TSTP Solution File: SYN503-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN503-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:56:00 EDT 2022
% Result : Unsatisfiable 2.03s 1.67s
% Output : Proof 2.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SYN503-1 : TPTP v8.1.0. Released v2.1.0.
% 0.02/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.06/0.33 % Computer : n011.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8042.1875MB
% 0.06/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Mon Sep 5 04:41:15 EDT 2022
% 0.06/0.34 % CPUTime :
% 0.06/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.06/0.36 Usage: tptp [options] [-file:]file
% 0.06/0.36 -h, -? prints this message.
% 0.06/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.06/0.36 -m, -model generate model.
% 0.06/0.36 -p, -proof generate proof.
% 0.06/0.36 -c, -core generate unsat core of named formulas.
% 0.06/0.36 -st, -statistics display statistics.
% 0.06/0.36 -t:timeout set timeout (in second).
% 0.06/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.06/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.06/0.36 -<param>:<value> configuration parameter and value.
% 0.06/0.36 -o:<output-file> file to place output in.
% 2.03/1.67 % SZS status Unsatisfiable
% 2.03/1.67 % SZS output start Proof
% 2.03/1.67 tff(c2_1_type, type, (
% 2.03/1.67 c2_1: $i > $o)).
% 2.03/1.67 tff(a234_type, type, (
% 2.03/1.67 a234: $i)).
% 2.03/1.67 tff(c0_1_type, type, (
% 2.03/1.67 c0_1: $i > $o)).
% 2.03/1.67 tff(hskp26_type, type, (
% 2.03/1.67 hskp26: $o)).
% 2.03/1.67 tff(c3_1_type, type, (
% 2.03/1.67 c3_1: $i > $o)).
% 2.03/1.67 tff(a252_type, type, (
% 2.03/1.67 a252: $i)).
% 2.03/1.67 tff(c1_1_type, type, (
% 2.03/1.67 c1_1: $i > $o)).
% 2.03/1.67 tff(ndr1_0_type, type, (
% 2.03/1.67 ndr1_0: $o)).
% 2.03/1.67 tff(hskp10_type, type, (
% 2.03/1.67 hskp10: $o)).
% 2.03/1.67 tff(a214_type, type, (
% 2.03/1.67 a214: $i)).
% 2.03/1.67 tff(hskp1_type, type, (
% 2.03/1.67 hskp1: $o)).
% 2.03/1.67 tff(a226_type, type, (
% 2.03/1.67 a226: $i)).
% 2.03/1.67 tff(hskp9_type, type, (
% 2.03/1.67 hskp9: $o)).
% 2.03/1.67 tff(a255_type, type, (
% 2.03/1.67 a255: $i)).
% 2.03/1.67 tff(a261_type, type, (
% 2.03/1.67 a261: $i)).
% 2.03/1.67 tff(hskp27_type, type, (
% 2.03/1.67 hskp27: $o)).
% 2.03/1.67 tff(a274_type, type, (
% 2.03/1.67 a274: $i)).
% 2.03/1.67 tff(a218_type, type, (
% 2.03/1.67 a218: $i)).
% 2.03/1.67 tff(hskp5_type, type, (
% 2.03/1.67 hskp5: $o)).
% 2.03/1.67 tff(hskp12_type, type, (
% 2.03/1.67 hskp12: $o)).
% 2.03/1.67 tff(hskp23_type, type, (
% 2.03/1.67 hskp23: $o)).
% 2.03/1.67 tff(a215_type, type, (
% 2.03/1.67 a215: $i)).
% 2.03/1.67 tff(hskp2_type, type, (
% 2.03/1.67 hskp2: $o)).
% 2.03/1.67 tff(hskp17_type, type, (
% 2.03/1.67 hskp17: $o)).
% 2.03/1.67 tff(hskp18_type, type, (
% 2.03/1.67 hskp18: $o)).
% 2.03/1.67 tff(a237_type, type, (
% 2.03/1.67 a237: $i)).
% 2.03/1.67 tff(a241_type, type, (
% 2.03/1.67 a241: $i)).
% 2.03/1.67 tff(a220_type, type, (
% 2.03/1.67 a220: $i)).
% 2.03/1.67 tff(hskp6_type, type, (
% 2.03/1.67 hskp6: $o)).
% 2.03/1.67 tff(a320_type, type, (
% 2.03/1.67 a320: $i)).
% 2.03/1.67 tff(hskp19_type, type, (
% 2.03/1.67 hskp19: $o)).
% 2.03/1.67 tff(hskp4_type, type, (
% 2.03/1.67 hskp4: $o)).
% 2.03/1.67 tff(a217_type, type, (
% 2.03/1.67 a217: $i)).
% 2.03/1.67 tff(hskp3_type, type, (
% 2.03/1.67 hskp3: $o)).
% 2.03/1.67 tff(a216_type, type, (
% 2.03/1.67 a216: $i)).
% 2.03/1.67 tff(a242_type, type, (
% 2.03/1.67 a242: $i)).
% 2.03/1.67 tff(hskp15_type, type, (
% 2.03/1.67 hskp15: $o)).
% 2.03/1.67 tff(hskp24_type, type, (
% 2.03/1.67 hskp24: $o)).
% 2.03/1.67 tff(hskp25_type, type, (
% 2.03/1.67 hskp25: $o)).
% 2.03/1.67 tff(a280_type, type, (
% 2.03/1.67 a280: $i)).
% 2.03/1.67 tff(a245_type, type, (
% 2.03/1.67 a245: $i)).
% 2.03/1.67 tff(hskp16_type, type, (
% 2.03/1.67 hskp16: $o)).
% 2.03/1.67 tff(a259_type, type, (
% 2.03/1.67 a259: $i)).
% 2.03/1.67 tff(hskp21_type, type, (
% 2.03/1.67 hskp21: $o)).
% 2.03/1.67 tff(a248_type, type, (
% 2.03/1.67 a248: $i)).
% 2.03/1.67 tff(a271_type, type, (
% 2.03/1.67 a271: $i)).
% 2.03/1.67 tff(a231_type, type, (
% 2.03/1.67 a231: $i)).
% 2.03/1.67 tff(a213_type, type, (
% 2.03/1.67 a213: $i)).
% 2.03/1.67 tff(hskp0_type, type, (
% 2.03/1.67 hskp0: $o)).
% 2.03/1.67 tff(hskp13_type, type, (
% 2.03/1.67 hskp13: $o)).
% 2.03/1.67 tff(a239_type, type, (
% 2.03/1.67 a239: $i)).
% 2.03/1.67 tff(a225_type, type, (
% 2.03/1.67 a225: $i)).
% 2.03/1.67 tff(hskp8_type, type, (
% 2.03/1.67 hskp8: $o)).
% 2.03/1.67 tff(hskp22_type, type, (
% 2.03/1.67 hskp22: $o)).
% 2.03/1.67 tff(a296_type, type, (
% 2.03/1.67 a296: $i)).
% 2.03/1.67 tff(hskp29_type, type, (
% 2.03/1.67 hskp29: $o)).
% 2.03/1.67 tff(a223_type, type, (
% 2.03/1.67 a223: $i)).
% 2.03/1.67 tff(hskp7_type, type, (
% 2.03/1.67 hskp7: $o)).
% 2.03/1.67 tff(hskp14_type, type, (
% 2.03/1.67 hskp14: $o)).
% 2.03/1.67 tff(a236_type, type, (
% 2.03/1.67 a236: $i)).
% 2.03/1.67 tff(hskp11_type, type, (
% 2.03/1.67 hskp11: $o)).
% 2.03/1.67 tff(1,assumption,(~hskp26), introduced(assumption)).
% 2.03/1.67 tff(2,plain,
% 2.03/1.67 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 2.03/1.67 inference(bind,[status(th)],[])).
% 2.03/1.67 tff(3,plain,
% 2.03/1.67 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.03/1.67 inference(quant_intro,[status(thm)],[2])).
% 2.03/1.67 tff(4,plain,
% 2.03/1.67 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.03/1.67 inference(rewrite,[status(thm)],[])).
% 2.03/1.67 tff(5,plain,
% 2.03/1.67 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 2.03/1.68 inference(bind,[status(th)],[])).
% 2.03/1.68 tff(6,plain,
% 2.03/1.68 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.03/1.68 inference(quant_intro,[status(thm)],[5])).
% 2.03/1.68 tff(7,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 2.03/1.68 tff(8,plain,
% 2.03/1.68 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.03/1.68 inference(modus_ponens,[status(thm)],[7, 6])).
% 2.03/1.68 tff(9,plain,
% 2.03/1.68 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.03/1.68 inference(modus_ponens,[status(thm)],[8, 4])).
% 2.03/1.68 tff(10,plain,(
% 2.03/1.68 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.03/1.68 inference(skolemize,[status(sab)],[9])).
% 2.03/1.68 tff(11,plain,
% 2.03/1.68 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.03/1.68 inference(modus_ponens,[status(thm)],[10, 3])).
% 2.03/1.68 tff(12,assumption,(~c3_1(a252)), introduced(assumption)).
% 2.03/1.68 tff(13,plain,
% 2.03/1.68 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))))),
% 2.03/1.68 inference(bind,[status(th)],[])).
% 2.03/1.68 tff(14,plain,
% 2.03/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.03/1.68 inference(quant_intro,[status(thm)],[13])).
% 2.03/1.68 tff(15,plain,
% 2.03/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.03/1.68 inference(rewrite,[status(thm)],[])).
% 2.03/1.68 tff(16,plain,
% 2.03/1.68 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))))),
% 2.05/1.68 inference(bind,[status(th)],[])).
% 2.05/1.68 tff(17,plain,
% 2.05/1.68 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.05/1.68 inference(quant_intro,[status(thm)],[16])).
% 2.05/1.68 tff(18,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 2.05/1.68 tff(19,plain,
% 2.05/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.05/1.68 inference(modus_ponens,[status(thm)],[18, 17])).
% 2.05/1.68 tff(20,plain,
% 2.05/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.05/1.68 inference(modus_ponens,[status(thm)],[19, 15])).
% 2.05/1.68 tff(21,plain,(
% 2.05/1.68 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.05/1.68 inference(skolemize,[status(sab)],[20])).
% 2.05/1.68 tff(22,plain,
% 2.05/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.05/1.68 inference(modus_ponens,[status(thm)],[21, 14])).
% 2.05/1.68 tff(23,assumption,(~hskp9), introduced(assumption)).
% 2.05/1.68 tff(24,plain,
% 2.05/1.68 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W))))),
% 2.05/1.68 inference(bind,[status(th)],[])).
% 2.05/1.68 tff(25,plain,
% 2.05/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 2.05/1.68 inference(quant_intro,[status(thm)],[24])).
% 2.05/1.68 tff(26,plain,
% 2.05/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 2.05/1.68 inference(rewrite,[status(thm)],[])).
% 2.05/1.68 tff(27,plain,
% 2.05/1.68 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))))),
% 2.05/1.68 inference(bind,[status(th)],[])).
% 2.05/1.68 tff(28,plain,
% 2.05/1.68 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 2.05/1.68 inference(quant_intro,[status(thm)],[27])).
% 2.05/1.68 tff(29,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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','clause200')).
% 2.05/1.68 tff(30,plain,
% 2.05/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 2.05/1.68 inference(modus_ponens,[status(thm)],[29, 28])).
% 2.05/1.68 tff(31,plain,
% 2.05/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 2.05/1.68 inference(modus_ponens,[status(thm)],[30, 26])).
% 2.05/1.68 tff(32,plain,(
% 2.05/1.68 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 2.05/1.68 inference(skolemize,[status(sab)],[31])).
% 2.05/1.68 tff(33,plain,
% 2.05/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 2.05/1.68 inference(modus_ponens,[status(thm)],[32, 25])).
% 2.05/1.68 tff(34,assumption,(~hskp27), introduced(assumption)).
% 2.05/1.68 tff(35,plain,
% 2.05/1.68 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 2.05/1.68 inference(bind,[status(th)],[])).
% 2.05/1.68 tff(36,plain,
% 2.05/1.68 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.05/1.68 inference(quant_intro,[status(thm)],[35])).
% 2.05/1.68 tff(37,plain,
% 2.05/1.68 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.05/1.68 inference(rewrite,[status(thm)],[])).
% 2.05/1.68 tff(38,plain,
% 2.05/1.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(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) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 2.05/1.69 inference(bind,[status(th)],[])).
% 2.05/1.69 tff(39,plain,
% 2.05/1.69 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.05/1.69 inference(quant_intro,[status(thm)],[38])).
% 2.05/1.69 tff(40,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 2.05/1.69 tff(41,plain,
% 2.05/1.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[40, 39])).
% 2.05/1.69 tff(42,plain,
% 2.05/1.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[41, 37])).
% 2.05/1.69 tff(43,plain,(
% 2.05/1.69 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.05/1.69 inference(skolemize,[status(sab)],[42])).
% 2.05/1.69 tff(44,plain,
% 2.05/1.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[43, 36])).
% 2.05/1.69 tff(45,assumption,(~hskp5), introduced(assumption)).
% 2.05/1.69 tff(46,assumption,(hskp26), introduced(assumption)).
% 2.05/1.69 tff(47,plain,
% 2.05/1.69 (^[U: $i] : refl((hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 2.05/1.69 inference(bind,[status(th)],[])).
% 2.05/1.69 tff(48,plain,
% 2.05/1.69 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.05/1.69 inference(quant_intro,[status(thm)],[47])).
% 2.05/1.69 tff(49,plain,
% 2.05/1.69 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(50,plain,
% 2.05/1.69 (^[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)) | hskp27) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp2) <=> ((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2))), rewrite(((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp2) <=> (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 2.05/1.69 inference(bind,[status(th)],[])).
% 2.05/1.69 tff(51,plain,
% 2.05/1.69 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp2) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.05/1.69 inference(quant_intro,[status(thm)],[50])).
% 2.05/1.69 tff(52,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 2.05/1.69 tff(53,plain,
% 2.05/1.69 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[52, 51])).
% 2.05/1.69 tff(54,plain,
% 2.05/1.69 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[53, 49])).
% 2.05/1.69 tff(55,plain,(
% 2.05/1.69 ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.05/1.69 inference(skolemize,[status(sab)],[54])).
% 2.05/1.69 tff(56,plain,
% 2.05/1.69 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[55, 48])).
% 2.05/1.69 tff(57,plain,
% 2.05/1.69 (((~hskp26) | c3_1(a234)) <=> ((~hskp26) | c3_1(a234))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(58,axiom,((~hskp26) | c3_1(a234)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 2.05/1.69 tff(59,plain,
% 2.05/1.69 ((~hskp26) | c3_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[58, 57])).
% 2.05/1.69 tff(60,plain,
% 2.05/1.69 ((~hskp26) | c3_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[59, 57])).
% 2.05/1.69 tff(61,plain,
% 2.05/1.69 ((~hskp26) | c3_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[60, 57])).
% 2.05/1.69 tff(62,plain,
% 2.05/1.69 ((~hskp26) | c3_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[61, 57])).
% 2.05/1.69 tff(63,plain,
% 2.05/1.69 ((~hskp26) | c3_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[62, 57])).
% 2.05/1.69 tff(64,plain,
% 2.05/1.69 ((~hskp26) | c3_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[63, 57])).
% 2.05/1.69 tff(65,plain,
% 2.05/1.69 ((~hskp26) | c3_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[64, 57])).
% 2.05/1.69 tff(66,plain,
% 2.05/1.69 ((~hskp26) | c3_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[65, 57])).
% 2.05/1.69 tff(67,plain,
% 2.05/1.69 (c3_1(a234)),
% 2.05/1.69 inference(unit_resolution,[status(thm)],[66, 46])).
% 2.05/1.69 tff(68,plain,
% 2.05/1.69 (((~hskp26) | c1_1(a234)) <=> ((~hskp26) | c1_1(a234))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(69,axiom,((~hskp26) | c1_1(a234)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 2.05/1.69 tff(70,plain,
% 2.05/1.69 ((~hskp26) | c1_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[69, 68])).
% 2.05/1.69 tff(71,plain,
% 2.05/1.69 ((~hskp26) | c1_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[70, 68])).
% 2.05/1.69 tff(72,plain,
% 2.05/1.69 ((~hskp26) | c1_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[71, 68])).
% 2.05/1.69 tff(73,plain,
% 2.05/1.69 ((~hskp26) | c1_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[72, 68])).
% 2.05/1.69 tff(74,plain,
% 2.05/1.69 ((~hskp26) | c1_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[73, 68])).
% 2.05/1.69 tff(75,plain,
% 2.05/1.69 ((~hskp26) | c1_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[74, 68])).
% 2.05/1.69 tff(76,plain,
% 2.05/1.69 ((~hskp26) | c1_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[75, 68])).
% 2.05/1.69 tff(77,plain,
% 2.05/1.69 ((~hskp26) | c1_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[76, 68])).
% 2.05/1.69 tff(78,plain,
% 2.05/1.69 (c1_1(a234)),
% 2.05/1.69 inference(unit_resolution,[status(thm)],[77, 46])).
% 2.05/1.69 tff(79,plain,
% 2.05/1.69 (((~hskp26) | c0_1(a234)) <=> ((~hskp26) | c0_1(a234))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(80,axiom,((~hskp26) | c0_1(a234)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 2.05/1.69 tff(81,plain,
% 2.05/1.69 ((~hskp26) | c0_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[80, 79])).
% 2.05/1.69 tff(82,plain,
% 2.05/1.69 ((~hskp26) | c0_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[81, 79])).
% 2.05/1.69 tff(83,plain,
% 2.05/1.69 ((~hskp26) | c0_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[82, 79])).
% 2.05/1.69 tff(84,plain,
% 2.05/1.69 ((~hskp26) | c0_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[83, 79])).
% 2.05/1.69 tff(85,plain,
% 2.05/1.69 ((~hskp26) | c0_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[84, 79])).
% 2.05/1.69 tff(86,plain,
% 2.05/1.69 ((~hskp26) | c0_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[85, 79])).
% 2.05/1.69 tff(87,plain,
% 2.05/1.69 ((~hskp26) | c0_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[86, 79])).
% 2.05/1.69 tff(88,plain,
% 2.05/1.69 ((~hskp26) | c0_1(a234)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[87, 79])).
% 2.05/1.69 tff(89,plain,
% 2.05/1.69 (c0_1(a234)),
% 2.05/1.69 inference(unit_resolution,[status(thm)],[88, 46])).
% 2.05/1.69 tff(90,assumption,(~hskp2), introduced(assumption)).
% 2.05/1.69 tff(91,assumption,(~ndr1_0), introduced(assumption)).
% 2.05/1.69 tff(92,plain,
% 2.05/1.69 ((ndr1_0 | (~hskp17)) <=> (ndr1_0 | (~hskp17))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(93,plain,
% 2.05/1.69 (((~hskp17) | ndr1_0) <=> (ndr1_0 | (~hskp17))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(94,axiom,((~hskp17) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause15')).
% 2.05/1.69 tff(95,plain,
% 2.05/1.69 (ndr1_0 | (~hskp17)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[94, 93])).
% 2.05/1.69 tff(96,plain,
% 2.05/1.69 (ndr1_0 | (~hskp17)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[95, 92])).
% 2.05/1.69 tff(97,plain,
% 2.05/1.69 (~hskp17),
% 2.05/1.69 inference(unit_resolution,[status(thm)],[96, 91])).
% 2.05/1.69 tff(98,plain,
% 2.05/1.69 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(99,plain,
% 2.05/1.69 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(100,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 2.05/1.69 tff(101,plain,
% 2.05/1.69 (ndr1_0 | (~hskp27)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[100, 99])).
% 2.05/1.69 tff(102,plain,
% 2.05/1.69 (ndr1_0 | (~hskp27)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[101, 98])).
% 2.05/1.69 tff(103,plain,
% 2.05/1.69 (~hskp27),
% 2.05/1.69 inference(unit_resolution,[status(thm)],[102, 91])).
% 2.05/1.69 tff(104,plain,
% 2.05/1.69 ((ndr1_0 | (~hskp18)) <=> (ndr1_0 | (~hskp18))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(105,plain,
% 2.05/1.69 (((~hskp18) | ndr1_0) <=> (ndr1_0 | (~hskp18))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(106,axiom,((~hskp18) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause14')).
% 2.05/1.69 tff(107,plain,
% 2.05/1.69 (ndr1_0 | (~hskp18)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[106, 105])).
% 2.05/1.69 tff(108,plain,
% 2.05/1.69 (ndr1_0 | (~hskp18)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[107, 104])).
% 2.05/1.69 tff(109,plain,
% 2.05/1.69 (~hskp18),
% 2.05/1.69 inference(unit_resolution,[status(thm)],[108, 91])).
% 2.05/1.69 tff(110,plain,
% 2.05/1.69 ((hskp27 | hskp18 | hskp17) <=> (hskp27 | hskp18 | hskp17)),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(111,plain,
% 2.05/1.69 (((hskp18 | hskp27) | hskp17) <=> (hskp27 | hskp18 | hskp17)),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(112,axiom,((hskp18 | hskp27) | hskp17), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 2.05/1.69 tff(113,plain,
% 2.05/1.69 (hskp27 | hskp18 | hskp17),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[112, 111])).
% 2.05/1.69 tff(114,plain,
% 2.05/1.69 (hskp27 | hskp18 | hskp17),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[113, 110])).
% 2.05/1.69 tff(115,plain,
% 2.05/1.69 (hskp27 | hskp18 | hskp17),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[114, 110])).
% 2.05/1.69 tff(116,plain,
% 2.05/1.69 (hskp27 | hskp18 | hskp17),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[115, 110])).
% 2.05/1.69 tff(117,plain,
% 2.05/1.69 (hskp27 | hskp18 | hskp17),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[116, 110])).
% 2.05/1.69 tff(118,plain,
% 2.05/1.69 (hskp27 | hskp18 | hskp17),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[117, 110])).
% 2.05/1.69 tff(119,plain,
% 2.05/1.69 (hskp27 | hskp18 | hskp17),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[118, 110])).
% 2.05/1.69 tff(120,plain,
% 2.05/1.69 (hskp27 | hskp18 | hskp17),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[119, 110])).
% 2.05/1.69 tff(121,plain,
% 2.05/1.69 ($false),
% 2.05/1.69 inference(unit_resolution,[status(thm)],[120, 109, 103, 97])).
% 2.05/1.69 tff(122,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 2.05/1.69 tff(123,plain,
% 2.05/1.69 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(124,plain,
% 2.05/1.69 ((hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234))) <=> (hskp27 | hskp2 | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(125,plain,
% 2.05/1.69 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234))))),
% 2.05/1.69 inference(monotonicity,[status(thm)],[124])).
% 2.05/1.69 tff(126,plain,
% 2.05/1.69 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))),
% 2.05/1.69 inference(transitivity,[status(thm)],[125, 123])).
% 2.05/1.69 tff(127,plain,
% 2.05/1.69 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)))),
% 2.05/1.69 inference(quant_inst,[status(thm)],[])).
% 2.05/1.69 tff(128,plain,
% 2.05/1.69 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234))),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[127, 126])).
% 2.05/1.69 tff(129,plain,
% 2.05/1.69 ($false),
% 2.05/1.69 inference(unit_resolution,[status(thm)],[128, 122, 34, 90, 89, 78, 67, 56])).
% 2.05/1.69 tff(130,plain,((~hskp26) | hskp27 | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.05/1.69 tff(131,plain,
% 2.05/1.69 (hskp2),
% 2.05/1.69 inference(unit_resolution,[status(thm)],[130, 46, 34])).
% 2.05/1.69 tff(132,plain,
% 2.05/1.69 (((~hskp2) | (~c1_1(a215))) <=> ((~hskp2) | (~c1_1(a215)))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(133,plain,
% 2.05/1.69 (((~c1_1(a215)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a215)))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(134,axiom,((~c1_1(a215)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 2.05/1.69 tff(135,plain,
% 2.05/1.69 ((~hskp2) | (~c1_1(a215))),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[134, 133])).
% 2.05/1.69 tff(136,plain,
% 2.05/1.69 ((~hskp2) | (~c1_1(a215))),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[135, 132])).
% 2.05/1.69 tff(137,plain,
% 2.05/1.69 (~c1_1(a215)),
% 2.05/1.69 inference(unit_resolution,[status(thm)],[136, 131])).
% 2.05/1.69 tff(138,plain,
% 2.05/1.69 (((~hskp2) | c2_1(a215)) <=> ((~hskp2) | c2_1(a215))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(139,axiom,((~hskp2) | c2_1(a215)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 2.05/1.69 tff(140,plain,
% 2.05/1.69 ((~hskp2) | c2_1(a215)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[139, 138])).
% 2.05/1.69 tff(141,plain,
% 2.05/1.69 ((~hskp2) | c2_1(a215)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[140, 138])).
% 2.05/1.69 tff(142,plain,
% 2.05/1.69 ((~hskp2) | c2_1(a215)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[141, 138])).
% 2.05/1.69 tff(143,plain,
% 2.05/1.69 ((~hskp2) | c2_1(a215)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[142, 138])).
% 2.05/1.69 tff(144,plain,
% 2.05/1.69 ((~hskp2) | c2_1(a215)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[143, 138])).
% 2.05/1.69 tff(145,plain,
% 2.05/1.69 ((~hskp2) | c2_1(a215)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[144, 138])).
% 2.05/1.69 tff(146,plain,
% 2.05/1.69 ((~hskp2) | c2_1(a215)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[145, 138])).
% 2.05/1.69 tff(147,plain,
% 2.05/1.69 ((~hskp2) | c2_1(a215)),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[146, 138])).
% 2.05/1.69 tff(148,plain,
% 2.05/1.69 (c2_1(a215)),
% 2.05/1.69 inference(unit_resolution,[status(thm)],[147, 131])).
% 2.05/1.69 tff(149,plain,
% 2.05/1.69 (((~hskp2) | (~c0_1(a215))) <=> ((~hskp2) | (~c0_1(a215)))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(150,plain,
% 2.05/1.69 (((~c0_1(a215)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a215)))),
% 2.05/1.69 inference(rewrite,[status(thm)],[])).
% 2.05/1.69 tff(151,axiom,((~c0_1(a215)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 2.05/1.69 tff(152,plain,
% 2.05/1.69 ((~hskp2) | (~c0_1(a215))),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[151, 150])).
% 2.05/1.69 tff(153,plain,
% 2.05/1.69 ((~hskp2) | (~c0_1(a215))),
% 2.05/1.69 inference(modus_ponens,[status(thm)],[152, 149])).
% 2.05/1.69 tff(154,plain,
% 2.05/1.69 (~c0_1(a215)),
% 2.05/1.69 inference(unit_resolution,[status(thm)],[153, 131])).
% 2.05/1.69 tff(155,plain,
% 2.05/1.69 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 2.05/1.69 inference(bind,[status(th)],[])).
% 2.05/1.69 tff(156,plain,
% 2.05/1.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.05/1.69 inference(quant_intro,[status(thm)],[155])).
% 2.05/1.69 tff(157,plain,
% 2.05/1.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.05/1.70 inference(rewrite,[status(thm)],[])).
% 2.05/1.70 tff(158,plain,
% 2.05/1.70 (^[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))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_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)) | (~c2_1(V))) | c0_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)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_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)) | (~c2_1(V))) | c0_1(V)) | c1_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)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~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)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 2.05/1.70 inference(bind,[status(th)],[])).
% 2.05/1.70 tff(159,plain,
% 2.05/1.70 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.05/1.70 inference(quant_intro,[status(thm)],[158])).
% 2.05/1.70 tff(160,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 2.05/1.70 tff(161,plain,
% 2.05/1.70 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.05/1.70 inference(modus_ponens,[status(thm)],[160, 159])).
% 2.05/1.70 tff(162,plain,
% 2.05/1.70 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.05/1.70 inference(modus_ponens,[status(thm)],[161, 157])).
% 2.05/1.70 tff(163,plain,(
% 2.05/1.70 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.05/1.70 inference(skolemize,[status(sab)],[162])).
% 2.05/1.70 tff(164,plain,
% 2.05/1.70 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.05/1.70 inference(modus_ponens,[status(thm)],[163, 156])).
% 2.05/1.70 tff(165,assumption,(~c1_1(a215)), introduced(assumption)).
% 2.05/1.70 tff(166,assumption,(~c0_1(a215)), introduced(assumption)).
% 2.05/1.70 tff(167,assumption,(c2_1(a215)), introduced(assumption)).
% 2.05/1.70 tff(168,plain,
% 2.05/1.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))),
% 2.05/1.70 inference(rewrite,[status(thm)],[])).
% 2.05/1.70 tff(169,plain,
% 2.05/1.70 ((hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215))) <=> (hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))),
% 2.05/1.70 inference(rewrite,[status(thm)],[])).
% 2.05/1.70 tff(170,plain,
% 2.05/1.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234))))),
% 2.05/1.70 inference(monotonicity,[status(thm)],[169])).
% 2.05/1.70 tff(171,plain,
% 2.05/1.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))),
% 2.05/1.70 inference(transitivity,[status(thm)],[170, 168])).
% 2.05/1.70 tff(172,plain,
% 2.05/1.70 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))),
% 2.05/1.70 inference(quant_inst,[status(thm)],[])).
% 2.05/1.70 tff(173,plain,
% 2.05/1.70 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234))),
% 2.05/1.70 inference(modus_ponens,[status(thm)],[172, 171])).
% 2.05/1.70 tff(174,plain,
% 2.05/1.70 ($false),
% 2.05/1.70 inference(unit_resolution,[status(thm)],[173, 122, 45, 89, 78, 67, 167, 166, 165, 164])).
% 2.05/1.70 tff(175,plain,((~hskp26) | hskp5 | (~c2_1(a215)) | c0_1(a215) | c1_1(a215)), inference(lemma,lemma(discharge,[]))).
% 2.05/1.70 tff(176,plain,
% 2.05/1.70 ($false),
% 2.05/1.70 inference(unit_resolution,[status(thm)],[175, 154, 148, 45, 46, 137])).
% 2.05/1.70 tff(177,plain,((~hskp26) | hskp5 | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.05/1.70 tff(178,plain,
% 2.05/1.70 (~hskp26),
% 2.05/1.70 inference(unit_resolution,[status(thm)],[177, 45, 34])).
% 2.05/1.70 tff(179,assumption,(~c3_1(a237)), introduced(assumption)).
% 2.05/1.70 tff(180,plain,
% 2.05/1.70 (^[U: $i] : refl((hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 2.05/1.70 inference(bind,[status(th)],[])).
% 2.05/1.70 tff(181,plain,
% 2.05/1.70 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.05/1.70 inference(quant_intro,[status(thm)],[180])).
% 2.05/1.70 tff(182,plain,
% 2.05/1.70 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.05/1.70 inference(rewrite,[status(thm)],[])).
% 2.05/1.70 tff(183,plain,
% 2.05/1.70 (^[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)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp2) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp2))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp2) <=> (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp2) <=> (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 2.05/1.70 inference(bind,[status(th)],[])).
% 2.05/1.70 tff(184,plain,
% 2.05/1.70 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp2) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.05/1.70 inference(quant_intro,[status(thm)],[183])).
% 2.05/1.70 tff(185,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 2.05/1.70 tff(186,plain,
% 2.05/1.70 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.05/1.70 inference(modus_ponens,[status(thm)],[185, 184])).
% 2.05/1.70 tff(187,plain,
% 2.05/1.70 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.05/1.70 inference(modus_ponens,[status(thm)],[186, 182])).
% 2.05/1.70 tff(188,plain,(
% 2.05/1.70 ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.05/1.70 inference(skolemize,[status(sab)],[187])).
% 2.05/1.70 tff(189,plain,
% 2.05/1.70 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.05/1.70 inference(modus_ponens,[status(thm)],[188, 181])).
% 2.05/1.70 tff(190,assumption,(hskp4), introduced(assumption)).
% 2.05/1.70 tff(191,plain,
% 2.05/1.70 (((~hskp4) | (~c3_1(a217))) <=> ((~hskp4) | (~c3_1(a217)))),
% 2.05/1.70 inference(rewrite,[status(thm)],[])).
% 2.05/1.70 tff(192,plain,
% 2.05/1.70 (((~c3_1(a217)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a217)))),
% 2.05/1.70 inference(rewrite,[status(thm)],[])).
% 2.05/1.70 tff(193,axiom,((~c3_1(a217)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 2.05/1.70 tff(194,plain,
% 2.05/1.70 ((~hskp4) | (~c3_1(a217))),
% 2.05/1.70 inference(modus_ponens,[status(thm)],[193, 192])).
% 2.05/1.70 tff(195,plain,
% 2.05/1.70 ((~hskp4) | (~c3_1(a217))),
% 2.05/1.70 inference(modus_ponens,[status(thm)],[194, 191])).
% 2.05/1.70 tff(196,plain,
% 2.05/1.70 (~c3_1(a217)),
% 2.05/1.70 inference(unit_resolution,[status(thm)],[195, 190])).
% 2.05/1.70 tff(197,plain,
% 2.05/1.70 (((~hskp4) | (~c2_1(a217))) <=> ((~hskp4) | (~c2_1(a217)))),
% 2.05/1.70 inference(rewrite,[status(thm)],[])).
% 2.05/1.70 tff(198,plain,
% 2.05/1.70 (((~c2_1(a217)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a217)))),
% 2.05/1.70 inference(rewrite,[status(thm)],[])).
% 2.05/1.70 tff(199,axiom,((~c2_1(a217)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 2.05/1.70 tff(200,plain,
% 2.05/1.70 ((~hskp4) | (~c2_1(a217))),
% 2.05/1.70 inference(modus_ponens,[status(thm)],[199, 198])).
% 2.05/1.70 tff(201,plain,
% 2.05/1.70 ((~hskp4) | (~c2_1(a217))),
% 2.05/1.70 inference(modus_ponens,[status(thm)],[200, 197])).
% 2.05/1.70 tff(202,plain,
% 2.05/1.70 (~c2_1(a217)),
% 2.05/1.70 inference(unit_resolution,[status(thm)],[201, 190])).
% 2.05/1.70 tff(203,plain,
% 2.05/1.70 (((~hskp4) | (~c1_1(a217))) <=> ((~hskp4) | (~c1_1(a217)))),
% 2.05/1.70 inference(rewrite,[status(thm)],[])).
% 2.05/1.70 tff(204,plain,
% 2.05/1.70 (((~c1_1(a217)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a217)))),
% 2.05/1.70 inference(rewrite,[status(thm)],[])).
% 2.05/1.70 tff(205,axiom,((~c1_1(a217)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 2.05/1.70 tff(206,plain,
% 2.05/1.70 ((~hskp4) | (~c1_1(a217))),
% 2.05/1.70 inference(modus_ponens,[status(thm)],[205, 204])).
% 2.05/1.70 tff(207,plain,
% 2.05/1.70 ((~hskp4) | (~c1_1(a217))),
% 2.05/1.70 inference(modus_ponens,[status(thm)],[206, 203])).
% 2.05/1.71 tff(208,plain,
% 2.05/1.71 (~c1_1(a217)),
% 2.05/1.71 inference(unit_resolution,[status(thm)],[207, 190])).
% 2.05/1.71 tff(209,plain,
% 2.05/1.71 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | c1_1(a217) | c2_1(a217) | c3_1(a217) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp2 | c1_1(a217) | c2_1(a217) | c3_1(a217) | (~ndr1_0))),
% 2.05/1.71 inference(rewrite,[status(thm)],[])).
