 2.89/2.25 inference(monotonicity,[status(thm)],[4151])).
% 2.89/2.25 tff(4153,plain,
% 2.89/2.25 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c0_1(a808)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c0_1(a808)))),
% 2.89/2.25 inference(transitivity,[status(thm)],[4152, 4150])).
% 2.89/2.25 tff(4154,plain,
% 2.89/2.25 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c0_1(a808)))),
% 2.89/2.25 inference(quant_inst,[status(thm)],[])).
% 2.89/2.25 tff(4155,plain,
% 2.89/2.25 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c0_1(a808))),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4154, 4153])).
% 2.89/2.25 tff(4156,plain,
% 2.89/2.25 (hskp1 | (~c0_1(a808))),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4155, 151, 346, 878, 877, 1646])).
% 2.89/2.25 tff(4157,plain,
% 2.89/2.25 (hskp1),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4156, 4147])).
% 2.89/2.25 tff(4158,plain,
% 2.89/2.25 (~c2_1(a794)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[280, 4157])).
% 2.89/2.25 tff(4159,plain,
% 2.89/2.25 (~c0_1(a794)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[297, 4157])).
% 2.89/2.25 tff(4160,plain,
% 2.89/2.25 (c3_1(a794)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[291, 4157])).
% 2.89/2.25 tff(4161,plain,
% 2.89/2.25 (c0_1(a806)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[67, 4148])).
% 2.89/2.25 tff(4162,plain,
% 2.89/2.25 (~c3_1(a806)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[75, 4148])).
% 2.89/2.25 tff(4163,plain,
% 2.89/2.25 ($false),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4068, 4162, 4161, 22, 4160, 4159, 4158, 4149, 346])).
% 2.89/2.25 tff(4164,plain,((~c0_1(a808)) | c3_1(a832) | hskp20 | c1_1(a808) | c2_1(a808) | (~c3_1(a808))), inference(lemma,lemma(discharge,[]))).
% 2.89/2.25 tff(4165,plain,
% 2.89/2.25 (~c0_1(a808)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4164, 3795, 3762, 22, 3794, 3796])).
% 2.89/2.25 tff(4166,plain,
% 2.89/2.25 (hskp7 | c0_1(a808)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[2980, 151, 2567, 2538, 2527, 3796, 3795, 1515])).
% 2.89/2.25 tff(4167,plain,
% 2.89/2.25 (hskp7),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4166, 4165])).
% 2.89/2.25 tff(4168,plain,
% 2.89/2.25 (c1_1(a832)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[1504, 4167, 22, 1458])).
% 2.89/2.25 tff(4169,plain,
% 2.89/2.25 (hskp12 | (~c1_1(a832))),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[3007, 151, 3791, 3792, 3790, 1458, 22, 110])).
% 2.89/2.25 tff(4170,plain,
% 2.89/2.25 (hskp12),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4169, 4168])).
% 2.89/2.25 tff(4171,plain,
% 2.89/2.25 (~c0_1(a809)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[164, 4170])).
% 2.89/2.25 tff(4172,plain,
% 2.89/2.25 (c2_1(a809)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[176, 4170])).
% 2.89/2.25 tff(4173,plain,
% 2.89/2.25 (c1_1(a809)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[187, 4170])).
% 2.89/2.25 tff(4174,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a832) | (~c0_1(a833)) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c0_1(a833)) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c1_1(a833)))),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4175,plain,
% 2.89/2.25 (((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809))) <=> (c2_1(a832) | (~c0_1(a833)) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c1_1(a833)))),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4176,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a832) | (~c0_1(a833)) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c1_1(a833))))),
% 2.89/2.25 inference(monotonicity,[status(thm)],[4175])).
% 2.89/2.25 tff(4177,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c0_1(a833)) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c1_1(a833)))),
% 2.89/2.25 inference(transitivity,[status(thm)],[4176, 4174])).
% 2.89/2.25 tff(4178,plain,
% 2.89/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.89/2.25 inference(quant_inst,[status(thm)],[])).
% 2.89/2.25 tff(4179,plain,
% 2.89/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c0_1(a833)) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c1_1(a833))),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4178, 4177])).
% 2.89/2.25 tff(4180,plain,
% 2.89/2.25 ($false),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4179, 151, 4095, 1458, 4173, 4172, 3761, 309, 4168, 22, 4171, 99])).
% 2.89/2.25 tff(4181,plain,(c2_1(a832) | c2_1(a833) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.25 tff(4182,plain,
% 2.89/2.25 (c2_1(a832)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4181, 22, 309])).
% 2.89/2.25 tff(4183,plain,
% 2.89/2.25 (hskp15),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[3354, 1069, 4182])).
% 2.89/2.25 tff(4184,plain,
% 2.89/2.25 (~c1_1(a817)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[1342, 4183])).
% 2.89/2.25 tff(4185,plain,
% 2.89/2.25 (c3_1(a817)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[1353, 4183])).
% 2.89/2.25 tff(4186,plain,
% 2.89/2.25 (c2_1(a817)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[1364, 4183])).
% 2.89/2.25 tff(4187,plain,
% 2.89/2.25 (~c2_1(a814)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4145, 151, 4095, 3610, 3761, 309, 3618, 99, 310])).
% 2.89/2.25 tff(4188,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a817) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)) | (~c1_1(a814)) | (~c2_1(a817)) | (~c3_1(a817)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a817) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)) | (~c1_1(a814)) | (~c2_1(a817)) | (~c3_1(a817)))),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4189,plain,
% 2.89/2.25 (((~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814))) <=> (c1_1(a817) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)) | (~c1_1(a814)) | (~c2_1(a817)) | (~c3_1(a817)))),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4190,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a817) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)) | (~c1_1(a814)) | (~c2_1(a817)) | (~c3_1(a817))))),
% 2.89/2.25 inference(monotonicity,[status(thm)],[4189])).
% 2.89/2.25 tff(4191,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a817) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)) | (~c1_1(a814)) | (~c2_1(a817)) | (~c3_1(a817)))),
% 2.89/2.25 inference(transitivity,[status(thm)],[4190, 4188])).
% 2.89/2.25 tff(4192,plain,
% 2.89/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814)))),
% 2.89/2.25 inference(quant_inst,[status(thm)],[])).
% 2.89/2.25 tff(4193,plain,
% 2.89/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a817) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)) | (~c1_1(a814)) | (~c2_1(a817)) | (~c3_1(a817))),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4192, 4191])).
% 2.89/2.25 tff(4194,plain,
% 2.89/2.25 (~c0_1(a797)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4193, 151, 2538, 2527, 2849, 2848, 3610, 2847, 3618, 3609, 800])).
% 2.89/2.25 tff(4195,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a814) | (~c1_1(a814)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a814) | (~c1_1(a814)) | (~c1_1(a833)))),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4196,plain,
% 2.89/2.25 (((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a814) | c2_1(a814) | (~c1_1(a814)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797))) <=> ((~c0_1(a833)) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a814) | (~c1_1(a814)) | (~c1_1(a833)))),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4197,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a814) | c2_1(a814) | (~c1_1(a814)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a814) | (~c1_1(a814)) | (~c1_1(a833))))),
% 2.89/2.25 inference(monotonicity,[status(thm)],[4196])).
% 2.89/2.25 tff(4198,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a814) | c2_1(a814) | (~c1_1(a814)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a814) | (~c1_1(a814)) | (~c1_1(a833)))),
% 2.89/2.25 inference(transitivity,[status(thm)],[4197, 4195])).
% 2.89/2.25 tff(4199,plain,
% 2.89/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a814) | c2_1(a814) | (~c1_1(a814)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))),
% 2.89/2.25 inference(quant_inst,[status(thm)],[])).
% 2.89/2.25 tff(4200,plain,
% 2.89/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a814) | (~c1_1(a814)) | (~c1_1(a833))),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4199, 4198])).
% 2.89/2.25 tff(4201,plain,
% 2.89/2.25 ($false),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4200, 151, 2567, 2538, 4095, 3610, 3761, 309, 3609, 99, 4194, 4187])).