% 2.05/1.71 tff(210,plain,
% 2.05/1.71 ((hskp27 | hskp2 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c3_1(a217)) <=> (hskp27 | hskp2 | c1_1(a217) | c2_1(a217) | c3_1(a217) | (~ndr1_0))),
% 2.05/1.71 inference(rewrite,[status(thm)],[])).
% 2.05/1.71 tff(211,plain,
% 2.05/1.71 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c3_1(a217))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | c1_1(a217) | c2_1(a217) | c3_1(a217) | (~ndr1_0)))),
% 2.05/1.71 inference(monotonicity,[status(thm)],[210])).
% 2.05/1.71 tff(212,plain,
% 2.05/1.71 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c3_1(a217))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp2 | c1_1(a217) | c2_1(a217) | c3_1(a217) | (~ndr1_0))),
% 2.05/1.71 inference(transitivity,[status(thm)],[211, 209])).
% 2.05/1.71 tff(213,plain,
% 2.05/1.71 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c3_1(a217))),
% 2.05/1.71 inference(quant_inst,[status(thm)],[])).
% 2.05/1.71 tff(214,plain,
% 2.05/1.71 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp2 | c1_1(a217) | c2_1(a217) | c3_1(a217) | (~ndr1_0)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[213, 212])).
% 2.05/1.71 tff(215,plain,
% 2.05/1.71 ($false),
% 2.05/1.71 inference(unit_resolution,[status(thm)],[214, 122, 34, 90, 208, 202, 196, 189])).
% 2.05/1.71 tff(216,plain,((~hskp4) | hskp27 | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.05/1.71 tff(217,plain,
% 2.05/1.71 (~hskp4),
% 2.05/1.71 inference(unit_resolution,[status(thm)],[216, 90, 34])).
% 2.05/1.71 tff(218,assumption,(hskp3), introduced(assumption)).
% 2.05/1.71 tff(219,plain,
% 2.05/1.71 (((~hskp3) | c1_1(a216)) <=> ((~hskp3) | c1_1(a216))),
% 2.05/1.71 inference(rewrite,[status(thm)],[])).
% 2.05/1.71 tff(220,axiom,((~hskp3) | c1_1(a216)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 2.05/1.71 tff(221,plain,
% 2.05/1.71 ((~hskp3) | c1_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[220, 219])).
% 2.05/1.71 tff(222,plain,
% 2.05/1.71 ((~hskp3) | c1_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[221, 219])).
% 2.05/1.71 tff(223,plain,
% 2.05/1.71 ((~hskp3) | c1_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[222, 219])).
% 2.05/1.71 tff(224,plain,
% 2.05/1.71 ((~hskp3) | c1_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[223, 219])).
% 2.05/1.71 tff(225,plain,
% 2.05/1.71 ((~hskp3) | c1_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[224, 219])).
% 2.05/1.71 tff(226,plain,
% 2.05/1.71 ((~hskp3) | c1_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[225, 219])).
% 2.05/1.71 tff(227,plain,
% 2.05/1.71 ((~hskp3) | c1_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[226, 219])).
% 2.05/1.71 tff(228,plain,
% 2.05/1.71 ((~hskp3) | c1_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[227, 219])).
% 2.05/1.71 tff(229,plain,
% 2.05/1.71 (c1_1(a216)),
% 2.05/1.71 inference(unit_resolution,[status(thm)],[228, 218])).
% 2.05/1.71 tff(230,plain,
% 2.05/1.71 (((~hskp3) | c0_1(a216)) <=> ((~hskp3) | c0_1(a216))),
% 2.05/1.71 inference(rewrite,[status(thm)],[])).
% 2.05/1.71 tff(231,axiom,((~hskp3) | c0_1(a216)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 2.05/1.71 tff(232,plain,
% 2.05/1.71 ((~hskp3) | c0_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[231, 230])).
% 2.05/1.71 tff(233,plain,
% 2.05/1.71 ((~hskp3) | c0_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[232, 230])).
% 2.05/1.71 tff(234,plain,
% 2.05/1.71 ((~hskp3) | c0_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[233, 230])).
% 2.05/1.71 tff(235,plain,
% 2.05/1.71 ((~hskp3) | c0_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[234, 230])).
% 2.05/1.71 tff(236,plain,
% 2.05/1.71 ((~hskp3) | c0_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[235, 230])).
% 2.05/1.71 tff(237,plain,
% 2.05/1.71 ((~hskp3) | c0_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[236, 230])).
% 2.05/1.71 tff(238,plain,
% 2.05/1.71 ((~hskp3) | c0_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[237, 230])).
% 2.05/1.71 tff(239,plain,
% 2.05/1.71 ((~hskp3) | c0_1(a216)),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[238, 230])).
% 2.05/1.71 tff(240,plain,
% 2.05/1.71 (c0_1(a216)),
% 2.05/1.71 inference(unit_resolution,[status(thm)],[239, 218])).
% 2.05/1.71 tff(241,plain,
% 2.05/1.71 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | (~c1_1(a216)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | (~c1_1(a216)))),
% 2.05/1.71 inference(rewrite,[status(thm)],[])).
% 2.05/1.71 tff(242,plain,
% 2.05/1.71 ((hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c1_1(a216)) | (~c0_1(a216))) <=> (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | (~c1_1(a216)))),
% 2.05/1.71 inference(rewrite,[status(thm)],[])).
% 2.05/1.71 tff(243,plain,
% 2.05/1.71 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c1_1(a216)) | (~c0_1(a216)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | (~c1_1(a216))))),
% 2.05/1.71 inference(monotonicity,[status(thm)],[242])).
% 2.05/1.71 tff(244,plain,
% 2.05/1.71 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c1_1(a216)) | (~c0_1(a216)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | (~c1_1(a216)))),
% 2.05/1.71 inference(transitivity,[status(thm)],[243, 241])).
% 2.05/1.71 tff(245,plain,
% 2.05/1.71 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c1_1(a216)) | (~c0_1(a216)))),
% 2.05/1.71 inference(quant_inst,[status(thm)],[])).
% 2.05/1.71 tff(246,plain,
% 2.05/1.71 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | (~c1_1(a216))),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[245, 244])).
% 2.05/1.71 tff(247,plain,
% 2.05/1.71 (~c3_1(a216)),
% 2.05/1.71 inference(unit_resolution,[status(thm)],[246, 122, 34, 90, 240, 229, 56])).
% 2.05/1.71 tff(248,plain,
% 2.05/1.71 (^[U: $i] : refl((hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 2.05/1.71 inference(bind,[status(th)],[])).
% 2.05/1.71 tff(249,plain,
% 2.05/1.71 (![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.05/1.71 inference(quant_intro,[status(thm)],[248])).
% 2.05/1.71 tff(250,plain,
% 2.05/1.71 (![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.05/1.71 inference(rewrite,[status(thm)],[])).
% 2.05/1.71 tff(251,plain,
% 2.05/1.71 (^[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)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp9) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp9) <=> (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp9) <=> (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 2.05/1.71 inference(bind,[status(th)],[])).
% 2.05/1.71 tff(252,plain,
% 2.05/1.71 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp9) <=> ![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.05/1.71 inference(quant_intro,[status(thm)],[251])).
% 2.05/1.71 tff(253,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 2.05/1.71 tff(254,plain,
% 2.05/1.71 (![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[253, 252])).
% 2.05/1.71 tff(255,plain,
% 2.05/1.71 (![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[254, 250])).
% 2.05/1.71 tff(256,plain,(
% 2.05/1.71 ![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.05/1.71 inference(skolemize,[status(sab)],[255])).
% 2.05/1.71 tff(257,plain,
% 2.05/1.71 (![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[256, 249])).
% 2.05/1.71 tff(258,plain,
% 2.05/1.71 (((~hskp3) | (~c2_1(a216))) <=> ((~hskp3) | (~c2_1(a216)))),
% 2.05/1.71 inference(rewrite,[status(thm)],[])).
% 2.05/1.71 tff(259,plain,
% 2.05/1.71 (((~c2_1(a216)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a216)))),
% 2.05/1.71 inference(rewrite,[status(thm)],[])).
% 2.05/1.71 tff(260,axiom,((~c2_1(a216)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 2.05/1.71 tff(261,plain,
% 2.05/1.71 ((~hskp3) | (~c2_1(a216))),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[260, 259])).
% 2.05/1.71 tff(262,plain,
% 2.05/1.71 ((~hskp3) | (~c2_1(a216))),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[261, 258])).
% 2.05/1.71 tff(263,plain,
% 2.05/1.71 (~c2_1(a216)),
% 2.05/1.71 inference(unit_resolution,[status(thm)],[262, 218])).
% 2.05/1.71 tff(264,plain,
% 2.05/1.71 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c1_1(a216)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c1_1(a216)))),
% 2.05/1.71 inference(rewrite,[status(thm)],[])).
% 2.05/1.71 tff(265,plain,
% 2.05/1.71 ((hskp26 | hskp9 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c1_1(a216))) <=> (hskp26 | hskp9 | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c1_1(a216)))),
% 2.05/1.71 inference(rewrite,[status(thm)],[])).
% 2.05/1.71 tff(266,plain,
% 2.05/1.71 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c1_1(a216)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c1_1(a216))))),
% 2.05/1.71 inference(monotonicity,[status(thm)],[265])).
% 2.05/1.71 tff(267,plain,
% 2.05/1.71 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c1_1(a216)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c1_1(a216)))),
% 2.05/1.71 inference(transitivity,[status(thm)],[266, 264])).
% 2.05/1.71 tff(268,plain,
% 2.05/1.71 ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c1_1(a216)))),
% 2.05/1.71 inference(quant_inst,[status(thm)],[])).
% 2.05/1.71 tff(269,plain,
% 2.05/1.71 ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c1_1(a216))),
% 2.05/1.71 inference(modus_ponens,[status(thm)],[268, 267])).
% 2.05/1.71 tff(270,plain,
% 2.05/1.71 ($false),
% 2.05/1.71 inference(unit_resolution,[status(thm)],[269, 122, 1, 23, 229, 263, 257, 247])).
% 2.05/1.71 tff(271,plain,((~hskp3) | hskp26 | hskp9 | hskp27 | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.05/1.71 tff(272,plain,
% 2.05/1.71 (~hskp3),
% 2.05/1.71 inference(unit_resolution,[status(thm)],[271, 90, 23, 34, 1])).
% 2.05/1.72 tff(273,plain,
% 2.05/1.72 (^[U: $i] : refl((hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))),
% 2.05/1.72 inference(bind,[status(th)],[])).
% 2.05/1.72 tff(274,plain,
% 2.05/1.72 (![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.05/1.72 inference(quant_intro,[status(thm)],[273])).
% 2.05/1.72 tff(275,plain,
% 2.05/1.72 (![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.05/1.72 inference(rewrite,[status(thm)],[])).
% 2.05/1.72 tff(276,plain,
% 2.05/1.72 (^[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) <=> (hskp3 | hskp4 | (~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 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))))),
% 2.05/1.72 inference(bind,[status(th)],[])).
% 2.05/1.72 tff(277,plain,
% 2.05/1.72 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.05/1.72 inference(quant_intro,[status(thm)],[276])).
% 2.05/1.72 tff(278,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 2.05/1.72 tff(279,plain,
% 2.05/1.72 (![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[278, 277])).
% 2.05/1.72 tff(280,plain,
% 2.05/1.72 (![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[279, 275])).
% 2.05/1.72 tff(281,plain,(
% 2.05/1.72 ![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.05/1.72 inference(skolemize,[status(sab)],[280])).
% 2.05/1.72 tff(282,plain,
% 2.05/1.72 (![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[281, 274])).
% 2.05/1.72 tff(283,assumption,(hskp19), introduced(assumption)).
% 2.05/1.72 tff(284,plain,
% 2.05/1.72 (((~hskp19) | (~c3_1(a255))) <=> ((~hskp19) | (~c3_1(a255)))),
% 2.05/1.72 inference(rewrite,[status(thm)],[])).
% 2.05/1.72 tff(285,plain,
% 2.05/1.72 (((~c3_1(a255)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a255)))),
% 2.05/1.72 inference(rewrite,[status(thm)],[])).
% 2.05/1.72 tff(286,axiom,((~c3_1(a255)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 2.05/1.72 tff(287,plain,
% 2.05/1.72 ((~hskp19) | (~c3_1(a255))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[286, 285])).
% 2.05/1.72 tff(288,plain,
% 2.05/1.72 ((~hskp19) | (~c3_1(a255))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[287, 284])).
% 2.05/1.72 tff(289,plain,
% 2.05/1.72 (~c3_1(a255)),
% 2.05/1.72 inference(unit_resolution,[status(thm)],[288, 283])).
% 2.05/1.72 tff(290,plain,
% 2.05/1.72 (((~hskp19) | (~c1_1(a255))) <=> ((~hskp19) | (~c1_1(a255)))),
% 2.05/1.72 inference(rewrite,[status(thm)],[])).
% 2.05/1.72 tff(291,plain,
% 2.05/1.72 (((~c1_1(a255)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a255)))),
% 2.05/1.72 inference(rewrite,[status(thm)],[])).
% 2.05/1.72 tff(292,axiom,((~c1_1(a255)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 2.05/1.72 tff(293,plain,
% 2.05/1.72 ((~hskp19) | (~c1_1(a255))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[292, 291])).
% 2.05/1.72 tff(294,plain,
% 2.05/1.72 ((~hskp19) | (~c1_1(a255))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[293, 290])).
% 2.05/1.72 tff(295,plain,
% 2.05/1.72 (~c1_1(a255)),
% 2.05/1.72 inference(unit_resolution,[status(thm)],[294, 283])).
% 2.05/1.72 tff(296,plain,
% 2.05/1.72 (((~hskp19) | (~c0_1(a255))) <=> ((~hskp19) | (~c0_1(a255)))),
% 2.05/1.72 inference(rewrite,[status(thm)],[])).
% 2.05/1.72 tff(297,plain,
% 2.05/1.72 (((~c0_1(a255)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a255)))),
% 2.05/1.72 inference(rewrite,[status(thm)],[])).
% 2.05/1.72 tff(298,axiom,((~c0_1(a255)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 2.05/1.72 tff(299,plain,
% 2.05/1.72 ((~hskp19) | (~c0_1(a255))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[298, 297])).
% 2.05/1.72 tff(300,plain,
% 2.05/1.72 ((~hskp19) | (~c0_1(a255))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[299, 296])).
% 2.05/1.72 tff(301,plain,
% 2.05/1.72 (~c0_1(a255)),
% 2.05/1.72 inference(unit_resolution,[status(thm)],[300, 283])).
% 2.05/1.72 tff(302,assumption,(~hskp4), introduced(assumption)).
% 2.05/1.72 tff(303,assumption,(~hskp3), introduced(assumption)).
% 2.05/1.72 tff(304,plain,
% 2.05/1.72 (((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp3 | hskp4 | c0_1(a255) | c1_1(a255) | c3_1(a255) | (~ndr1_0))) <=> ((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp3 | hskp4 | c0_1(a255) | c1_1(a255) | c3_1(a255) | (~ndr1_0))),
% 2.05/1.72 inference(rewrite,[status(thm)],[])).
% 2.05/1.72 tff(305,plain,
% 2.05/1.72 ((hskp3 | hskp4 | (~ndr1_0) | c1_1(a255) | c0_1(a255) | c3_1(a255)) <=> (hskp3 | hskp4 | c0_1(a255) | c1_1(a255) | c3_1(a255) | (~ndr1_0))),
% 2.05/1.72 inference(rewrite,[status(thm)],[])).
% 2.05/1.72 tff(306,plain,
% 2.05/1.72 (((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp3 | hskp4 | (~ndr1_0) | c1_1(a255) | c0_1(a255) | c3_1(a255))) <=> ((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp3 | hskp4 | c0_1(a255) | c1_1(a255) | c3_1(a255) | (~ndr1_0)))),
% 2.05/1.72 inference(monotonicity,[status(thm)],[305])).
% 2.05/1.72 tff(307,plain,
% 2.05/1.72 (((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp3 | hskp4 | (~ndr1_0) | c1_1(a255) | c0_1(a255) | c3_1(a255))) <=> ((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp3 | hskp4 | c0_1(a255) | c1_1(a255) | c3_1(a255) | (~ndr1_0))),
% 2.05/1.72 inference(transitivity,[status(thm)],[306, 304])).
% 2.05/1.72 tff(308,plain,
% 2.05/1.72 ((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp3 | hskp4 | (~ndr1_0) | c1_1(a255) | c0_1(a255) | c3_1(a255))),
% 2.05/1.72 inference(quant_inst,[status(thm)],[])).
% 2.05/1.72 tff(309,plain,
% 2.05/1.72 ((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp3 | hskp4 | c0_1(a255) | c1_1(a255) | c3_1(a255) | (~ndr1_0)),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[308, 307])).
% 2.05/1.72 tff(310,plain,
% 2.05/1.72 ($false),
% 2.05/1.72 inference(unit_resolution,[status(thm)],[309, 303, 122, 302, 301, 295, 289, 282])).
% 2.05/1.72 tff(311,plain,((~hskp19) | hskp3 | hskp4), inference(lemma,lemma(discharge,[]))).
% 2.05/1.72 tff(312,plain,
% 2.05/1.72 (~hskp19),
% 2.05/1.72 inference(unit_resolution,[status(thm)],[311, 272, 217])).
% 2.05/1.72 tff(313,plain,
% 2.05/1.72 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 2.05/1.72 inference(bind,[status(th)],[])).
% 2.05/1.72 tff(314,plain,
% 2.05/1.72 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.05/1.72 inference(quant_intro,[status(thm)],[313])).
% 2.05/1.72 tff(315,plain,
% 2.05/1.72 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.05/1.72 inference(rewrite,[status(thm)],[])).
% 2.05/1.72 tff(316,plain,
% 2.05/1.72 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 2.05/1.72 inference(bind,[status(th)],[])).
% 2.05/1.72 tff(317,plain,
% 2.05/1.72 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.05/1.72 inference(quant_intro,[status(thm)],[316])).
% 2.05/1.72 tff(318,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 2.05/1.72 tff(319,plain,
% 2.05/1.72 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[318, 317])).
% 2.05/1.72 tff(320,plain,
% 2.05/1.72 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[319, 315])).
% 2.05/1.72 tff(321,plain,(
% 2.05/1.72 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.05/1.72 inference(skolemize,[status(sab)],[320])).
% 2.05/1.72 tff(322,plain,
% 2.05/1.72 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[321, 314])).
% 2.05/1.72 tff(323,assumption,(~c1_1(a320)), introduced(assumption)).
% 2.05/1.72 tff(324,plain,
% 2.05/1.72 (^[U: $i] : refl((hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 2.05/1.72 inference(bind,[status(th)],[])).
% 2.05/1.72 tff(325,plain,
% 2.05/1.72 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.05/1.72 inference(quant_intro,[status(thm)],[324])).
% 2.05/1.72 tff(326,plain,
% 2.05/1.72 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.05/1.72 inference(rewrite,[status(thm)],[])).
% 2.05/1.72 tff(327,plain,
% 2.05/1.72 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24) <=> ((hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp24))), rewrite(((hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp24) <=> (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24) <=> (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 2.05/1.72 inference(bind,[status(th)],[])).
% 2.05/1.72 tff(328,plain,
% 2.05/1.72 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.05/1.72 inference(quant_intro,[status(thm)],[327])).
% 2.05/1.72 tff(329,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 2.05/1.72 tff(330,plain,
% 2.05/1.72 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[329, 328])).
% 2.05/1.72 tff(331,plain,
% 2.05/1.72 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[330, 326])).
% 2.05/1.72 tff(332,plain,(
% 2.05/1.72 ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.05/1.72 inference(skolemize,[status(sab)],[331])).
% 2.05/1.72 tff(333,plain,
% 2.05/1.72 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[332, 325])).
% 2.05/1.72 tff(334,assumption,(~hskp19), introduced(assumption)).
% 2.05/1.72 tff(335,plain,
% 2.05/1.72 ((hskp25 | hskp19) <=> (hskp25 | hskp19)),
% 2.05/1.72 inference(rewrite,[status(thm)],[])).
% 2.05/1.72 tff(336,axiom,(hskp25 | hskp19), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 2.05/1.72 tff(337,plain,
% 2.05/1.72 (hskp25 | hskp19),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[336, 335])).
% 2.05/1.72 tff(338,plain,
% 2.05/1.72 (hskp25 | hskp19),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[337, 335])).
% 2.05/1.72 tff(339,plain,
% 2.05/1.72 (hskp25 | hskp19),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[338, 335])).
% 2.05/1.72 tff(340,plain,
% 2.05/1.72 (hskp25 | hskp19),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[339, 335])).
% 2.05/1.72 tff(341,plain,
% 2.05/1.72 (hskp25 | hskp19),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[340, 335])).
% 2.05/1.72 tff(342,plain,
% 2.05/1.72 (hskp25 | hskp19),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[341, 335])).
% 2.05/1.72 tff(343,plain,
% 2.05/1.72 (hskp25 | hskp19),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[342, 335])).
% 2.05/1.72 tff(344,plain,
% 2.05/1.72 (hskp25 | hskp19),
% 2.05/1.72 inference(modus_ponens,[status(thm)],[343, 335])).
% 2.05/1.72 tff(345,plain,
% 2.05/1.72 (hskp25),
% 2.05/1.72 inference(unit_resolution,[status(thm)],[344, 334])).
% 2.05/1.73 tff(346,plain,
% 2.05/1.73 (((~hskp25) | c3_1(a320)) <=> ((~hskp25) | c3_1(a320))),
% 2.05/1.73 inference(rewrite,[status(thm)],[])).
% 2.05/1.73 tff(347,axiom,((~hskp25) | c3_1(a320)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 2.05/1.73 tff(348,plain,
% 2.05/1.73 ((~hskp25) | c3_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[347, 346])).
% 2.05/1.73 tff(349,plain,
% 2.05/1.73 ((~hskp25) | c3_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[348, 346])).
% 2.05/1.73 tff(350,plain,
% 2.05/1.73 ((~hskp25) | c3_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[349, 346])).
% 2.05/1.73 tff(351,plain,
% 2.05/1.73 ((~hskp25) | c3_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[350, 346])).
% 2.05/1.73 tff(352,plain,
% 2.05/1.73 ((~hskp25) | c3_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[351, 346])).
% 2.05/1.73 tff(353,plain,
% 2.05/1.73 ((~hskp25) | c3_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[352, 346])).
% 2.05/1.73 tff(354,plain,
% 2.05/1.73 ((~hskp25) | c3_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[353, 346])).
% 2.05/1.73 tff(355,plain,
% 2.05/1.73 ((~hskp25) | c3_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[354, 346])).
% 2.05/1.73 tff(356,plain,
% 2.05/1.73 (c3_1(a320)),
% 2.05/1.73 inference(unit_resolution,[status(thm)],[355, 345])).
% 2.05/1.73 tff(357,plain,
% 2.05/1.73 (((~hskp25) | c2_1(a320)) <=> ((~hskp25) | c2_1(a320))),
% 2.05/1.73 inference(rewrite,[status(thm)],[])).
% 2.05/1.73 tff(358,axiom,((~hskp25) | c2_1(a320)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 2.05/1.73 tff(359,plain,
% 2.05/1.73 ((~hskp25) | c2_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[358, 357])).
% 2.05/1.73 tff(360,plain,
% 2.05/1.73 ((~hskp25) | c2_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[359, 357])).
% 2.05/1.73 tff(361,plain,
% 2.05/1.73 ((~hskp25) | c2_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[360, 357])).
% 2.05/1.73 tff(362,plain,
% 2.05/1.73 ((~hskp25) | c2_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[361, 357])).
% 2.05/1.73 tff(363,plain,
% 2.05/1.73 ((~hskp25) | c2_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[362, 357])).
% 2.05/1.73 tff(364,plain,
% 2.05/1.73 ((~hskp25) | c2_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[363, 357])).
% 2.05/1.73 tff(365,plain,
% 2.05/1.73 ((~hskp25) | c2_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[364, 357])).
% 2.05/1.73 tff(366,plain,
% 2.05/1.73 ((~hskp25) | c2_1(a320)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[365, 357])).
% 2.05/1.73 tff(367,plain,
% 2.05/1.73 (c2_1(a320)),
% 2.05/1.73 inference(unit_resolution,[status(thm)],[366, 345])).
% 2.05/1.73 tff(368,assumption,(hskp24), introduced(assumption)).
% 2.05/1.73 tff(369,plain,
% 2.05/1.73 (((~hskp24) | (~c3_1(a280))) <=> ((~hskp24) | (~c3_1(a280)))),
% 2.05/1.73 inference(rewrite,[status(thm)],[])).
% 2.05/1.73 tff(370,plain,
% 2.05/1.73 (((~c3_1(a280)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a280)))),
% 2.05/1.73 inference(rewrite,[status(thm)],[])).
% 2.05/1.73 tff(371,axiom,((~c3_1(a280)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 2.05/1.73 tff(372,plain,
% 2.05/1.73 ((~hskp24) | (~c3_1(a280))),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[371, 370])).
% 2.05/1.73 tff(373,plain,
% 2.05/1.73 ((~hskp24) | (~c3_1(a280))),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[372, 369])).
% 2.05/1.73 tff(374,plain,
% 2.05/1.73 (~c3_1(a280)),
% 2.05/1.73 inference(unit_resolution,[status(thm)],[373, 368])).
% 2.05/1.73 tff(375,plain,
% 2.05/1.73 (((~hskp24) | (~c2_1(a280))) <=> ((~hskp24) | (~c2_1(a280)))),
% 2.05/1.73 inference(rewrite,[status(thm)],[])).
% 2.05/1.73 tff(376,plain,
% 2.05/1.73 (((~c2_1(a280)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a280)))),
% 2.05/1.73 inference(rewrite,[status(thm)],[])).
% 2.05/1.73 tff(377,axiom,((~c2_1(a280)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 2.05/1.73 tff(378,plain,
% 2.05/1.73 ((~hskp24) | (~c2_1(a280))),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[377, 376])).
% 2.05/1.73 tff(379,plain,
% 2.05/1.73 ((~hskp24) | (~c2_1(a280))),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[378, 375])).
% 2.05/1.73 tff(380,plain,
% 2.05/1.73 (~c2_1(a280)),
% 2.05/1.73 inference(unit_resolution,[status(thm)],[379, 368])).
% 2.05/1.73 tff(381,plain,
% 2.05/1.73 (((~hskp25) | (~c0_1(a320))) <=> ((~hskp25) | (~c0_1(a320)))),
% 2.05/1.73 inference(rewrite,[status(thm)],[])).
% 2.05/1.73 tff(382,plain,
% 2.05/1.73 (((~c0_1(a320)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a320)))),
% 2.05/1.73 inference(rewrite,[status(thm)],[])).
% 2.05/1.73 tff(383,axiom,((~c0_1(a320)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 2.05/1.73 tff(384,plain,
% 2.05/1.73 ((~hskp25) | (~c0_1(a320))),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[383, 382])).
% 2.05/1.73 tff(385,plain,
% 2.05/1.73 ((~hskp25) | (~c0_1(a320))),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[384, 381])).
% 2.05/1.73 tff(386,plain,
% 2.05/1.73 (~c0_1(a320)),
% 2.05/1.73 inference(unit_resolution,[status(thm)],[385, 345])).
% 2.05/1.73 tff(387,plain,
% 2.05/1.73 (((~hskp24) | c1_1(a280)) <=> ((~hskp24) | c1_1(a280))),
% 2.05/1.73 inference(rewrite,[status(thm)],[])).
% 2.05/1.73 tff(388,axiom,((~hskp24) | c1_1(a280)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 2.05/1.73 tff(389,plain,
% 2.05/1.73 ((~hskp24) | c1_1(a280)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[388, 387])).
% 2.05/1.73 tff(390,plain,
% 2.05/1.73 ((~hskp24) | c1_1(a280)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[389, 387])).
% 2.05/1.73 tff(391,plain,
% 2.05/1.73 ((~hskp24) | c1_1(a280)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[390, 387])).
% 2.05/1.73 tff(392,plain,
% 2.05/1.73 ((~hskp24) | c1_1(a280)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[391, 387])).
% 2.05/1.73 tff(393,plain,
% 2.05/1.73 ((~hskp24) | c1_1(a280)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[392, 387])).
% 2.05/1.73 tff(394,plain,
% 2.05/1.73 ((~hskp24) | c1_1(a280)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[393, 387])).
% 2.05/1.73 tff(395,plain,
% 2.05/1.73 ((~hskp24) | c1_1(a280)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[394, 387])).
% 2.05/1.73 tff(396,plain,
% 2.05/1.73 ((~hskp24) | c1_1(a280)),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[395, 387])).
% 2.05/1.73 tff(397,plain,
% 2.05/1.73 (c1_1(a280)),
% 2.05/1.73 inference(unit_resolution,[status(thm)],[396, 368])).
% 2.05/1.73 tff(398,plain,
% 2.05/1.73 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a320) | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c1_1(a280)) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a320) | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c1_1(a280)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.05/1.73 inference(rewrite,[status(thm)],[])).
% 2.05/1.73 tff(399,plain,
% 2.05/1.73 ((hskp19 | (~ndr1_0) | c2_1(a280) | c3_1(a280) | (~c1_1(a280)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320))) <=> (hskp19 | c0_1(a320) | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c1_1(a280)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.05/1.73 inference(rewrite,[status(thm)],[])).
% 2.05/1.73 tff(400,plain,
% 2.05/1.73 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a280) | c3_1(a280) | (~c1_1(a280)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a320) | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c1_1(a280)) | (~c2_1(a320)) | (~c3_1(a320))))),
% 2.05/1.73 inference(monotonicity,[status(thm)],[399])).
% 2.05/1.73 tff(401,plain,
% 2.05/1.73 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a280) | c3_1(a280) | (~c1_1(a280)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a320) | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c1_1(a280)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.05/1.73 inference(transitivity,[status(thm)],[400, 398])).
% 2.05/1.73 tff(402,plain,
% 2.05/1.73 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a280) | c3_1(a280) | (~c1_1(a280)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320)))),
% 2.05/1.73 inference(quant_inst,[status(thm)],[])).
% 2.05/1.73 tff(403,plain,
% 2.05/1.73 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a320) | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c1_1(a280)) | (~c2_1(a320)) | (~c3_1(a320))),
% 2.05/1.73 inference(modus_ponens,[status(thm)],[402, 401])).
% 2.05/1.73 tff(404,plain,
% 2.05/1.73 ($false),
% 2.05/1.73 inference(unit_resolution,[status(thm)],[403, 334, 122, 367, 356, 397, 386, 380, 374, 322])).
% 2.05/1.73 tff(405,plain,((~hskp24) | hskp19), inference(lemma,lemma(discharge,[]))).
% 2.05/1.73 tff(406,plain,
% 2.05/1.73 (~hskp24),
% 2.05/1.73 inference(unit_resolution,[status(thm)],[405, 334])).
% 2.05/1.73 tff(407,plain,
% 2.05/1.73 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp24 | hskp15 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.10/1.73 inference(rewrite,[status(thm)],[])).
% 2.10/1.73 tff(408,plain,
% 2.10/1.73 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.10/1.73 inference(quant_inst,[status(thm)],[])).
% 2.10/1.73 tff(409,plain,
% 2.10/1.73 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp24 | hskp15 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320))),
% 2.10/1.73 inference(modus_ponens,[status(thm)],[408, 407])).
% 2.10/1.73 tff(410,plain,
% 2.10/1.73 (hskp15 | c1_1(a320)),
% 2.10/1.73 inference(unit_resolution,[status(thm)],[409, 122, 406, 367, 356, 333])).
% 2.10/1.73 tff(411,plain,
% 2.10/1.73 (hskp15),
% 2.10/1.73 inference(unit_resolution,[status(thm)],[410, 323])).
% 2.10/1.73 tff(412,plain,
% 2.10/1.73 (((~hskp15) | (~c2_1(a242))) <=> ((~hskp15) | (~c2_1(a242)))),
% 2.10/1.73 inference(rewrite,[status(thm)],[])).
% 2.10/1.73 tff(413,plain,
% 2.10/1.73 (((~c2_1(a242)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a242)))),
% 2.10/1.73 inference(rewrite,[status(thm)],[])).
% 2.10/1.73 tff(414,axiom,((~c2_1(a242)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 2.10/1.73 tff(415,plain,
% 2.10/1.73 ((~hskp15) | (~c2_1(a242))),
% 2.10/1.73 inference(modus_ponens,[status(thm)],[414, 413])).
% 2.10/1.73 tff(416,plain,
% 2.10/1.73 ((~hskp15) | (~c2_1(a242))),
% 2.10/1.73 inference(modus_ponens,[status(thm)],[415, 412])).
% 2.10/1.73 tff(417,plain,
% 2.10/1.73 (~c2_1(a242)),
% 2.10/1.73 inference(unit_resolution,[status(thm)],[416, 411])).
% 2.10/1.73 tff(418,plain,
% 2.10/1.73 (((~hskp15) | c1_1(a242)) <=> ((~hskp15) | c1_1(a242))),
% 2.10/1.73 inference(rewrite,[status(thm)],[])).
% 2.10/1.73 tff(419,axiom,((~hskp15) | c1_1(a242)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 2.10/1.73 tff(420,plain,
% 2.10/1.73 ((~hskp15) | c1_1(a242)),
% 2.10/1.73 inference(modus_ponens,[status(thm)],[419, 418])).
% 2.10/1.73 tff(421,plain,
% 2.10/1.73 ((~hskp15) | c1_1(a242)),
% 2.10/1.73 inference(modus_ponens,[status(thm)],[420, 418])).
% 2.10/1.73 tff(422,plain,
% 2.10/1.73 ((~hskp15) | c1_1(a242)),
% 2.10/1.73 inference(modus_ponens,[status(thm)],[421, 418])).
% 2.10/1.73 tff(423,plain,
% 2.10/1.73 ((~hskp15) | c1_1(a242)),
% 2.10/1.73 inference(modus_ponens,[status(thm)],[422, 418])).
% 2.10/1.73 tff(424,plain,
% 2.10/1.73 ((~hskp15) | c1_1(a242)),
% 2.10/1.73 inference(modus_ponens,[status(thm)],[423, 418])).
% 2.10/1.73 tff(425,plain,
% 2.10/1.73 ((~hskp15) | c1_1(a242)),
% 2.10/1.73 inference(modus_ponens,[status(thm)],[424, 418])).
% 2.10/1.73 tff(426,plain,
% 2.10/1.73 ((~hskp15) | c1_1(a242)),
% 2.10/1.73 inference(modus_ponens,[status(thm)],[425, 418])).
% 2.10/1.73 tff(427,plain,
% 2.10/1.73 ((~hskp15) | c1_1(a242)),
% 2.10/1.73 inference(modus_ponens,[status(thm)],[426, 418])).
% 2.10/1.73 tff(428,plain,
% 2.10/1.73 (c1_1(a242)),
% 2.10/1.73 inference(unit_resolution,[status(thm)],[427, 411])).
% 2.10/1.73 tff(429,plain,
% 2.10/1.73 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a320) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a320) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.10/1.73 inference(rewrite,[status(thm)],[])).
% 2.10/1.73 tff(430,plain,
% 2.10/1.73 ((hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320))) <=> (hskp19 | c0_1(a320) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.10/1.73 inference(rewrite,[status(thm)],[])).
% 2.10/1.73 tff(431,plain,
% 2.10/1.73 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a320) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | (~c2_1(a320)) | (~c3_1(a320))))),
% 2.10/1.73 inference(monotonicity,[status(thm)],[430])).
% 2.10/1.73 tff(432,plain,
% 2.10/1.73 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a320) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.10/1.73 inference(transitivity,[status(thm)],[431, 429])).
% 2.10/1.73 tff(433,plain,
% 2.10/1.73 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320)))),
% 2.10/1.73 inference(quant_inst,[status(thm)],[])).
% 2.10/1.73 tff(434,plain,
% 2.10/1.73 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a320) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | (~c2_1(a320)) | (~c3_1(a320))),
% 2.10/1.73 inference(modus_ponens,[status(thm)],[433, 432])).
% 2.10/1.73 tff(435,plain,
% 2.10/1.73 (c3_1(a242)),
% 2.10/1.73 inference(unit_resolution,[status(thm)],[434, 334, 122, 367, 356, 428, 386, 417, 322])).
% 2.10/1.73 tff(436,plain,
% 2.10/1.73 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 2.10/1.73 inference(bind,[status(th)],[])).
% 2.10/1.73 tff(437,plain,
% 2.10/1.73 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.10/1.73 inference(quant_intro,[status(thm)],[436])).
% 2.10/1.73 tff(438,plain,
% 2.10/1.73 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.10/1.73 inference(rewrite,[status(thm)],[])).
% 2.10/1.73 tff(439,plain,
% 2.10/1.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_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) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_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) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 2.10/1.74 inference(bind,[status(th)],[])).
% 2.10/1.74 tff(440,plain,
% 2.10/1.74 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.10/1.74 inference(quant_intro,[status(thm)],[439])).
% 2.10/1.74 tff(441,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)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 2.10/1.74 tff(442,plain,
% 2.10/1.74 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[441, 440])).
% 2.10/1.74 tff(443,plain,
% 2.10/1.74 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[442, 438])).
% 2.10/1.74 tff(444,plain,(
% 2.10/1.74 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.10/1.74 inference(skolemize,[status(sab)],[443])).
% 2.10/1.74 tff(445,plain,
% 2.10/1.74 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[444, 437])).
% 2.10/1.74 tff(446,plain,
% 2.10/1.74 (((~hskp15) | (~c0_1(a242))) <=> ((~hskp15) | (~c0_1(a242)))),
% 2.10/1.74 inference(rewrite,[status(thm)],[])).
% 2.10/1.74 tff(447,plain,
% 2.10/1.74 (((~c0_1(a242)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a242)))),
% 2.10/1.74 inference(rewrite,[status(thm)],[])).
% 2.10/1.74 tff(448,axiom,((~c0_1(a242)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 2.10/1.74 tff(449,plain,
% 2.10/1.74 ((~hskp15) | (~c0_1(a242))),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[448, 447])).
% 2.10/1.74 tff(450,plain,
% 2.10/1.74 ((~hskp15) | (~c0_1(a242))),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[449, 446])).
% 2.10/1.74 tff(451,plain,
% 2.10/1.74 (~c0_1(a242)),
% 2.10/1.74 inference(unit_resolution,[status(thm)],[450, 411])).
% 2.10/1.74 tff(452,plain,
% 2.10/1.74 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.10/1.74 inference(rewrite,[status(thm)],[])).
% 2.10/1.74 tff(453,plain,
% 2.10/1.74 ((hskp9 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242))) <=> (hskp9 | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.10/1.74 inference(rewrite,[status(thm)],[])).
% 2.10/1.74 tff(454,plain,
% 2.10/1.74 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320))))),
% 2.10/1.74 inference(monotonicity,[status(thm)],[453])).
% 2.10/1.74 tff(455,plain,
% 2.10/1.74 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.10/1.74 inference(transitivity,[status(thm)],[454, 452])).
% 2.10/1.74 tff(456,plain,
% 2.10/1.74 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))),
% 2.10/1.74 inference(quant_inst,[status(thm)],[])).
% 2.10/1.74 tff(457,plain,
% 2.10/1.74 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320))),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[456, 455])).
% 2.10/1.74 tff(458,plain,
% 2.10/1.74 ($false),
% 2.10/1.74 inference(unit_resolution,[status(thm)],[457, 122, 23, 367, 356, 428, 451, 445, 323, 435])).
% 2.10/1.74 tff(459,plain,(c1_1(a320) | hskp9 | hskp19), inference(lemma,lemma(discharge,[]))).
% 2.10/1.74 tff(460,plain,
% 2.10/1.74 (c1_1(a320)),
% 2.10/1.74 inference(unit_resolution,[status(thm)],[459, 312, 23])).
% 2.10/1.74 tff(461,plain,
% 2.10/1.74 (^[U: $i] : refl((hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 2.10/1.74 inference(bind,[status(th)],[])).
% 2.10/1.74 tff(462,plain,
% 2.10/1.74 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.10/1.74 inference(quant_intro,[status(thm)],[461])).
% 2.10/1.74 tff(463,plain,
% 2.10/1.74 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.10/1.74 inference(rewrite,[status(thm)],[])).
% 2.10/1.74 tff(464,plain,
% 2.10/1.74 (^[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)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6) <=> ((hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp6))), rewrite(((hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6) <=> (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 2.10/1.74 inference(bind,[status(th)],[])).
% 2.10/1.74 tff(465,plain,
% 2.10/1.74 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6) <=> ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.10/1.74 inference(quant_intro,[status(thm)],[464])).
% 2.10/1.74 tff(466,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 2.10/1.74 tff(467,plain,
% 2.10/1.74 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[466, 465])).
% 2.10/1.74 tff(468,plain,
% 2.10/1.74 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[467, 463])).
% 2.10/1.74 tff(469,plain,(
% 2.10/1.74 ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.10/1.74 inference(skolemize,[status(sab)],[468])).
% 2.10/1.74 tff(470,plain,
% 2.10/1.74 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[469, 462])).
% 2.10/1.74 tff(471,plain,
% 2.10/1.74 (hskp25),
% 2.10/1.74 inference(unit_resolution,[status(thm)],[344, 312])).
% 2.10/1.74 tff(472,plain,
% 2.10/1.74 (~c0_1(a320)),
% 2.10/1.74 inference(unit_resolution,[status(thm)],[385, 471])).
% 2.10/1.74 tff(473,plain,
% 2.10/1.74 (c3_1(a320)),
% 2.10/1.74 inference(unit_resolution,[status(thm)],[355, 471])).
% 2.10/1.74 tff(474,plain,
% 2.10/1.74 (((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp3 | hskp6 | c0_1(a320) | (~ndr1_0) | (~c1_1(a320)) | (~c3_1(a320)))) <=> ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp3 | hskp6 | c0_1(a320) | (~ndr1_0) | (~c1_1(a320)) | (~c3_1(a320)))),
% 2.10/1.74 inference(rewrite,[status(thm)],[])).
% 2.10/1.74 tff(475,plain,
% 2.10/1.74 ((hskp3 | hskp6 | (~ndr1_0) | c0_1(a320) | (~c3_1(a320)) | (~c1_1(a320))) <=> (hskp3 | hskp6 | c0_1(a320) | (~ndr1_0) | (~c1_1(a320)) | (~c3_1(a320)))),
% 2.10/1.74 inference(rewrite,[status(thm)],[])).
% 2.10/1.74 tff(476,plain,
% 2.10/1.74 (((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp3 | hskp6 | (~ndr1_0) | c0_1(a320) | (~c3_1(a320)) | (~c1_1(a320)))) <=> ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp3 | hskp6 | c0_1(a320) | (~ndr1_0) | (~c1_1(a320)) | (~c3_1(a320))))),
% 2.10/1.74 inference(monotonicity,[status(thm)],[475])).
% 2.10/1.74 tff(477,plain,
% 2.10/1.74 (((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp3 | hskp6 | (~ndr1_0) | c0_1(a320) | (~c3_1(a320)) | (~c1_1(a320)))) <=> ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp3 | hskp6 | c0_1(a320) | (~ndr1_0) | (~c1_1(a320)) | (~c3_1(a320)))),
% 2.10/1.74 inference(transitivity,[status(thm)],[476, 474])).
% 2.10/1.74 tff(478,plain,
% 2.10/1.74 ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp3 | hskp6 | (~ndr1_0) | c0_1(a320) | (~c3_1(a320)) | (~c1_1(a320)))),
% 2.10/1.74 inference(quant_inst,[status(thm)],[])).
% 2.10/1.74 tff(479,plain,
% 2.10/1.74 ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp3 | hskp6 | c0_1(a320) | (~ndr1_0) | (~c1_1(a320)) | (~c3_1(a320))),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[478, 477])).
% 2.10/1.74 tff(480,plain,
% 2.10/1.74 (hskp6),
% 2.10/1.74 inference(unit_resolution,[status(thm)],[479, 272, 122, 473, 472, 470, 460])).
% 2.10/1.74 tff(481,plain,
% 2.10/1.74 (((~hskp6) | (~c3_1(a220))) <=> ((~hskp6) | (~c3_1(a220)))),
% 2.10/1.74 inference(rewrite,[status(thm)],[])).
% 2.10/1.74 tff(482,plain,
% 2.10/1.74 (((~c3_1(a220)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a220)))),
% 2.10/1.74 inference(rewrite,[status(thm)],[])).
% 2.10/1.74 tff(483,axiom,((~c3_1(a220)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 2.10/1.74 tff(484,plain,
% 2.10/1.74 ((~hskp6) | (~c3_1(a220))),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[483, 482])).
% 2.10/1.74 tff(485,plain,
% 2.10/1.74 ((~hskp6) | (~c3_1(a220))),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[484, 481])).
% 2.10/1.74 tff(486,plain,
% 2.10/1.74 (~c3_1(a220)),
% 2.10/1.74 inference(unit_resolution,[status(thm)],[485, 480])).
% 2.10/1.74 tff(487,plain,
% 2.10/1.74 ((hskp3 | hskp16) <=> (hskp3 | hskp16)),
% 2.10/1.74 inference(rewrite,[status(thm)],[])).
% 2.10/1.74 tff(488,axiom,(hskp3 | hskp16), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 2.10/1.74 tff(489,plain,
% 2.10/1.74 (hskp3 | hskp16),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[488, 487])).
% 2.10/1.74 tff(490,plain,
% 2.10/1.74 (hskp3 | hskp16),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[489, 487])).
% 2.10/1.74 tff(491,plain,
% 2.10/1.74 (hskp3 | hskp16),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[490, 487])).
% 2.10/1.74 tff(492,plain,
% 2.10/1.74 (hskp3 | hskp16),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[491, 487])).
% 2.10/1.74 tff(493,plain,
% 2.10/1.74 (hskp3 | hskp16),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[492, 487])).
% 2.10/1.74 tff(494,plain,
% 2.10/1.74 (hskp3 | hskp16),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[493, 487])).
% 2.10/1.74 tff(495,plain,
% 2.10/1.74 (hskp3 | hskp16),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[494, 487])).
% 2.10/1.74 tff(496,plain,
% 2.10/1.74 (hskp3 | hskp16),
% 2.10/1.74 inference(modus_ponens,[status(thm)],[495, 487])).
% 2.10/1.74 tff(497,plain,
% 2.10/1.74 (hskp16),
% 2.10/1.74 inference(unit_resolution,[status(thm)],[496, 272])).
% 2.10/1.75 tff(498,plain,
% 2.10/1.75 (((~hskp16) | (~c3_1(a245))) <=> ((~hskp16) | (~c3_1(a245)))),
% 2.10/1.75 inference(rewrite,[status(thm)],[])).
% 2.10/1.75 tff(499,plain,
% 2.10/1.75 (((~c3_1(a245)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a245)))),
% 2.10/1.75 inference(rewrite,[status(thm)],[])).
% 2.10/1.75 tff(500,axiom,((~c3_1(a245)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 2.10/1.75 tff(501,plain,
% 2.10/1.75 ((~hskp16) | (~c3_1(a245))),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[500, 499])).
% 2.10/1.75 tff(502,plain,
% 2.10/1.75 ((~hskp16) | (~c3_1(a245))),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[501, 498])).
% 2.10/1.75 tff(503,plain,
% 2.10/1.75 (~c3_1(a245)),
% 2.10/1.75 inference(unit_resolution,[status(thm)],[502, 497])).
% 2.10/1.75 tff(504,plain,
% 2.10/1.75 (((~hskp16) | (~c1_1(a245))) <=> ((~hskp16) | (~c1_1(a245)))),
% 2.10/1.75 inference(rewrite,[status(thm)],[])).
% 2.10/1.75 tff(505,plain,
% 2.10/1.75 (((~c1_1(a245)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a245)))),
% 2.10/1.75 inference(rewrite,[status(thm)],[])).
% 2.10/1.75 tff(506,axiom,((~c1_1(a245)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 2.10/1.75 tff(507,plain,
% 2.10/1.75 ((~hskp16) | (~c1_1(a245))),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[506, 505])).
% 2.10/1.75 tff(508,plain,
% 2.10/1.75 ((~hskp16) | (~c1_1(a245))),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[507, 504])).
% 2.10/1.75 tff(509,plain,
% 2.10/1.75 (~c1_1(a245)),
% 2.10/1.75 inference(unit_resolution,[status(thm)],[508, 497])).
% 2.10/1.75 tff(510,plain,
% 2.10/1.75 (((~hskp16) | c0_1(a245)) <=> ((~hskp16) | c0_1(a245))),
% 2.10/1.75 inference(rewrite,[status(thm)],[])).
% 2.10/1.75 tff(511,axiom,((~hskp16) | c0_1(a245)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 2.10/1.75 tff(512,plain,
% 2.10/1.75 ((~hskp16) | c0_1(a245)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[511, 510])).
% 2.10/1.75 tff(513,plain,
% 2.10/1.75 ((~hskp16) | c0_1(a245)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[512, 510])).
% 2.10/1.75 tff(514,plain,
% 2.10/1.75 ((~hskp16) | c0_1(a245)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[513, 510])).
% 2.10/1.75 tff(515,plain,
% 2.10/1.75 ((~hskp16) | c0_1(a245)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[514, 510])).
% 2.10/1.75 tff(516,plain,
% 2.10/1.75 ((~hskp16) | c0_1(a245)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[515, 510])).
% 2.10/1.75 tff(517,plain,
% 2.10/1.75 ((~hskp16) | c0_1(a245)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[516, 510])).
% 2.10/1.75 tff(518,plain,
% 2.10/1.75 ((~hskp16) | c0_1(a245)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[517, 510])).
% 2.10/1.75 tff(519,plain,
% 2.10/1.75 ((~hskp16) | c0_1(a245)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[518, 510])).
% 2.10/1.75 tff(520,plain,
% 2.10/1.75 (c0_1(a245)),
% 2.10/1.75 inference(unit_resolution,[status(thm)],[519, 497])).
% 2.10/1.75 tff(521,plain,
% 2.10/1.75 (((~hskp6) | c1_1(a220)) <=> ((~hskp6) | c1_1(a220))),
% 2.10/1.75 inference(rewrite,[status(thm)],[])).
% 2.10/1.75 tff(522,axiom,((~hskp6) | c1_1(a220)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 2.10/1.75 tff(523,plain,
% 2.10/1.75 ((~hskp6) | c1_1(a220)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[522, 521])).
% 2.10/1.75 tff(524,plain,
% 2.10/1.75 ((~hskp6) | c1_1(a220)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[523, 521])).
% 2.10/1.75 tff(525,plain,
% 2.10/1.75 ((~hskp6) | c1_1(a220)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[524, 521])).
% 2.10/1.75 tff(526,plain,
% 2.10/1.75 ((~hskp6) | c1_1(a220)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[525, 521])).
% 2.10/1.75 tff(527,plain,
% 2.10/1.75 ((~hskp6) | c1_1(a220)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[526, 521])).
% 2.10/1.75 tff(528,plain,
% 2.10/1.75 ((~hskp6) | c1_1(a220)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[527, 521])).
% 2.10/1.75 tff(529,plain,
% 2.10/1.75 ((~hskp6) | c1_1(a220)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[528, 521])).
% 2.10/1.75 tff(530,plain,
% 2.10/1.75 ((~hskp6) | c1_1(a220)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[529, 521])).
% 2.10/1.75 tff(531,plain,
% 2.10/1.75 (c1_1(a220)),
% 2.10/1.75 inference(unit_resolution,[status(thm)],[530, 480])).
% 2.10/1.75 tff(532,plain,
% 2.10/1.75 (((~hskp6) | c2_1(a220)) <=> ((~hskp6) | c2_1(a220))),
% 2.10/1.75 inference(rewrite,[status(thm)],[])).
% 2.10/1.75 tff(533,axiom,((~hskp6) | c2_1(a220)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 2.10/1.75 tff(534,plain,
% 2.10/1.75 ((~hskp6) | c2_1(a220)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[533, 532])).
% 2.10/1.75 tff(535,plain,
% 2.10/1.75 ((~hskp6) | c2_1(a220)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[534, 532])).
% 2.10/1.75 tff(536,plain,
% 2.10/1.75 ((~hskp6) | c2_1(a220)),
% 2.10/1.75 inference(modus_ponens,[status(thm)],[535, 532])).
% 2.10/1.75 tff(537,plain,
% 2.11/1.75 ((~hskp6) | c2_1(a220)),
% 2.11/1.75 inference(modus_ponens,[status(thm)],[536, 532])).
% 2.11/1.75 tff(538,plain,
% 2.11/1.75 ((~hskp6) | c2_1(a220)),
% 2.11/1.75 inference(modus_ponens,[status(thm)],[537, 532])).
% 2.11/1.75 tff(539,plain,
% 2.11/1.75 ((~hskp6) | c2_1(a220)),
% 2.11/1.75 inference(modus_ponens,[status(thm)],[538, 532])).
% 2.11/1.75 tff(540,plain,
% 2.11/1.75 ((~hskp6) | c2_1(a220)),
% 2.11/1.75 inference(modus_ponens,[status(thm)],[539, 532])).
% 2.11/1.75 tff(541,plain,
% 2.11/1.75 ((~hskp6) | c2_1(a220)),
% 2.11/1.75 inference(modus_ponens,[status(thm)],[540, 532])).
% 2.11/1.75 tff(542,plain,
% 2.11/1.75 (c2_1(a220)),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[541, 480])).
% 2.11/1.75 tff(543,plain,
% 2.11/1.75 (c1_1(a320)),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[459, 334, 23])).
% 2.11/1.75 tff(544,plain,
% 2.11/1.75 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))))),
% 2.11/1.75 inference(bind,[status(th)],[])).
% 2.11/1.75 tff(545,plain,
% 2.11/1.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.75 inference(quant_intro,[status(thm)],[544])).
% 2.11/1.75 tff(546,plain,
% 2.11/1.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.75 inference(rewrite,[status(thm)],[])).
% 2.11/1.75 tff(547,plain,
% 2.11/1.75 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~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)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))))),
% 2.11/1.75 inference(bind,[status(th)],[])).
% 2.11/1.75 tff(548,plain,
% 2.11/1.75 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.75 inference(quant_intro,[status(thm)],[547])).
% 2.11/1.75 tff(549,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 2.11/1.75 tff(550,plain,
% 2.11/1.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.75 inference(modus_ponens,[status(thm)],[549, 548])).
% 2.11/1.75 tff(551,plain,
% 2.11/1.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.75 inference(modus_ponens,[status(thm)],[550, 546])).
% 2.11/1.75 tff(552,plain,(
% 2.11/1.75 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.75 inference(skolemize,[status(sab)],[551])).
% 2.11/1.75 tff(553,plain,
% 2.11/1.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.75 inference(modus_ponens,[status(thm)],[552, 545])).
% 2.11/1.75 tff(554,assumption,(~c3_1(a220)), introduced(assumption)).
% 2.11/1.75 tff(555,assumption,(~c3_1(a245)), introduced(assumption)).
% 2.11/1.75 tff(556,assumption,(~c1_1(a245)), introduced(assumption)).
% 2.11/1.75 tff(557,assumption,(c2_1(a220)), introduced(assumption)).
% 2.11/1.75 tff(558,assumption,(c1_1(a220)), introduced(assumption)).
% 2.11/1.75 tff(559,assumption,(c0_1(a245)), introduced(assumption)).
% 2.11/1.75 tff(560,plain,
% 2.11/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a245) | c3_1(a245) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c0_1(a245)) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a245) | c3_1(a245) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c0_1(a245)) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 2.11/1.75 inference(rewrite,[status(thm)],[])).
% 2.11/1.75 tff(561,plain,
% 2.11/1.75 (((~ndr1_0) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245))) <=> (c1_1(a245) | c3_1(a245) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c0_1(a245)) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 2.11/1.75 inference(rewrite,[status(thm)],[])).
% 2.11/1.75 tff(562,plain,
% 2.11/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a245) | c3_1(a245) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c0_1(a245)) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320))))),
% 2.11/1.75 inference(monotonicity,[status(thm)],[561])).
% 2.11/1.75 tff(563,plain,
% 2.11/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a245) | c3_1(a245) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c0_1(a245)) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 2.11/1.75 inference(transitivity,[status(thm)],[562, 560])).
% 2.11/1.75 tff(564,plain,
% 2.11/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))),
% 2.11/1.75 inference(quant_inst,[status(thm)],[])).
% 2.11/1.75 tff(565,plain,
% 2.11/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a245) | c3_1(a245) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c0_1(a245)) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320))),
% 2.11/1.75 inference(modus_ponens,[status(thm)],[564, 563])).
% 2.11/1.75 tff(566,plain,
% 2.11/1.75 ($false),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[565, 122, 367, 356, 559, 558, 557, 556, 555, 554, 553, 543])).
% 2.11/1.75 tff(567,plain,(hskp19 | (~c0_1(a245)) | (~c1_1(a220)) | (~c2_1(a220)) | c1_1(a245) | c3_1(a245) | c3_1(a220) | hskp9), inference(lemma,lemma(discharge,[]))).
% 2.11/1.75 tff(568,plain,
% 2.11/1.75 ($false),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[567, 542, 531, 520, 312, 509, 503, 486, 23])).
% 2.11/1.75 tff(569,plain,(hskp2 | hskp9 | hskp27 | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.11/1.75 tff(570,plain,
% 2.11/1.75 (hskp2),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[569, 178, 34, 23])).
% 2.11/1.75 tff(571,plain,
% 2.11/1.75 (~c1_1(a215)),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[136, 570])).
% 2.11/1.75 tff(572,plain,
% 2.11/1.75 (~c0_1(a215)),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[153, 570])).
% 2.11/1.75 tff(573,plain,
% 2.11/1.75 (c2_1(a215)),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[147, 570])).
% 2.11/1.75 tff(574,assumption,(~hskp12), introduced(assumption)).
% 2.11/1.75 tff(575,assumption,(~c2_1(a237)), introduced(assumption)).
% 2.11/1.75 tff(576,plain,
% 2.11/1.75 (~hskp26),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[130, 90, 34])).
% 2.11/1.75 tff(577,plain,
% 2.11/1.75 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp2 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237))),
% 2.11/1.76 inference(rewrite,[status(thm)],[])).
% 2.11/1.76 tff(578,plain,
% 2.11/1.76 ((hskp27 | hskp2 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c3_1(a237)) <=> (hskp27 | hskp2 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237))),
% 2.11/1.76 inference(rewrite,[status(thm)],[])).
% 2.11/1.76 tff(579,plain,
% 2.11/1.76 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c3_1(a237))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237)))),
% 2.11/1.76 inference(monotonicity,[status(thm)],[578])).
% 2.11/1.76 tff(580,plain,
% 2.11/1.76 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c3_1(a237))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp2 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237))),
% 2.11/1.76 inference(transitivity,[status(thm)],[579, 577])).
% 2.11/1.76 tff(581,plain,
% 2.11/1.76 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c3_1(a237))),
% 2.11/1.76 inference(quant_inst,[status(thm)],[])).
% 2.11/1.76 tff(582,plain,
% 2.11/1.76 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp2 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[581, 580])).
% 2.11/1.76 tff(583,plain,
% 2.11/1.76 (hskp2 | c2_1(a237) | c1_1(a237)),
% 2.11/1.76 inference(unit_resolution,[status(thm)],[582, 122, 34, 179, 189])).
% 2.11/1.76 tff(584,plain,
% 2.11/1.76 (c1_1(a237)),
% 2.11/1.76 inference(unit_resolution,[status(thm)],[583, 575, 90])).
% 2.11/1.76 tff(585,plain,
% 2.11/1.76 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c1_1(a237)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c1_1(a237)))),
% 2.11/1.76 inference(rewrite,[status(thm)],[])).
% 2.11/1.76 tff(586,plain,
% 2.11/1.76 ((hskp26 | hskp9 | (~ndr1_0) | c2_1(a237) | c3_1(a237) | (~c1_1(a237))) <=> (hskp26 | hskp9 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c1_1(a237)))),
% 2.11/1.76 inference(rewrite,[status(thm)],[])).
% 2.11/1.76 tff(587,plain,
% 2.11/1.76 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a237) | c3_1(a237) | (~c1_1(a237)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c1_1(a237))))),
% 2.11/1.76 inference(monotonicity,[status(thm)],[586])).
% 2.11/1.76 tff(588,plain,
% 2.11/1.76 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a237) | c3_1(a237) | (~c1_1(a237)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c1_1(a237)))),
% 2.11/1.76 inference(transitivity,[status(thm)],[587, 585])).
% 2.11/1.76 tff(589,plain,
% 2.11/1.76 ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a237) | c3_1(a237) | (~c1_1(a237)))),
% 2.11/1.76 inference(quant_inst,[status(thm)],[])).
% 2.11/1.76 tff(590,plain,
% 2.11/1.76 ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c1_1(a237))),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[589, 588])).
% 2.11/1.76 tff(591,plain,
% 2.11/1.76 (hskp26 | c2_1(a237) | (~c1_1(a237))),
% 2.11/1.76 inference(unit_resolution,[status(thm)],[590, 122, 23, 179, 257])).
% 2.11/1.76 tff(592,plain,
% 2.11/1.76 ($false),
% 2.11/1.76 inference(unit_resolution,[status(thm)],[591, 584, 575, 576])).
% 2.11/1.76 tff(593,plain,(c2_1(a237) | hskp9 | c3_1(a237) | hskp2 | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.11/1.76 tff(594,plain,
% 2.11/1.76 (hskp2),
% 2.11/1.76 inference(unit_resolution,[status(thm)],[593, 575, 179, 23, 34])).
% 2.11/1.76 tff(595,plain,
% 2.11/1.76 (~c1_1(a215)),
% 2.11/1.76 inference(unit_resolution,[status(thm)],[136, 594])).
% 2.11/1.76 tff(596,plain,
% 2.11/1.76 (~c0_1(a215)),
% 2.11/1.76 inference(unit_resolution,[status(thm)],[153, 594])).
% 2.11/1.76 tff(597,plain,
% 2.11/1.76 (c2_1(a215)),
% 2.11/1.76 inference(unit_resolution,[status(thm)],[147, 594])).
% 2.11/1.76 tff(598,plain,
% 2.11/1.76 (((~hskp12) | c2_1(a237)) <=> ((~hskp12) | c2_1(a237))),
% 2.11/1.76 inference(rewrite,[status(thm)],[])).
% 2.11/1.76 tff(599,axiom,((~hskp12) | c2_1(a237)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 2.11/1.76 tff(600,plain,
% 2.11/1.76 ((~hskp12) | c2_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[599, 598])).
% 2.11/1.76 tff(601,plain,
% 2.11/1.76 ((~hskp12) | c2_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[600, 598])).
% 2.11/1.76 tff(602,plain,
% 2.11/1.76 ((~hskp12) | c2_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[601, 598])).
% 2.11/1.76 tff(603,plain,
% 2.11/1.76 ((~hskp12) | c2_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[602, 598])).
% 2.11/1.76 tff(604,plain,
% 2.11/1.76 ((~hskp12) | c2_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[603, 598])).
% 2.11/1.76 tff(605,plain,
% 2.11/1.76 ((~hskp12) | c2_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[604, 598])).
% 2.11/1.76 tff(606,plain,
% 2.11/1.76 ((~hskp12) | c2_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[605, 598])).
% 2.11/1.76 tff(607,plain,
% 2.11/1.76 ((~hskp12) | c2_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[606, 598])).
% 2.11/1.76 tff(608,plain,
% 2.11/1.76 (~hskp12),
% 2.11/1.76 inference(unit_resolution,[status(thm)],[607, 575])).
% 2.11/1.76 tff(609,plain,
% 2.11/1.76 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 2.11/1.76 inference(bind,[status(th)],[])).
% 2.11/1.76 tff(610,plain,
% 2.11/1.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.11/1.76 inference(quant_intro,[status(thm)],[609])).
% 2.11/1.76 tff(611,plain,
% 2.11/1.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.11/1.76 inference(rewrite,[status(thm)],[])).
% 2.11/1.76 tff(612,plain,
% 2.11/1.76 (^[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)) | (~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(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_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)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | 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) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 2.11/1.76 inference(bind,[status(th)],[])).
% 2.11/1.76 tff(613,plain,
% 2.11/1.76 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.11/1.76 inference(quant_intro,[status(thm)],[612])).
% 2.11/1.76 tff(614,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 2.11/1.76 tff(615,plain,
% 2.11/1.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[614, 613])).
% 2.11/1.76 tff(616,plain,
% 2.11/1.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[615, 611])).
% 2.11/1.76 tff(617,plain,(
% 2.11/1.76 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.11/1.76 inference(skolemize,[status(sab)],[616])).
% 2.11/1.76 tff(618,plain,
% 2.11/1.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[617, 610])).
% 2.11/1.76 tff(619,assumption,(~c0_1(a237)), introduced(assumption)).
% 2.11/1.76 tff(620,plain,
% 2.11/1.76 (((~hskp12) | c0_1(a237)) <=> ((~hskp12) | c0_1(a237))),
% 2.11/1.76 inference(rewrite,[status(thm)],[])).
% 2.11/1.76 tff(621,axiom,((~hskp12) | c0_1(a237)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 2.11/1.76 tff(622,plain,
% 2.11/1.76 ((~hskp12) | c0_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[621, 620])).
% 2.11/1.76 tff(623,plain,
% 2.11/1.76 ((~hskp12) | c0_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[622, 620])).
% 2.11/1.76 tff(624,plain,
% 2.11/1.76 ((~hskp12) | c0_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[623, 620])).
% 2.11/1.76 tff(625,plain,
% 2.11/1.76 ((~hskp12) | c0_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[624, 620])).
% 2.11/1.76 tff(626,plain,
% 2.11/1.76 ((~hskp12) | c0_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[625, 620])).
% 2.11/1.76 tff(627,plain,
% 2.11/1.76 ((~hskp12) | c0_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[626, 620])).
% 2.11/1.76 tff(628,plain,
% 2.11/1.76 ((~hskp12) | c0_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[627, 620])).
% 2.11/1.76 tff(629,plain,
% 2.11/1.76 ((~hskp12) | c0_1(a237)),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[628, 620])).
% 2.11/1.76 tff(630,plain,
% 2.11/1.76 (~hskp12),
% 2.11/1.76 inference(unit_resolution,[status(thm)],[629, 619])).
% 2.11/1.76 tff(631,plain,
% 2.11/1.76 (c2_1(a237)),
% 2.11/1.76 inference(unit_resolution,[status(thm)],[593, 90, 179, 23, 34])).
% 2.11/1.76 tff(632,plain,
% 2.11/1.76 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)))),
% 2.11/1.76 inference(rewrite,[status(thm)],[])).
% 2.11/1.76 tff(633,plain,
% 2.11/1.76 ((hskp12 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237))) <=> (hskp12 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)))),
% 2.11/1.76 inference(rewrite,[status(thm)],[])).
% 2.11/1.76 tff(634,plain,
% 2.11/1.76 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237))))),
% 2.11/1.76 inference(monotonicity,[status(thm)],[633])).
% 2.11/1.76 tff(635,plain,
% 2.11/1.76 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)))),
% 2.11/1.76 inference(transitivity,[status(thm)],[634, 632])).
% 2.11/1.76 tff(636,plain,
% 2.11/1.76 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237)))),
% 2.11/1.76 inference(quant_inst,[status(thm)],[])).
% 2.11/1.76 tff(637,plain,
% 2.11/1.76 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237))),
% 2.11/1.76 inference(modus_ponens,[status(thm)],[636, 635])).
% 2.11/1.76 tff(638,plain,
% 2.11/1.76 (hskp12 | c0_1(a237) | (~c2_1(a237)) | (~c1_1(a237))),
% 2.11/1.76 inference(unit_resolution,[status(thm)],[637, 122, 179, 44])).
% 2.11/1.76 tff(639,plain,
% 2.11/1.76 (~c1_1(a237)),
% 2.11/1.76 inference(unit_resolution,[status(thm)],[638, 631, 619, 630])).
% 2.11/1.76 tff(640,plain,
% 2.11/1.76 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 2.11/1.76 inference(bind,[status(th)],[])).
% 2.11/1.76 tff(641,plain,
% 2.11/1.76 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.11/1.76 inference(quant_intro,[status(thm)],[640])).
% 2.11/1.76 tff(642,plain,
% 2.11/1.76 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.11/1.76 inference(rewrite,[status(thm)],[])).
% 2.11/1.76 tff(643,plain,
% 2.11/1.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 2.11/1.77 inference(bind,[status(th)],[])).
% 2.11/1.77 tff(644,plain,
% 2.11/1.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.11/1.77 inference(quant_intro,[status(thm)],[643])).
% 2.11/1.77 tff(645,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 2.11/1.77 tff(646,plain,
% 2.11/1.77 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[645, 644])).
% 2.11/1.77 tff(647,plain,
% 2.11/1.77 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[646, 642])).
% 2.11/1.77 tff(648,plain,(
% 2.11/1.77 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.11/1.77 inference(skolemize,[status(sab)],[647])).
% 2.11/1.77 tff(649,plain,
% 2.11/1.77 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[648, 641])).
% 2.11/1.77 tff(650,assumption,(~hskp18), introduced(assumption)).
% 2.11/1.77 tff(651,assumption,(hskp10), introduced(assumption)).
% 2.11/1.77 tff(652,plain,
% 2.11/1.77 (((~hskp10) | c1_1(a231)) <=> ((~hskp10) | c1_1(a231))),
% 2.11/1.77 inference(rewrite,[status(thm)],[])).
% 2.11/1.77 tff(653,axiom,((~hskp10) | c1_1(a231)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 2.11/1.77 tff(654,plain,
% 2.11/1.77 ((~hskp10) | c1_1(a231)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[653, 652])).
% 2.11/1.77 tff(655,plain,
% 2.11/1.77 ((~hskp10) | c1_1(a231)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[654, 652])).
% 2.11/1.77 tff(656,plain,
% 2.11/1.77 ((~hskp10) | c1_1(a231)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[655, 652])).
% 2.11/1.77 tff(657,plain,
% 2.11/1.77 ((~hskp10) | c1_1(a231)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[656, 652])).
% 2.11/1.77 tff(658,plain,
% 2.11/1.77 ((~hskp10) | c1_1(a231)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[657, 652])).
% 2.11/1.77 tff(659,plain,
% 2.11/1.77 ((~hskp10) | c1_1(a231)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[658, 652])).
% 2.11/1.77 tff(660,plain,
% 2.11/1.77 ((~hskp10) | c1_1(a231)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[659, 652])).
% 2.11/1.77 tff(661,plain,
% 2.11/1.77 ((~hskp10) | c1_1(a231)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[660, 652])).