% 2.89/2.25 tff(4202,plain,((~hskp13) | c2_1(a833) | c3_1(a833) | (~c2_1(a817)) | (~c3_1(a817)) | c1_1(a817)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.25 tff(4203,plain,
% 2.89/2.25 (~hskp13),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4202, 4186, 310, 309, 4185, 4184])).
% 2.89/2.25 tff(4204,plain,
% 2.89/2.25 (hskp1),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4136, 4203, 4095, 310])).
% 2.89/2.25 tff(4205,plain,
% 2.89/2.25 (~c0_1(a794)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[297, 4204])).
% 2.89/2.25 tff(4206,plain,
% 2.89/2.25 (c3_1(a794)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[291, 4204])).
% 2.89/2.25 tff(4207,plain,
% 2.89/2.25 (~c2_1(a794)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[280, 4204])).
% 2.89/2.25 tff(4208,plain,
% 2.89/2.25 ($false),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[3989, 4207, 4206, 4182, 22, 322, 1069, 4205])).
% 2.89/2.25 tff(4209,plain,(c0_1(a832) | c3_1(a832) | c1_1(a832) | c3_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.25 tff(4210,plain,
% 2.89/2.25 (c0_1(a832)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4209, 310, 322, 22, 309])).
% 2.89/2.25 tff(4211,plain,
% 2.89/2.25 (~c3_1(a814)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[3589, 4137])).
% 2.89/2.25 tff(4212,assumption,(~c2_1(a814)), introduced(assumption)).
% 2.89/2.25 tff(4213,assumption,(~c3_1(a814)), introduced(assumption)).
% 2.89/2.25 tff(4214,assumption,(~c0_1(a814)), introduced(assumption)).
% 2.89/2.25 tff(4215,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c2_1(a814) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c2_1(a814) | (~c0_1(a832)))),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4216,plain,
% 2.89/2.25 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a814) | c0_1(a814) | c3_1(a814)) <=> (c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c2_1(a814) | (~c0_1(a832)))),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4217,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a814) | c0_1(a814) | c3_1(a814))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c2_1(a814) | (~c0_1(a832))))),
% 2.89/2.25 inference(monotonicity,[status(thm)],[4216])).
% 2.89/2.25 tff(4218,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a814) | c0_1(a814) | c3_1(a814))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c2_1(a814) | (~c0_1(a832)))),
% 2.89/2.25 inference(transitivity,[status(thm)],[4217, 4215])).
% 2.89/2.25 tff(4219,plain,
% 2.89/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a814) | c0_1(a814) | c3_1(a814))),
% 2.89/2.25 inference(quant_inst,[status(thm)],[])).
% 2.89/2.25 tff(4220,plain,
% 2.89/2.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c2_1(a814) | (~c0_1(a832))),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4219, 4218])).
% 2.89/2.25 tff(4221,plain,
% 2.89/2.25 ($false),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4220, 151, 1518, 322, 22, 4214, 4213, 1517, 1527, 876, 456, 4212])).
% 2.89/2.25 tff(4222,plain,((~hskp11) | c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | (~c0_1(a832)) | c2_1(a814)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.25 tff(4223,plain,
% 2.89/2.25 (~hskp11),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4222, 4138, 22, 322, 4211, 4210, 4146])).
% 2.89/2.25 tff(4224,plain,
% 2.89/2.25 (hskp21),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[2574, 4223])).
% 2.89/2.25 tff(4225,plain,
% 2.89/2.25 (hskp9),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[2948, 4224, 3762])).
% 2.89/2.25 tff(4226,plain,
% 2.89/2.25 (~c3_1(a806)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[75, 4225])).
% 2.89/2.25 tff(4227,plain,
% 2.89/2.25 ((hskp22 | hskp11 | hskp1) <=> (hskp22 | hskp11 | hskp1)),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4228,plain,
% 2.89/2.25 (((hskp22 | hskp1) | hskp11) <=> (hskp22 | hskp11 | hskp1)),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4229,plain,
% 2.89/2.25 ((hskp22 | hskp1) <=> (hskp22 | hskp1)),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4230,plain,
% 2.89/2.25 (((hskp22 | hskp1) | hskp11) <=> ((hskp22 | hskp1) | hskp11)),
% 2.89/2.25 inference(monotonicity,[status(thm)],[4229])).
% 2.89/2.25 tff(4231,plain,
% 2.89/2.25 (((hskp22 | hskp1) | hskp11) <=> (hskp22 | hskp11 | hskp1)),
% 2.89/2.25 inference(transitivity,[status(thm)],[4230, 4228])).
% 2.89/2.25 tff(4232,axiom,((hskp22 | hskp1) | hskp11), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 2.89/2.25 tff(4233,plain,
% 2.89/2.25 (hskp22 | hskp11 | hskp1),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4232, 4231])).
% 2.89/2.25 tff(4234,plain,
% 2.89/2.25 (hskp22 | hskp11 | hskp1),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4233, 4227])).
% 2.89/2.25 tff(4235,plain,
% 2.89/2.25 (hskp22 | hskp11 | hskp1),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4234, 4227])).
% 2.89/2.25 tff(4236,plain,
% 2.89/2.25 (hskp22 | hskp11 | hskp1),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4235, 4227])).
% 2.89/2.25 tff(4237,plain,
% 2.89/2.25 (hskp22 | hskp11 | hskp1),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4236, 4227])).
% 2.89/2.25 tff(4238,plain,
% 2.89/2.25 (hskp22 | hskp11 | hskp1),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4237, 4227])).
% 2.89/2.25 tff(4239,plain,
% 2.89/2.25 (hskp22 | hskp11 | hskp1),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4238, 4227])).
% 2.89/2.25 tff(4240,plain,
% 2.89/2.25 (hskp22 | hskp11 | hskp1),
% 2.89/2.25 inference(modus_ponens,[status(thm)],[4239, 4227])).
% 2.89/2.25 tff(4241,plain,
% 2.89/2.25 (hskp22),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[4240, 4223, 4119])).
% 2.89/2.25 tff(4242,plain,
% 2.89/2.25 (~c0_1(a840)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[1934, 4241])).
% 2.89/2.25 tff(4243,plain,
% 2.89/2.25 (c1_1(a806)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[87, 4225])).
% 2.89/2.25 tff(4244,plain,
% 2.89/2.25 (c0_1(a806)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[67, 4225])).
% 2.89/2.25 tff(4245,plain,
% 2.89/2.25 (c3_1(a840)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[1945, 4241])).
% 2.89/2.25 tff(4246,plain,
% 2.89/2.25 (c1_1(a840)),
% 2.89/2.25 inference(unit_resolution,[status(thm)],[1974, 4241])).
% 2.89/2.25 tff(4247,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a840) | c0_1(a814) | c3_1(a814) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | c2_1(a814) | (~c1_1(a840)) | (~c3_1(a840)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a840) | c0_1(a814) | c3_1(a814) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | c2_1(a814) | (~c1_1(a840)) | (~c3_1(a840)))),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4248,plain,
% 2.89/2.25 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a814) | c0_1(a814) | c3_1(a814)) <=> (c0_1(a840) | c0_1(a814) | c3_1(a814) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | c2_1(a814) | (~c1_1(a840)) | (~c3_1(a840)))),
% 2.89/2.25 inference(rewrite,[status(thm)],[])).
% 2.89/2.25 tff(4249,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a814) | c0_1(a814) | c3_1(a814))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a840) | c0_1(a814) | c3_1(a814) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | c2_1(a814) | (~c1_1(a840)) | (~c3_1(a840))))),
% 2.89/2.25 inference(monotonicity,[status(thm)],[4248])).
% 2.89/2.25 tff(4250,plain,
% 2.89/2.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a814) | c0_1(a814) | c3_1(a814))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a840) | c0_1(a814) | c3_1(a814) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | c2_1(a814) | (~c1_1(a840)) | (~c3_1(a840)))),
% 2.89/2.26 inference(transitivity,[status(thm)],[4249, 4247])).
% 2.89/2.26 tff(4251,plain,
% 2.89/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a814) | c0_1(a814) | c3_1(a814))),
% 2.89/2.26 inference(quant_inst,[status(thm)],[])).