% 2.11/1.77 tff(662,plain,
% 2.11/1.77 (c1_1(a231)),
% 2.11/1.77 inference(unit_resolution,[status(thm)],[661, 651])).
% 2.11/1.77 tff(663,plain,
% 2.11/1.77 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 2.11/1.77 inference(bind,[status(th)],[])).
% 2.11/1.77 tff(664,plain,
% 2.11/1.77 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.11/1.77 inference(quant_intro,[status(thm)],[663])).
% 2.11/1.77 tff(665,plain,
% 2.11/1.77 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.11/1.77 inference(rewrite,[status(thm)],[])).
% 2.11/1.77 tff(666,plain,
% 2.11/1.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 2.11/1.77 inference(bind,[status(th)],[])).
% 2.11/1.77 tff(667,plain,
% 2.11/1.77 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.11/1.77 inference(quant_intro,[status(thm)],[666])).
% 2.11/1.77 tff(668,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 2.11/1.77 tff(669,plain,
% 2.11/1.77 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[668, 667])).
% 2.11/1.77 tff(670,plain,
% 2.11/1.77 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[669, 665])).
% 2.11/1.77 tff(671,plain,(
% 2.11/1.77 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.11/1.77 inference(skolemize,[status(sab)],[670])).
% 2.11/1.77 tff(672,plain,
% 2.11/1.77 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[671, 664])).
% 2.11/1.77 tff(673,plain,
% 2.11/1.77 (hskp17),
% 2.11/1.77 inference(unit_resolution,[status(thm)],[120, 34, 650])).
% 2.11/1.77 tff(674,plain,
% 2.11/1.77 (((~hskp17) | c1_1(a248)) <=> ((~hskp17) | c1_1(a248))),
% 2.11/1.77 inference(rewrite,[status(thm)],[])).
% 2.11/1.77 tff(675,axiom,((~hskp17) | c1_1(a248)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 2.11/1.77 tff(676,plain,
% 2.11/1.77 ((~hskp17) | c1_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[675, 674])).
% 2.11/1.77 tff(677,plain,
% 2.11/1.77 ((~hskp17) | c1_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[676, 674])).
% 2.11/1.77 tff(678,plain,
% 2.11/1.77 ((~hskp17) | c1_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[677, 674])).
% 2.11/1.77 tff(679,plain,
% 2.11/1.77 ((~hskp17) | c1_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[678, 674])).
% 2.11/1.77 tff(680,plain,
% 2.11/1.77 ((~hskp17) | c1_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[679, 674])).
% 2.11/1.77 tff(681,plain,
% 2.11/1.77 ((~hskp17) | c1_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[680, 674])).
% 2.11/1.77 tff(682,plain,
% 2.11/1.77 ((~hskp17) | c1_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[681, 674])).
% 2.11/1.77 tff(683,plain,
% 2.11/1.77 ((~hskp17) | c1_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[682, 674])).
% 2.11/1.77 tff(684,plain,
% 2.11/1.77 (c1_1(a248)),
% 2.11/1.77 inference(unit_resolution,[status(thm)],[683, 673])).
% 2.11/1.77 tff(685,plain,
% 2.11/1.77 (((~hskp17) | (~c2_1(a248))) <=> ((~hskp17) | (~c2_1(a248)))),
% 2.11/1.77 inference(rewrite,[status(thm)],[])).
% 2.11/1.77 tff(686,plain,
% 2.11/1.77 (((~c2_1(a248)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a248)))),
% 2.11/1.77 inference(rewrite,[status(thm)],[])).
% 2.11/1.77 tff(687,axiom,((~c2_1(a248)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 2.11/1.77 tff(688,plain,
% 2.11/1.77 ((~hskp17) | (~c2_1(a248))),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[687, 686])).
% 2.11/1.77 tff(689,plain,
% 2.11/1.77 ((~hskp17) | (~c2_1(a248))),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[688, 685])).
% 2.11/1.77 tff(690,plain,
% 2.11/1.77 (~c2_1(a248)),
% 2.11/1.77 inference(unit_resolution,[status(thm)],[689, 673])).
% 2.11/1.77 tff(691,plain,
% 2.11/1.77 (((~hskp17) | c3_1(a248)) <=> ((~hskp17) | c3_1(a248))),
% 2.11/1.77 inference(rewrite,[status(thm)],[])).
% 2.11/1.77 tff(692,axiom,((~hskp17) | c3_1(a248)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 2.11/1.77 tff(693,plain,
% 2.11/1.77 ((~hskp17) | c3_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[692, 691])).
% 2.11/1.77 tff(694,plain,
% 2.11/1.77 ((~hskp17) | c3_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[693, 691])).
% 2.11/1.77 tff(695,plain,
% 2.11/1.77 ((~hskp17) | c3_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[694, 691])).
% 2.11/1.77 tff(696,plain,
% 2.11/1.77 ((~hskp17) | c3_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[695, 691])).
% 2.11/1.77 tff(697,plain,
% 2.11/1.77 ((~hskp17) | c3_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[696, 691])).
% 2.11/1.77 tff(698,plain,
% 2.11/1.77 ((~hskp17) | c3_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[697, 691])).
% 2.11/1.77 tff(699,plain,
% 2.11/1.77 ((~hskp17) | c3_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[698, 691])).
% 2.11/1.77 tff(700,plain,
% 2.11/1.77 ((~hskp17) | c3_1(a248)),
% 2.11/1.77 inference(modus_ponens,[status(thm)],[699, 691])).
% 2.11/1.77 tff(701,plain,
% 2.11/1.77 (c3_1(a248)),
% 2.11/1.77 inference(unit_resolution,[status(thm)],[700, 673])).
% 2.11/1.77 tff(702,assumption,(~c0_1(a248)), introduced(assumption)).
% 2.11/1.77 tff(703,assumption,(~c2_1(a248)), introduced(assumption)).
% 2.11/1.77 tff(704,assumption,(c3_1(a248)), introduced(assumption)).
% 2.11/1.77 tff(705,assumption,(c1_1(a248)), introduced(assumption)).
% 2.11/1.77 tff(706,plain,
% 2.11/1.77 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))),
% 2.11/1.77 inference(rewrite,[status(thm)],[])).
% 2.11/1.77 tff(707,plain,
% 2.11/1.77 ((hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248))) <=> (hskp18 | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))),
% 2.11/1.77 inference(rewrite,[status(thm)],[])).
% 2.11/1.77 tff(708,plain,
% 2.11/1.77 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248))))),
% 2.11/1.78 inference(monotonicity,[status(thm)],[707])).
% 2.11/1.78 tff(709,plain,
% 2.11/1.78 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))),
% 2.11/1.78 inference(transitivity,[status(thm)],[708, 706])).
% 2.11/1.78 tff(710,plain,
% 2.11/1.78 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))),
% 2.11/1.78 inference(quant_inst,[status(thm)],[])).
% 2.11/1.78 tff(711,plain,
% 2.11/1.78 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248))),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[710, 709])).
% 2.11/1.78 tff(712,plain,
% 2.11/1.78 ($false),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[711, 122, 650, 705, 704, 703, 672, 702])).
% 2.11/1.78 tff(713,plain,(c0_1(a248) | hskp18 | (~c1_1(a248)) | (~c3_1(a248)) | c2_1(a248)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.78 tff(714,plain,
% 2.11/1.78 (c0_1(a248)),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[713, 684, 650, 701, 690])).
% 2.11/1.78 tff(715,plain,
% 2.11/1.78 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(716,plain,
% 2.11/1.78 ((hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248))) <=> (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(717,plain,
% 2.11/1.78 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248))))),
% 2.11/1.78 inference(monotonicity,[status(thm)],[716])).
% 2.11/1.78 tff(718,plain,
% 2.11/1.78 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))),
% 2.11/1.78 inference(transitivity,[status(thm)],[717, 715])).
% 2.11/1.78 tff(719,plain,
% 2.11/1.78 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)))),
% 2.11/1.78 inference(quant_inst,[status(thm)],[])).
% 2.11/1.78 tff(720,plain,
% 2.11/1.78 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248))),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[719, 718])).
% 2.11/1.78 tff(721,plain,
% 2.11/1.78 (hskp2 | (~c0_1(a248))),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[720, 122, 34, 684, 701, 56])).
% 2.11/1.78 tff(722,plain,
% 2.11/1.78 (hskp2),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[721, 714])).
% 2.11/1.78 tff(723,plain,
% 2.11/1.78 (~c1_1(a215)),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[136, 722])).
% 2.11/1.78 tff(724,plain,
% 2.11/1.78 (~c0_1(a215)),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[153, 722])).
% 2.11/1.78 tff(725,plain,
% 2.11/1.78 (c2_1(a215)),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[147, 722])).
% 2.11/1.78 tff(726,plain,
% 2.11/1.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(727,plain,
% 2.11/1.78 ((hskp5 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215))) <=> (hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(728,plain,
% 2.11/1.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248))))),
% 2.11/1.78 inference(monotonicity,[status(thm)],[727])).
% 2.11/1.78 tff(729,plain,
% 2.11/1.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))),
% 2.11/1.78 inference(transitivity,[status(thm)],[728, 726])).
% 2.11/1.78 tff(730,plain,
% 2.11/1.78 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))),
% 2.11/1.78 inference(quant_inst,[status(thm)],[])).
% 2.11/1.78 tff(731,plain,
% 2.11/1.78 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248))),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[730, 729])).
% 2.11/1.78 tff(732,plain,
% 2.11/1.78 (hskp5),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[731, 122, 684, 701, 725, 724, 723, 164, 714])).
% 2.11/1.78 tff(733,plain,
% 2.11/1.78 (((~hskp5) | (~c2_1(a218))) <=> ((~hskp5) | (~c2_1(a218)))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(734,plain,
% 2.11/1.78 (((~c2_1(a218)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a218)))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(735,axiom,((~c2_1(a218)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 2.11/1.78 tff(736,plain,
% 2.11/1.78 ((~hskp5) | (~c2_1(a218))),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[735, 734])).
% 2.11/1.78 tff(737,plain,
% 2.11/1.78 ((~hskp5) | (~c2_1(a218))),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[736, 733])).
% 2.11/1.78 tff(738,plain,
% 2.11/1.78 (~c2_1(a218)),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[737, 732])).
% 2.11/1.78 tff(739,plain,
% 2.11/1.78 (((~hskp5) | (~c1_1(a218))) <=> ((~hskp5) | (~c1_1(a218)))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(740,plain,
% 2.11/1.78 (((~c1_1(a218)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a218)))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(741,axiom,((~c1_1(a218)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 2.11/1.78 tff(742,plain,
% 2.11/1.78 ((~hskp5) | (~c1_1(a218))),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[741, 740])).
% 2.11/1.78 tff(743,plain,
% 2.11/1.78 ((~hskp5) | (~c1_1(a218))),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[742, 739])).
% 2.11/1.78 tff(744,plain,
% 2.11/1.78 (~c1_1(a218)),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[743, 732])).
% 2.11/1.78 tff(745,plain,
% 2.11/1.78 (((~hskp5) | c3_1(a218)) <=> ((~hskp5) | c3_1(a218))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(746,axiom,((~hskp5) | c3_1(a218)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 2.11/1.78 tff(747,plain,
% 2.11/1.78 ((~hskp5) | c3_1(a218)),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[746, 745])).
% 2.11/1.78 tff(748,plain,
% 2.11/1.78 ((~hskp5) | c3_1(a218)),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[747, 745])).
% 2.11/1.78 tff(749,plain,
% 2.11/1.78 ((~hskp5) | c3_1(a218)),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[748, 745])).
% 2.11/1.78 tff(750,plain,
% 2.11/1.78 ((~hskp5) | c3_1(a218)),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[749, 745])).
% 2.11/1.78 tff(751,plain,
% 2.11/1.78 ((~hskp5) | c3_1(a218)),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[750, 745])).
% 2.11/1.78 tff(752,plain,
% 2.11/1.78 ((~hskp5) | c3_1(a218)),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[751, 745])).
% 2.11/1.78 tff(753,plain,
% 2.11/1.78 ((~hskp5) | c3_1(a218)),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[752, 745])).
% 2.11/1.78 tff(754,plain,
% 2.11/1.78 ((~hskp5) | c3_1(a218)),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[753, 745])).
% 2.11/1.78 tff(755,plain,
% 2.11/1.78 (c3_1(a218)),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[754, 732])).
% 2.11/1.78 tff(756,assumption,(c0_1(a248)), introduced(assumption)).
% 2.11/1.78 tff(757,assumption,(hskp12), introduced(assumption)).
% 2.11/1.78 tff(758,plain,
% 2.11/1.78 (((~hskp12) | (~c3_1(a237))) <=> ((~hskp12) | (~c3_1(a237)))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(759,plain,
% 2.11/1.78 (((~c3_1(a237)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a237)))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(760,axiom,((~c3_1(a237)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 2.11/1.78 tff(761,plain,
% 2.11/1.78 ((~hskp12) | (~c3_1(a237))),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[760, 759])).
% 2.11/1.78 tff(762,plain,
% 2.11/1.78 ((~hskp12) | (~c3_1(a237))),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[761, 758])).
% 2.11/1.78 tff(763,plain,
% 2.11/1.78 (~c3_1(a237)),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[762, 757])).
% 2.11/1.78 tff(764,plain,
% 2.11/1.78 (c2_1(a237)),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[607, 757])).
% 2.11/1.78 tff(765,plain,
% 2.11/1.78 (c0_1(a237)),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[629, 757])).
% 2.11/1.78 tff(766,plain,
% 2.11/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(767,plain,
% 2.11/1.78 (((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237))) <=> (c2_1(a248) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(768,plain,
% 2.11/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248))))),
% 2.11/1.78 inference(monotonicity,[status(thm)],[767])).
% 2.11/1.78 tff(769,plain,
% 2.11/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 2.11/1.78 inference(transitivity,[status(thm)],[768, 766])).
% 2.11/1.78 tff(770,plain,
% 2.11/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))),
% 2.11/1.78 inference(quant_inst,[status(thm)],[])).
% 2.11/1.78 tff(771,plain,
% 2.11/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248))),
% 2.11/1.78 inference(modus_ponens,[status(thm)],[770, 769])).
% 2.11/1.78 tff(772,plain,
% 2.11/1.78 (c1_1(a237)),
% 2.11/1.78 inference(unit_resolution,[status(thm)],[771, 122, 704, 765, 764, 703, 763, 22, 756])).
% 2.11/1.78 tff(773,plain,
% 2.11/1.78 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_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)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 2.11/1.78 inference(bind,[status(th)],[])).
% 2.11/1.78 tff(774,plain,
% 2.11/1.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_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)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.78 inference(quant_intro,[status(thm)],[773])).
% 2.11/1.78 tff(775,plain,
% 2.11/1.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_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)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.78 inference(rewrite,[status(thm)],[])).
% 2.11/1.78 tff(776,plain,
% 2.11/1.78 (^[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)) | (~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(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 2.11/1.79 inference(bind,[status(th)],[])).
% 2.11/1.79 tff(777,plain,
% 2.11/1.79 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.79 inference(quant_intro,[status(thm)],[776])).
% 2.11/1.79 tff(778,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 2.11/1.79 tff(779,plain,
% 2.11/1.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[778, 777])).
% 2.11/1.79 tff(780,plain,
% 2.11/1.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[779, 775])).
% 2.11/1.79 tff(781,plain,(
% 2.11/1.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.79 inference(skolemize,[status(sab)],[780])).
% 2.11/1.79 tff(782,plain,
% 2.11/1.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[781, 774])).
% 2.11/1.79 tff(783,assumption,(~c2_1(a218)), introduced(assumption)).
% 2.11/1.79 tff(784,assumption,(~c1_1(a218)), introduced(assumption)).
% 2.11/1.79 tff(785,assumption,(c3_1(a218)), introduced(assumption)).
% 2.11/1.79 tff(786,plain,
% 2.11/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c3_1(a237) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a237)) | (~c1_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c3_1(a237) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a237)) | (~c1_1(a237)))),
% 2.11/1.79 inference(rewrite,[status(thm)],[])).
% 2.11/1.79 tff(787,plain,
% 2.11/1.79 (((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215))) <=> (c3_1(a237) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a237)) | (~c1_1(a237)))),
% 2.11/1.79 inference(rewrite,[status(thm)],[])).
% 2.11/1.79 tff(788,plain,
% 2.11/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c3_1(a237) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a237)) | (~c1_1(a237))))),
% 2.11/1.79 inference(monotonicity,[status(thm)],[787])).
% 2.11/1.79 tff(789,plain,
% 2.11/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c3_1(a237) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a237)) | (~c1_1(a237)))),
% 2.11/1.79 inference(transitivity,[status(thm)],[788, 786])).
% 2.11/1.79 tff(790,plain,
% 2.11/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))),
% 2.11/1.79 inference(quant_inst,[status(thm)],[])).
% 2.11/1.79 tff(791,plain,
% 2.11/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c3_1(a237) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a237)) | (~c1_1(a237))),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[790, 789])).
% 2.11/1.79 tff(792,plain,
% 2.11/1.79 ($false),
% 2.11/1.79 inference(unit_resolution,[status(thm)],[791, 122, 765, 785, 167, 763, 784, 783, 166, 165, 782, 772])).
% 2.11/1.79 tff(793,plain,((~hskp12) | (~c3_1(a218)) | (~c2_1(a215)) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~c3_1(a248)) | c2_1(a248) | (~c0_1(a248))), inference(lemma,lemma(discharge,[]))).
% 2.11/1.79 tff(794,plain,
% 2.11/1.79 (~hskp12),
% 2.11/1.79 inference(unit_resolution,[status(thm)],[793, 755, 725, 744, 738, 724, 723, 701, 690, 714])).
% 2.11/1.79 tff(795,plain,
% 2.11/1.79 (^[U: $i] : refl((hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 2.11/1.79 inference(bind,[status(th)],[])).
% 2.11/1.79 tff(796,plain,
% 2.11/1.79 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.11/1.79 inference(quant_intro,[status(thm)],[795])).
% 2.11/1.79 tff(797,plain,
% 2.11/1.79 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.11/1.79 inference(rewrite,[status(thm)],[])).
% 2.11/1.79 tff(798,plain,
% 2.11/1.79 (^[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)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp21) <=> ((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21))), rewrite(((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21) <=> (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp21) <=> (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 2.11/1.79 inference(bind,[status(th)],[])).
% 2.11/1.79 tff(799,plain,
% 2.11/1.79 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp21) <=> ![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.11/1.79 inference(quant_intro,[status(thm)],[798])).
% 2.11/1.79 tff(800,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 2.11/1.79 tff(801,plain,
% 2.11/1.79 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[800, 799])).
% 2.11/1.79 tff(802,plain,
% 2.11/1.79 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[801, 797])).
% 2.11/1.79 tff(803,plain,(
% 2.11/1.79 ![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.11/1.79 inference(skolemize,[status(sab)],[802])).
% 2.11/1.79 tff(804,plain,
% 2.11/1.79 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[803, 796])).
% 2.11/1.79 tff(805,assumption,(hskp0), introduced(assumption)).
% 2.11/1.79 tff(806,plain,
% 2.11/1.79 (((~hskp0) | (~c3_1(a213))) <=> ((~hskp0) | (~c3_1(a213)))),
% 2.11/1.79 inference(rewrite,[status(thm)],[])).
% 2.11/1.79 tff(807,plain,
% 2.11/1.79 (((~c3_1(a213)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a213)))),
% 2.11/1.79 inference(rewrite,[status(thm)],[])).
% 2.11/1.79 tff(808,axiom,((~c3_1(a213)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 2.11/1.79 tff(809,plain,
% 2.11/1.79 ((~hskp0) | (~c3_1(a213))),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[808, 807])).
% 2.11/1.79 tff(810,plain,
% 2.11/1.79 ((~hskp0) | (~c3_1(a213))),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[809, 806])).
% 2.11/1.79 tff(811,plain,
% 2.11/1.79 (~c3_1(a213)),
% 2.11/1.79 inference(unit_resolution,[status(thm)],[810, 805])).
% 2.11/1.79 tff(812,plain,
% 2.11/1.79 (((~hskp0) | (~c1_1(a213))) <=> ((~hskp0) | (~c1_1(a213)))),
% 2.11/1.79 inference(rewrite,[status(thm)],[])).
% 2.11/1.79 tff(813,plain,
% 2.11/1.79 (((~c1_1(a213)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a213)))),
% 2.11/1.79 inference(rewrite,[status(thm)],[])).
% 2.11/1.79 tff(814,axiom,((~c1_1(a213)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 2.11/1.79 tff(815,plain,
% 2.11/1.79 ((~hskp0) | (~c1_1(a213))),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[814, 813])).
% 2.11/1.79 tff(816,plain,
% 2.11/1.79 ((~hskp0) | (~c1_1(a213))),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[815, 812])).
% 2.11/1.79 tff(817,plain,
% 2.11/1.79 (~c1_1(a213)),
% 2.11/1.79 inference(unit_resolution,[status(thm)],[816, 805])).
% 2.11/1.79 tff(818,plain,
% 2.11/1.79 (((~hskp0) | c2_1(a213)) <=> ((~hskp0) | c2_1(a213))),
% 2.11/1.79 inference(rewrite,[status(thm)],[])).
% 2.11/1.79 tff(819,axiom,((~hskp0) | c2_1(a213)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 2.11/1.79 tff(820,plain,
% 2.11/1.79 ((~hskp0) | c2_1(a213)),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[819, 818])).
% 2.11/1.79 tff(821,plain,
% 2.11/1.79 ((~hskp0) | c2_1(a213)),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[820, 818])).
% 2.11/1.79 tff(822,plain,
% 2.11/1.79 ((~hskp0) | c2_1(a213)),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[821, 818])).
% 2.11/1.79 tff(823,plain,
% 2.11/1.79 ((~hskp0) | c2_1(a213)),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[822, 818])).
% 2.11/1.79 tff(824,plain,
% 2.11/1.79 ((~hskp0) | c2_1(a213)),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[823, 818])).
% 2.11/1.79 tff(825,plain,
% 2.11/1.79 ((~hskp0) | c2_1(a213)),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[824, 818])).
% 2.11/1.79 tff(826,plain,
% 2.11/1.79 ((~hskp0) | c2_1(a213)),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[825, 818])).
% 2.11/1.79 tff(827,plain,
% 2.11/1.79 ((~hskp0) | c2_1(a213)),
% 2.11/1.79 inference(modus_ponens,[status(thm)],[826, 818])).
% 2.11/1.79 tff(828,plain,
% 2.11/1.79 (c2_1(a213)),
% 2.11/1.79 inference(unit_resolution,[status(thm)],[827, 805])).
% 2.11/1.79 tff(829,plain,
% 2.11/1.79 (c0_1(a248)),
% 2.11/1.79 inference(unit_resolution,[status(thm)],[713, 705, 650, 704, 703])).
% 2.11/1.79 tff(830,plain,
% 2.11/1.79 (hskp5),
% 2.11/1.79 inference(unit_resolution,[status(thm)],[731, 122, 705, 704, 167, 166, 165, 164, 829])).
% 2.11/1.79 tff(831,plain,
% 2.11/1.79 (~c2_1(a218)),
% 2.11/1.79 inference(unit_resolution,[status(thm)],[737, 830])).
% 2.11/1.79 tff(832,plain,
% 2.11/1.79 (~c1_1(a218)),
% 2.11/1.79 inference(unit_resolution,[status(thm)],[743, 830])).
% 2.11/1.79 tff(833,plain,
% 2.11/1.79 (c3_1(a218)),
% 2.11/1.79 inference(unit_resolution,[status(thm)],[754, 830])).
% 2.11/1.79 tff(834,plain,
% 2.11/1.79 (~hskp12),
% 2.11/1.79 inference(unit_resolution,[status(thm)],[793, 833, 167, 832, 831, 166, 165, 704, 703, 829])).
% 2.11/1.80 tff(835,assumption,(~c3_1(a213)), introduced(assumption)).
% 2.11/1.80 tff(836,assumption,(~c1_1(a213)), introduced(assumption)).
% 2.11/1.80 tff(837,assumption,(c2_1(a213)), introduced(assumption)).
% 2.11/1.80 tff(838,plain,
% 2.11/1.80 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)))),
% 2.11/1.80 inference(rewrite,[status(thm)],[])).
% 2.11/1.80 tff(839,plain,
% 2.11/1.80 ((hskp21 | hskp12 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c2_1(a213))) <=> (hskp21 | hskp12 | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)))),
% 2.11/1.80 inference(rewrite,[status(thm)],[])).
% 2.11/1.80 tff(840,plain,
% 2.11/1.80 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c2_1(a213)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213))))),
% 2.11/1.80 inference(monotonicity,[status(thm)],[839])).
% 2.11/1.80 tff(841,plain,
% 2.11/1.80 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c2_1(a213)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)))),
% 2.11/1.80 inference(transitivity,[status(thm)],[840, 838])).
% 2.11/1.80 tff(842,plain,
% 2.11/1.80 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c2_1(a213)))),
% 2.11/1.80 inference(quant_inst,[status(thm)],[])).
% 2.11/1.80 tff(843,plain,
% 2.11/1.80 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213))),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[842, 841])).
% 2.11/1.80 tff(844,plain,
% 2.11/1.80 (hskp21 | c1_1(a213) | (~c2_1(a213))),
% 2.11/1.80 inference(unit_resolution,[status(thm)],[843, 122, 834, 835, 804])).
% 2.11/1.80 tff(845,plain,
% 2.11/1.80 (hskp21),
% 2.11/1.80 inference(unit_resolution,[status(thm)],[844, 836, 837])).
% 2.11/1.80 tff(846,plain,
% 2.11/1.80 (((~hskp21) | c0_1(a259)) <=> ((~hskp21) | c0_1(a259))),
% 2.11/1.80 inference(rewrite,[status(thm)],[])).
% 2.11/1.80 tff(847,axiom,((~hskp21) | c0_1(a259)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 2.11/1.80 tff(848,plain,
% 2.11/1.80 ((~hskp21) | c0_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[847, 846])).
% 2.11/1.80 tff(849,plain,
% 2.11/1.80 ((~hskp21) | c0_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[848, 846])).
% 2.11/1.80 tff(850,plain,
% 2.11/1.80 ((~hskp21) | c0_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[849, 846])).
% 2.11/1.80 tff(851,plain,
% 2.11/1.80 ((~hskp21) | c0_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[850, 846])).
% 2.11/1.80 tff(852,plain,
% 2.11/1.80 ((~hskp21) | c0_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[851, 846])).
% 2.11/1.80 tff(853,plain,
% 2.11/1.80 ((~hskp21) | c0_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[852, 846])).
% 2.11/1.80 tff(854,plain,
% 2.11/1.80 ((~hskp21) | c0_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[853, 846])).
% 2.11/1.80 tff(855,plain,
% 2.11/1.80 ((~hskp21) | c0_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[854, 846])).
% 2.11/1.80 tff(856,plain,
% 2.11/1.80 (c0_1(a259)),
% 2.11/1.80 inference(unit_resolution,[status(thm)],[855, 845])).
% 2.11/1.80 tff(857,assumption,(~c2_1(a259)), introduced(assumption)).
% 2.11/1.80 tff(858,plain,
% 2.11/1.80 (((~hskp21) | c3_1(a259)) <=> ((~hskp21) | c3_1(a259))),
% 2.11/1.80 inference(rewrite,[status(thm)],[])).
% 2.11/1.80 tff(859,axiom,((~hskp21) | c3_1(a259)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 2.11/1.80 tff(860,plain,
% 2.11/1.80 ((~hskp21) | c3_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[859, 858])).
% 2.11/1.80 tff(861,plain,
% 2.11/1.80 ((~hskp21) | c3_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[860, 858])).
% 2.11/1.80 tff(862,plain,
% 2.11/1.80 ((~hskp21) | c3_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[861, 858])).
% 2.11/1.80 tff(863,plain,
% 2.11/1.80 ((~hskp21) | c3_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[862, 858])).
% 2.11/1.80 tff(864,plain,
% 2.11/1.80 ((~hskp21) | c3_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[863, 858])).
% 2.11/1.80 tff(865,plain,
% 2.11/1.80 ((~hskp21) | c3_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[864, 858])).
% 2.11/1.80 tff(866,plain,
% 2.11/1.80 ((~hskp21) | c3_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[865, 858])).
% 2.11/1.80 tff(867,plain,
% 2.11/1.80 ((~hskp21) | c3_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[866, 858])).
% 2.11/1.80 tff(868,plain,
% 2.11/1.80 (c3_1(a259)),
% 2.11/1.80 inference(unit_resolution,[status(thm)],[867, 845])).
% 2.11/1.80 tff(869,plain,
% 2.11/1.80 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 2.11/1.80 inference(bind,[status(th)],[])).
% 2.11/1.80 tff(870,plain,
% 2.11/1.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.80 inference(quant_intro,[status(thm)],[869])).
% 2.11/1.80 tff(871,plain,
% 2.11/1.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.80 inference(rewrite,[status(thm)],[])).
% 2.11/1.80 tff(872,plain,
% 2.11/1.80 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 2.11/1.80 inference(bind,[status(th)],[])).
% 2.11/1.80 tff(873,plain,
% 2.11/1.80 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.80 inference(quant_intro,[status(thm)],[872])).
% 2.11/1.80 tff(874,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 2.11/1.80 tff(875,plain,
% 2.11/1.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[874, 873])).
% 2.11/1.80 tff(876,plain,
% 2.11/1.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[875, 871])).
% 2.11/1.80 tff(877,plain,(
% 2.11/1.80 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.80 inference(skolemize,[status(sab)],[876])).
% 2.11/1.80 tff(878,plain,
% 2.11/1.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[877, 870])).
% 2.11/1.80 tff(879,plain,
% 2.11/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c2_1(a248) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a259)) | c1_1(a259))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c2_1(a248) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a259)) | c1_1(a259))),
% 2.11/1.80 inference(rewrite,[status(thm)],[])).
% 2.11/1.80 tff(880,plain,
% 2.11/1.80 (((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259))) <=> (c2_1(a259) | c2_1(a248) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a259)) | c1_1(a259))),
% 2.11/1.80 inference(rewrite,[status(thm)],[])).
% 2.11/1.80 tff(881,plain,
% 2.11/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c2_1(a248) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a259)) | c1_1(a259)))),
% 2.11/1.80 inference(monotonicity,[status(thm)],[880])).
% 2.11/1.80 tff(882,plain,
% 2.11/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c2_1(a248) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a259)) | c1_1(a259))),
% 2.11/1.80 inference(transitivity,[status(thm)],[881, 879])).
% 2.11/1.80 tff(883,plain,
% 2.11/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))),
% 2.11/1.80 inference(quant_inst,[status(thm)],[])).
% 2.11/1.80 tff(884,plain,
% 2.11/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c2_1(a248) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a259)) | c1_1(a259)),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[883, 882])).
% 2.11/1.80 tff(885,plain,
% 2.11/1.80 (c1_1(a213) | (~c2_1(a213)) | (~c0_1(a259)) | c1_1(a259)),
% 2.11/1.80 inference(unit_resolution,[status(thm)],[884, 122, 705, 704, 857, 703, 835, 878])).
% 2.11/1.80 tff(886,plain,
% 2.11/1.80 (c1_1(a259)),
% 2.11/1.80 inference(unit_resolution,[status(thm)],[885, 856, 837, 836])).
% 2.11/1.80 tff(887,assumption,(c1_1(a259)), introduced(assumption)).
% 2.11/1.80 tff(888,assumption,(hskp9), introduced(assumption)).
% 2.11/1.80 tff(889,plain,
% 2.11/1.80 (((~hskp9) | (~c2_1(a226))) <=> ((~hskp9) | (~c2_1(a226)))),
% 2.11/1.80 inference(rewrite,[status(thm)],[])).
% 2.11/1.80 tff(890,plain,
% 2.11/1.80 (((~c2_1(a226)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a226)))),
% 2.11/1.80 inference(rewrite,[status(thm)],[])).
% 2.11/1.80 tff(891,axiom,((~c2_1(a226)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 2.11/1.80 tff(892,plain,
% 2.11/1.80 ((~hskp9) | (~c2_1(a226))),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[891, 890])).
% 2.11/1.80 tff(893,plain,
% 2.11/1.80 ((~hskp9) | (~c2_1(a226))),
% 2.11/1.80 inference(modus_ponens,[status(thm)],[892, 889])).
% 2.11/1.80 tff(894,plain,
% 2.11/1.80 (~c2_1(a226)),
% 2.11/1.80 inference(unit_resolution,[status(thm)],[893, 888])).
% 2.11/1.80 tff(895,plain,
% 2.11/1.80 (((~hskp9) | (~c1_1(a226))) <=> ((~hskp9) | (~c1_1(a226)))),
% 2.11/1.81 inference(rewrite,[status(thm)],[])).
% 2.11/1.81 tff(896,plain,
% 2.11/1.81 (((~c1_1(a226)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a226)))),
% 2.11/1.81 inference(rewrite,[status(thm)],[])).
% 2.11/1.81 tff(897,axiom,((~c1_1(a226)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 2.11/1.81 tff(898,plain,
% 2.11/1.81 ((~hskp9) | (~c1_1(a226))),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[897, 896])).
% 2.11/1.81 tff(899,plain,
% 2.11/1.81 ((~hskp9) | (~c1_1(a226))),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[898, 895])).
% 2.11/1.81 tff(900,plain,
% 2.11/1.81 (~c1_1(a226)),
% 2.11/1.81 inference(unit_resolution,[status(thm)],[899, 888])).
% 2.11/1.81 tff(901,plain,
% 2.11/1.81 (((~hskp9) | c0_1(a226)) <=> ((~hskp9) | c0_1(a226))),
% 2.11/1.81 inference(rewrite,[status(thm)],[])).
% 2.11/1.81 tff(902,axiom,((~hskp9) | c0_1(a226)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 2.11/1.81 tff(903,plain,
% 2.11/1.81 ((~hskp9) | c0_1(a226)),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[902, 901])).
% 2.11/1.81 tff(904,plain,
% 2.11/1.81 ((~hskp9) | c0_1(a226)),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[903, 901])).
% 2.11/1.81 tff(905,plain,
% 2.11/1.81 ((~hskp9) | c0_1(a226)),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[904, 901])).
% 2.11/1.81 tff(906,plain,
% 2.11/1.81 ((~hskp9) | c0_1(a226)),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[905, 901])).
% 2.11/1.81 tff(907,plain,
% 2.11/1.81 ((~hskp9) | c0_1(a226)),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[906, 901])).
% 2.11/1.81 tff(908,plain,
% 2.11/1.81 ((~hskp9) | c0_1(a226)),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[907, 901])).
% 2.11/1.81 tff(909,plain,
% 2.11/1.81 ((~hskp9) | c0_1(a226)),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[908, 901])).
% 2.11/1.81 tff(910,plain,
% 2.11/1.81 ((~hskp9) | c0_1(a226)),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[909, 901])).
% 2.11/1.81 tff(911,plain,
% 2.11/1.81 (c0_1(a226)),
% 2.11/1.81 inference(unit_resolution,[status(thm)],[910, 888])).
% 2.11/1.81 tff(912,assumption,(c3_1(a259)), introduced(assumption)).
% 2.11/1.81 tff(913,plain,
% 2.11/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a226)) | (~c3_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a226)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 2.11/1.81 inference(rewrite,[status(thm)],[])).
% 2.11/1.81 tff(914,plain,
% 2.11/1.81 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226))) <=> (c2_1(a259) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a226)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 2.11/1.81 inference(rewrite,[status(thm)],[])).