% 2.89/2.26 tff(4252,plain,
% 2.89/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a840) | c0_1(a814) | c3_1(a814) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | c2_1(a814) | (~c1_1(a840)) | (~c3_1(a840))),
% 2.89/2.26 inference(modus_ponens,[status(thm)],[4251, 4250])).
% 2.89/2.26 tff(4253,plain,
% 2.89/2.26 ($false),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4252, 151, 4246, 4245, 4244, 4243, 4242, 4138, 4211, 4226, 2556, 4146])).
% 2.89/2.26 tff(4254,plain,(hskp1 | c3_1(a832) | c1_1(a832) | c2_1(a833) | c3_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.26 tff(4255,plain,
% 2.89/2.26 (c3_1(a833)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4254, 322, 4118, 309, 22])).
% 2.89/2.26 tff(4256,plain,
% 2.89/2.26 (hskp9),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[3959, 750, 3762, 3761])).
% 2.89/2.26 tff(4257,plain,
% 2.89/2.26 (~c3_1(a806)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[75, 4256])).
% 2.89/2.26 tff(4258,plain,
% 2.89/2.26 (c1_1(a806)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[87, 4256])).
% 2.89/2.26 tff(4259,plain,
% 2.89/2.26 (c0_1(a806)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[67, 4256])).
% 2.89/2.26 tff(4260,plain,
% 2.89/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a833) | c3_1(a832) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a833) | c3_1(a832) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4261,plain,
% 2.89/2.26 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c0_1(a832) | c3_1(a832) | (~c2_1(a832))) <=> (c2_1(a833) | c3_1(a832) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4262,plain,
% 2.89/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a833) | c3_1(a832) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.89/2.26 inference(monotonicity,[status(thm)],[4261])).
% 2.89/2.26 tff(4263,plain,
% 2.89/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a833) | c3_1(a832) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.26 inference(transitivity,[status(thm)],[4262, 4260])).
% 2.89/2.26 tff(4264,plain,
% 2.89/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)))),
% 2.89/2.26 inference(quant_inst,[status(thm)],[])).
% 2.89/2.26 tff(4265,plain,
% 2.89/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a833) | c3_1(a832) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.89/2.26 inference(modus_ponens,[status(thm)],[4264, 4263])).
% 2.89/2.26 tff(4266,plain,
% 2.89/2.26 ($false),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4265, 151, 4095, 4182, 4259, 4258, 309, 22, 4257, 308, 1069, 750])).
% 2.89/2.26 tff(4267,plain,(c0_1(a832) | c2_1(a833) | c3_1(a832) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 2.89/2.26 tff(4268,plain,
% 2.89/2.26 (c0_1(a832)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4267, 4255, 22, 309])).
% 2.89/2.26 tff(4269,plain,
% 2.89/2.26 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~c0_1(a833)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~c0_1(a833)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4270,plain,
% 2.89/2.26 ((hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832))) <=> (hskp5 | (~c0_1(a833)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4271,plain,
% 2.89/2.26 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~c0_1(a833)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.89/2.26 inference(monotonicity,[status(thm)],[4270])).
% 2.89/2.26 tff(4272,plain,
% 2.89/2.26 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~c0_1(a833)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.26 inference(transitivity,[status(thm)],[4271, 4269])).
% 2.89/2.26 tff(4273,plain,
% 2.89/2.26 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))),
% 2.89/2.26 inference(quant_inst,[status(thm)],[])).
% 2.89/2.26 tff(4274,plain,
% 2.89/2.26 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~c0_1(a833)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.89/2.26 inference(modus_ponens,[status(thm)],[4273, 4272])).
% 2.89/2.26 tff(4275,plain,
% 2.89/2.26 (hskp5 | (~c0_1(a832))),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4274, 151, 4095, 4182, 3761, 22, 217, 4255])).
% 2.89/2.26 tff(4276,plain,
% 2.89/2.26 (hskp5),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4275, 4268])).
% 2.89/2.26 tff(4277,plain,
% 2.89/2.26 (~c1_1(a800)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[263, 4276])).
% 2.89/2.26 tff(4278,plain,
% 2.89/2.26 (~c0_1(a800)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[229, 4276])).
% 2.89/2.26 tff(4279,plain,
% 2.89/2.26 (c3_1(a800)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[240, 4276])).
% 2.89/2.26 tff(4280,plain,
% 2.89/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c1_1(a832) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c1_1(a832) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c1_1(a833)))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4281,plain,
% 2.89/2.26 (((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> ((~c0_1(a833)) | c2_1(a833) | c1_1(a832) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c1_1(a833)))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4282,plain,
% 2.89/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c1_1(a832) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c1_1(a833))))),
% 2.89/2.26 inference(monotonicity,[status(thm)],[4281])).
% 2.89/2.26 tff(4283,plain,
% 2.89/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c1_1(a832) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c1_1(a833)))),
% 2.89/2.26 inference(transitivity,[status(thm)],[4282, 4280])).
% 2.89/2.26 tff(4284,plain,
% 2.89/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 2.89/2.26 inference(quant_inst,[status(thm)],[])).
% 2.89/2.26 tff(4285,plain,
% 2.89/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c1_1(a832) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c1_1(a833))),
% 2.89/2.26 inference(modus_ponens,[status(thm)],[4284, 4283])).
% 2.89/2.26 tff(4286,plain,
% 2.89/2.26 ($false),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4285, 151, 4095, 4182, 4279, 3761, 309, 322, 4278, 4277, 320, 4268])).
% 2.89/2.26 tff(4287,plain,(c1_1(a832) | c2_1(a833) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.26 tff(4288,plain,
% 2.89/2.26 (c1_1(a832)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4287, 22, 309])).
% 2.89/2.26 tff(4289,plain,
% 2.89/2.26 (~hskp19),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[391, 4288])).
% 2.89/2.26 tff(4290,plain,
% 2.89/2.26 (hskp27),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[2596, 4289])).
% 2.89/2.26 tff(4291,plain,
% 2.89/2.26 (c3_1(a796)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[594, 4290])).
% 2.89/2.26 tff(4292,plain,
% 2.89/2.26 (hskp30),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[2588, 4290, 3762])).
% 2.89/2.26 tff(4293,plain,
% 2.89/2.26 (c3_1(a867)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[33, 4292])).
% 2.89/2.26 tff(4294,plain,
% 2.89/2.26 (c0_1(a867)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[55, 4292])).
% 2.89/2.26 tff(4295,plain,
% 2.89/2.26 (c0_1(a796)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[616, 4290])).
% 2.89/2.26 tff(4296,plain,
% 2.89/2.26 (c2_1(a796)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[605, 4290])).
% 2.89/2.26 tff(4297,plain,
% 2.89/2.26 (c1_1(a867)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[44, 4292])).
% 2.89/2.26 tff(4298,plain,
% 2.89/2.26 (hskp11),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[2971, 4297, 3762, 4296, 4295, 4294, 4293, 4291])).
% 2.89/2.26 tff(4299,plain,
% 2.89/2.26 (~c2_1(a808)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[857, 4298])).
% 2.89/2.26 tff(4300,plain,
% 2.89/2.26 (~c1_1(a808)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[851, 4298])).
% 2.89/2.26 tff(4301,plain,
% 2.89/2.26 (c3_1(a808)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[896, 4298])).
% 2.89/2.26 tff(4302,plain,
% 2.89/2.26 (~c0_1(a808)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4164, 4301, 3762, 4300, 4299, 22])).
% 2.89/2.26 tff(4303,plain,
% 2.89/2.26 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | c0_1(a808))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | c0_1(a808))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4304,plain,
% 2.89/2.26 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | c0_1(a808)) <=> (hskp2 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | c0_1(a808))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4305,plain,
% 2.89/2.26 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | c0_1(a808))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | c0_1(a808)))),
% 2.89/2.26 inference(monotonicity,[status(thm)],[4304])).
% 2.89/2.26 tff(4306,plain,
% 2.89/2.26 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | c0_1(a808))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | c0_1(a808))),
% 2.89/2.26 inference(transitivity,[status(thm)],[4305, 4303])).
% 2.89/2.26 tff(4307,plain,
% 2.89/2.26 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | c0_1(a808))),
% 2.89/2.26 inference(quant_inst,[status(thm)],[])).
% 2.89/2.26 tff(4308,plain,
% 2.89/2.26 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | c0_1(a808)),
% 2.89/2.26 inference(modus_ponens,[status(thm)],[4307, 4306])).
% 2.89/2.26 tff(4309,plain,
% 2.89/2.26 (hskp2),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4308, 151, 4118, 4300, 4299, 2445, 4302])).
% 2.89/2.26 tff(4310,plain,
% 2.89/2.26 (~c3_1(a795)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[1417, 4309])).
% 2.89/2.26 tff(4311,plain,
% 2.89/2.26 (~c0_1(a795)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[1449, 4309])).
% 2.89/2.26 tff(4312,plain,
% 2.89/2.26 (hskp7),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[2980, 151, 2567, 2538, 2527, 4301, 4300, 1515, 4302])).
% 2.89/2.26 tff(4313,plain,
% 2.89/2.26 (~c2_1(a803)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[1473, 4312])).
% 2.89/2.26 tff(4314,plain,
% 2.89/2.26 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~c0_1(a833)) | c2_1(a833) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | (~c0_1(a833)) | c2_1(a833) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c1_1(a833)))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4315,plain,
% 2.89/2.26 ((hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (hskp9 | (~c0_1(a833)) | c2_1(a833) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c1_1(a833)))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4316,plain,
% 2.89/2.26 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~c0_1(a833)) | c2_1(a833) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c1_1(a833))))),
% 2.89/2.26 inference(monotonicity,[status(thm)],[4315])).
% 2.89/2.26 tff(4317,plain,
% 2.89/2.26 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | (~c0_1(a833)) | c2_1(a833) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c1_1(a833)))),
% 2.89/2.26 inference(transitivity,[status(thm)],[4316, 4314])).
% 2.89/2.26 tff(4318,plain,
% 2.89/2.26 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 2.89/2.26 inference(quant_inst,[status(thm)],[])).
% 2.89/2.26 tff(4319,plain,
% 2.89/2.26 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | (~c0_1(a833)) | c2_1(a833) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c1_1(a833))),
% 2.89/2.26 inference(modus_ponens,[status(thm)],[4318, 4317])).
% 2.89/2.26 tff(4320,plain,
% 2.89/2.26 (hskp9),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4319, 151, 4095, 4301, 3761, 309, 4299, 4105, 4302])).
% 2.89/2.26 tff(4321,plain,
% 2.89/2.26 (~c3_1(a806)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[75, 4320])).
% 2.89/2.26 tff(4322,plain,
% 2.89/2.26 (c3_1(a803)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[1484, 4312])).
% 2.89/2.26 tff(4323,plain,
% 2.89/2.26 (c1_1(a803)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[1495, 4312])).
% 2.89/2.26 tff(4324,plain,
% 2.89/2.26 (c1_1(a806)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[87, 4320])).
% 2.89/2.26 tff(4325,plain,
% 2.89/2.26 (c0_1(a806)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[67, 4320])).
% 2.89/2.26 tff(4326,plain,
% 2.89/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a806) | c2_1(a803) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a806) | c2_1(a803) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4327,plain,
% 2.89/2.26 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a795) | c3_1(a795) | (~c2_1(a795))) <=> (c3_1(a806) | c2_1(a803) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4328,plain,
% 2.89/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a806) | c2_1(a803) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806))))),
% 2.89/2.26 inference(monotonicity,[status(thm)],[4327])).
% 2.89/2.26 tff(4329,plain,
% 2.89/2.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a806) | c2_1(a803) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 2.89/2.26 inference(transitivity,[status(thm)],[4328, 4326])).
% 2.89/2.26 tff(4330,plain,
% 2.89/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)))),
% 2.89/2.26 inference(quant_inst,[status(thm)],[])).
% 2.89/2.26 tff(4331,plain,
% 2.89/2.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a806) | c2_1(a803) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806))),
% 2.89/2.26 inference(modus_ponens,[status(thm)],[4330, 4329])).
% 2.89/2.26 tff(4332,plain,
% 2.89/2.26 (~c2_1(a795)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4331, 151, 4325, 4324, 4323, 4322, 4321, 4313, 4311, 4310, 308])).
% 2.89/2.26 tff(4333,plain,
% 2.89/2.26 (~c1_1(a795)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[1423, 4309])).
% 2.89/2.26 tff(4334,plain,
% 2.89/2.26 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a803) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a803)) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a803) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a803)) | (~c1_1(a803)))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4335,plain,
% 2.89/2.26 ((hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a795) | c2_1(a795) | c1_1(a795)) <=> (hskp19 | c2_1(a803) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a803)) | (~c1_1(a803)))),
% 2.89/2.26 inference(rewrite,[status(thm)],[])).
% 2.89/2.26 tff(4336,plain,
% 2.89/2.26 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a795) | c2_1(a795) | c1_1(a795))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a803) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a803)) | (~c1_1(a803))))),
% 2.89/2.26 inference(monotonicity,[status(thm)],[4335])).
% 2.89/2.26 tff(4337,plain,
% 2.89/2.26 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a795) | c2_1(a795) | c1_1(a795))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a803) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a803)) | (~c1_1(a803)))),
% 2.89/2.26 inference(transitivity,[status(thm)],[4336, 4334])).
% 2.89/2.26 tff(4338,plain,
% 2.89/2.26 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a795) | c2_1(a795) | c1_1(a795))),
% 2.89/2.26 inference(quant_inst,[status(thm)],[])).
% 2.89/2.26 tff(4339,plain,
% 2.89/2.26 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a803) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a803)) | (~c1_1(a803))),
% 2.89/2.26 inference(modus_ponens,[status(thm)],[4338, 4337])).
% 2.89/2.26 tff(4340,plain,
% 2.89/2.26 ($false),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4339, 151, 4289, 4323, 4322, 4313, 4333, 4310, 10, 4332])).
% 2.89/2.26 tff(4341,plain,(c3_1(a832) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.26 tff(4342,plain,
% 2.89/2.26 (c3_1(a832)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[4341, 309])).
% 2.89/2.26 tff(4343,plain,
% 2.89/2.26 (~hskp19),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[385, 4342])).
% 2.89/2.26 tff(4344,plain,
% 2.89/2.26 (hskp27),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[2596, 4343])).
% 2.89/2.26 tff(4345,plain,
% 2.89/2.26 (hskp30),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[2588, 4344, 3762])).
% 2.89/2.26 tff(4346,plain,
% 2.89/2.26 (c3_1(a867)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[33, 4345])).
% 2.89/2.26 tff(4347,plain,
% 2.89/2.26 (c1_1(a867)),
% 2.89/2.26 inference(unit_resolution,[status(thm)],[44, 4345])).
% 2.89/2.27 tff(4348,plain,
% 2.89/2.27 (c0_1(a867)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[55, 4345])).
% 2.89/2.27 tff(4349,plain,
% 2.89/2.27 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c3_1(a833) | (~c1_1(a833)))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4350,plain,
% 2.89/2.27 ((hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833))) <=> (hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c3_1(a833) | (~c1_1(a833)))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4351,plain,
% 2.89/2.27 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c3_1(a833) | (~c1_1(a833))))),
% 2.89/2.27 inference(monotonicity,[status(thm)],[4350])).
% 2.89/2.27 tff(4352,plain,
% 2.89/2.27 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c3_1(a833) | (~c1_1(a833)))),
% 2.89/2.27 inference(transitivity,[status(thm)],[4351, 4349])).
% 2.89/2.27 tff(4353,plain,
% 2.89/2.27 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)))),
% 2.89/2.27 inference(quant_inst,[status(thm)],[])).
% 2.89/2.27 tff(4354,plain,
% 2.89/2.27 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c3_1(a833) | (~c1_1(a833))),
% 2.89/2.27 inference(modus_ponens,[status(thm)],[4353, 4352])).