% 2.11/1.81 tff(915,plain,
% 2.11/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a226)) | (~c3_1(a259)) | (~c1_1(a259))))),
% 2.11/1.81 inference(monotonicity,[status(thm)],[914])).
% 2.11/1.81 tff(916,plain,
% 2.11/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a226)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 2.11/1.81 inference(transitivity,[status(thm)],[915, 913])).
% 2.11/1.81 tff(917,plain,
% 2.11/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))),
% 2.11/1.81 inference(quant_inst,[status(thm)],[])).
% 2.11/1.81 tff(918,plain,
% 2.11/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a226)) | (~c3_1(a259)) | (~c1_1(a259))),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[917, 916])).
% 2.11/1.81 tff(919,plain,
% 2.11/1.81 ($false),
% 2.11/1.81 inference(unit_resolution,[status(thm)],[918, 122, 912, 911, 837, 857, 900, 894, 836, 835, 878, 887])).
% 2.11/1.81 tff(920,plain,((~hskp9) | (~c3_1(a259)) | (~c2_1(a213)) | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~c1_1(a259))), inference(lemma,lemma(discharge,[]))).
% 2.11/1.81 tff(921,plain,
% 2.11/1.81 (~hskp9),
% 2.11/1.81 inference(unit_resolution,[status(thm)],[920, 886, 837, 857, 836, 835, 868])).
% 2.11/1.81 tff(922,plain,
% 2.11/1.81 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 2.11/1.81 inference(bind,[status(th)],[])).
% 2.11/1.81 tff(923,plain,
% 2.11/1.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.81 inference(quant_intro,[status(thm)],[922])).
% 2.11/1.81 tff(924,plain,
% 2.11/1.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.81 inference(rewrite,[status(thm)],[])).
% 2.11/1.81 tff(925,plain,
% 2.11/1.81 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 2.11/1.81 inference(bind,[status(th)],[])).
% 2.11/1.81 tff(926,plain,
% 2.11/1.81 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.81 inference(quant_intro,[status(thm)],[925])).
% 2.11/1.81 tff(927,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 2.11/1.81 tff(928,plain,
% 2.11/1.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[927, 926])).
% 2.11/1.81 tff(929,plain,
% 2.11/1.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[928, 924])).
% 2.11/1.81 tff(930,plain,(
% 2.11/1.81 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.81 inference(skolemize,[status(sab)],[929])).
% 2.11/1.81 tff(931,plain,
% 2.11/1.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.11/1.81 inference(modus_ponens,[status(thm)],[930, 923])).
% 2.11/1.81 tff(932,assumption,(hskp13), introduced(assumption)).
% 2.11/1.81 tff(933,plain,
% 2.11/1.81 (((~hskp13) | c3_1(a239)) <=> ((~hskp13) | c3_1(a239))),
% 2.11/1.81 inference(rewrite,[status(thm)],[])).
% 2.11/1.81 tff(934,axiom,((~hskp13) | c3_1(a239)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 2.18/1.81 tff(935,plain,
% 2.18/1.81 ((~hskp13) | c3_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[934, 933])).
% 2.18/1.81 tff(936,plain,
% 2.18/1.81 ((~hskp13) | c3_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[935, 933])).
% 2.18/1.81 tff(937,plain,
% 2.18/1.81 ((~hskp13) | c3_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[936, 933])).
% 2.18/1.81 tff(938,plain,
% 2.18/1.81 ((~hskp13) | c3_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[937, 933])).
% 2.18/1.81 tff(939,plain,
% 2.18/1.81 ((~hskp13) | c3_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[938, 933])).
% 2.18/1.81 tff(940,plain,
% 2.18/1.81 ((~hskp13) | c3_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[939, 933])).
% 2.18/1.81 tff(941,plain,
% 2.18/1.81 ((~hskp13) | c3_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[940, 933])).
% 2.18/1.81 tff(942,plain,
% 2.18/1.81 ((~hskp13) | c3_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[941, 933])).
% 2.18/1.81 tff(943,plain,
% 2.18/1.81 (c3_1(a239)),
% 2.18/1.81 inference(unit_resolution,[status(thm)],[942, 932])).
% 2.18/1.81 tff(944,plain,
% 2.18/1.81 (((~hskp13) | c2_1(a239)) <=> ((~hskp13) | c2_1(a239))),
% 2.18/1.81 inference(rewrite,[status(thm)],[])).
% 2.18/1.81 tff(945,axiom,((~hskp13) | c2_1(a239)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 2.18/1.81 tff(946,plain,
% 2.18/1.81 ((~hskp13) | c2_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[945, 944])).
% 2.18/1.81 tff(947,plain,
% 2.18/1.81 ((~hskp13) | c2_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[946, 944])).
% 2.18/1.81 tff(948,plain,
% 2.18/1.81 ((~hskp13) | c2_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[947, 944])).
% 2.18/1.81 tff(949,plain,
% 2.18/1.81 ((~hskp13) | c2_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[948, 944])).
% 2.18/1.81 tff(950,plain,
% 2.18/1.81 ((~hskp13) | c2_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[949, 944])).
% 2.18/1.81 tff(951,plain,
% 2.18/1.81 ((~hskp13) | c2_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[950, 944])).
% 2.18/1.81 tff(952,plain,
% 2.18/1.81 ((~hskp13) | c2_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[951, 944])).
% 2.18/1.81 tff(953,plain,
% 2.18/1.81 ((~hskp13) | c2_1(a239)),
% 2.18/1.81 inference(modus_ponens,[status(thm)],[952, 944])).
% 2.18/1.81 tff(954,plain,
% 2.18/1.81 (c2_1(a239)),
% 2.18/1.81 inference(unit_resolution,[status(thm)],[953, 932])).
% 2.18/1.81 tff(955,assumption,(c0_1(a259)), introduced(assumption)).
% 2.18/1.81 tff(956,plain,
% 2.18/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a239)) | (~c0_1(a239)) | (~c2_1(a239)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a239)) | (~c0_1(a239)) | (~c2_1(a239)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.18/1.81 inference(rewrite,[status(thm)],[])).
% 2.18/1.81 tff(957,plain,
% 2.18/1.81 (((~ndr1_0) | (~c2_1(a239)) | (~c3_1(a239)) | (~c0_1(a239)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215))) <=> (c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a239)) | (~c0_1(a239)) | (~c2_1(a239)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.18/1.81 inference(rewrite,[status(thm)],[])).
% 2.18/1.81 tff(958,plain,
% 2.18/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a239)) | (~c3_1(a239)) | (~c0_1(a239)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a239)) | (~c0_1(a239)) | (~c2_1(a239)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 2.18/1.81 inference(monotonicity,[status(thm)],[957])).
% 2.18/1.81 tff(959,plain,
% 2.18/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a239)) | (~c3_1(a239)) | (~c0_1(a239)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a239)) | (~c0_1(a239)) | (~c2_1(a239)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.18/1.82 inference(transitivity,[status(thm)],[958, 956])).
% 2.18/1.82 tff(960,plain,
% 2.18/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a239)) | (~c3_1(a239)) | (~c0_1(a239)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))),
% 2.18/1.82 inference(quant_inst,[status(thm)],[])).
% 2.18/1.82 tff(961,plain,
% 2.18/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a239)) | (~c0_1(a239)) | (~c2_1(a239)) | (~c3_1(a259)) | (~c0_1(a259))),
% 2.18/1.82 inference(modus_ponens,[status(thm)],[960, 959])).
% 2.18/1.82 tff(962,plain,
% 2.18/1.82 (~c0_1(a239)),
% 2.18/1.82 inference(unit_resolution,[status(thm)],[961, 122, 955, 912, 954, 943, 167, 857, 166, 165, 931])).
% 2.18/1.82 tff(963,plain,
% 2.18/1.82 (((~hskp13) | (~c1_1(a239))) <=> ((~hskp13) | (~c1_1(a239)))),
% 2.18/1.82 inference(rewrite,[status(thm)],[])).
% 2.18/1.82 tff(964,plain,
% 2.18/1.82 (((~c1_1(a239)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a239)))),
% 2.18/1.82 inference(rewrite,[status(thm)],[])).
% 2.18/1.82 tff(965,axiom,((~c1_1(a239)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 2.18/1.82 tff(966,plain,
% 2.18/1.82 ((~hskp13) | (~c1_1(a239))),
% 2.18/1.82 inference(modus_ponens,[status(thm)],[965, 964])).
% 2.18/1.82 tff(967,plain,
% 2.18/1.82 ((~hskp13) | (~c1_1(a239))),
% 2.18/1.82 inference(modus_ponens,[status(thm)],[966, 963])).
% 2.18/1.82 tff(968,plain,
% 2.18/1.82 (~c1_1(a239)),
% 2.18/1.82 inference(unit_resolution,[status(thm)],[967, 932])).
% 2.18/1.82 tff(969,assumption,(hskp15), introduced(assumption)).
% 2.18/1.82 tff(970,plain,
% 2.18/1.82 (~c0_1(a242)),
% 2.18/1.82 inference(unit_resolution,[status(thm)],[450, 969])).
% 2.18/1.82 tff(971,plain,
% 2.18/1.82 (c1_1(a242)),
% 2.18/1.82 inference(unit_resolution,[status(thm)],[427, 969])).
% 2.18/1.82 tff(972,plain,
% 2.18/1.82 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a259) | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | (~c3_1(a259)) | (~c1_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 2.18/1.82 inference(rewrite,[status(thm)],[])).
% 2.18/1.82 tff(973,plain,
% 2.18/1.82 ((hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242))) <=> (hskp18 | c2_1(a259) | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 2.18/1.82 inference(rewrite,[status(thm)],[])).
% 2.18/1.82 tff(974,plain,
% 2.18/1.82 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a259) | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | (~c3_1(a259)) | (~c1_1(a259))))),
% 2.18/1.82 inference(monotonicity,[status(thm)],[973])).
% 2.18/1.82 tff(975,plain,
% 2.18/1.82 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 2.18/1.82 inference(transitivity,[status(thm)],[974, 972])).
% 2.18/1.82 tff(976,plain,
% 2.18/1.82 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))),
% 2.18/1.82 inference(quant_inst,[status(thm)],[])).
% 2.18/1.82 tff(977,plain,
% 2.18/1.82 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | (~c3_1(a259)) | (~c1_1(a259))),
% 2.18/1.82 inference(modus_ponens,[status(thm)],[976, 975])).
% 2.18/1.82 tff(978,plain,
% 2.18/1.82 (~c3_1(a242)),
% 2.18/1.82 inference(unit_resolution,[status(thm)],[977, 122, 650, 912, 971, 857, 970, 672, 887])).
% 2.18/1.82 tff(979,assumption,(~c0_1(a239)), introduced(assumption)).
% 2.18/1.82 tff(980,plain,
% 2.18/1.82 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 2.18/1.82 inference(bind,[status(th)],[])).
% 2.18/1.82 tff(981,plain,
% 2.18/1.82 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.18/1.82 inference(quant_intro,[status(thm)],[980])).
% 2.18/1.82 tff(982,plain,
% 2.18/1.82 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.18/1.82 inference(rewrite,[status(thm)],[])).
% 2.18/1.82 tff(983,plain,
% 2.18/1.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 2.18/1.82 inference(bind,[status(th)],[])).
% 2.18/1.82 tff(984,plain,
% 2.18/1.82 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.18/1.82 inference(quant_intro,[status(thm)],[983])).
% 2.18/1.82 tff(985,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 2.18/1.82 tff(986,plain,
% 2.18/1.82 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.18/1.82 inference(modus_ponens,[status(thm)],[985, 984])).
% 2.18/1.82 tff(987,plain,
% 2.18/1.82 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.18/1.82 inference(modus_ponens,[status(thm)],[986, 982])).
% 2.18/1.82 tff(988,plain,(
% 2.18/1.82 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.18/1.82 inference(skolemize,[status(sab)],[987])).
% 2.18/1.82 tff(989,plain,
% 2.18/1.82 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.18/1.82 inference(modus_ponens,[status(thm)],[988, 981])).
% 2.18/1.82 tff(990,plain,
% 2.18/1.82 (~c2_1(a242)),
% 2.18/1.82 inference(unit_resolution,[status(thm)],[416, 969])).
% 2.18/1.82 tff(991,assumption,(c3_1(a239)), introduced(assumption)).
% 2.18/1.82 tff(992,assumption,(c2_1(a239)), introduced(assumption)).
% 2.18/1.82 tff(993,plain,
% 2.18/1.82 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c3_1(a242))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c3_1(a242))),
% 2.18/1.82 inference(rewrite,[status(thm)],[])).
% 2.18/1.82 tff(994,plain,
% 2.18/1.82 ((hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a242) | c0_1(a242) | c2_1(a242)) <=> (hskp9 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c3_1(a242))),
% 2.18/1.82 inference(rewrite,[status(thm)],[])).
% 2.18/1.82 tff(995,plain,
% 2.18/1.82 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a242) | c0_1(a242) | c2_1(a242))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c3_1(a242)))),
% 2.18/1.82 inference(monotonicity,[status(thm)],[994])).
% 2.18/1.82 tff(996,plain,
% 2.18/1.82 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a242) | c0_1(a242) | c2_1(a242))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c3_1(a242))),
% 2.18/1.82 inference(transitivity,[status(thm)],[995, 993])).
% 2.18/1.82 tff(997,plain,
% 2.18/1.82 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a242) | c0_1(a242) | c2_1(a242))),
% 2.18/1.82 inference(quant_inst,[status(thm)],[])).
% 2.18/1.82 tff(998,plain,
% 2.18/1.82 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c3_1(a242)),
% 2.18/1.82 inference(modus_ponens,[status(thm)],[997, 996])).
% 2.18/1.82 tff(999,plain,
% 2.18/1.82 ($false),
% 2.18/1.82 inference(unit_resolution,[status(thm)],[998, 122, 23, 992, 991, 970, 990, 989, 979, 978])).
% 2.18/1.82 tff(1000,plain,((~hskp15) | hskp9 | (~c2_1(a239)) | (~c3_1(a239)) | c0_1(a239) | hskp18 | (~c3_1(a259)) | c2_1(a259) | (~c1_1(a259))), inference(lemma,lemma(discharge,[]))).
% 2.18/1.83 tff(1001,plain,
% 2.18/1.83 (~hskp15),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[1000, 962, 887, 943, 954, 650, 912, 857, 23])).
% 2.18/1.83 tff(1002,assumption,(~hskp15), introduced(assumption)).
% 2.18/1.83 tff(1003,assumption,(~hskp24), introduced(assumption)).
% 2.18/1.83 tff(1004,assumption,(~c1_1(a239)), introduced(assumption)).
% 2.18/1.83 tff(1005,plain,
% 2.18/1.83 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c2_1(a239)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp24 | hskp15 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c2_1(a239)))),
% 2.18/1.83 inference(rewrite,[status(thm)],[])).
% 2.18/1.83 tff(1006,plain,
% 2.18/1.83 ((hskp24 | hskp15 | (~ndr1_0) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a239))) <=> (hskp24 | hskp15 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c2_1(a239)))),
% 2.18/1.83 inference(rewrite,[status(thm)],[])).
% 2.18/1.83 tff(1007,plain,
% 2.18/1.83 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a239)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c2_1(a239))))),
% 2.18/1.83 inference(monotonicity,[status(thm)],[1006])).
% 2.18/1.83 tff(1008,plain,
% 2.18/1.83 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a239)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp24 | hskp15 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c2_1(a239)))),
% 2.18/1.83 inference(transitivity,[status(thm)],[1007, 1005])).
% 2.18/1.83 tff(1009,plain,
% 2.18/1.83 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a239)))),
% 2.18/1.83 inference(quant_inst,[status(thm)],[])).
% 2.18/1.83 tff(1010,plain,
% 2.18/1.83 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp24 | hskp15 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c2_1(a239))),
% 2.18/1.83 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 2.18/1.83 tff(1011,plain,
% 2.18/1.83 (hskp24 | hskp15 | (~c3_1(a239)) | (~c2_1(a239))),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[1010, 122, 1004, 333])).
% 2.18/1.83 tff(1012,plain,
% 2.18/1.83 ($false),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[1011, 943, 954, 1003, 1002])).
% 2.18/1.83 tff(1013,plain,((~hskp13) | hskp24 | hskp15 | c1_1(a239)), inference(lemma,lemma(discharge,[]))).
% 2.18/1.83 tff(1014,plain,
% 2.18/1.83 (hskp24),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[1013, 1001, 932, 968])).
% 2.18/1.83 tff(1015,plain,
% 2.18/1.83 (~c3_1(a280)),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[373, 1014])).
% 2.18/1.83 tff(1016,plain,
% 2.18/1.83 (c1_1(a280)),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[396, 1014])).
% 2.18/1.83 tff(1017,plain,
% 2.18/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c3_1(a280) | c1_1(a239) | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a239) | (~c2_1(a239)) | (~c0_1(a280)) | (~c1_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c3_1(a280) | c1_1(a239) | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a239) | (~c2_1(a239)) | (~c0_1(a280)) | (~c1_1(a280)))),
% 2.18/1.83 inference(rewrite,[status(thm)],[])).
% 2.18/1.83 tff(1018,plain,
% 2.18/1.83 (((~ndr1_0) | c3_1(a280) | (~c1_1(a280)) | (~c0_1(a280)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a239) | c1_1(a239) | (~c2_1(a239))) <=> (c3_1(a280) | c1_1(a239) | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a239) | (~c2_1(a239)) | (~c0_1(a280)) | (~c1_1(a280)))),
% 2.18/1.83 inference(rewrite,[status(thm)],[])).
% 2.18/1.83 tff(1019,plain,
% 2.18/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a280) | (~c1_1(a280)) | (~c0_1(a280)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a239) | c1_1(a239) | (~c2_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c3_1(a280) | c1_1(a239) | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a239) | (~c2_1(a239)) | (~c0_1(a280)) | (~c1_1(a280))))),
% 2.18/1.83 inference(monotonicity,[status(thm)],[1018])).
% 2.18/1.83 tff(1020,plain,
% 2.18/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a280) | (~c1_1(a280)) | (~c0_1(a280)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a239) | c1_1(a239) | (~c2_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c3_1(a280) | c1_1(a239) | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a239) | (~c2_1(a239)) | (~c0_1(a280)) | (~c1_1(a280)))),
% 2.18/1.83 inference(transitivity,[status(thm)],[1019, 1017])).
% 2.18/1.83 tff(1021,plain,
% 2.18/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a280) | (~c1_1(a280)) | (~c0_1(a280)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a239) | c1_1(a239) | (~c2_1(a239)))),
% 2.18/1.83 inference(quant_inst,[status(thm)],[])).
% 2.18/1.83 tff(1022,plain,
% 2.18/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c3_1(a280) | c1_1(a239) | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a239) | (~c2_1(a239)) | (~c0_1(a280)) | (~c1_1(a280))),
% 2.18/1.83 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 2.18/1.83 tff(1023,plain,
% 2.18/1.83 (~c0_1(a280)),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[1022, 122, 1016, 954, 785, 1015, 968, 784, 783, 782, 962])).
% 2.18/1.83 tff(1024,plain,
% 2.18/1.83 (~c2_1(a280)),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[379, 1014])).
% 2.18/1.83 tff(1025,plain,
% 2.18/1.83 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c0_1(a280))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c0_1(a280))),
% 2.18/1.83 inference(rewrite,[status(thm)],[])).
% 2.18/1.83 tff(1026,plain,
% 2.18/1.83 ((hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a280) | c0_1(a280) | c2_1(a280)) <=> (hskp9 | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c0_1(a280))),
% 2.18/1.83 inference(rewrite,[status(thm)],[])).
% 2.18/1.83 tff(1027,plain,
% 2.18/1.83 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a280) | c0_1(a280) | c2_1(a280))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c0_1(a280)))),
% 2.18/1.83 inference(monotonicity,[status(thm)],[1026])).
% 2.18/1.83 tff(1028,plain,
% 2.18/1.83 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a280) | c0_1(a280) | c2_1(a280))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c0_1(a280))),
% 2.18/1.83 inference(transitivity,[status(thm)],[1027, 1025])).
% 2.18/1.83 tff(1029,plain,
% 2.18/1.83 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a280) | c0_1(a280) | c2_1(a280))),
% 2.18/1.83 inference(quant_inst,[status(thm)],[])).
% 2.18/1.83 tff(1030,plain,
% 2.18/1.83 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c0_1(a280)),
% 2.18/1.83 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 2.18/1.83 tff(1031,plain,
% 2.18/1.83 ($false),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[1030, 122, 23, 954, 943, 1024, 1015, 989, 962, 1023])).
% 2.18/1.83 tff(1032,plain,((~hskp13) | hskp9 | (~c3_1(a218)) | c1_1(a218) | c2_1(a218) | (~c1_1(a259)) | hskp18 | (~c3_1(a259)) | c2_1(a259) | (~c0_1(a259)) | (~c2_1(a215)) | c0_1(a215) | c1_1(a215)), inference(lemma,lemma(discharge,[]))).
% 2.18/1.83 tff(1033,plain,
% 2.18/1.83 (~hskp13),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[1032, 921, 833, 832, 831, 886, 650, 868, 857, 856, 167, 166, 165])).
% 2.18/1.83 tff(1034,plain,
% 2.18/1.83 ((hskp16 | hskp13 | hskp12) <=> (hskp16 | hskp13 | hskp12)),
% 2.18/1.83 inference(rewrite,[status(thm)],[])).
% 2.18/1.83 tff(1035,plain,
% 2.18/1.83 (((hskp12 | hskp16) | hskp13) <=> (hskp16 | hskp13 | hskp12)),
% 2.18/1.83 inference(rewrite,[status(thm)],[])).
% 2.18/1.83 tff(1036,axiom,((hskp12 | hskp16) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 2.18/1.83 tff(1037,plain,
% 2.18/1.83 (hskp16 | hskp13 | hskp12),
% 2.18/1.83 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 2.18/1.83 tff(1038,plain,
% 2.18/1.83 (hskp16 | hskp13 | hskp12),
% 2.18/1.83 inference(modus_ponens,[status(thm)],[1037, 1034])).
% 2.18/1.83 tff(1039,plain,
% 2.18/1.83 (hskp16 | hskp13 | hskp12),
% 2.18/1.83 inference(modus_ponens,[status(thm)],[1038, 1034])).
% 2.18/1.83 tff(1040,plain,
% 2.18/1.83 (hskp16 | hskp13 | hskp12),
% 2.18/1.83 inference(modus_ponens,[status(thm)],[1039, 1034])).
% 2.18/1.83 tff(1041,plain,
% 2.18/1.83 (hskp16 | hskp13 | hskp12),
% 2.18/1.83 inference(modus_ponens,[status(thm)],[1040, 1034])).
% 2.18/1.83 tff(1042,plain,
% 2.18/1.83 (hskp16 | hskp13 | hskp12),
% 2.18/1.83 inference(modus_ponens,[status(thm)],[1041, 1034])).
% 2.18/1.83 tff(1043,plain,
% 2.18/1.83 (hskp16 | hskp13 | hskp12),
% 2.18/1.83 inference(modus_ponens,[status(thm)],[1042, 1034])).
% 2.18/1.83 tff(1044,plain,
% 2.18/1.83 (hskp16 | hskp13 | hskp12),
% 2.18/1.83 inference(modus_ponens,[status(thm)],[1043, 1034])).
% 2.18/1.83 tff(1045,plain,
% 2.18/1.83 (hskp16),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[1044, 1033, 834])).
% 2.18/1.83 tff(1046,plain,
% 2.18/1.83 (~c3_1(a245)),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[502, 1045])).
% 2.18/1.83 tff(1047,plain,
% 2.18/1.83 (~c1_1(a245)),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[508, 1045])).
% 2.18/1.83 tff(1048,plain,
% 2.18/1.83 (c0_1(a245)),
% 2.18/1.83 inference(unit_resolution,[status(thm)],[519, 1045])).
% 2.18/1.83 tff(1049,plain,
% 2.18/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.18/1.83 inference(rewrite,[status(thm)],[])).
% 2.18/1.83 tff(1050,plain,
% 2.18/1.83 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245))) <=> (c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.18/1.83 inference(rewrite,[status(thm)],[])).
% 2.18/1.83 tff(1051,plain,
% 2.18/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 2.18/1.83 inference(monotonicity,[status(thm)],[1050])).
% 2.18/1.83 tff(1052,plain,
% 2.18/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.18/1.84 inference(transitivity,[status(thm)],[1051, 1049])).
% 2.18/1.84 tff(1053,plain,
% 2.18/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))),
% 2.18/1.84 inference(quant_inst,[status(thm)],[])).
% 2.18/1.84 tff(1054,plain,
% 2.18/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259))),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 2.18/1.84 tff(1055,plain,
% 2.18/1.84 ($false),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[1054, 122, 856, 868, 1048, 837, 857, 1047, 1046, 836, 835, 22])).
% 2.18/1.84 tff(1056,plain,(c1_1(a213) | (~c2_1(a213)) | c2_1(a259) | c3_1(a213) | hskp18 | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | (~c1_1(a248)) | (~c3_1(a248)) | c2_1(a248)), inference(lemma,lemma(discharge,[]))).
% 2.18/1.84 tff(1057,plain,
% 2.18/1.84 (c2_1(a259)),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[1056, 817, 828, 811, 650, 167, 166, 165, 705, 704, 703])).
% 2.18/1.84 tff(1058,plain,
% 2.18/1.84 (((~hskp21) | (~c2_1(a259))) <=> ((~hskp21) | (~c2_1(a259)))),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1059,plain,
% 2.18/1.84 (((~c2_1(a259)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a259)))),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1060,axiom,((~c2_1(a259)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 2.18/1.84 tff(1061,plain,
% 2.18/1.84 ((~hskp21) | (~c2_1(a259))),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 2.18/1.84 tff(1062,plain,
% 2.18/1.84 ((~hskp21) | (~c2_1(a259))),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1061, 1058])).
% 2.18/1.84 tff(1063,plain,
% 2.18/1.84 (~hskp21),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[1062, 1057])).
% 2.18/1.84 tff(1064,plain,
% 2.18/1.84 ($false),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[843, 122, 1063, 834, 828, 817, 811, 804])).
% 2.18/1.84 tff(1065,plain,((~hskp0) | hskp18 | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | (~c1_1(a248)) | (~c3_1(a248)) | c2_1(a248)), inference(lemma,lemma(discharge,[]))).
% 2.18/1.84 tff(1066,plain,
% 2.18/1.84 (~hskp0),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[1065, 725, 650, 724, 723, 684, 701, 690])).
% 2.18/1.84 tff(1067,assumption,(~hskp0), introduced(assumption)).
% 2.18/1.84 tff(1068,plain,
% 2.18/1.84 ((hskp12 | hskp1 | hskp0) <=> (hskp12 | hskp1 | hskp0)),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1069,plain,
% 2.18/1.84 (((hskp12 | hskp1) | hskp0) <=> (hskp12 | hskp1 | hskp0)),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1070,plain,
% 2.18/1.84 ((hskp12 | hskp1) <=> (hskp12 | hskp1)),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1071,plain,
% 2.18/1.84 (((hskp12 | hskp1) | hskp0) <=> ((hskp12 | hskp1) | hskp0)),
% 2.18/1.84 inference(monotonicity,[status(thm)],[1070])).
% 2.18/1.84 tff(1072,plain,
% 2.18/1.84 (((hskp12 | hskp1) | hskp0) <=> (hskp12 | hskp1 | hskp0)),
% 2.18/1.84 inference(transitivity,[status(thm)],[1071, 1069])).
% 2.18/1.84 tff(1073,axiom,((hskp12 | hskp1) | hskp0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 2.18/1.84 tff(1074,plain,
% 2.18/1.84 (hskp12 | hskp1 | hskp0),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1073, 1072])).
% 2.18/1.84 tff(1075,plain,
% 2.18/1.84 (hskp12 | hskp1 | hskp0),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1074, 1068])).
% 2.18/1.84 tff(1076,plain,
% 2.18/1.84 (hskp12 | hskp1 | hskp0),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1075, 1068])).
% 2.18/1.84 tff(1077,plain,
% 2.18/1.84 (hskp12 | hskp1 | hskp0),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1076, 1068])).
% 2.18/1.84 tff(1078,plain,
% 2.18/1.84 (hskp12 | hskp1 | hskp0),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1077, 1068])).
% 2.18/1.84 tff(1079,plain,
% 2.18/1.84 (hskp12 | hskp1 | hskp0),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1078, 1068])).
% 2.18/1.84 tff(1080,plain,
% 2.18/1.84 (hskp12 | hskp1 | hskp0),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1079, 1068])).
% 2.18/1.84 tff(1081,plain,
% 2.18/1.84 (hskp12 | hskp1 | hskp0),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1080, 1068])).
% 2.18/1.84 tff(1082,plain,
% 2.18/1.84 (hskp1),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[1081, 1067, 574])).
% 2.18/1.84 tff(1083,plain,
% 2.18/1.84 (((~hskp1) | (~c3_1(a214))) <=> ((~hskp1) | (~c3_1(a214)))),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1084,plain,
% 2.18/1.84 (((~c3_1(a214)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a214)))),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1085,axiom,((~c3_1(a214)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 2.18/1.84 tff(1086,plain,
% 2.18/1.84 ((~hskp1) | (~c3_1(a214))),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 2.18/1.84 tff(1087,plain,
% 2.18/1.84 ((~hskp1) | (~c3_1(a214))),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1086, 1083])).
% 2.18/1.84 tff(1088,plain,
% 2.18/1.84 (~c3_1(a214)),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[1087, 1082])).
% 2.18/1.84 tff(1089,plain,
% 2.18/1.84 (^[U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 2.18/1.84 inference(bind,[status(th)],[])).
% 2.18/1.84 tff(1090,plain,
% 2.18/1.84 (![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.18/1.84 inference(quant_intro,[status(thm)],[1089])).
% 2.18/1.84 tff(1091,plain,
% 2.18/1.84 (![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1092,plain,
% 2.18/1.84 (^[U: $i] : 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)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 2.18/1.84 inference(bind,[status(th)],[])).
% 2.18/1.84 tff(1093,plain,
% 2.18/1.84 (![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.18/1.84 inference(quant_intro,[status(thm)],[1092])).
% 2.18/1.84 tff(1094,axiom,(![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 2.18/1.84 tff(1095,plain,
% 2.18/1.84 (![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 2.18/1.84 tff(1096,plain,
% 2.18/1.84 (![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1095, 1091])).
% 2.18/1.84 tff(1097,plain,(
% 2.18/1.84 ![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.18/1.84 inference(skolemize,[status(sab)],[1096])).
% 2.18/1.84 tff(1098,plain,
% 2.18/1.84 (![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1097, 1090])).
% 2.18/1.84 tff(1099,plain,
% 2.18/1.84 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | c0_1(a218))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | c0_1(a218))),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1100,plain,
% 2.18/1.84 ((hskp0 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | c0_1(a218)) <=> (hskp0 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | c0_1(a218))),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1101,plain,
% 2.18/1.84 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | c0_1(a218))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | c0_1(a218)))),
% 2.18/1.84 inference(monotonicity,[status(thm)],[1100])).
% 2.18/1.84 tff(1102,plain,
% 2.18/1.84 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | c0_1(a218))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | c0_1(a218))),
% 2.18/1.84 inference(transitivity,[status(thm)],[1101, 1099])).
% 2.18/1.84 tff(1103,plain,
% 2.18/1.84 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | c0_1(a218))),
% 2.18/1.84 inference(quant_inst,[status(thm)],[])).
% 2.18/1.84 tff(1104,plain,
% 2.18/1.84 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | c0_1(a218)),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 2.18/1.84 tff(1105,plain,
% 2.18/1.84 (hskp0 | c0_1(a218)),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[1104, 122, 784, 783, 1098])).
% 2.18/1.84 tff(1106,plain,
% 2.18/1.84 (c0_1(a218)),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[1105, 1067])).
% 2.18/1.84 tff(1107,plain,
% 2.18/1.84 (^[U: $i] : refl((hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.18/1.84 inference(bind,[status(th)],[])).
% 2.18/1.84 tff(1108,plain,
% 2.18/1.84 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.18/1.84 inference(quant_intro,[status(thm)],[1107])).
% 2.18/1.84 tff(1109,plain,
% 2.18/1.84 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1110,plain,
% 2.18/1.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp4) <=> ((hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4))), rewrite(((hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp4) <=> (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.18/1.84 inference(bind,[status(th)],[])).
% 2.18/1.84 tff(1111,plain,
% 2.18/1.84 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp4) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.18/1.84 inference(quant_intro,[status(thm)],[1110])).
% 2.18/1.84 tff(1112,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 2.18/1.84 tff(1113,plain,
% 2.18/1.84 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1112, 1111])).
% 2.18/1.84 tff(1114,plain,
% 2.18/1.84 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1113, 1109])).
% 2.18/1.84 tff(1115,plain,(
% 2.18/1.84 ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.18/1.84 inference(skolemize,[status(sab)],[1114])).
% 2.18/1.84 tff(1116,plain,
% 2.18/1.84 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1115, 1108])).
% 2.18/1.84 tff(1117,plain,
% 2.18/1.84 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp4 | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)))),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1118,plain,
% 2.18/1.84 ((hskp16 | hskp4 | (~ndr1_0) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218))) <=> (hskp16 | hskp4 | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)))),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1119,plain,
% 2.18/1.84 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218))))),
% 2.18/1.84 inference(monotonicity,[status(thm)],[1118])).
% 2.18/1.84 tff(1120,plain,
% 2.18/1.84 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp4 | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)))),
% 2.18/1.84 inference(transitivity,[status(thm)],[1119, 1117])).
% 2.18/1.84 tff(1121,plain,
% 2.18/1.84 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218)))),
% 2.18/1.84 inference(quant_inst,[status(thm)],[])).
% 2.18/1.84 tff(1122,plain,
% 2.18/1.84 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp4 | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218))),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 2.18/1.84 tff(1123,plain,
% 2.18/1.84 (hskp16 | hskp4 | (~c0_1(a218))),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[1122, 122, 785, 784, 1116])).
% 2.18/1.84 tff(1124,plain,
% 2.18/1.84 (hskp16),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[1123, 1106, 302])).
% 2.18/1.84 tff(1125,plain,
% 2.18/1.84 (~c3_1(a245)),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[502, 1124])).
% 2.18/1.84 tff(1126,plain,
% 2.18/1.84 (~c1_1(a245)),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[508, 1124])).
% 2.18/1.84 tff(1127,plain,
% 2.18/1.84 (((~hskp1) | c2_1(a214)) <=> ((~hskp1) | c2_1(a214))),
% 2.18/1.84 inference(rewrite,[status(thm)],[])).
% 2.18/1.84 tff(1128,axiom,((~hskp1) | c2_1(a214)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 2.18/1.84 tff(1129,plain,
% 2.18/1.84 ((~hskp1) | c2_1(a214)),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 2.18/1.84 tff(1130,plain,
% 2.18/1.84 ((~hskp1) | c2_1(a214)),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1129, 1127])).
% 2.18/1.84 tff(1131,plain,
% 2.18/1.84 ((~hskp1) | c2_1(a214)),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1130, 1127])).
% 2.18/1.84 tff(1132,plain,
% 2.18/1.84 ((~hskp1) | c2_1(a214)),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1131, 1127])).
% 2.18/1.84 tff(1133,plain,
% 2.18/1.84 ((~hskp1) | c2_1(a214)),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1132, 1127])).