% 2.89/2.27 tff(4355,plain,
% 2.89/2.27 (hskp12),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4354, 151, 4348, 4347, 4346, 4095, 309, 110, 310])).
% 2.89/2.27 tff(4356,plain,
% 2.89/2.27 (~c0_1(a809)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[164, 4355])).
% 2.89/2.27 tff(4357,plain,
% 2.89/2.27 (c2_1(a809)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[176, 4355])).
% 2.89/2.27 tff(4358,plain,
% 2.89/2.27 (c1_1(a809)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[187, 4355])).
% 2.89/2.27 tff(4359,plain,
% 2.89/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | c3_1(a833) | (~c1_1(a833)))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4360,plain,
% 2.89/2.27 (((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809))) <=> ((~c0_1(a833)) | c2_1(a833) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | c3_1(a833) | (~c1_1(a833)))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4361,plain,
% 2.89/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | c3_1(a833) | (~c1_1(a833))))),
% 2.89/2.27 inference(monotonicity,[status(thm)],[4360])).
% 2.89/2.27 tff(4362,plain,
% 2.89/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | c3_1(a833) | (~c1_1(a833)))),
% 2.89/2.27 inference(transitivity,[status(thm)],[4361, 4359])).
% 2.89/2.27 tff(4363,plain,
% 2.89/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))),
% 2.89/2.27 inference(quant_inst,[status(thm)],[])).
% 2.89/2.27 tff(4364,plain,
% 2.89/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | c3_1(a833) | (~c1_1(a833))),
% 2.89/2.27 inference(modus_ponens,[status(thm)],[4363, 4362])).
% 2.89/2.27 tff(4365,plain,
% 2.89/2.27 ($false),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4364, 151, 4095, 4358, 4357, 3761, 309, 4356, 99, 310])).
% 2.89/2.27 tff(4366,plain,(c3_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.27 tff(4367,plain,
% 2.89/2.27 (c3_1(a833)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4366, 309])).
% 2.89/2.27 tff(4368,plain,
% 2.89/2.27 (hskp9),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[3959, 4367, 3762, 3761])).
% 2.89/2.27 tff(4369,plain,
% 2.89/2.27 (c0_1(a806)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[67, 4368])).
% 2.89/2.27 tff(4370,plain,
% 2.89/2.27 (~c3_1(a806)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[75, 4368])).
% 2.89/2.27 tff(4371,plain,
% 2.89/2.27 (c1_1(a806)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[87, 4368])).
% 2.89/2.27 tff(4372,plain,
% 2.89/2.27 (c2_1(a806)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[196, 4371, 4346, 4370, 4348, 4347, 4369])).
% 2.89/2.27 tff(4373,plain,
% 2.89/2.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~c0_1(a833)) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~c0_1(a833)) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4374,plain,
% 2.89/2.27 ((hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806))) <=> (hskp5 | (~c0_1(a833)) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4375,plain,
% 2.89/2.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~c0_1(a833)) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 2.89/2.27 inference(monotonicity,[status(thm)],[4374])).
% 2.89/2.27 tff(4376,plain,
% 2.89/2.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~c0_1(a833)) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 2.89/2.27 inference(transitivity,[status(thm)],[4375, 4373])).
% 2.89/2.27 tff(4377,plain,
% 2.89/2.27 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806)))),
% 2.89/2.27 inference(quant_inst,[status(thm)],[])).
% 2.89/2.27 tff(4378,plain,
% 2.89/2.27 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~c0_1(a833)) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)) | (~c3_1(a833)) | (~c1_1(a833))),
% 2.89/2.27 inference(modus_ponens,[status(thm)],[4377, 4376])).
% 2.89/2.27 tff(4379,plain,
% 2.89/2.27 (hskp5),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4378, 151, 4095, 4369, 3761, 4370, 217, 4367, 4372])).
% 2.89/2.27 tff(4380,plain,
% 2.89/2.27 (~c1_1(a800)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[263, 4379])).
% 2.89/2.27 tff(4381,plain,
% 2.89/2.27 (~c0_1(a800)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[229, 4379])).
% 2.89/2.27 tff(4382,plain,
% 2.89/2.27 (c3_1(a800)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[240, 4379])).
% 2.89/2.27 tff(4383,plain,
% 2.89/2.27 (hskp6),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[3382, 151, 4095, 4382, 309, 4381, 4380, 1964, 4367])).
% 2.89/2.27 tff(4384,plain,
% 2.89/2.27 (~c0_1(a802)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1987, 4383])).
% 2.89/2.27 tff(4385,plain,
% 2.89/2.27 (hskp7),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2924, 151, 2567, 2538, 2527, 4382, 4381, 4380, 1515])).
% 2.89/2.27 tff(4386,plain,
% 2.89/2.27 (~c2_1(a803)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1473, 4385])).
% 2.89/2.27 tff(4387,plain,
% 2.89/2.27 (c2_1(a802)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1998, 4383])).
% 2.89/2.27 tff(4388,plain,
% 2.89/2.27 (c3_1(a803)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1484, 4385])).
% 2.89/2.27 tff(4389,plain,
% 2.89/2.27 (c1_1(a803)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1495, 4385])).
% 2.89/2.27 tff(4390,plain,
% 2.89/2.27 (c3_1(a802)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2059, 151, 4369, 4371, 4389, 4388, 4387, 4370, 4386, 4384, 308])).
% 2.89/2.27 tff(4391,plain,
% 2.89/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4392,plain,
% 2.89/2.27 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802))) <=> (c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4393,plain,
% 2.89/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806))))),
% 2.89/2.27 inference(monotonicity,[status(thm)],[4392])).
% 2.89/2.27 tff(4394,plain,
% 2.89/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 2.89/2.27 inference(transitivity,[status(thm)],[4393, 4391])).
% 2.89/2.27 tff(4395,plain,
% 2.89/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))),
% 2.89/2.27 inference(quant_inst,[status(thm)],[])).
% 2.89/2.27 tff(4396,plain,
% 2.89/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806))),
% 2.89/2.27 inference(modus_ponens,[status(thm)],[4395, 4394])).
% 2.89/2.27 tff(4397,plain,
% 2.89/2.27 ($false),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4396, 151, 4348, 4347, 4346, 4369, 4371, 4387, 4384, 207, 4372, 4390])).
% 2.89/2.27 tff(4398,plain,(c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.27 tff(4399,plain,
% 2.89/2.27 (~hskp20),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[626, 4398])).
% 2.89/2.27 tff(4400,plain,
% 2.89/2.27 (c3_1(a832) | (~c0_1(a806)) | c3_1(a806) | (~c3_1(a794)) | c0_1(a794) | c2_1(a794) | (~c1_1(a806))),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4068, 4399])).
% 2.89/2.27 tff(4401,plain,
% 2.89/2.27 ($false),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4400, 298, 292, 22, 166, 100, 281, 111])).
% 2.89/2.27 tff(4402,plain,((~hskp1) | c3_1(a832) | (~c0_1(a806)) | c3_1(a806) | (~c1_1(a806))), inference(lemma,lemma(discharge,[]))).
% 2.89/2.27 tff(4403,plain,
% 2.89/2.27 (~hskp1),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4402, 76, 22, 68, 88])).
% 2.89/2.27 tff(4404,plain,
% 2.89/2.27 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | c0_1(a800) | (~ndr1_0) | (~c3_1(a800)) | c2_1(a800))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp1 | c0_1(a800) | (~ndr1_0) | (~c3_1(a800)) | c2_1(a800))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4405,plain,
% 2.89/2.27 ((hskp10 | hskp1 | (~ndr1_0) | c2_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (hskp10 | hskp1 | c0_1(a800) | (~ndr1_0) | (~c3_1(a800)) | c2_1(a800))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4406,plain,
% 2.89/2.27 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | c0_1(a800) | (~ndr1_0) | (~c3_1(a800)) | c2_1(a800)))),
% 2.89/2.27 inference(monotonicity,[status(thm)],[4405])).
% 2.89/2.27 tff(4407,plain,
% 2.89/2.27 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp1 | c0_1(a800) | (~ndr1_0) | (~c3_1(a800)) | c2_1(a800))),
% 2.89/2.27 inference(transitivity,[status(thm)],[4406, 4404])).