% 2.18/1.84 tff(1134,plain,
% 2.18/1.84 ((~hskp1) | c2_1(a214)),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1133, 1127])).
% 2.18/1.84 tff(1135,plain,
% 2.18/1.84 ((~hskp1) | c2_1(a214)),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1134, 1127])).
% 2.18/1.84 tff(1136,plain,
% 2.18/1.84 ((~hskp1) | c2_1(a214)),
% 2.18/1.84 inference(modus_ponens,[status(thm)],[1135, 1127])).
% 2.18/1.84 tff(1137,plain,
% 2.18/1.84 (c2_1(a214)),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[1136, 1082])).
% 2.18/1.84 tff(1138,plain,
% 2.18/1.84 (c0_1(a245)),
% 2.18/1.84 inference(unit_resolution,[status(thm)],[519, 1124])).
% 2.18/1.84 tff(1139,plain,
% 2.18/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c1_1(a245) | c3_1(a245) | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)) | (~c0_1(a245)) | (~c3_1(a248)) | (~c0_1(a248)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c1_1(a245) | c3_1(a245) | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)) | (~c0_1(a245)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 2.18/1.85 inference(rewrite,[status(thm)],[])).
% 2.18/1.85 tff(1140,plain,
% 2.18/1.85 (((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245))) <=> (c2_1(a248) | c1_1(a245) | c3_1(a245) | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)) | (~c0_1(a245)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 2.18/1.85 inference(rewrite,[status(thm)],[])).
% 2.18/1.85 tff(1141,plain,
% 2.18/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c1_1(a245) | c3_1(a245) | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)) | (~c0_1(a245)) | (~c3_1(a248)) | (~c0_1(a248))))),
% 2.18/1.85 inference(monotonicity,[status(thm)],[1140])).
% 2.18/1.85 tff(1142,plain,
% 2.18/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c1_1(a245) | c3_1(a245) | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)) | (~c0_1(a245)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 2.18/1.85 inference(transitivity,[status(thm)],[1141, 1139])).
% 2.18/1.85 tff(1143,plain,
% 2.18/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))),
% 2.18/1.85 inference(quant_inst,[status(thm)],[])).
% 2.18/1.85 tff(1144,plain,
% 2.18/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c1_1(a245) | c3_1(a245) | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)) | (~c0_1(a245)) | (~c3_1(a248)) | (~c0_1(a248))),
% 2.18/1.85 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 2.18/1.85 tff(1145,plain,
% 2.18/1.85 (c1_1(a214)),
% 2.18/1.85 inference(unit_resolution,[status(thm)],[1144, 122, 704, 1138, 1137, 703, 1126, 1125, 1088, 22, 756])).
% 2.18/1.85 tff(1146,plain,
% 2.18/1.85 (((~hskp1) | (~c0_1(a214))) <=> ((~hskp1) | (~c0_1(a214)))),
% 2.18/1.85 inference(rewrite,[status(thm)],[])).
% 2.18/1.85 tff(1147,plain,
% 2.18/1.85 (((~c0_1(a214)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a214)))),
% 2.18/1.85 inference(rewrite,[status(thm)],[])).
% 2.18/1.85 tff(1148,axiom,((~c0_1(a214)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 2.18/1.85 tff(1149,plain,
% 2.18/1.85 ((~hskp1) | (~c0_1(a214))),
% 2.18/1.85 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 2.18/1.85 tff(1150,plain,
% 2.18/1.85 ((~hskp1) | (~c0_1(a214))),
% 2.18/1.85 inference(modus_ponens,[status(thm)],[1149, 1146])).
% 2.18/1.85 tff(1151,plain,
% 2.18/1.85 (~c0_1(a214)),
% 2.18/1.85 inference(unit_resolution,[status(thm)],[1150, 1082])).
% 2.18/1.85 tff(1152,plain,
% 2.18/1.85 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214)))),
% 2.18/1.85 inference(rewrite,[status(thm)],[])).
% 2.18/1.85 tff(1153,plain,
% 2.18/1.85 ((hskp12 | (~ndr1_0) | c3_1(a214) | (~c2_1(a214)) | (~c1_1(a214)) | c3_1(a214) | c0_1(a214) | (~c1_1(a214))) <=> (hskp12 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214)))),
% 2.18/1.85 inference(rewrite,[status(thm)],[])).
% 2.18/1.85 tff(1154,plain,
% 2.18/1.85 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a214) | (~c2_1(a214)) | (~c1_1(a214)) | c3_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214))))),
% 2.18/1.85 inference(monotonicity,[status(thm)],[1153])).
% 2.18/1.85 tff(1155,plain,
% 2.18/1.85 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a214) | (~c2_1(a214)) | (~c1_1(a214)) | c3_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214)))),
% 2.18/1.85 inference(transitivity,[status(thm)],[1154, 1152])).
% 2.18/1.85 tff(1156,plain,
% 2.18/1.85 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a214) | (~c2_1(a214)) | (~c1_1(a214)) | c3_1(a214) | c0_1(a214) | (~c1_1(a214)))),
% 2.18/1.85 inference(quant_inst,[status(thm)],[])).
% 2.18/1.85 tff(1157,plain,
% 2.18/1.85 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214))),
% 2.18/1.85 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 2.18/1.85 tff(1158,plain,
% 2.18/1.85 ($false),
% 2.18/1.85 inference(unit_resolution,[status(thm)],[1157, 122, 574, 1137, 1151, 1088, 44, 1145])).
% 2.18/1.85 tff(1159,plain,(hskp0 | hskp12 | (~c3_1(a248)) | c2_1(a248) | (~c0_1(a248)) | hskp4 | (~c3_1(a218)) | c1_1(a218) | c2_1(a218)), inference(lemma,lemma(discharge,[]))).
% 2.18/1.85 tff(1160,plain,
% 2.18/1.85 (hskp4),
% 2.18/1.85 inference(unit_resolution,[status(thm)],[1159, 1066, 701, 690, 714, 794, 755, 744, 738])).
% 2.18/1.85 tff(1161,plain,
% 2.18/1.85 (~c2_1(a217)),
% 2.18/1.85 inference(unit_resolution,[status(thm)],[201, 1160])).
% 2.18/1.85 tff(1162,plain,
% 2.18/1.85 (~c1_1(a217)),
% 2.18/1.85 inference(unit_resolution,[status(thm)],[207, 1160])).
% 2.18/1.85 tff(1163,plain,
% 2.18/1.85 (~c3_1(a217)),
% 2.18/1.85 inference(unit_resolution,[status(thm)],[195, 1160])).
% 2.18/1.85 tff(1164,assumption,(~c1_1(a217)), introduced(assumption)).
% 2.18/1.85 tff(1165,assumption,(~c2_1(a217)), introduced(assumption)).
% 2.18/1.85 tff(1166,assumption,(~c3_1(a217)), introduced(assumption)).
% 2.18/1.85 tff(1167,assumption,(c0_1(a217)), introduced(assumption)).
% 2.18/1.85 tff(1168,plain,
% 2.18/1.85 (^[U: $i] : refl((hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 2.18/1.85 inference(bind,[status(th)],[])).
% 2.18/1.85 tff(1169,plain,
% 2.18/1.85 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.18/1.85 inference(quant_intro,[status(thm)],[1168])).
% 2.18/1.85 tff(1170,plain,
% 2.18/1.85 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.18/1.85 inference(rewrite,[status(thm)],[])).
% 2.18/1.85 tff(1171,plain,
% 2.18/1.85 (^[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)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19) <=> ((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 2.18/1.85 inference(bind,[status(th)],[])).
% 2.18/1.85 tff(1172,plain,
% 2.18/1.85 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.18/1.85 inference(quant_intro,[status(thm)],[1171])).
% 2.18/1.85 tff(1173,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 2.18/1.85 tff(1174,plain,
% 2.18/1.85 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.18/1.85 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 2.18/1.85 tff(1175,plain,
% 2.18/1.85 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.18/1.85 inference(modus_ponens,[status(thm)],[1174, 1170])).
% 2.18/1.85 tff(1176,plain,(
% 2.18/1.85 ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.18/1.85 inference(skolemize,[status(sab)],[1175])).
% 2.18/1.85 tff(1177,plain,
% 2.18/1.85 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.18/1.85 inference(modus_ponens,[status(thm)],[1176, 1169])).
% 2.18/1.85 tff(1178,plain,
% 2.18/1.85 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | (~c0_1(a217)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | (~c0_1(a217)))),
% 2.18/1.85 inference(rewrite,[status(thm)],[])).
% 2.18/1.85 tff(1179,plain,
% 2.18/1.85 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | (~c0_1(a217))) <=> (hskp19 | hskp18 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | (~c0_1(a217)))),
% 2.18/1.85 inference(rewrite,[status(thm)],[])).
% 2.18/1.85 tff(1180,plain,
% 2.18/1.85 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | (~c0_1(a217)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | (~c0_1(a217))))),
% 2.18/1.85 inference(monotonicity,[status(thm)],[1179])).
% 2.18/1.85 tff(1181,plain,
% 2.18/1.85 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | (~c0_1(a217)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | (~c0_1(a217)))),
% 2.18/1.85 inference(transitivity,[status(thm)],[1180, 1178])).
% 2.18/1.85 tff(1182,plain,
% 2.18/1.85 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | (~c0_1(a217)))),
% 2.18/1.85 inference(quant_inst,[status(thm)],[])).
% 2.18/1.85 tff(1183,plain,
% 2.18/1.85 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | (~c0_1(a217))),
% 2.18/1.85 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 2.18/1.85 tff(1184,plain,
% 2.18/1.85 (hskp19 | c1_1(a217) | (~c0_1(a217))),
% 2.18/1.85 inference(unit_resolution,[status(thm)],[1183, 122, 650, 1165, 1177])).
% 2.18/1.85 tff(1185,plain,
% 2.18/1.85 (hskp19),
% 2.18/1.85 inference(unit_resolution,[status(thm)],[1184, 1167, 1164])).
% 2.18/1.85 tff(1186,plain,
% 2.18/1.85 (~c0_1(a255)),
% 2.18/1.85 inference(unit_resolution,[status(thm)],[300, 1185])).
% 2.18/1.85 tff(1187,plain,
% 2.18/1.85 (~c1_1(a255)),
% 2.18/1.85 inference(unit_resolution,[status(thm)],[294, 1185])).
% 2.18/1.85 tff(1188,plain,
% 2.18/1.85 (~c3_1(a255)),
% 2.18/1.85 inference(unit_resolution,[status(thm)],[288, 1185])).
% 2.18/1.85 tff(1189,assumption,(~c1_1(a255)), introduced(assumption)).
% 2.18/1.86 tff(1190,assumption,(~c0_1(a255)), introduced(assumption)).
% 2.18/1.86 tff(1191,plain,
% 2.18/1.86 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | c2_1(a255))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | c2_1(a255))),
% 2.18/1.86 inference(rewrite,[status(thm)],[])).
% 2.18/1.86 tff(1192,plain,
% 2.18/1.86 ((hskp0 | (~ndr1_0) | c2_1(a255) | c1_1(a255) | c0_1(a255)) <=> (hskp0 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | c2_1(a255))),
% 2.18/1.86 inference(rewrite,[status(thm)],[])).
% 2.18/1.86 tff(1193,plain,
% 2.18/1.86 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a255) | c1_1(a255) | c0_1(a255))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | c2_1(a255)))),
% 2.18/1.86 inference(monotonicity,[status(thm)],[1192])).
% 2.18/1.86 tff(1194,plain,
% 2.18/1.86 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a255) | c1_1(a255) | c0_1(a255))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | c2_1(a255))),
% 2.18/1.86 inference(transitivity,[status(thm)],[1193, 1191])).
% 2.18/1.86 tff(1195,plain,
% 2.18/1.86 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a255) | c1_1(a255) | c0_1(a255))),
% 2.18/1.86 inference(quant_inst,[status(thm)],[])).
% 2.18/1.86 tff(1196,plain,
% 2.18/1.86 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | c2_1(a255)),
% 2.18/1.86 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 2.18/1.86 tff(1197,plain,
% 2.18/1.86 (hskp0 | c2_1(a255)),
% 2.18/1.86 inference(unit_resolution,[status(thm)],[1196, 122, 1190, 1189, 1098])).
% 2.18/1.86 tff(1198,plain,
% 2.18/1.86 (c2_1(a255)),
% 2.18/1.86 inference(unit_resolution,[status(thm)],[1197, 1067])).
% 2.18/1.86 tff(1199,plain,
% 2.18/1.86 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | c0_1(a217))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | c0_1(a217))),
% 2.18/1.86 inference(rewrite,[status(thm)],[])).
% 2.18/1.86 tff(1200,plain,
% 2.18/1.86 ((hskp0 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c0_1(a217)) <=> (hskp0 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | c0_1(a217))),
% 2.18/1.86 inference(rewrite,[status(thm)],[])).
% 2.18/1.86 tff(1201,plain,
% 2.18/1.86 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c0_1(a217))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | c0_1(a217)))),
% 2.18/1.86 inference(monotonicity,[status(thm)],[1200])).
% 2.18/1.86 tff(1202,plain,
% 2.18/1.86 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c0_1(a217))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | c0_1(a217))),
% 2.18/1.86 inference(transitivity,[status(thm)],[1201, 1199])).
% 2.18/1.86 tff(1203,plain,
% 2.18/1.86 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c0_1(a217))),
% 2.18/1.86 inference(quant_inst,[status(thm)],[])).
% 2.18/1.86 tff(1204,plain,
% 2.18/1.86 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | c0_1(a217)),
% 2.18/1.86 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 2.18/1.86 tff(1205,plain,
% 2.18/1.86 (hskp0 | c1_1(a217) | c0_1(a217)),
% 2.18/1.86 inference(unit_resolution,[status(thm)],[1204, 122, 1165, 1098])).
% 2.18/1.86 tff(1206,plain,
% 2.18/1.86 (c0_1(a217)),
% 2.18/1.86 inference(unit_resolution,[status(thm)],[1205, 1067, 1164])).
% 2.18/1.86 tff(1207,assumption,(~c3_1(a255)), introduced(assumption)).
% 2.18/1.86 tff(1208,plain,
% 2.18/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a255)))),
% 2.18/1.86 inference(rewrite,[status(thm)],[])).
% 2.18/1.86 tff(1209,plain,
% 2.18/1.86 (((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217))) <=> (c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a255)))),
% 2.18/1.86 inference(rewrite,[status(thm)],[])).
% 2.18/1.86 tff(1210,plain,
% 2.18/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a255))))),
% 2.18/1.86 inference(monotonicity,[status(thm)],[1209])).
% 2.18/1.86 tff(1211,plain,
% 2.18/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a255)))),
% 2.18/1.86 inference(transitivity,[status(thm)],[1210, 1208])).
% 2.18/1.86 tff(1212,plain,
% 2.18/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217)))),
% 2.18/1.86 inference(quant_inst,[status(thm)],[])).
% 2.18/1.86 tff(1213,plain,
% 2.18/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a255))),
% 2.18/1.86 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 2.18/1.86 tff(1214,plain,
% 2.18/1.86 ((~c0_1(a217)) | (~c0_1(a218)) | (~c2_1(a255))),
% 2.18/1.86 inference(unit_resolution,[status(thm)],[1213, 122, 785, 1189, 1207, 783, 1164, 1166, 22])).
% 2.18/1.86 tff(1215,plain,
% 2.18/1.86 ($false),
% 2.18/1.86 inference(unit_resolution,[status(thm)],[1214, 1206, 1106, 1198])).
% 2.18/1.86 tff(1216,plain,(hskp0 | (~c3_1(a218)) | c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | c0_1(a255) | c2_1(a217) | c1_1(a218)), inference(lemma,lemma(discharge,[]))).
% 2.18/1.86 tff(1217,plain,
% 2.18/1.86 (hskp0),
% 2.18/1.86 inference(unit_resolution,[status(thm)],[1216, 1188, 785, 1187, 783, 1164, 1166, 1186, 1165, 784])).
% 2.18/1.86 tff(1218,plain,
% 2.18/1.86 (~c3_1(a213)),
% 2.18/1.86 inference(unit_resolution,[status(thm)],[810, 1217])).
% 2.18/1.86 tff(1219,plain,
% 2.18/1.86 (~c1_1(a213)),
% 2.18/1.86 inference(unit_resolution,[status(thm)],[816, 1217])).
% 2.18/1.86 tff(1220,plain,
% 2.18/1.86 (c2_1(a213)),
% 2.18/1.86 inference(unit_resolution,[status(thm)],[827, 1217])).
% 2.18/1.86 tff(1221,plain,
% 2.18/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c1_1(a217) | c3_1(a217) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a217)) | (~c3_1(a248)) | (~c0_1(a248)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c1_1(a217) | c3_1(a217) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a217)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 2.18/1.86 inference(rewrite,[status(thm)],[])).
% 2.22/1.86 tff(1222,plain,
% 2.22/1.86 (((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217))) <=> (c2_1(a248) | c1_1(a217) | c3_1(a217) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a217)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 2.22/1.86 inference(rewrite,[status(thm)],[])).
% 2.22/1.86 tff(1223,plain,
% 2.22/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c1_1(a217) | c3_1(a217) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a217)) | (~c3_1(a248)) | (~c0_1(a248))))),
% 2.22/1.86 inference(monotonicity,[status(thm)],[1222])).
% 2.22/1.86 tff(1224,plain,
% 2.22/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c1_1(a217) | c3_1(a217) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a217)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 2.22/1.86 inference(transitivity,[status(thm)],[1223, 1221])).
% 2.22/1.86 tff(1225,plain,
% 2.22/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217)))),
% 2.22/1.86 inference(quant_inst,[status(thm)],[])).
% 2.22/1.86 tff(1226,plain,
% 2.22/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c1_1(a217) | c3_1(a217) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a217)) | (~c3_1(a248)) | (~c0_1(a248))),
% 2.22/1.86 inference(modus_ponens,[status(thm)],[1225, 1224])).
% 2.22/1.86 tff(1227,plain,
% 2.22/1.86 ($false),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[1226, 122, 704, 1220, 703, 1164, 1166, 1219, 1218, 22, 756, 1167])).
% 2.22/1.86 tff(1228,plain,((~c0_1(a217)) | (~c3_1(a248)) | c2_1(a248) | c1_1(a217) | c3_1(a217) | (~c0_1(a248)) | (~c3_1(a218)) | c2_1(a218) | c2_1(a217) | c1_1(a218) | hskp18), inference(lemma,lemma(discharge,[]))).
% 2.22/1.86 tff(1229,plain,
% 2.22/1.86 (~c0_1(a217)),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[1228, 1164, 703, 704, 1166, 829, 833, 831, 1165, 832, 650])).
% 2.22/1.86 tff(1230,plain,
% 2.22/1.86 (hskp0),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[1205, 1229, 1164])).
% 2.22/1.86 tff(1231,plain,
% 2.22/1.86 (~c3_1(a213)),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[810, 1230])).
% 2.22/1.86 tff(1232,plain,
% 2.22/1.86 (~c1_1(a213)),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[816, 1230])).
% 2.22/1.86 tff(1233,assumption,(~c0_1(a217)), introduced(assumption)).
% 2.22/1.86 tff(1234,plain,
% 2.22/1.86 (hskp0),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[1205, 1233, 1164])).
% 2.22/1.86 tff(1235,plain,
% 2.22/1.86 (~c3_1(a213)),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[810, 1234])).
% 2.22/1.86 tff(1236,plain,
% 2.22/1.86 (c2_1(a213)),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[827, 1234])).
% 2.22/1.86 tff(1237,plain,
% 2.22/1.86 (~c1_1(a213)),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[816, 1234])).
% 2.22/1.86 tff(1238,plain,
% 2.22/1.86 (hskp21 | hskp12),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[843, 122, 837, 836, 835, 804])).
% 2.22/1.86 tff(1239,plain,
% 2.22/1.86 (hskp21),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[1238, 574])).
% 2.22/1.86 tff(1240,plain,
% 2.22/1.86 (~c2_1(a259)),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[1062, 1239])).
% 2.22/1.86 tff(1241,plain,
% 2.22/1.86 (c0_1(a259)),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[855, 1239])).
% 2.22/1.86 tff(1242,plain,
% 2.22/1.86 (c1_1(a259)),
% 2.22/1.86 inference(unit_resolution,[status(thm)],[884, 122, 1241, 705, 704, 837, 1240, 703, 836, 835, 878])).
% 2.22/1.87 tff(1243,plain,
% 2.22/1.87 (c3_1(a259)),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[867, 1239])).
% 2.22/1.87 tff(1244,plain,
% 2.22/1.87 (~hskp9),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[920, 1243, 837, 1240, 836, 835, 1242])).
% 2.22/1.87 tff(1245,plain,
% 2.22/1.87 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | c0_1(a217))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | c0_1(a217))),
% 2.22/1.87 inference(rewrite,[status(thm)],[])).
% 2.22/1.87 tff(1246,plain,
% 2.22/1.87 ((hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a217) | c0_1(a217) | c2_1(a217)) <=> (hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | c0_1(a217))),
% 2.22/1.87 inference(rewrite,[status(thm)],[])).
% 2.22/1.87 tff(1247,plain,
% 2.22/1.87 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a217) | c0_1(a217) | c2_1(a217))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | c0_1(a217)))),
% 2.22/1.87 inference(monotonicity,[status(thm)],[1246])).
% 2.22/1.87 tff(1248,plain,
% 2.22/1.87 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a217) | c0_1(a217) | c2_1(a217))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | c0_1(a217))),
% 2.22/1.87 inference(transitivity,[status(thm)],[1247, 1245])).
% 2.22/1.87 tff(1249,plain,
% 2.22/1.87 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a217) | c0_1(a217) | c2_1(a217))),
% 2.22/1.87 inference(quant_inst,[status(thm)],[])).
% 2.22/1.87 tff(1250,plain,
% 2.22/1.87 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | c0_1(a217)),
% 2.22/1.87 inference(modus_ponens,[status(thm)],[1249, 1248])).
% 2.22/1.87 tff(1251,plain,
% 2.22/1.87 (hskp9 | c2_1(a217) | (~c3_1(a215)) | c0_1(a217)),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[1250, 122, 167, 1166, 166, 989])).
% 2.22/1.87 tff(1252,plain,
% 2.22/1.87 (~c3_1(a215)),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[1251, 1244, 1165, 1233])).
% 2.22/1.87 tff(1253,assumption,(~hskp16), introduced(assumption)).
% 2.22/1.87 tff(1254,plain,
% 2.22/1.87 (hskp13),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[1044, 574, 1253])).
% 2.22/1.87 tff(1255,plain,
% 2.22/1.87 (c3_1(a239)),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[942, 1254])).
% 2.22/1.87 tff(1256,plain,
% 2.22/1.87 (c2_1(a239)),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[953, 1254])).
% 2.22/1.87 tff(1257,plain,
% 2.22/1.87 (~c3_1(a215)),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[1251, 23, 1165, 1233])).
% 2.22/1.87 tff(1258,plain,
% 2.22/1.87 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)))),
% 2.22/1.87 inference(rewrite,[status(thm)],[])).
% 2.22/1.87 tff(1259,plain,
% 2.22/1.87 ((hskp21 | hskp12 | (~ndr1_0) | c1_1(a215) | c3_1(a215) | (~c2_1(a215))) <=> (hskp21 | hskp12 | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)))),
% 2.22/1.87 inference(rewrite,[status(thm)],[])).
% 2.22/1.87 tff(1260,plain,
% 2.22/1.87 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a215) | c3_1(a215) | (~c2_1(a215)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215))))),
% 2.22/1.87 inference(monotonicity,[status(thm)],[1259])).
% 2.22/1.87 tff(1261,plain,
% 2.22/1.87 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a215) | c3_1(a215) | (~c2_1(a215)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)))),
% 2.22/1.87 inference(transitivity,[status(thm)],[1260, 1258])).
% 2.22/1.87 tff(1262,plain,
% 2.22/1.87 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a215) | c3_1(a215) | (~c2_1(a215)))),
% 2.22/1.87 inference(quant_inst,[status(thm)],[])).
% 2.22/1.87 tff(1263,plain,
% 2.22/1.87 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215))),
% 2.22/1.87 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 2.22/1.87 tff(1264,plain,
% 2.22/1.87 (hskp21 | hskp12 | c3_1(a215)),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[1263, 122, 167, 165, 804])).
% 2.22/1.87 tff(1265,plain,
% 2.22/1.87 (hskp21),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[1264, 574, 1257])).
% 2.22/1.87 tff(1266,plain,
% 2.22/1.87 (c3_1(a259)),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[867, 1265])).
% 2.22/1.87 tff(1267,plain,
% 2.22/1.87 (c0_1(a259)),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[855, 1265])).
% 2.22/1.87 tff(1268,plain,
% 2.22/1.87 (~c0_1(a239)),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[961, 122, 1267, 1266, 1256, 1255, 167, 857, 166, 165, 931])).
% 2.22/1.87 tff(1269,plain,
% 2.22/1.87 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c0_1(a217) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c0_1(a217) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)))),
% 2.22/1.87 inference(rewrite,[status(thm)],[])).
% 2.22/1.87 tff(1270,plain,
% 2.22/1.87 ((hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a217) | c0_1(a217) | c2_1(a217)) <=> (hskp9 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c0_1(a217) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)))),
% 2.22/1.87 inference(rewrite,[status(thm)],[])).
% 2.22/1.87 tff(1271,plain,
% 2.22/1.87 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a217) | c0_1(a217) | c2_1(a217))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c0_1(a217) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239))))),
% 2.22/1.87 inference(monotonicity,[status(thm)],[1270])).
% 2.22/1.87 tff(1272,plain,
% 2.22/1.87 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a217) | c0_1(a217) | c2_1(a217))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c0_1(a217) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)))),
% 2.22/1.87 inference(transitivity,[status(thm)],[1271, 1269])).
% 2.22/1.87 tff(1273,plain,
% 2.22/1.87 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a217) | c0_1(a217) | c2_1(a217))),
% 2.22/1.87 inference(quant_inst,[status(thm)],[])).
% 2.22/1.87 tff(1274,plain,
% 2.22/1.87 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c0_1(a217) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239))),
% 2.22/1.87 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 2.22/1.87 tff(1275,plain,
% 2.22/1.87 ($false),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[1274, 122, 23, 1256, 1255, 1165, 1166, 989, 1233, 1268])).
% 2.22/1.87 tff(1276,plain,(hskp12 | hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a217) | (~c2_1(a215)) | c2_1(a259) | c0_1(a215) | c1_1(a215) | hskp16), inference(lemma,lemma(discharge,[]))).
% 2.22/1.87 tff(1277,plain,
% 2.22/1.87 (hskp16),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[1276, 1244, 1165, 1166, 1233, 167, 574, 166, 165, 1240])).
% 2.22/1.87 tff(1278,plain,
% 2.22/1.87 (~c3_1(a245)),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[502, 1277])).
% 2.22/1.87 tff(1279,plain,
% 2.22/1.87 (~c1_1(a245)),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[508, 1277])).
% 2.22/1.87 tff(1280,plain,
% 2.22/1.87 (c0_1(a245)),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[519, 1277])).
% 2.22/1.87 tff(1281,plain,
% 2.22/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.22/1.87 inference(rewrite,[status(thm)],[])).
% 2.22/1.87 tff(1282,plain,
% 2.22/1.87 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245))) <=> (c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.22/1.87 inference(rewrite,[status(thm)],[])).
% 2.22/1.87 tff(1283,plain,
% 2.22/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 2.22/1.87 inference(monotonicity,[status(thm)],[1282])).
% 2.22/1.87 tff(1284,plain,
% 2.22/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.22/1.87 inference(transitivity,[status(thm)],[1283, 1281])).
% 2.22/1.87 tff(1285,plain,
% 2.22/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))),
% 2.22/1.87 inference(quant_inst,[status(thm)],[])).
% 2.22/1.87 tff(1286,plain,
% 2.22/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259))),
% 2.22/1.87 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 2.22/1.87 tff(1287,plain,
% 2.22/1.87 ($false),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[1286, 122, 1241, 1243, 1280, 167, 1240, 1279, 1278, 165, 22, 1252])).
% 2.22/1.87 tff(1288,plain,(hskp12 | (~c2_1(a215)) | c1_1(a215) | c2_1(a217) | c3_1(a217) | c0_1(a217) | c0_1(a215) | (~c2_1(a213)) | c1_1(a213) | c3_1(a213) | (~c1_1(a248)) | (~c3_1(a248)) | c2_1(a248)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.87 tff(1289,plain,
% 2.22/1.87 ($false),
% 2.22/1.87 inference(unit_resolution,[status(thm)],[1288, 1237, 1236, 165, 1165, 1166, 167, 166, 574, 1233, 1235, 705, 704, 703])).
% 2.22/1.88 tff(1290,plain,(c0_1(a217) | c1_1(a215) | c2_1(a217) | c3_1(a217) | (~c2_1(a215)) | c0_1(a215) | hskp12 | (~c1_1(a248)) | (~c3_1(a248)) | c2_1(a248) | c1_1(a217)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.88 tff(1291,plain,
% 2.22/1.88 (hskp12),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[1290, 1229, 1165, 1166, 167, 166, 165, 705, 704, 703, 1164])).
% 2.22/1.88 tff(1292,plain,
% 2.22/1.88 (~c3_1(a237)),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[762, 1291])).
% 2.22/1.88 tff(1293,plain,
% 2.22/1.88 (c2_1(a213)),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[827, 1230])).
% 2.22/1.88 tff(1294,plain,
% 2.22/1.88 (c0_1(a237)),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[629, 1291])).
% 2.22/1.88 tff(1295,plain,
% 2.22/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c3_1(a237) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c3_1(a237) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 2.22/1.88 inference(rewrite,[status(thm)],[])).
% 2.22/1.88 tff(1296,plain,
% 2.22/1.88 (((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237))) <=> (c2_1(a248) | c3_1(a237) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 2.22/1.88 inference(rewrite,[status(thm)],[])).
% 2.22/1.88 tff(1297,plain,
% 2.22/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c3_1(a237) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248))))),
% 2.22/1.88 inference(monotonicity,[status(thm)],[1296])).
% 2.22/1.88 tff(1298,plain,
% 2.22/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c3_1(a237) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 2.22/1.88 inference(transitivity,[status(thm)],[1297, 1295])).
% 2.22/1.88 tff(1299,plain,
% 2.22/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))),
% 2.22/1.88 inference(quant_inst,[status(thm)],[])).
% 2.22/1.88 tff(1300,plain,
% 2.22/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c3_1(a237) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248))),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 2.22/1.88 tff(1301,plain,
% 2.22/1.88 (c1_1(a237)),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[1300, 122, 704, 1294, 1293, 703, 1292, 1232, 1231, 22, 829])).
% 2.22/1.88 tff(1302,plain,
% 2.22/1.88 ($false),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[791, 122, 1294, 833, 167, 1292, 832, 831, 166, 165, 782, 1301])).
% 2.22/1.88 tff(1303,plain,(c1_1(a217) | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | (~c3_1(a248)) | c2_1(a248) | c2_1(a217) | c3_1(a217) | (~c1_1(a248)) | hskp18), inference(lemma,lemma(discharge,[]))).
% 2.22/1.88 tff(1304,plain,
% 2.22/1.88 ($false),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[1303, 1163, 1162, 724, 723, 701, 690, 725, 1161, 684, 650])).
% 2.22/1.88 tff(1305,plain,(hskp27 | hskp18), inference(lemma,lemma(discharge,[]))).
% 2.22/1.88 tff(1306,plain,
% 2.22/1.88 (hskp27),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[1305, 650])).
% 2.22/1.88 tff(1307,plain,
% 2.22/1.88 (((~hskp27) | c3_1(a261)) <=> ((~hskp27) | c3_1(a261))),
% 2.22/1.88 inference(rewrite,[status(thm)],[])).
% 2.22/1.88 tff(1308,axiom,((~hskp27) | c3_1(a261)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 2.22/1.88 tff(1309,plain,
% 2.22/1.88 ((~hskp27) | c3_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1308, 1307])).
% 2.22/1.88 tff(1310,plain,
% 2.22/1.88 ((~hskp27) | c3_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1309, 1307])).
% 2.22/1.88 tff(1311,plain,
% 2.22/1.88 ((~hskp27) | c3_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1310, 1307])).
% 2.22/1.88 tff(1312,plain,
% 2.22/1.88 ((~hskp27) | c3_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1311, 1307])).
% 2.22/1.88 tff(1313,plain,
% 2.22/1.88 ((~hskp27) | c3_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1312, 1307])).
% 2.22/1.88 tff(1314,plain,
% 2.22/1.88 ((~hskp27) | c3_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1313, 1307])).
% 2.22/1.88 tff(1315,plain,
% 2.22/1.88 ((~hskp27) | c3_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1314, 1307])).
% 2.22/1.88 tff(1316,plain,
% 2.22/1.88 ((~hskp27) | c3_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1315, 1307])).
% 2.22/1.88 tff(1317,plain,
% 2.22/1.88 (c3_1(a261)),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[1316, 1306])).
% 2.22/1.88 tff(1318,plain,
% 2.22/1.88 (((~hskp27) | c2_1(a261)) <=> ((~hskp27) | c2_1(a261))),
% 2.22/1.88 inference(rewrite,[status(thm)],[])).
% 2.22/1.88 tff(1319,axiom,((~hskp27) | c2_1(a261)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 2.22/1.88 tff(1320,plain,
% 2.22/1.88 ((~hskp27) | c2_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 2.22/1.88 tff(1321,plain,
% 2.22/1.88 ((~hskp27) | c2_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1320, 1318])).
% 2.22/1.88 tff(1322,plain,
% 2.22/1.88 ((~hskp27) | c2_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1321, 1318])).
% 2.22/1.88 tff(1323,plain,
% 2.22/1.88 ((~hskp27) | c2_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1322, 1318])).
% 2.22/1.88 tff(1324,plain,
% 2.22/1.88 ((~hskp27) | c2_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1323, 1318])).
% 2.22/1.88 tff(1325,plain,
% 2.22/1.88 ((~hskp27) | c2_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1324, 1318])).
% 2.22/1.88 tff(1326,plain,
% 2.22/1.88 ((~hskp27) | c2_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1325, 1318])).
% 2.22/1.88 tff(1327,plain,
% 2.22/1.88 ((~hskp27) | c2_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1326, 1318])).
% 2.22/1.88 tff(1328,plain,
% 2.22/1.88 (c2_1(a261)),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[1327, 1306])).
% 2.22/1.88 tff(1329,plain,
% 2.22/1.88 (((~hskp27) | c1_1(a261)) <=> ((~hskp27) | c1_1(a261))),
% 2.22/1.88 inference(rewrite,[status(thm)],[])).
% 2.22/1.88 tff(1330,axiom,((~hskp27) | c1_1(a261)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 2.22/1.88 tff(1331,plain,
% 2.22/1.88 ((~hskp27) | c1_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 2.22/1.88 tff(1332,plain,
% 2.22/1.88 ((~hskp27) | c1_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1331, 1329])).
% 2.22/1.88 tff(1333,plain,
% 2.22/1.88 ((~hskp27) | c1_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1332, 1329])).
% 2.22/1.88 tff(1334,plain,
% 2.22/1.88 ((~hskp27) | c1_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1333, 1329])).
% 2.22/1.88 tff(1335,plain,
% 2.22/1.88 ((~hskp27) | c1_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1334, 1329])).