% 2.89/2.27 tff(4408,plain,
% 2.89/2.27 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 2.89/2.27 inference(quant_inst,[status(thm)],[])).
% 2.89/2.27 tff(4409,plain,
% 2.89/2.27 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp1 | c0_1(a800) | (~ndr1_0) | (~c3_1(a800)) | c2_1(a800)),
% 2.89/2.27 inference(modus_ponens,[status(thm)],[4408, 4407])).
% 2.89/2.27 tff(4410,plain,
% 2.89/2.27 (hskp10 | c2_1(a800)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4409, 151, 4403, 241, 230, 274])).
% 2.89/2.27 tff(4411,plain,
% 2.89/2.27 (hskp10),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4410, 248])).
% 2.89/2.27 tff(4412,plain,
% 2.89/2.27 (~c3_1(a807)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[509, 4411])).
% 2.89/2.27 tff(4413,plain,
% 2.89/2.27 (~c2_1(a807)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[552, 4411])).
% 2.89/2.27 tff(4414,plain,
% 2.89/2.27 (~c0_1(a807)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[515, 4411])).
% 2.89/2.27 tff(4415,plain,
% 2.89/2.27 (hskp25 | hskp1),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2471, 151, 70, 69, 77, 2465])).
% 2.89/2.27 tff(4416,plain,
% 2.89/2.27 (hskp25),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4415, 4403])).
% 2.89/2.27 tff(4417,plain,
% 2.89/2.27 (~c3_1(a865)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2478, 4416])).
% 2.89/2.27 tff(4418,plain,
% 2.89/2.27 (c2_1(a865)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2489, 4416])).
% 2.89/2.27 tff(4419,plain,
% 2.89/2.27 (c1_1(a865)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2500, 4416])).
% 2.89/2.27 tff(4420,plain,
% 2.89/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a865) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | c2_1(a800) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a865) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | c2_1(a800) | (~c2_1(a865)) | (~c1_1(a865)))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4421,plain,
% 2.89/2.27 (((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a807) | c2_1(a807) | c0_1(a807) | c2_1(a800) | c1_1(a800) | c0_1(a800)) <=> (c3_1(a865) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | c2_1(a800) | (~c2_1(a865)) | (~c1_1(a865)))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4422,plain,
% 2.89/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a807) | c2_1(a807) | c0_1(a807) | c2_1(a800) | c1_1(a800) | c0_1(a800))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a865) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | c2_1(a800) | (~c2_1(a865)) | (~c1_1(a865))))),
% 2.89/2.27 inference(monotonicity,[status(thm)],[4421])).
% 2.89/2.27 tff(4423,plain,
% 2.89/2.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a807) | c2_1(a807) | c0_1(a807) | c2_1(a800) | c1_1(a800) | c0_1(a800))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a865) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | c2_1(a800) | (~c2_1(a865)) | (~c1_1(a865)))),
% 2.89/2.27 inference(transitivity,[status(thm)],[4422, 4420])).
% 2.89/2.27 tff(4424,plain,
% 2.89/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a807) | c2_1(a807) | c0_1(a807) | c2_1(a800) | c1_1(a800) | c0_1(a800))),
% 2.89/2.27 inference(quant_inst,[status(thm)],[])).
% 2.89/2.27 tff(4425,plain,
% 2.89/2.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a865) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | c2_1(a800) | (~c2_1(a865)) | (~c1_1(a865))),
% 2.89/2.27 inference(modus_ponens,[status(thm)],[4424, 4423])).
% 2.89/2.27 tff(4426,plain,
% 2.89/2.27 ($false),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4425, 151, 4419, 4418, 4417, 4414, 4413, 4412, 230, 264, 258, 248])).
% 2.89/2.27 tff(4427,plain,((~hskp9) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a867)) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.27 tff(4428,plain,
% 2.89/2.27 (~hskp9),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4427, 56, 45, 34, 22])).
% 2.89/2.27 tff(4429,plain,
% 2.89/2.27 ((~hskp21) | hskp9),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2948, 4399])).
% 2.89/2.27 tff(4430,plain,
% 2.89/2.27 (~hskp21),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4429, 4428])).
% 2.89/2.27 tff(4431,plain,
% 2.89/2.27 (hskp11),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2574, 4430])).
% 2.89/2.27 tff(4432,plain,
% 2.89/2.27 (~c2_1(a808)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[857, 4431])).
% 2.89/2.27 tff(4433,plain,
% 2.89/2.27 (~c1_1(a808)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[851, 4431])).
% 2.89/2.27 tff(4434,plain,
% 2.89/2.27 (c3_1(a808)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[896, 4431])).
% 2.89/2.27 tff(4435,plain,
% 2.89/2.27 ((~c0_1(a808)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~c3_1(a808))),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4164, 4399])).
% 2.89/2.27 tff(4436,plain,
% 2.89/2.27 (~c0_1(a808)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4435, 4434, 4433, 4432, 22])).
% 2.89/2.27 tff(4437,plain,
% 2.89/2.27 (hskp9 | c2_1(a867)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[3059, 151, 4399, 56, 34, 21])).
% 2.89/2.27 tff(4438,plain,
% 2.89/2.27 (c2_1(a867)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4437, 4428])).
% 2.89/2.27 tff(4439,plain,
% 2.89/2.27 (hskp7),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1524, 151, 45, 34, 4434, 4433, 1515, 4438, 4436])).
% 2.89/2.27 tff(4440,plain,
% 2.89/2.27 (~c2_1(a803)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1473, 4439])).
% 2.89/2.27 tff(4441,plain,
% 2.89/2.27 (hskp18),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2365, 4438, 4430, 45, 34])).
% 2.89/2.27 tff(4442,plain,
% 2.89/2.27 (~c3_1(a828)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1197, 4441])).
% 2.89/2.27 tff(4443,plain,
% 2.89/2.27 (~c2_1(a828)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1191, 4441])).
% 2.89/2.27 tff(4444,plain,
% 2.89/2.27 (~c1_1(a828)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1203, 4441])).
% 2.89/2.27 tff(4445,plain,
% 2.89/2.27 (c3_1(a803)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1484, 4439])).
% 2.89/2.27 tff(4446,plain,
% 2.89/2.27 (c1_1(a803)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1495, 4439])).
% 2.89/2.27 tff(4447,plain,
% 2.89/2.27 (~hskp21),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4429, 11])).
% 2.89/2.27 tff(4448,plain,
% 2.89/2.27 (hskp30),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2884, 4447])).
% 2.89/2.27 tff(4449,plain,
% 2.89/2.27 (c3_1(a867)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[33, 4448])).
% 2.89/2.27 tff(4450,plain,
% 2.89/2.27 (c1_1(a867)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[44, 4448])).
% 2.89/2.27 tff(4451,plain,
% 2.89/2.27 (c0_1(a867)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[55, 4448])).
% 2.89/2.27 tff(4452,plain,
% 2.89/2.27 (hskp11),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2574, 4447])).
% 2.89/2.27 tff(4453,plain,
% 2.89/2.27 (c3_1(a808)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[896, 4452])).
% 2.89/2.27 tff(4454,plain,
% 2.89/2.27 ((~hskp27) | hskp30),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2588, 4399])).
% 2.89/2.27 tff(4455,plain,
% 2.89/2.27 (hskp30),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4454, 2953])).
% 2.89/2.27 tff(4456,plain,
% 2.89/2.27 (c3_1(a867)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[33, 4455])).
% 2.89/2.27 tff(4457,plain,
% 2.89/2.27 (c0_1(a867)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[55, 4455])).
% 2.89/2.27 tff(4458,plain,
% 2.89/2.27 (c1_1(a867)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[44, 4455])).
% 2.89/2.27 tff(4459,plain,
% 2.89/2.27 (hskp11 | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a867)) | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796))),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2971, 4399])).
% 2.89/2.27 tff(4460,plain,
% 2.89/2.27 (hskp11),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4459, 4458, 2955, 2956, 4457, 4456, 2954])).
% 2.89/2.27 tff(4461,plain,
% 2.89/2.27 (~c2_1(a808)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[857, 4460])).