% 2.22/1.88 tff(1336,plain,
% 2.22/1.88 ((~hskp27) | c1_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1335, 1329])).
% 2.22/1.88 tff(1337,plain,
% 2.22/1.88 ((~hskp27) | c1_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1336, 1329])).
% 2.22/1.88 tff(1338,plain,
% 2.22/1.88 ((~hskp27) | c1_1(a261)),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1337, 1329])).
% 2.22/1.88 tff(1339,plain,
% 2.22/1.88 (c1_1(a261)),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[1338, 1306])).
% 2.22/1.88 tff(1340,plain,
% 2.22/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c3_1(a261)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c3_1(a261)))),
% 2.22/1.88 inference(rewrite,[status(thm)],[])).
% 2.22/1.88 tff(1341,plain,
% 2.22/1.88 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c1_1(a261))) <=> ((~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c3_1(a261)))),
% 2.22/1.88 inference(rewrite,[status(thm)],[])).
% 2.22/1.88 tff(1342,plain,
% 2.22/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c1_1(a261)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c3_1(a261))))),
% 2.22/1.88 inference(monotonicity,[status(thm)],[1341])).
% 2.22/1.88 tff(1343,plain,
% 2.22/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c1_1(a261)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c3_1(a261)))),
% 2.22/1.88 inference(transitivity,[status(thm)],[1342, 1340])).
% 2.22/1.88 tff(1344,plain,
% 2.22/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c1_1(a261)))),
% 2.22/1.88 inference(quant_inst,[status(thm)],[])).
% 2.22/1.88 tff(1345,plain,
% 2.22/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c3_1(a261))),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 2.22/1.88 tff(1346,plain,
% 2.22/1.88 (~c0_1(a261)),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[1345, 122, 1339, 1328, 1317, 33])).
% 2.22/1.88 tff(1347,plain,
% 2.22/1.88 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 2.22/1.88 inference(bind,[status(th)],[])).
% 2.22/1.88 tff(1348,plain,
% 2.22/1.88 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.22/1.88 inference(quant_intro,[status(thm)],[1347])).
% 2.22/1.88 tff(1349,plain,
% 2.22/1.88 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.22/1.88 inference(rewrite,[status(thm)],[])).
% 2.22/1.88 tff(1350,plain,
% 2.22/1.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 2.22/1.88 inference(bind,[status(th)],[])).
% 2.22/1.88 tff(1351,plain,
% 2.22/1.88 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.22/1.88 inference(quant_intro,[status(thm)],[1350])).
% 2.22/1.88 tff(1352,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 2.22/1.88 tff(1353,plain,
% 2.22/1.88 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 2.22/1.88 tff(1354,plain,
% 2.22/1.88 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1353, 1349])).
% 2.22/1.88 tff(1355,plain,(
% 2.22/1.88 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.22/1.88 inference(skolemize,[status(sab)],[1354])).
% 2.22/1.88 tff(1356,plain,
% 2.22/1.88 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.22/1.88 inference(modus_ponens,[status(thm)],[1355, 1348])).
% 2.22/1.88 tff(1357,assumption,(hskp5), introduced(assumption)).
% 2.22/1.88 tff(1358,plain,
% 2.22/1.88 (~c2_1(a218)),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[737, 1357])).
% 2.22/1.88 tff(1359,plain,
% 2.22/1.88 (~c1_1(a218)),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[743, 1357])).
% 2.22/1.88 tff(1360,plain,
% 2.22/1.88 (c3_1(a218)),
% 2.22/1.88 inference(unit_resolution,[status(thm)],[754, 1357])).
% 2.22/1.88 tff(1361,plain,
% 2.22/1.88 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c3_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c3_1(a218)))),
% 2.22/1.89 inference(rewrite,[status(thm)],[])).
% 2.22/1.89 tff(1362,plain,
% 2.22/1.89 ((hskp15 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | (~c3_1(a218)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261))) <=> (hskp15 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c3_1(a218)))),
% 2.22/1.89 inference(rewrite,[status(thm)],[])).
% 2.22/1.89 tff(1363,plain,
% 2.22/1.89 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | (~c3_1(a218)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c3_1(a218))))),
% 2.22/1.89 inference(monotonicity,[status(thm)],[1362])).
% 2.22/1.89 tff(1364,plain,
% 2.22/1.89 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | (~c3_1(a218)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c3_1(a218)))),
% 2.22/1.89 inference(transitivity,[status(thm)],[1363, 1361])).
% 2.22/1.89 tff(1365,plain,
% 2.22/1.89 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | (~c3_1(a218)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))),
% 2.22/1.89 inference(quant_inst,[status(thm)],[])).
% 2.22/1.89 tff(1366,plain,
% 2.22/1.89 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c3_1(a218))),
% 2.22/1.89 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 2.22/1.89 tff(1367,plain,
% 2.22/1.89 (hskp15),
% 2.22/1.89 inference(unit_resolution,[status(thm)],[1366, 122, 1339, 1328, 1360, 1359, 1358, 1356, 1346])).
% 2.22/1.89 tff(1368,plain,
% 2.22/1.89 (~c2_1(a242)),
% 2.22/1.89 inference(unit_resolution,[status(thm)],[416, 1367])).
% 2.22/1.89 tff(1369,plain,
% 2.22/1.89 (~c0_1(a242)),
% 2.22/1.89 inference(unit_resolution,[status(thm)],[450, 1367])).
% 2.22/1.89 tff(1370,plain,
% 2.22/1.89 (c1_1(a242)),
% 2.22/1.89 inference(unit_resolution,[status(thm)],[427, 1367])).
% 2.22/1.89 tff(1371,plain,
% 2.22/1.89 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)))),
% 2.22/1.89 inference(rewrite,[status(thm)],[])).
% 2.22/1.89 tff(1372,plain,
% 2.22/1.89 ((hskp18 | (~ndr1_0) | c2_1(a242) | (~c3_1(a242)) | (~c1_1(a242)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242))) <=> (hskp18 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)))),
% 2.22/1.89 inference(rewrite,[status(thm)],[])).
% 2.22/1.89 tff(1373,plain,
% 2.22/1.89 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a242) | (~c3_1(a242)) | (~c1_1(a242)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242))))),
% 2.22/1.89 inference(monotonicity,[status(thm)],[1372])).
% 2.22/1.89 tff(1374,plain,
% 2.22/1.89 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a242) | (~c3_1(a242)) | (~c1_1(a242)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)))),
% 2.22/1.89 inference(transitivity,[status(thm)],[1373, 1371])).
% 2.22/1.89 tff(1375,plain,
% 2.22/1.89 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a242) | (~c3_1(a242)) | (~c1_1(a242)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))),
% 2.22/1.89 inference(quant_inst,[status(thm)],[])).
% 2.22/1.89 tff(1376,plain,
% 2.22/1.89 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242))),
% 2.22/1.89 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 2.22/1.89 tff(1377,plain,
% 2.22/1.89 (~c3_1(a242)),
% 2.22/1.89 inference(unit_resolution,[status(thm)],[1376, 122, 650, 1370, 1369, 1368, 672])).
% 2.22/1.89 tff(1378,plain,
% 2.22/1.89 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 2.22/1.89 inference(bind,[status(th)],[])).
% 2.22/1.89 tff(1379,plain,
% 2.22/1.89 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.89 inference(quant_intro,[status(thm)],[1378])).
% 2.22/1.89 tff(1380,plain,
% 2.22/1.89 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.89 inference(rewrite,[status(thm)],[])).
% 2.22/1.89 tff(1381,plain,
% 2.22/1.89 (^[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)) | (~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))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~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))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~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))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 2.22/1.89 inference(bind,[status(th)],[])).
% 2.22/1.89 tff(1382,plain,
% 2.22/1.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.89 inference(quant_intro,[status(thm)],[1381])).
% 2.22/1.89 tff(1383,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 2.22/1.89 tff(1384,plain,
% 2.22/1.89 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.89 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 2.22/1.89 tff(1385,plain,
% 2.22/1.89 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.89 inference(modus_ponens,[status(thm)],[1384, 1380])).
% 2.22/1.89 tff(1386,plain,(
% 2.22/1.89 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.89 inference(skolemize,[status(sab)],[1385])).
% 2.22/1.89 tff(1387,plain,
% 2.22/1.89 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.89 inference(modus_ponens,[status(thm)],[1386, 1379])).
% 2.22/1.89 tff(1388,plain,
% 2.22/1.89 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | (~c1_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | (~c1_1(a259)))),
% 2.22/1.89 inference(rewrite,[status(thm)],[])).
% 2.22/1.89 tff(1389,plain,
% 2.22/1.89 ((hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261))) <=> (hskp18 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | (~c1_1(a259)))),
% 2.22/1.89 inference(rewrite,[status(thm)],[])).
% 2.22/1.89 tff(1390,plain,
% 2.22/1.89 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | (~c1_1(a259))))),
% 2.22/1.89 inference(monotonicity,[status(thm)],[1389])).
% 2.22/1.89 tff(1391,plain,
% 2.22/1.89 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | (~c1_1(a259)))),
% 2.22/1.89 inference(transitivity,[status(thm)],[1390, 1388])).
% 2.22/1.89 tff(1392,plain,
% 2.22/1.89 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))),
% 2.22/1.89 inference(quant_inst,[status(thm)],[])).
% 2.22/1.89 tff(1393,plain,
% 2.22/1.89 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | (~c1_1(a259))),
% 2.22/1.90 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 2.22/1.90 tff(1394,plain,
% 2.22/1.90 (~c1_1(a259)),
% 2.22/1.90 inference(unit_resolution,[status(thm)],[1393, 122, 650, 1339, 1317, 1243, 1240, 672, 1346])).
% 2.22/1.90 tff(1395,plain,
% 2.22/1.90 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 2.22/1.90 inference(bind,[status(th)],[])).
% 2.22/1.90 tff(1396,plain,
% 2.22/1.90 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.22/1.90 inference(quant_intro,[status(thm)],[1395])).
% 2.22/1.90 tff(1397,plain,
% 2.22/1.90 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.22/1.90 inference(rewrite,[status(thm)],[])).
% 2.22/1.90 tff(1398,plain,
% 2.22/1.90 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 2.22/1.90 inference(bind,[status(th)],[])).
% 2.22/1.90 tff(1399,plain,
% 2.22/1.90 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.22/1.90 inference(quant_intro,[status(thm)],[1398])).
% 2.22/1.90 tff(1400,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 2.22/1.90 tff(1401,plain,
% 2.22/1.90 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.22/1.90 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 2.22/1.90 tff(1402,plain,
% 2.22/1.90 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.22/1.90 inference(modus_ponens,[status(thm)],[1401, 1397])).
% 2.22/1.90 tff(1403,plain,(
% 2.22/1.90 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.22/1.90 inference(skolemize,[status(sab)],[1402])).
% 2.22/1.90 tff(1404,plain,
% 2.22/1.90 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.22/1.90 inference(modus_ponens,[status(thm)],[1403, 1396])).
% 2.22/1.90 tff(1405,plain,
% 2.22/1.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | c1_1(a259))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | c1_1(a259))),
% 2.22/1.90 inference(rewrite,[status(thm)],[])).
% 2.22/1.90 tff(1406,plain,
% 2.22/1.90 ((hskp10 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c3_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261))) <=> (hskp10 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | c1_1(a259))),
% 2.22/1.90 inference(rewrite,[status(thm)],[])).
% 2.22/1.90 tff(1407,plain,
% 2.22/1.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c3_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | c1_1(a259)))),
% 2.22/1.90 inference(monotonicity,[status(thm)],[1406])).
% 2.22/1.90 tff(1408,plain,
% 2.22/1.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c3_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | c1_1(a259))),
% 2.22/1.90 inference(transitivity,[status(thm)],[1407, 1405])).
% 2.22/1.90 tff(1409,plain,
% 2.22/1.90 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c3_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))),
% 2.22/1.90 inference(quant_inst,[status(thm)],[])).
% 2.22/1.90 tff(1410,plain,
% 2.22/1.90 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | c1_1(a259)),
% 2.22/1.90 inference(modus_ponens,[status(thm)],[1409, 1408])).
% 2.22/1.90 tff(1411,plain,
% 2.22/1.90 (hskp10),
% 2.22/1.90 inference(unit_resolution,[status(thm)],[1410, 122, 1339, 1317, 1243, 1240, 1404, 1394, 1346])).
% 2.22/1.90 tff(1412,plain,
% 2.22/1.90 (((~hskp10) | (~c0_1(a231))) <=> ((~hskp10) | (~c0_1(a231)))),
% 2.22/1.90 inference(rewrite,[status(thm)],[])).
% 2.22/1.90 tff(1413,plain,
% 2.22/1.90 (((~c0_1(a231)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a231)))),
% 2.22/1.90 inference(rewrite,[status(thm)],[])).
% 2.22/1.90 tff(1414,axiom,((~c0_1(a231)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 2.22/1.90 tff(1415,plain,
% 2.22/1.90 ((~hskp10) | (~c0_1(a231))),
% 2.22/1.90 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 2.22/1.90 tff(1416,plain,
% 2.22/1.90 ((~hskp10) | (~c0_1(a231))),
% 2.22/1.90 inference(modus_ponens,[status(thm)],[1415, 1412])).
% 2.22/1.90 tff(1417,plain,
% 2.22/1.90 (~c0_1(a231)),
% 2.22/1.90 inference(unit_resolution,[status(thm)],[1416, 1411])).
% 2.22/1.90 tff(1418,plain,
% 2.22/1.90 (^[U: $i] : refl((hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 2.22/1.90 inference(bind,[status(th)],[])).
% 2.22/1.90 tff(1419,plain,
% 2.22/1.90 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.22/1.90 inference(quant_intro,[status(thm)],[1418])).
% 2.22/1.90 tff(1420,plain,
% 2.22/1.90 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.22/1.90 inference(rewrite,[status(thm)],[])).
% 2.22/1.90 tff(1421,plain,
% 2.22/1.90 (^[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)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17) <=> ((hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17))), rewrite(((hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17) <=> (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 2.22/1.90 inference(bind,[status(th)],[])).
% 2.22/1.90 tff(1422,plain,
% 2.22/1.90 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17) <=> ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.22/1.90 inference(quant_intro,[status(thm)],[1421])).
% 2.22/1.90 tff(1423,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 2.22/1.90 tff(1424,plain,
% 2.22/1.90 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.22/1.90 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 2.22/1.90 tff(1425,plain,
% 2.22/1.90 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.22/1.90 inference(modus_ponens,[status(thm)],[1424, 1420])).
% 2.22/1.90 tff(1426,plain,(
% 2.22/1.90 ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.22/1.90 inference(skolemize,[status(sab)],[1425])).
% 2.22/1.90 tff(1427,plain,
% 2.22/1.90 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.22/1.90 inference(modus_ponens,[status(thm)],[1426, 1419])).
% 2.22/1.90 tff(1428,plain,
% 2.22/1.90 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))),
% 2.22/1.90 inference(rewrite,[status(thm)],[])).
% 2.22/1.90 tff(1429,plain,
% 2.22/1.90 ((hskp17 | hskp12 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259))) <=> (hskp17 | hskp12 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))),
% 2.22/1.90 inference(rewrite,[status(thm)],[])).
% 2.22/1.91 tff(1430,plain,
% 2.22/1.91 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259)))),
% 2.22/1.91 inference(monotonicity,[status(thm)],[1429])).
% 2.22/1.91 tff(1431,plain,
% 2.22/1.91 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))),
% 2.22/1.91 inference(transitivity,[status(thm)],[1430, 1428])).
% 2.22/1.91 tff(1432,plain,
% 2.22/1.91 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))),
% 2.22/1.91 inference(quant_inst,[status(thm)],[])).
% 2.22/1.91 tff(1433,plain,
% 2.22/1.91 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259)),
% 2.22/1.91 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 2.22/1.91 tff(1434,plain,
% 2.22/1.91 (hskp17 | c1_1(a259)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1433, 122, 574, 1241, 1240, 1427])).
% 2.22/1.91 tff(1435,plain,
% 2.22/1.91 (hskp17),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1434, 1394])).
% 2.22/1.91 tff(1436,plain,
% 2.22/1.91 (~c2_1(a248)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[689, 1435])).
% 2.22/1.91 tff(1437,plain,
% 2.22/1.91 (((~hskp10) | c3_1(a231)) <=> ((~hskp10) | c3_1(a231))),
% 2.22/1.91 inference(rewrite,[status(thm)],[])).
% 2.22/1.91 tff(1438,axiom,((~hskp10) | c3_1(a231)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 2.22/1.91 tff(1439,plain,
% 2.22/1.91 ((~hskp10) | c3_1(a231)),
% 2.22/1.91 inference(modus_ponens,[status(thm)],[1438, 1437])).
% 2.22/1.91 tff(1440,plain,
% 2.22/1.91 ((~hskp10) | c3_1(a231)),
% 2.22/1.91 inference(modus_ponens,[status(thm)],[1439, 1437])).
% 2.22/1.91 tff(1441,plain,
% 2.22/1.91 ((~hskp10) | c3_1(a231)),
% 2.22/1.91 inference(modus_ponens,[status(thm)],[1440, 1437])).
% 2.22/1.91 tff(1442,plain,
% 2.22/1.91 ((~hskp10) | c3_1(a231)),
% 2.22/1.91 inference(modus_ponens,[status(thm)],[1441, 1437])).
% 2.22/1.91 tff(1443,plain,
% 2.22/1.91 ((~hskp10) | c3_1(a231)),
% 2.22/1.91 inference(modus_ponens,[status(thm)],[1442, 1437])).
% 2.22/1.91 tff(1444,plain,
% 2.22/1.91 ((~hskp10) | c3_1(a231)),
% 2.22/1.91 inference(modus_ponens,[status(thm)],[1443, 1437])).
% 2.22/1.91 tff(1445,plain,
% 2.22/1.91 ((~hskp10) | c3_1(a231)),
% 2.22/1.91 inference(modus_ponens,[status(thm)],[1444, 1437])).
% 2.22/1.91 tff(1446,plain,
% 2.22/1.91 ((~hskp10) | c3_1(a231)),
% 2.22/1.91 inference(modus_ponens,[status(thm)],[1445, 1437])).
% 2.22/1.91 tff(1447,plain,
% 2.22/1.91 (c3_1(a231)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1446, 1411])).
% 2.22/1.91 tff(1448,plain,
% 2.22/1.91 (c1_1(a231)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[661, 1411])).
% 2.22/1.91 tff(1449,plain,
% 2.22/1.91 (c3_1(a248)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[700, 1435])).
% 2.22/1.91 tff(1450,plain,
% 2.22/1.91 (c1_1(a248)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[683, 1435])).
% 2.22/1.91 tff(1451,plain,
% 2.22/1.91 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a248) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a248)) | (~c1_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a248) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a248)) | (~c1_1(a248)))),
% 2.22/1.91 inference(rewrite,[status(thm)],[])).
% 2.22/1.91 tff(1452,plain,
% 2.22/1.91 ((hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231))) <=> (hskp18 | c2_1(a248) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a248)) | (~c1_1(a248)))),
% 2.22/1.91 inference(rewrite,[status(thm)],[])).
% 2.22/1.91 tff(1453,plain,
% 2.22/1.91 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a248) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a248)) | (~c1_1(a248))))),
% 2.22/1.91 inference(monotonicity,[status(thm)],[1452])).
% 2.22/1.91 tff(1454,plain,
% 2.22/1.91 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a248) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a248)) | (~c1_1(a248)))),
% 2.22/1.91 inference(transitivity,[status(thm)],[1453, 1451])).
% 2.22/1.91 tff(1455,plain,
% 2.22/1.91 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))),
% 2.22/1.91 inference(quant_inst,[status(thm)],[])).
% 2.22/1.91 tff(1456,plain,
% 2.22/1.91 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a248) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a248)) | (~c1_1(a248))),
% 2.22/1.91 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 2.22/1.91 tff(1457,plain,
% 2.22/1.91 ($false),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1456, 122, 650, 1450, 1449, 1448, 1447, 1436, 1417, 672])).
% 2.22/1.91 tff(1458,plain,(hskp12 | hskp18 | (~c2_1(a213)) | c1_1(a213) | c3_1(a213)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.91 tff(1459,plain,
% 2.22/1.91 ($false),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1458, 817, 828, 650, 574, 811])).
% 2.22/1.91 tff(1460,plain,((~hskp0) | hskp18 | hskp12), inference(lemma,lemma(discharge,[]))).
% 2.22/1.91 tff(1461,plain,
% 2.22/1.91 (~hskp0),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1460, 574, 650])).
% 2.22/1.91 tff(1462,plain,
% 2.22/1.91 (hskp1),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1081, 1461, 574])).
% 2.22/1.91 tff(1463,plain,
% 2.22/1.91 (~c3_1(a214)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1087, 1462])).
% 2.22/1.91 tff(1464,plain,
% 2.22/1.91 (~c0_1(a214)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1150, 1462])).
% 2.22/1.91 tff(1465,plain,
% 2.22/1.91 (c2_1(a214)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1136, 1462])).
% 2.22/1.91 tff(1466,plain,
% 2.22/1.91 (~c1_1(a214)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1157, 122, 574, 1465, 1464, 1463, 44])).
% 2.22/1.91 tff(1467,plain,
% 2.22/1.91 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)))),
% 2.22/1.91 inference(rewrite,[status(thm)],[])).
% 2.22/1.91 tff(1468,plain,
% 2.22/1.91 ((hskp21 | hskp12 | (~ndr1_0) | c1_1(a214) | c3_1(a214) | (~c2_1(a214))) <=> (hskp21 | hskp12 | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)))),
% 2.22/1.91 inference(rewrite,[status(thm)],[])).
% 2.22/1.91 tff(1469,plain,
% 2.22/1.91 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a214) | c3_1(a214) | (~c2_1(a214)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214))))),
% 2.22/1.91 inference(monotonicity,[status(thm)],[1468])).
% 2.22/1.91 tff(1470,plain,
% 2.22/1.91 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a214) | c3_1(a214) | (~c2_1(a214)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)))),
% 2.22/1.91 inference(transitivity,[status(thm)],[1469, 1467])).
% 2.22/1.91 tff(1471,plain,
% 2.22/1.91 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a214) | c3_1(a214) | (~c2_1(a214)))),
% 2.22/1.91 inference(quant_inst,[status(thm)],[])).
% 2.22/1.91 tff(1472,plain,
% 2.22/1.91 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214))),
% 2.22/1.91 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 2.22/1.91 tff(1473,plain,
% 2.22/1.91 (hskp21 | c1_1(a214)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1472, 122, 574, 1465, 1463, 804])).
% 2.22/1.91 tff(1474,plain,
% 2.22/1.91 (hskp21),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1473, 1466])).
% 2.22/1.91 tff(1475,plain,
% 2.22/1.91 (~c2_1(a259)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1062, 1474])).
% 2.22/1.91 tff(1476,plain,
% 2.22/1.91 (c3_1(a259)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[867, 1474])).
% 2.22/1.91 tff(1477,plain,
% 2.22/1.91 (~c1_1(a259)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1393, 122, 650, 1339, 1317, 1476, 1475, 672, 1346])).
% 2.22/1.91 tff(1478,plain,
% 2.22/1.91 (c0_1(a259)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[855, 1474])).
% 2.22/1.91 tff(1479,plain,
% 2.22/1.91 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))),
% 2.22/1.91 inference(rewrite,[status(thm)],[])).
% 2.22/1.91 tff(1480,plain,
% 2.22/1.91 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259))) <=> (hskp19 | hskp18 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))),
% 2.22/1.91 inference(rewrite,[status(thm)],[])).
% 2.22/1.91 tff(1481,plain,
% 2.22/1.91 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259)))),
% 2.22/1.91 inference(monotonicity,[status(thm)],[1480])).
% 2.22/1.91 tff(1482,plain,
% 2.22/1.91 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))),
% 2.22/1.91 inference(transitivity,[status(thm)],[1481, 1479])).
% 2.22/1.91 tff(1483,plain,
% 2.22/1.91 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))),
% 2.22/1.91 inference(quant_inst,[status(thm)],[])).
% 2.22/1.91 tff(1484,plain,
% 2.22/1.91 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259)),
% 2.22/1.91 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 2.22/1.91 tff(1485,plain,
% 2.22/1.91 (hskp19 | c1_1(a259)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1484, 122, 650, 1478, 1475, 1177])).
% 2.22/1.91 tff(1486,plain,
% 2.22/1.91 (hskp19),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1485, 1477])).
% 2.22/1.91 tff(1487,plain,
% 2.22/1.91 (~c1_1(a255)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[294, 1486])).
% 2.22/1.91 tff(1488,plain,
% 2.22/1.91 (~c0_1(a255)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[300, 1486])).
% 2.22/1.91 tff(1489,plain,
% 2.22/1.91 (c2_1(a255)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1196, 122, 1461, 1488, 1487, 1098])).
% 2.22/1.91 tff(1490,plain,
% 2.22/1.91 (hskp17 | c1_1(a259)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1433, 122, 574, 1478, 1475, 1427])).
% 2.22/1.91 tff(1491,plain,
% 2.22/1.91 (hskp17),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[1490, 1477])).
% 2.22/1.91 tff(1492,plain,
% 2.22/1.91 (~c2_1(a248)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[689, 1491])).
% 2.22/1.91 tff(1493,plain,
% 2.22/1.91 (~c3_1(a255)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[288, 1486])).
% 2.22/1.91 tff(1494,plain,
% 2.22/1.91 (c3_1(a248)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[700, 1491])).
% 2.22/1.91 tff(1495,plain,
% 2.22/1.91 (c1_1(a248)),
% 2.22/1.91 inference(unit_resolution,[status(thm)],[683, 1491])).
% 2.22/1.91 tff(1496,plain,
% 2.22/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a255) | c3_1(a255) | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c2_1(a255)) | (~c0_1(a259)) | c1_1(a259))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a255) | c3_1(a255) | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c2_1(a255)) | (~c0_1(a259)) | c1_1(a259))),
% 2.22/1.92 inference(rewrite,[status(thm)],[])).
% 2.22/1.92 tff(1497,plain,
% 2.22/1.92 (((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259))) <=> (c2_1(a259) | c1_1(a255) | c3_1(a255) | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c2_1(a255)) | (~c0_1(a259)) | c1_1(a259))),
% 2.22/1.92 inference(rewrite,[status(thm)],[])).
% 2.22/1.92 tff(1498,plain,
% 2.22/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a255) | c3_1(a255) | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c2_1(a255)) | (~c0_1(a259)) | c1_1(a259)))),
% 2.22/1.92 inference(monotonicity,[status(thm)],[1497])).
% 2.22/1.92 tff(1499,plain,
% 2.22/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a255) | c3_1(a255) | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c2_1(a255)) | (~c0_1(a259)) | c1_1(a259))),
% 2.22/1.92 inference(transitivity,[status(thm)],[1498, 1496])).
% 2.22/1.92 tff(1500,plain,
% 2.22/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))),
% 2.22/1.92 inference(quant_inst,[status(thm)],[])).
% 2.22/1.92 tff(1501,plain,
% 2.22/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a255) | c3_1(a255) | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c2_1(a255)) | (~c0_1(a259)) | c1_1(a259)),
% 2.22/1.92 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 2.22/1.92 tff(1502,plain,
% 2.22/1.92 ($false),
% 2.22/1.92 inference(unit_resolution,[status(thm)],[1501, 122, 1478, 1495, 1494, 1475, 1487, 1493, 1492, 878, 1477, 1489])).
% 2.22/1.92 tff(1503,plain,(hskp12 | hskp18), inference(lemma,lemma(discharge,[]))).
% 2.22/1.92 tff(1504,plain,
% 2.22/1.92 (hskp12),
% 2.22/1.92 inference(unit_resolution,[status(thm)],[1503, 650])).
% 2.22/1.92 tff(1505,plain,
% 2.22/1.92 (~c3_1(a237)),
% 2.22/1.92 inference(unit_resolution,[status(thm)],[762, 1504])).
% 2.22/1.92 tff(1506,plain,
% 2.22/1.92 (c2_1(a237)),
% 2.22/1.92 inference(unit_resolution,[status(thm)],[607, 1504])).
% 2.22/1.92 tff(1507,plain,
% 2.22/1.92 (c0_1(a237)),
% 2.22/1.92 inference(unit_resolution,[status(thm)],[629, 1504])).
% 2.22/1.92 tff(1508,plain,
% 2.22/1.92 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c3_1(a237) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.22/1.92 inference(rewrite,[status(thm)],[])).
% 2.22/1.92 tff(1509,plain,
% 2.22/1.92 ((hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218))) <=> (hskp18 | c3_1(a237) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.22/1.92 inference(rewrite,[status(thm)],[])).
% 2.22/1.92 tff(1510,plain,
% 2.22/1.92 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c3_1(a237) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a237)) | (~c0_1(a237))))),
% 2.22/1.92 inference(monotonicity,[status(thm)],[1509])).
% 2.22/1.92 tff(1511,plain,
% 2.22/1.92 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.22/1.92 inference(transitivity,[status(thm)],[1510, 1508])).
% 2.22/1.92 tff(1512,plain,
% 2.22/1.92 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218)))),
% 2.22/1.92 inference(quant_inst,[status(thm)],[])).
% 2.22/1.92 tff(1513,plain,
% 2.22/1.92 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a237)) | (~c0_1(a237))),
% 2.22/1.92 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 2.22/1.92 tff(1514,plain,
% 2.22/1.92 (~c0_1(a218)),
% 2.22/1.92 inference(unit_resolution,[status(thm)],[1513, 122, 650, 1507, 1506, 1360, 1505, 1359, 1387])).
% 2.22/1.92 tff(1515,plain,
% 2.22/1.92 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 2.22/1.92 inference(bind,[status(th)],[])).
% 2.22/1.92 tff(1516,plain,
% 2.22/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 2.22/1.92 inference(quant_intro,[status(thm)],[1515])).
% 2.22/1.92 tff(1517,plain,
% 2.22/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 2.22/1.92 inference(rewrite,[status(thm)],[])).
% 2.22/1.92 tff(1518,plain,
% 2.22/1.92 (^[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)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c0_1(W))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c0_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 2.22/1.92 inference(bind,[status(th)],[])).
% 2.22/1.92 tff(1519,plain,
% 2.22/1.92 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 2.22/1.92 inference(quant_intro,[status(thm)],[1518])).
% 2.22/1.92 tff(1520,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 2.22/1.92 tff(1521,plain,
% 2.22/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 2.22/1.92 inference(modus_ponens,[status(thm)],[1520, 1519])).
% 2.22/1.92 tff(1522,plain,
% 2.22/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 2.22/1.92 inference(modus_ponens,[status(thm)],[1521, 1517])).
% 2.22/1.92 tff(1523,plain,(
% 2.22/1.92 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 2.22/1.92 inference(skolemize,[status(sab)],[1522])).
% 2.22/1.92 tff(1524,plain,
% 2.22/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 2.22/1.92 inference(modus_ponens,[status(thm)],[1523, 1516])).
% 2.22/1.92 tff(1525,plain,
% 2.22/1.92 (hskp0),
% 2.22/1.92 inference(unit_resolution,[status(thm)],[1104, 122, 1359, 1358, 1098, 1514])).
% 2.22/1.92 tff(1526,plain,
% 2.22/1.92 (~c3_1(a213)),
% 2.22/1.92 inference(unit_resolution,[status(thm)],[810, 1525])).
% 2.22/1.92 tff(1527,plain,
% 2.22/1.92 (~c1_1(a213)),
% 2.22/1.92 inference(unit_resolution,[status(thm)],[816, 1525])).
% 2.22/1.92 tff(1528,plain,
% 2.22/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a242) | c2_1(a242) | c1_1(a218) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a218)) | c0_1(a218) | c3_1(a242))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a242) | c2_1(a242) | c1_1(a218) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a218)) | c0_1(a218) | c3_1(a242))),
% 2.22/1.92 inference(rewrite,[status(thm)],[])).
% 2.22/1.92 tff(1529,plain,
% 2.22/1.92 (((~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a242) | c2_1(a242) | c0_1(a242)) <=> (c0_1(a242) | c2_1(a242) | c1_1(a218) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a218)) | c0_1(a218) | c3_1(a242))),
% 2.22/1.92 inference(rewrite,[status(thm)],[])).
% 2.22/1.92 tff(1530,plain,
% 2.22/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a242) | c2_1(a242) | c0_1(a242))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a242) | c2_1(a242) | c1_1(a218) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a218)) | c0_1(a218) | c3_1(a242)))),
% 2.22/1.92 inference(monotonicity,[status(thm)],[1529])).
% 2.22/1.92 tff(1531,plain,
% 2.22/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a242) | c2_1(a242) | c0_1(a242))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a242) | c2_1(a242) | c1_1(a218) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a218)) | c0_1(a218) | c3_1(a242))),
% 2.22/1.92 inference(transitivity,[status(thm)],[1530, 1528])).
% 2.22/1.92 tff(1532,plain,
% 2.22/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a242) | c2_1(a242) | c0_1(a242))),
% 2.22/1.92 inference(quant_inst,[status(thm)],[])).
% 2.22/1.92 tff(1533,plain,
% 2.22/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a242) | c2_1(a242) | c1_1(a218) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a218)) | c0_1(a218) | c3_1(a242)),
% 2.22/1.92 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 2.22/1.92 tff(1534,plain,
% 2.22/1.92 (~c0_1(a213)),
% 2.22/1.92 inference(unit_resolution,[status(thm)],[1533, 122, 1360, 1369, 1368, 1359, 1527, 1526, 1524, 1514, 1377])).
% 2.22/1.92 tff(1535,plain,
% 2.22/1.92 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 2.22/1.92 inference(bind,[status(th)],[])).
% 2.22/1.92 tff(1536,plain,
% 2.22/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.22/1.92 inference(quant_intro,[status(thm)],[1535])).
% 2.22/1.92 tff(1537,plain,
% 2.22/1.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.22/1.92 inference(rewrite,[status(thm)],[])).
% 2.22/1.92 tff(1538,plain,
% 2.22/1.92 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 2.22/1.93 inference(bind,[status(th)],[])).
% 2.22/1.93 tff(1539,plain,
% 2.22/1.93 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.22/1.93 inference(quant_intro,[status(thm)],[1538])).
% 2.22/1.93 tff(1540,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 2.22/1.93 tff(1541,plain,
% 2.22/1.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.22/1.93 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 2.22/1.93 tff(1542,plain,
% 2.22/1.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.22/1.93 inference(modus_ponens,[status(thm)],[1541, 1537])).
% 2.22/1.93 tff(1543,plain,(
% 2.22/1.93 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.22/1.93 inference(skolemize,[status(sab)],[1542])).
% 2.22/1.93 tff(1544,plain,
% 2.22/1.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.22/1.93 inference(modus_ponens,[status(thm)],[1543, 1536])).
% 2.22/1.93 tff(1545,plain,
% 2.22/1.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c2_1(a242) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a242) | (~c1_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a242) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a242) | (~c1_1(a242)))),
% 2.22/1.93 inference(rewrite,[status(thm)],[])).
% 2.22/1.93 tff(1546,plain,
% 2.22/1.93 ((hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a261) | (~c3_1(a261)) | (~c2_1(a261))) <=> (hskp19 | c2_1(a242) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a242) | (~c1_1(a242)))),
% 2.22/1.93 inference(rewrite,[status(thm)],[])).
% 2.22/1.93 tff(1547,plain,
% 2.22/1.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a261) | (~c3_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c2_1(a242) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a242) | (~c1_1(a242))))),
% 2.22/1.93 inference(monotonicity,[status(thm)],[1546])).