% 2.89/2.27 tff(4462,plain,
% 2.89/2.27 (~c1_1(a808)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[851, 4460])).
% 2.89/2.27 tff(4463,plain,
% 2.89/2.27 (c3_1(a808)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[896, 4460])).
% 2.89/2.27 tff(4464,plain,
% 2.89/2.27 (~c0_1(a808)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4435, 4463, 4462, 4461, 22])).
% 2.89/2.27 tff(4465,plain,
% 2.89/2.27 (~hskp7),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1504, 1458, 22, 322])).
% 2.89/2.27 tff(4466,plain,
% 2.89/2.27 ($false),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2980, 151, 4465, 2567, 2538, 2527, 4463, 4462, 1515, 4464])).
% 2.89/2.27 tff(4467,plain,(c2_1(a832) | c3_1(a832) | c1_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.27 tff(4468,plain,
% 2.89/2.27 (c2_1(a832)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4467, 322, 22])).
% 2.89/2.27 tff(4469,plain,
% 2.89/2.27 (~c1_1(a808)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[851, 4452])).
% 2.89/2.27 tff(4470,plain,
% 2.89/2.27 (~c2_1(a808)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[857, 4452])).
% 2.89/2.27 tff(4471,plain,
% 2.89/2.27 (c1_1(a808) | hskp9 | (~c3_1(a808)) | c2_1(a808) | (~c2_1(a832)) | c3_1(a832) | c1_1(a832) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a867))),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[3167, 4399])).
% 2.89/2.27 tff(4472,plain,
% 2.89/2.27 ($false),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4471, 4470, 4469, 322, 4468, 11, 22, 4453, 4451, 4450, 4449])).
% 2.89/2.27 tff(4473,plain,(hskp9 | c1_1(a832) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.27 tff(4474,plain,
% 2.89/2.27 (c1_1(a832)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4473, 4428, 22])).
% 2.89/2.27 tff(4475,plain,
% 2.89/2.27 (~hskp19),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[391, 4474])).
% 2.89/2.27 tff(4476,plain,
% 2.89/2.27 ($false),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[1815, 151, 4475, 4446, 4445, 4444, 4443, 4442, 4440, 10])).
% 2.89/2.27 tff(4477,plain,((~hskp30) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.27 tff(4478,plain,
% 2.89/2.27 (~hskp30),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4477, 22])).
% 2.89/2.27 tff(4479,plain,
% 2.89/2.27 (hskp21),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2884, 4478])).
% 2.89/2.27 tff(4480,plain,
% 2.89/2.27 (hskp9),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4429, 4479])).
% 2.89/2.27 tff(4481,plain,
% 2.89/2.27 (c1_1(a806)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[87, 4480])).
% 2.89/2.27 tff(4482,plain,
% 2.89/2.27 (c0_1(a806)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[67, 4480])).
% 2.89/2.27 tff(4483,plain,
% 2.89/2.27 (~c3_1(a806)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[75, 4480])).
% 2.89/2.27 tff(4484,plain,
% 2.89/2.27 (~hskp1),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4402, 4483, 22, 4482, 4481])).
% 2.89/2.27 tff(4485,plain,
% 2.89/2.27 (hskp30 | (~c0_1(a797))),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[2545, 4399])).
% 2.89/2.27 tff(4486,plain,
% 2.89/2.27 (~c0_1(a797)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4485, 345])).
% 2.89/2.27 tff(4487,plain,
% 2.89/2.27 (c0_1(a838)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[454, 2885])).
% 2.89/2.27 tff(4488,plain,
% 2.89/2.27 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | c1_1(a838))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | c1_1(a838))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4489,plain,
% 2.89/2.27 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a838) | c1_1(a838) | (~c0_1(a838))) <=> (hskp20 | hskp1 | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | c1_1(a838))),
% 2.89/2.27 inference(rewrite,[status(thm)],[])).
% 2.89/2.27 tff(4490,plain,
% 2.89/2.27 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a838) | c1_1(a838) | (~c0_1(a838)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | c1_1(a838)))),
% 2.89/2.27 inference(monotonicity,[status(thm)],[4489])).
% 2.89/2.27 tff(4491,plain,
% 2.89/2.27 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a838) | c1_1(a838) | (~c0_1(a838)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | c1_1(a838))),
% 2.89/2.27 inference(transitivity,[status(thm)],[4490, 4488])).
% 2.89/2.27 tff(4492,plain,
% 2.89/2.27 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a838) | c1_1(a838) | (~c0_1(a838)))),
% 2.89/2.27 inference(quant_inst,[status(thm)],[])).
% 2.89/2.27 tff(4493,plain,
% 2.89/2.27 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | c1_1(a838)),
% 2.89/2.27 inference(modus_ponens,[status(thm)],[4492, 4491])).
% 2.89/2.27 tff(4494,plain,
% 2.89/2.27 (c1_1(a838)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[4493, 151, 4399, 4119, 4487, 2886, 1646])).
% 2.89/2.27 tff(4495,plain,
% 2.89/2.27 (c3_1(a838)),
% 2.89/2.27 inference(unit_resolution,[status(thm)],[443, 2885])).
% 2.89/2.28 tff(4496,plain,
% 2.89/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 2.89/2.28 inference(rewrite,[status(thm)],[])).
% 2.89/2.28 tff(4497,plain,
% 2.89/2.28 (((~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797))) <=> ((~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 2.89/2.28 inference(rewrite,[status(thm)],[])).
% 2.89/2.28 tff(4498,plain,
% 2.89/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))))),
% 2.89/2.28 inference(monotonicity,[status(thm)],[4497])).
% 2.89/2.28 tff(4499,plain,
% 2.89/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 2.89/2.28 inference(transitivity,[status(thm)],[4498, 4496])).
% 2.89/2.28 tff(4500,plain,
% 2.89/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797)))),
% 2.89/2.28 inference(quant_inst,[status(thm)],[])).
% 2.89/2.28 tff(4501,plain,
% 2.89/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))),
% 2.89/2.28 inference(modus_ponens,[status(thm)],[4500, 4499])).
% 2.89/2.28 tff(4502,plain,
% 2.89/2.28 (~c2_1(a806)),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[4501, 151, 2538, 2527, 4487, 4495, 166, 111, 207, 4494, 4486])).
% 2.89/2.28 tff(4503,plain,
% 2.89/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a838) | c3_1(a806) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a838)) | (~c1_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a838) | c3_1(a806) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 2.89/2.28 inference(rewrite,[status(thm)],[])).
% 2.89/2.28 tff(4504,plain,
% 2.89/2.28 (((~ndr1_0) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797))) <=> (c2_1(a838) | c3_1(a806) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 2.89/2.28 inference(rewrite,[status(thm)],[])).
% 2.89/2.28 tff(4505,plain,
% 2.89/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a838) | c3_1(a806) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a838)) | (~c1_1(a838))))),
% 2.89/2.28 inference(monotonicity,[status(thm)],[4504])).
% 2.89/2.28 tff(4506,plain,
% 2.89/2.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a838) | c3_1(a806) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 2.89/2.28 inference(transitivity,[status(thm)],[4505, 4503])).
% 2.89/2.28 tff(4507,plain,
% 2.89/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))),
% 2.89/2.28 inference(quant_inst,[status(thm)],[])).
% 2.89/2.28 tff(4508,plain,
% 2.89/2.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a838) | c3_1(a806) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a838)) | (~c1_1(a838))),
% 2.89/2.28 inference(modus_ponens,[status(thm)],[4507, 4506])).
% 2.89/2.28 tff(4509,plain,
% 2.89/2.28 ($false),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[4508, 151, 2567, 2538, 4487, 111, 2886, 100, 99, 4494, 4502, 4486])).
% 2.89/2.28 tff(4510,plain,(hskp30 | (~c1_1(a806)) | c3_1(a806) | (~c0_1(a806)) | hskp1), inference(lemma,lemma(discharge,[]))).
% 2.89/2.28 tff(4511,plain,
% 2.89/2.28 ($false),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[4510, 4484, 4483, 4478, 4482, 4481])).
% 2.89/2.28 tff(4512,plain,(c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 2.89/2.28 tff(4513,plain,
% 2.89/2.28 (~hskp19),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[385, 4512])).
% 2.89/2.28 tff(4514,plain,
% 2.89/2.28 (hskp27),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[2596, 4513])).
% 2.89/2.28 tff(4515,plain,
% 2.89/2.28 (c3_1(a796)),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[594, 4514])).
% 2.89/2.28 tff(4516,plain,
% 2.89/2.28 (hskp30),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[4454, 4514])).
% 2.89/2.28 tff(4517,plain,
% 2.89/2.28 (c3_1(a867)),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[33, 4516])).
% 2.89/2.28 tff(4518,plain,
% 2.89/2.28 (c0_1(a867)),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[55, 4516])).
% 2.89/2.28 tff(4519,plain,
% 2.89/2.28 (c0_1(a796)),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[616, 4514])).
% 2.89/2.28 tff(4520,plain,
% 2.89/2.28 (c2_1(a796)),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[605, 4514])).
% 2.89/2.28 tff(4521,plain,
% 2.89/2.28 (c1_1(a867)),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[44, 4516])).
% 2.89/2.28 tff(4522,plain,
% 2.89/2.28 (hskp11),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[4459, 4521, 4520, 4519, 4518, 4517, 4515])).
% 2.89/2.28 tff(4523,plain,
% 2.89/2.28 (~c2_1(a808)),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[857, 4522])).
% 2.89/2.28 tff(4524,plain,
% 2.89/2.28 (c3_1(a808)),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[896, 4522])).
% 2.89/2.28 tff(4525,plain,
% 2.89/2.28 (hskp9 | (~c0_1(a808))),
% 2.89/2.28 inference(unit_resolution,[status(thm)],[1533, 151, 4399, 4524, 4523, 21])).
% 2.89/2.28 tff(4526,plain,
% 2.89/2.28 (~c0_1(a808)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[4525, 11])).
% 2.97/2.28 tff(4527,plain,
% 2.97/2.28 (hskp9 | c2_1(a867)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[3059, 151, 4399, 4518, 4517, 21])).
% 2.97/2.28 tff(4528,plain,
% 2.97/2.28 (c2_1(a867)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[4527, 11])).
% 2.97/2.28 tff(4529,plain,
% 2.97/2.28 (~c1_1(a808)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[851, 4522])).
% 2.97/2.28 tff(4530,plain,
% 2.97/2.28 (hskp7 | (~c2_1(a867)) | c0_1(a808)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[1524, 151, 4521, 4517, 4524, 4529, 1515])).
% 2.97/2.28 tff(4531,plain,
% 2.97/2.28 (hskp7),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[4530, 4528, 4526])).
% 2.97/2.28 tff(4532,plain,
% 2.97/2.28 (~c2_1(a803)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[1473, 4531])).
% 2.97/2.28 tff(4533,plain,
% 2.97/2.28 (hskp18),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[3301, 4447, 4524, 4523])).
% 2.97/2.28 tff(4534,plain,
% 2.97/2.28 (~c3_1(a828)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[1197, 4533])).
% 2.97/2.28 tff(4535,plain,
% 2.97/2.28 (~c2_1(a828)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[1191, 4533])).
% 2.97/2.28 tff(4536,plain,
% 2.97/2.28 (~c1_1(a828)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[1203, 4533])).
% 2.97/2.28 tff(4537,plain,
% 2.97/2.28 (c3_1(a803)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[1484, 4531])).
% 2.97/2.28 tff(4538,plain,
% 2.97/2.28 (c1_1(a803)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[1495, 4531])).
% 2.97/2.28 tff(4539,plain,
% 2.97/2.28 ($false),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[1815, 151, 4513, 4538, 4537, 4536, 4535, 4534, 4532, 10])).
% 2.97/2.28 tff(4540,plain,(hskp9), inference(lemma,lemma(discharge,[]))).
% 2.97/2.28 tff(4541,plain,
% 2.97/2.28 (c0_1(a806)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[67, 4540])).
% 2.97/2.28 tff(4542,plain,
% 2.97/2.28 (~c3_1(a806)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[75, 4540])).
% 2.97/2.28 tff(4543,plain,
% 2.97/2.28 (c1_1(a806)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[87, 4540])).
% 2.97/2.28 tff(4544,plain,
% 2.97/2.28 (c2_1(a806)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[196, 4543, 4517, 4542, 4518, 4521, 4541])).
% 2.97/2.28 tff(4545,plain,
% 2.97/2.28 (hskp5),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[223, 151, 4518, 4521, 4517, 4541, 4542, 217, 4544])).
% 2.97/2.28 tff(4546,plain,
% 2.97/2.28 (~c1_1(a800)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[263, 4545])).
% 2.97/2.28 tff(4547,plain,
% 2.97/2.28 (~c0_1(a800)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[229, 4545])).
% 2.97/2.28 tff(4548,plain,
% 2.97/2.28 (c3_1(a800)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[240, 4545])).
% 2.97/2.28 tff(4549,plain,
% 2.97/2.28 (hskp7),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[2924, 151, 2567, 2538, 2527, 4548, 4547, 4546, 1515])).
% 2.97/2.28 tff(4550,plain,
% 2.97/2.28 (~c2_1(a803)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[1473, 4549])).
% 2.97/2.28 tff(4551,plain,
% 2.97/2.28 (c3_1(a803)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[1484, 4549])).
% 2.97/2.28 tff(4552,plain,
% 2.97/2.28 (c1_1(a803)),
% 2.97/2.28 inference(unit_resolution,[status(thm)],[1495, 4549])).
% 2.97/2.28 tff(4553,plain,
% 2.97/2.28 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a803)) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a803)) | (~c1_1(a803)))),
% 2.97/2.28 inference(rewrite,[status(thm)],[])).
% 2.97/2.28 tff(4554,plain,
% 2.97/2.28 ((hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (hskp6 | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a803)) | (~c1_1(a803)))),
% 2.97/2.28 inference(rewrite,[status(thm)],[])).
% 2.97/2.28 tff(4555,plain,
% 2.97/2.28 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a803)) | (~c1_1(a803))))),
% 2.97/2.28 inference(monotonicity,[status(thm)],[4554])).
% 2.97/2.28 tff(4556,plain,
% 2.97/2.28 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a803)) | (~c1_1(a803)))),
% 2.97/2.29 inference(transitivity,[status(thm)],[4555, 4553])).
% 2.97/2.29 tff(4557,plain,
% 2.97/2.29 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 2.97/2.29 inference(quant_inst,[status(thm)],[])).
% 2.97/2.29 tff(4558,plain,
% 2.97/2.29 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a803)) | (~c1_1(a803))),
% 2.97/2.29 inference(modus_ponens,[status(thm)],[4557, 4556])).
% 2.97/2.29 tff(4559,plain,
% 2.97/2.29 (hskp6),
% 2.97/2.29 inference(unit_resolution,[status(thm)],[4558, 151, 4552, 4551, 4548, 4550, 4547, 4546, 1964])).
% 2.97/2.29 tff(4560,plain,
% 2.97/2.29 (~c0_1(a802)),
% 2.97/2.29 inference(unit_resolution,[status(thm)],[1987, 4559])).
% 2.97/2.29 tff(4561,plain,
% 2.97/2.29 (c2_1(a802)),
% 2.97/2.29 inference(unit_resolution,[status(thm)],[1998, 4559])).
% 2.97/2.29 tff(4562,plain,
% 2.97/2.29 (~c3_1(a802)),
% 2.97/2.29 inference(unit_resolution,[status(thm)],[4396, 151, 4518, 4521, 4517, 4541, 4543, 4561, 4560, 207, 4544])).
% 2.97/2.29 tff(4563,plain,
% 2.97/2.29 ($false),
% 2.97/2.29 inference(unit_resolution,[status(thm)],[2059, 151, 4541, 4543, 4552, 4551, 4561, 4542, 4550, 4560, 308, 4562])).
% 2.97/2.29 % SZS output end Proof
%------------------------------------------------------------------------------