% 2.22/1.93 tff(1548,plain,
% 2.22/1.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a261) | (~c3_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a242) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a242) | (~c1_1(a242)))),
% 2.22/1.93 inference(transitivity,[status(thm)],[1547, 1545])).
% 2.22/1.93 tff(1549,plain,
% 2.22/1.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a261) | (~c3_1(a261)) | (~c2_1(a261)))),
% 2.22/1.93 inference(quant_inst,[status(thm)],[])).
% 2.22/1.93 tff(1550,plain,
% 2.22/1.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a242) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a242) | (~c1_1(a242))),
% 2.22/1.93 inference(modus_ponens,[status(thm)],[1549, 1548])).
% 2.22/1.93 tff(1551,plain,
% 2.22/1.93 (hskp19),
% 2.22/1.93 inference(unit_resolution,[status(thm)],[1550, 122, 1328, 1317, 1370, 1368, 322, 1346, 1377])).
% 2.22/1.93 tff(1552,plain,
% 2.22/1.93 (~c1_1(a255)),
% 2.22/1.93 inference(unit_resolution,[status(thm)],[294, 1551])).
% 2.22/1.93 tff(1553,plain,
% 2.22/1.93 (~c0_1(a255)),
% 2.22/1.93 inference(unit_resolution,[status(thm)],[300, 1551])).
% 2.22/1.93 tff(1554,plain,
% 2.22/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a255)))),
% 2.22/1.93 inference(rewrite,[status(thm)],[])).
% 2.22/1.93 tff(1555,plain,
% 2.22/1.93 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255))) <=> (c0_1(a255) | c1_1(a255) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a255)))),
% 2.22/1.93 inference(rewrite,[status(thm)],[])).
% 2.22/1.93 tff(1556,plain,
% 2.22/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a255))))),
% 2.22/1.93 inference(monotonicity,[status(thm)],[1555])).
% 2.22/1.93 tff(1557,plain,
% 2.22/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a255)))),
% 2.22/1.93 inference(transitivity,[status(thm)],[1556, 1554])).
% 2.22/1.93 tff(1558,plain,
% 2.22/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))),
% 2.22/1.93 inference(quant_inst,[status(thm)],[])).
% 2.22/1.93 tff(1559,plain,
% 2.22/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a255))),
% 2.22/1.93 inference(modus_ponens,[status(thm)],[1558, 1557])).
% 2.22/1.93 tff(1560,plain,
% 2.22/1.93 (~c2_1(a255)),
% 2.22/1.93 inference(unit_resolution,[status(thm)],[1559, 122, 1339, 1328, 1317, 1360, 1553, 1552, 1358, 1544, 1514])).
% 2.22/1.93 tff(1561,plain,
% 2.22/1.93 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 2.22/1.93 inference(bind,[status(th)],[])).
% 2.22/1.93 tff(1562,plain,
% 2.22/1.93 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 2.22/1.93 inference(quant_intro,[status(thm)],[1561])).
% 2.22/1.93 tff(1563,plain,
% 2.22/1.93 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 2.22/1.93 inference(rewrite,[status(thm)],[])).
% 2.22/1.93 tff(1564,plain,
% 2.22/1.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | 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)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V)) | 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)) | c1_1(V) | c2_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_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) | c1_1(V) | c2_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_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) | c1_1(V) | c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 2.22/1.93 inference(bind,[status(th)],[])).
% 2.22/1.93 tff(1565,plain,
% 2.22/1.93 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 2.22/1.93 inference(quant_intro,[status(thm)],[1564])).
% 2.22/1.93 tff(1566,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 2.22/1.93 tff(1567,plain,
% 2.22/1.93 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 2.22/1.93 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 2.22/1.94 tff(1568,plain,
% 2.22/1.94 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1567, 1563])).
% 2.22/1.94 tff(1569,plain,(
% 2.22/1.94 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 2.22/1.94 inference(skolemize,[status(sab)],[1568])).
% 2.22/1.94 tff(1570,plain,
% 2.22/1.94 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1569, 1562])).
% 2.22/1.94 tff(1571,plain,
% 2.22/1.94 (~c3_1(a255)),
% 2.22/1.94 inference(unit_resolution,[status(thm)],[288, 1551])).
% 2.22/1.94 tff(1572,plain,
% 2.22/1.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a255) | c3_1(a255) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a255) | c3_1(a255) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | c2_1(a255))),
% 2.22/1.94 inference(rewrite,[status(thm)],[])).
% 2.22/1.94 tff(1573,plain,
% 2.22/1.94 ((hskp8 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c3_1(a255) | c1_1(a255) | c2_1(a255)) <=> (hskp8 | c1_1(a255) | c3_1(a255) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | c2_1(a255))),
% 2.22/1.94 inference(rewrite,[status(thm)],[])).
% 2.22/1.94 tff(1574,plain,
% 2.22/1.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c3_1(a255) | c1_1(a255) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a255) | c3_1(a255) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | c2_1(a255)))),
% 2.22/1.94 inference(monotonicity,[status(thm)],[1573])).
% 2.22/1.94 tff(1575,plain,
% 2.22/1.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c3_1(a255) | c1_1(a255) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a255) | c3_1(a255) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | c2_1(a255))),
% 2.22/1.94 inference(transitivity,[status(thm)],[1574, 1572])).
% 2.22/1.94 tff(1576,plain,
% 2.22/1.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c3_1(a255) | c1_1(a255) | c2_1(a255))),
% 2.22/1.94 inference(quant_inst,[status(thm)],[])).
% 2.22/1.94 tff(1577,plain,
% 2.22/1.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a255) | c3_1(a255) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | c2_1(a255)),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 2.22/1.94 tff(1578,plain,
% 2.22/1.94 (hskp8 | c2_1(a255)),
% 2.22/1.94 inference(unit_resolution,[status(thm)],[1577, 122, 1370, 1552, 1571, 1368, 1570, 1377])).
% 2.22/1.94 tff(1579,plain,
% 2.22/1.94 (hskp8),
% 2.22/1.94 inference(unit_resolution,[status(thm)],[1578, 1560])).
% 2.22/1.94 tff(1580,plain,
% 2.22/1.94 (((~hskp8) | (~c2_1(a225))) <=> ((~hskp8) | (~c2_1(a225)))),
% 2.22/1.94 inference(rewrite,[status(thm)],[])).
% 2.22/1.94 tff(1581,plain,
% 2.22/1.94 (((~c2_1(a225)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a225)))),
% 2.22/1.94 inference(rewrite,[status(thm)],[])).
% 2.22/1.94 tff(1582,axiom,((~c2_1(a225)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 2.22/1.94 tff(1583,plain,
% 2.22/1.94 ((~hskp8) | (~c2_1(a225))),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1582, 1581])).
% 2.22/1.94 tff(1584,plain,
% 2.22/1.94 ((~hskp8) | (~c2_1(a225))),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1583, 1580])).
% 2.22/1.94 tff(1585,plain,
% 2.22/1.94 (~c2_1(a225)),
% 2.22/1.94 inference(unit_resolution,[status(thm)],[1584, 1579])).
% 2.22/1.94 tff(1586,plain,
% 2.22/1.94 (((~hskp8) | (~c0_1(a225))) <=> ((~hskp8) | (~c0_1(a225)))),
% 2.22/1.94 inference(rewrite,[status(thm)],[])).
% 2.22/1.94 tff(1587,plain,
% 2.22/1.94 (((~c0_1(a225)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a225)))),
% 2.22/1.94 inference(rewrite,[status(thm)],[])).
% 2.22/1.94 tff(1588,axiom,((~c0_1(a225)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 2.22/1.94 tff(1589,plain,
% 2.22/1.94 ((~hskp8) | (~c0_1(a225))),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 2.22/1.94 tff(1590,plain,
% 2.22/1.94 ((~hskp8) | (~c0_1(a225))),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1589, 1586])).
% 2.22/1.94 tff(1591,plain,
% 2.22/1.94 (~c0_1(a225)),
% 2.22/1.94 inference(unit_resolution,[status(thm)],[1590, 1579])).
% 2.22/1.94 tff(1592,plain,
% 2.22/1.94 (c2_1(a213)),
% 2.22/1.94 inference(unit_resolution,[status(thm)],[827, 1525])).
% 2.22/1.94 tff(1593,plain,
% 2.22/1.94 (((~hskp8) | c3_1(a225)) <=> ((~hskp8) | c3_1(a225))),
% 2.22/1.94 inference(rewrite,[status(thm)],[])).
% 2.22/1.94 tff(1594,axiom,((~hskp8) | c3_1(a225)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 2.22/1.94 tff(1595,plain,
% 2.22/1.94 ((~hskp8) | c3_1(a225)),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 2.22/1.94 tff(1596,plain,
% 2.22/1.94 ((~hskp8) | c3_1(a225)),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1595, 1593])).
% 2.22/1.94 tff(1597,plain,
% 2.22/1.94 ((~hskp8) | c3_1(a225)),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1596, 1593])).
% 2.22/1.94 tff(1598,plain,
% 2.22/1.94 ((~hskp8) | c3_1(a225)),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1597, 1593])).
% 2.22/1.94 tff(1599,plain,
% 2.22/1.94 ((~hskp8) | c3_1(a225)),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1598, 1593])).
% 2.22/1.94 tff(1600,plain,
% 2.22/1.94 ((~hskp8) | c3_1(a225)),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1599, 1593])).
% 2.22/1.94 tff(1601,plain,
% 2.22/1.94 ((~hskp8) | c3_1(a225)),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1600, 1593])).
% 2.22/1.94 tff(1602,plain,
% 2.22/1.94 ((~hskp8) | c3_1(a225)),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1601, 1593])).
% 2.22/1.94 tff(1603,plain,
% 2.22/1.94 (c3_1(a225)),
% 2.22/1.94 inference(unit_resolution,[status(thm)],[1602, 1579])).
% 2.22/1.94 tff(1604,plain,
% 2.22/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a225) | c2_1(a225) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a225) | c2_1(a225) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a225)))),
% 2.22/1.94 inference(rewrite,[status(thm)],[])).
% 2.22/1.94 tff(1605,plain,
% 2.22/1.94 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213))) <=> (c0_1(a225) | c2_1(a225) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a225)))),
% 2.22/1.94 inference(rewrite,[status(thm)],[])).
% 2.22/1.94 tff(1606,plain,
% 2.22/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a225) | c2_1(a225) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a225))))),
% 2.22/1.94 inference(monotonicity,[status(thm)],[1605])).
% 2.22/1.94 tff(1607,plain,
% 2.22/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a225) | c2_1(a225) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a225)))),
% 2.22/1.94 inference(transitivity,[status(thm)],[1606, 1604])).
% 2.22/1.94 tff(1608,plain,
% 2.22/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213)))),
% 2.22/1.94 inference(quant_inst,[status(thm)],[])).
% 2.22/1.94 tff(1609,plain,
% 2.22/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a225) | c2_1(a225) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a225))),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 2.22/1.94 tff(1610,plain,
% 2.22/1.94 ($false),
% 2.22/1.94 inference(unit_resolution,[status(thm)],[1609, 122, 1339, 1328, 1317, 1603, 1592, 1591, 1585, 1527, 1544, 1534])).
% 2.22/1.94 tff(1611,plain,((~hskp5) | hskp18), inference(lemma,lemma(discharge,[]))).
% 2.22/1.94 tff(1612,plain,
% 2.22/1.94 (~hskp5),
% 2.22/1.94 inference(unit_resolution,[status(thm)],[1611, 650])).
% 2.22/1.94 tff(1613,plain,
% 2.22/1.94 (c3_1(a231)),
% 2.22/1.94 inference(unit_resolution,[status(thm)],[1446, 651])).
% 2.22/1.94 tff(1614,plain,
% 2.22/1.94 (~c0_1(a231)),
% 2.22/1.94 inference(unit_resolution,[status(thm)],[1416, 651])).
% 2.22/1.94 tff(1615,assumption,(~c0_1(a231)), introduced(assumption)).
% 2.22/1.94 tff(1616,assumption,(c3_1(a231)), introduced(assumption)).
% 2.22/1.94 tff(1617,assumption,(c1_1(a231)), introduced(assumption)).
% 2.22/1.94 tff(1618,plain,
% 2.22/1.94 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.22/1.94 inference(rewrite,[status(thm)],[])).
% 2.22/1.94 tff(1619,plain,
% 2.22/1.94 ((hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a226) | (~c3_1(a226)) | (~c0_1(a226))) <=> (hskp18 | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.22/1.94 inference(rewrite,[status(thm)],[])).
% 2.22/1.94 tff(1620,plain,
% 2.22/1.94 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a226) | (~c3_1(a226)) | (~c0_1(a226)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | (~c2_1(a237)) | (~c0_1(a237))))),
% 2.22/1.94 inference(monotonicity,[status(thm)],[1619])).
% 2.22/1.94 tff(1621,plain,
% 2.22/1.94 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a226) | (~c3_1(a226)) | (~c0_1(a226)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.22/1.94 inference(transitivity,[status(thm)],[1620, 1618])).
% 2.22/1.94 tff(1622,plain,
% 2.22/1.94 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a226) | (~c3_1(a226)) | (~c0_1(a226)))),
% 2.22/1.94 inference(quant_inst,[status(thm)],[])).
% 2.22/1.94 tff(1623,plain,
% 2.22/1.94 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | (~c2_1(a237)) | (~c0_1(a237))),
% 2.22/1.94 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 2.22/1.94 tff(1624,plain,
% 2.22/1.94 (~c3_1(a226)),
% 2.22/1.94 inference(unit_resolution,[status(thm)],[1623, 122, 650, 1507, 1506, 911, 1505, 900, 1387])).
% 2.22/1.94 tff(1625,plain,
% 2.22/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a237)) | (~c1_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a237)) | (~c1_1(a237)))),
% 2.30/1.95 inference(rewrite,[status(thm)],[])).
% 2.30/1.95 tff(1626,plain,
% 2.30/1.95 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a226) | c1_1(a226) | (~c0_1(a226))) <=> (c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a237)) | (~c1_1(a237)))),
% 2.30/1.95 inference(rewrite,[status(thm)],[])).
% 2.30/1.95 tff(1627,plain,
% 2.30/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a237)) | (~c1_1(a237))))),
% 2.30/1.95 inference(monotonicity,[status(thm)],[1626])).
% 2.30/1.95 tff(1628,plain,
% 2.30/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a237)) | (~c1_1(a237)))),
% 2.30/1.95 inference(transitivity,[status(thm)],[1627, 1625])).
% 2.30/1.95 tff(1629,plain,
% 2.30/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a226) | c1_1(a226) | (~c0_1(a226)))),
% 2.30/1.95 inference(quant_inst,[status(thm)],[])).
% 2.30/1.95 tff(1630,plain,
% 2.30/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a237)) | (~c1_1(a237))),
% 2.30/1.95 inference(modus_ponens,[status(thm)],[1629, 1628])).
% 2.30/1.95 tff(1631,plain,
% 2.30/1.95 (~c1_1(a237)),
% 2.30/1.95 inference(unit_resolution,[status(thm)],[1630, 122, 1339, 1328, 1317, 1506, 911, 1505, 900, 553, 1624])).
% 2.30/1.95 tff(1632,plain,
% 2.30/1.95 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)))),
% 2.30/1.95 inference(rewrite,[status(thm)],[])).
% 2.30/1.95 tff(1633,plain,
% 2.30/1.95 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | (~c0_1(a226))) <=> (hskp19 | hskp18 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)))),
% 2.30/1.95 inference(rewrite,[status(thm)],[])).
% 2.30/1.95 tff(1634,plain,
% 2.30/1.95 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226))))),
% 2.30/1.95 inference(monotonicity,[status(thm)],[1633])).
% 2.30/1.95 tff(1635,plain,
% 2.30/1.95 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)))),
% 2.30/1.95 inference(transitivity,[status(thm)],[1634, 1632])).
% 2.30/1.95 tff(1636,plain,
% 2.30/1.95 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))),
% 2.30/1.95 inference(quant_inst,[status(thm)],[])).
% 2.30/1.95 tff(1637,plain,
% 2.30/1.95 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226))),
% 2.30/1.95 inference(modus_ponens,[status(thm)],[1636, 1635])).
% 2.30/1.95 tff(1638,plain,
% 2.30/1.95 (hskp19),
% 2.30/1.95 inference(unit_resolution,[status(thm)],[1637, 122, 650, 911, 900, 894, 1177])).
% 2.30/1.95 tff(1639,plain,
% 2.30/1.95 (~c1_1(a255)),
% 2.30/1.95 inference(unit_resolution,[status(thm)],[294, 1638])).
% 2.30/1.95 tff(1640,plain,
% 2.30/1.95 (~c0_1(a255)),
% 2.30/1.95 inference(unit_resolution,[status(thm)],[300, 1638])).
% 2.30/1.95 tff(1641,plain,
% 2.30/1.95 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 2.30/1.95 inference(bind,[status(th)],[])).
% 2.30/1.95 tff(1642,plain,
% 2.30/1.95 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.30/1.95 inference(quant_intro,[status(thm)],[1641])).
% 2.30/1.95 tff(1643,plain,
% 2.30/1.95 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.30/1.95 inference(rewrite,[status(thm)],[])).
% 2.30/1.95 tff(1644,plain,
% 2.30/1.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 2.30/1.95 inference(bind,[status(th)],[])).
% 2.30/1.95 tff(1645,plain,
% 2.30/1.95 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.30/1.95 inference(quant_intro,[status(thm)],[1644])).
% 2.30/1.95 tff(1646,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 2.30/1.95 tff(1647,plain,
% 2.30/1.95 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.30/1.95 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 2.30/1.95 tff(1648,plain,
% 2.30/1.95 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.30/1.95 inference(modus_ponens,[status(thm)],[1647, 1643])).
% 2.30/1.95 tff(1649,plain,(
% 2.30/1.95 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.30/1.95 inference(skolemize,[status(sab)],[1648])).
% 2.30/1.95 tff(1650,plain,
% 2.30/1.95 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 2.30/1.95 inference(modus_ponens,[status(thm)],[1649, 1642])).
% 2.30/1.95 tff(1651,plain,
% 2.30/1.95 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c2_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | c3_1(a226) | (~c0_1(a226)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c2_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | c3_1(a226) | (~c0_1(a226)))),
% 2.30/1.95 inference(rewrite,[status(thm)],[])).
% 2.30/1.95 tff(1652,plain,
% 2.30/1.95 ((hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261))) <=> (hskp26 | c2_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | c3_1(a226) | (~c0_1(a226)))),
% 2.30/1.95 inference(rewrite,[status(thm)],[])).
% 2.30/1.95 tff(1653,plain,
% 2.30/1.95 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c2_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | c3_1(a226) | (~c0_1(a226))))),
% 2.30/1.95 inference(monotonicity,[status(thm)],[1652])).
% 2.30/1.95 tff(1654,plain,
% 2.30/1.95 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c2_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | c3_1(a226) | (~c0_1(a226)))),
% 2.30/1.95 inference(transitivity,[status(thm)],[1653, 1651])).
% 2.30/1.95 tff(1655,plain,
% 2.30/1.95 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))),
% 2.30/1.96 inference(quant_inst,[status(thm)],[])).
% 2.30/1.96 tff(1656,plain,
% 2.30/1.96 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c2_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | c3_1(a226) | (~c0_1(a226))),
% 2.30/1.96 inference(modus_ponens,[status(thm)],[1655, 1654])).
% 2.30/1.96 tff(1657,plain,
% 2.30/1.96 (hskp26),
% 2.30/1.96 inference(unit_resolution,[status(thm)],[1656, 122, 1339, 1328, 911, 894, 1650, 1346, 1624])).
% 2.30/1.96 tff(1658,plain,
% 2.30/1.96 (c3_1(a234)),
% 2.30/1.96 inference(unit_resolution,[status(thm)],[66, 1657])).
% 2.30/1.96 tff(1659,plain,
% 2.30/1.96 (c1_1(a234)),
% 2.30/1.96 inference(unit_resolution,[status(thm)],[77, 1657])).
% 2.30/1.96 tff(1660,plain,
% 2.30/1.96 (c0_1(a234)),
% 2.30/1.96 inference(unit_resolution,[status(thm)],[88, 1657])).
% 2.30/1.96 tff(1661,plain,
% 2.30/1.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a255)))),
% 2.30/1.96 inference(rewrite,[status(thm)],[])).
% 2.30/1.96 tff(1662,plain,
% 2.30/1.96 ((hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a255) | c0_1(a255) | (~c2_1(a255))) <=> (hskp5 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a255)))),
% 2.30/1.96 inference(rewrite,[status(thm)],[])).
% 2.30/1.96 tff(1663,plain,
% 2.30/1.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a255) | c0_1(a255) | (~c2_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a255))))),
% 2.30/1.96 inference(monotonicity,[status(thm)],[1662])).
% 2.30/1.96 tff(1664,plain,
% 2.30/1.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a255) | c0_1(a255) | (~c2_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a255)))),
% 2.30/1.96 inference(transitivity,[status(thm)],[1663, 1661])).
% 2.30/1.96 tff(1665,plain,
% 2.30/1.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a255) | c0_1(a255) | (~c2_1(a255)))),
% 2.30/1.96 inference(quant_inst,[status(thm)],[])).
% 2.30/1.96 tff(1666,plain,
% 2.30/1.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a255))),
% 2.30/1.96 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 2.30/1.96 tff(1667,plain,
% 2.30/1.96 (~c2_1(a255)),
% 2.30/1.96 inference(unit_resolution,[status(thm)],[1666, 122, 45, 1660, 1659, 1658, 1640, 1639, 164])).
% 2.30/1.96 tff(1668,plain,
% 2.30/1.96 (^[U: $i] : refl((hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 2.30/1.96 inference(bind,[status(th)],[])).
% 2.30/1.96 tff(1669,plain,
% 2.30/1.96 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.30/1.96 inference(quant_intro,[status(thm)],[1668])).
% 2.30/1.96 tff(1670,plain,
% 2.30/1.96 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.30/1.96 inference(rewrite,[status(thm)],[])).
% 2.30/1.96 tff(1671,plain,
% 2.30/1.96 (^[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)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp5) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp5))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp5) <=> (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp5) <=> (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 2.30/1.96 inference(bind,[status(th)],[])).
% 2.30/1.96 tff(1672,plain,
% 2.30/1.96 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp5) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.30/1.96 inference(quant_intro,[status(thm)],[1671])).
% 2.30/1.96 tff(1673,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 2.30/1.96 tff(1674,plain,
% 2.30/1.96 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.30/1.96 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 2.30/1.96 tff(1675,plain,
% 2.30/1.96 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.30/1.96 inference(modus_ponens,[status(thm)],[1674, 1670])).
% 2.30/1.96 tff(1676,plain,(
% 2.30/1.96 ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.30/1.96 inference(skolemize,[status(sab)],[1675])).
% 2.30/1.96 tff(1677,plain,
% 2.30/1.96 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 2.30/1.96 inference(modus_ponens,[status(thm)],[1676, 1669])).
% 2.30/1.96 tff(1678,plain,
% 2.30/1.96 (~c3_1(a255)),
% 2.30/1.96 inference(unit_resolution,[status(thm)],[288, 1638])).
% 2.30/1.96 tff(1679,plain,
% 2.30/1.96 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | c2_1(a255))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp6 | hskp5 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | c2_1(a255))),
% 2.30/1.96 inference(rewrite,[status(thm)],[])).
% 2.30/1.96 tff(1680,plain,
% 2.30/1.96 ((hskp6 | hskp5 | (~ndr1_0) | c2_1(a255) | c0_1(a255) | c3_1(a255)) <=> (hskp6 | hskp5 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | c2_1(a255))),
% 2.30/1.96 inference(rewrite,[status(thm)],[])).
% 2.30/1.96 tff(1681,plain,
% 2.30/1.96 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a255) | c0_1(a255) | c3_1(a255))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | c2_1(a255)))),
% 2.30/1.96 inference(monotonicity,[status(thm)],[1680])).
% 2.30/1.96 tff(1682,plain,
% 2.30/1.96 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a255) | c0_1(a255) | c3_1(a255))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp6 | hskp5 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | c2_1(a255))),
% 2.30/1.96 inference(transitivity,[status(thm)],[1681, 1679])).
% 2.30/1.96 tff(1683,plain,
% 2.30/1.96 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a255) | c0_1(a255) | c3_1(a255))),
% 2.30/1.96 inference(quant_inst,[status(thm)],[])).
% 2.30/1.96 tff(1684,plain,
% 2.30/1.96 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp6 | hskp5 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | c2_1(a255)),
% 2.30/1.96 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 2.30/1.96 tff(1685,plain,
% 2.30/1.96 (hskp6),
% 2.30/1.96 inference(unit_resolution,[status(thm)],[1684, 122, 45, 1640, 1678, 1677, 1667])).
% 2.30/1.96 tff(1686,plain,
% 2.30/1.96 (~c3_1(a220)),
% 2.30/1.96 inference(unit_resolution,[status(thm)],[485, 1685])).
% 2.30/1.96 tff(1687,plain,
% 2.30/1.96 (c2_1(a220)),
% 2.30/1.96 inference(unit_resolution,[status(thm)],[541, 1685])).
% 2.30/1.96 tff(1688,plain,
% 2.30/1.96 (c1_1(a220)),
% 2.30/1.96 inference(unit_resolution,[status(thm)],[530, 1685])).
% 2.30/1.96 tff(1689,plain,
% 2.30/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a220)) | (~c1_1(a220)) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a220)) | (~c1_1(a220)) | c1_1(a237) | (~c0_1(a237)))),
% 2.30/1.96 inference(rewrite,[status(thm)],[])).
% 2.30/1.96 tff(1690,plain,
% 2.30/1.96 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237))) <=> (c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a220)) | (~c1_1(a220)) | c1_1(a237) | (~c0_1(a237)))),
% 2.30/1.96 inference(rewrite,[status(thm)],[])).
% 2.30/1.96 tff(1691,plain,
% 2.30/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a220)) | (~c1_1(a220)) | c1_1(a237) | (~c0_1(a237))))),
% 2.30/1.96 inference(monotonicity,[status(thm)],[1690])).
% 2.30/1.96 tff(1692,plain,
% 2.30/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a220)) | (~c1_1(a220)) | c1_1(a237) | (~c0_1(a237)))),
% 2.30/1.96 inference(transitivity,[status(thm)],[1691, 1689])).
% 2.30/1.96 tff(1693,plain,
% 2.30/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))),
% 2.30/1.96 inference(quant_inst,[status(thm)],[])).
% 2.30/1.96 tff(1694,plain,
% 2.30/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a220)) | (~c1_1(a220)) | c1_1(a237) | (~c0_1(a237))),
% 2.30/1.96 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 2.30/1.96 tff(1695,plain,
% 2.30/1.96 ($false),
% 2.30/1.96 inference(unit_resolution,[status(thm)],[1694, 122, 1339, 1328, 1317, 1507, 1688, 1687, 1505, 1686, 553, 1631])).
% 2.30/1.96 tff(1696,plain,((~hskp9) | hskp5 | hskp18), inference(lemma,lemma(discharge,[]))).
% 2.30/1.96 tff(1697,plain,
% 2.30/1.96 (~hskp9),
% 2.30/1.96 inference(unit_resolution,[status(thm)],[1696, 45, 650])).
% 2.30/1.96 tff(1698,assumption,(~c3_1(a259)), introduced(assumption)).
% 2.30/1.96 tff(1699,plain,
% 2.30/1.96 (~hskp21),
% 2.30/1.96 inference(unit_resolution,[status(thm)],[867, 1698])).
% 2.30/1.96 tff(1700,assumption,(c3_1(a261)), introduced(assumption)).
% 2.30/1.97 tff(1701,assumption,(c2_1(a261)), introduced(assumption)).
% 2.30/1.97 tff(1702,assumption,(c1_1(a261)), introduced(assumption)).
% 2.30/1.97 tff(1703,plain,
% 2.30/1.97 (~c0_1(a261)),
% 2.30/1.97 inference(unit_resolution,[status(thm)],[1345, 122, 1702, 1701, 1700, 33])).
% 2.30/1.97 tff(1704,plain,
% 2.30/1.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a259) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a259) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261))),
% 2.30/1.97 inference(rewrite,[status(thm)],[])).
% 2.30/1.97 tff(1705,plain,
% 2.30/1.97 ((hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a259) | c0_1(a259) | c2_1(a259)) <=> (hskp9 | c0_1(a259) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261))),
% 2.30/1.97 inference(rewrite,[status(thm)],[])).
% 2.30/1.97 tff(1706,plain,
% 2.30/1.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a259) | c0_1(a259) | c2_1(a259))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a259) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261)))),
% 2.30/1.97 inference(monotonicity,[status(thm)],[1705])).
% 2.30/1.97 tff(1707,plain,
% 2.30/1.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a259) | c0_1(a259) | c2_1(a259))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a259) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261))),
% 2.30/1.97 inference(transitivity,[status(thm)],[1706, 1704])).
% 2.30/1.97 tff(1708,plain,
% 2.30/1.97 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a259) | c0_1(a259) | c2_1(a259))),
% 2.30/1.97 inference(quant_inst,[status(thm)],[])).
% 2.30/1.97 tff(1709,plain,
% 2.30/1.97 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a259) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261)),
% 2.30/1.97 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 2.30/1.97 tff(1710,plain,
% 2.30/1.97 (c0_1(a259)),
% 2.30/1.97 inference(unit_resolution,[status(thm)],[1709, 122, 23, 1701, 1700, 1698, 857, 989, 1703])).
% 2.30/1.97 tff(1711,plain,
% 2.30/1.97 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))))),
% 2.30/1.97 inference(bind,[status(th)],[])).
% 2.30/1.97 tff(1712,plain,
% 2.30/1.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 2.30/1.97 inference(quant_intro,[status(thm)],[1711])).
% 2.30/1.97 tff(1713,plain,
% 2.30/1.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 2.30/1.97 inference(rewrite,[status(thm)],[])).
% 2.30/1.97 tff(1714,plain,
% 2.30/1.97 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))))),
% 2.30/1.97 inference(bind,[status(th)],[])).
% 2.30/1.97 tff(1715,plain,
% 2.30/1.97 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 2.30/1.97 inference(quant_intro,[status(thm)],[1714])).
% 2.30/1.97 tff(1716,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 2.30/1.97 tff(1717,plain,
% 2.30/1.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 2.30/1.97 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 2.30/1.97 tff(1718,plain,
% 2.30/1.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 2.30/1.97 inference(modus_ponens,[status(thm)],[1717, 1713])).
% 2.30/1.97 tff(1719,plain,(
% 2.30/1.97 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 2.30/1.97 inference(skolemize,[status(sab)],[1718])).
% 2.30/1.97 tff(1720,plain,
% 2.30/1.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 2.30/1.97 inference(modus_ponens,[status(thm)],[1719, 1712])).
% 2.30/1.97 tff(1721,plain,
% 2.30/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 2.30/1.97 inference(rewrite,[status(thm)],[])).
% 2.30/1.97 tff(1722,plain,
% 2.30/1.97 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259))) <=> (c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 2.30/1.97 inference(rewrite,[status(thm)],[])).
% 2.30/1.97 tff(1723,plain,
% 2.30/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c0_1(a259)) | (~c1_1(a259))))),
% 2.30/1.97 inference(monotonicity,[status(thm)],[1722])).
% 2.30/1.97 tff(1724,plain,
% 2.30/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 2.30/1.97 inference(transitivity,[status(thm)],[1723, 1721])).
% 2.30/1.97 tff(1725,plain,
% 2.30/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259)))),
% 2.30/1.97 inference(quant_inst,[status(thm)],[])).
% 2.30/1.97 tff(1726,plain,
% 2.30/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c0_1(a259)) | (~c1_1(a259))),
% 2.30/1.97 inference(modus_ponens,[status(thm)],[1725, 1724])).
% 2.30/1.97 tff(1727,plain,
% 2.30/1.97 ((~c0_1(a259)) | (~c1_1(a259))),
% 2.30/1.97 inference(unit_resolution,[status(thm)],[1726, 122, 1702, 1701, 1700, 1698, 857, 1720])).
% 2.30/1.97 tff(1728,plain,
% 2.30/1.97 (~c1_1(a259)),
% 2.30/1.97 inference(unit_resolution,[status(thm)],[1727, 1710])).
% 2.30/1.97 tff(1729,plain,
% 2.30/1.97 (^[U: $i] : refl((hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 2.30/1.97 inference(bind,[status(th)],[])).
% 2.30/1.97 tff(1730,plain,
% 2.30/1.97 (![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.30/1.97 inference(quant_intro,[status(thm)],[1729])).
% 2.30/1.97 tff(1731,plain,
% 2.30/1.97 (![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.30/1.97 inference(rewrite,[status(thm)],[])).
% 2.30/1.97 tff(1732,plain,
% 2.30/1.97 (^[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)) | 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))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp19) <=> ((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp19))), rewrite(((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp19) <=> (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp19) <=> (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 2.30/1.97 inference(bind,[status(th)],[])).
% 2.30/1.97 tff(1733,plain,
% 2.30/1.97 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp19) <=> ![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.30/1.97 inference(quant_intro,[status(thm)],[1732])).
% 2.30/1.97 tff(1734,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 2.30/1.97 tff(1735,plain,
% 2.30/1.97 (![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.30/1.97 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 2.30/1.97 tff(1736,plain,
% 2.30/1.97 (![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.30/1.97 inference(modus_ponens,[status(thm)],[1735, 1731])).
% 2.30/1.97 tff(1737,plain,(
% 2.30/1.97 ![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.30/1.97 inference(skolemize,[status(sab)],[1736])).
% 2.30/1.97 tff(1738,plain,
% 2.30/1.97 (![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 2.30/1.97 inference(modus_ponens,[status(thm)],[1737, 1730])).
% 2.30/1.97 tff(1739,plain,
% 2.30/1.97 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | c1_1(a259))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | c1_1(a259))),
% 2.30/1.98 inference(rewrite,[status(thm)],[])).
% 2.30/1.98 tff(1740,plain,
% 2.30/1.98 ((hskp19 | hskp21 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | c3_1(a259)) <=> (hskp19 | hskp21 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | c1_1(a259))),
% 2.30/1.98 inference(rewrite,[status(thm)],[])).
% 2.30/1.98 tff(1741,plain,
% 2.30/1.98 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | c3_1(a259))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | c1_1(a259)))),
% 2.30/1.98 inference(monotonicity,[status(thm)],[1740])).
% 2.30/1.98 tff(1742,plain,
% 2.30/1.98 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | c3_1(a259))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | c1_1(a259))),
% 2.30/1.98 inference(transitivity,[status(thm)],[1741, 1739])).
% 2.30/1.98 tff(1743,plain,
% 2.30/1.98 ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | c3_1(a259))),
% 2.30/1.98 inference(quant_inst,[status(thm)],[])).
% 2.30/1.98 tff(1744,plain,
% 2.30/1.98 ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | c1_1(a259)),
% 2.30/1.98 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 2.30/1.98 tff(1745,plain,
% 2.30/1.98 (hskp19 | hskp21 | c3_1(a259) | c1_1(a259)),
% 2.30/1.98 inference(unit_resolution,[status(thm)],[1744, 122, 857, 1738])).
% 2.30/1.98 tff(1746,plain,
% 2.30/1.98 (hskp19),
% 2.30/1.98 inference(unit_resolution,[status(thm)],[1745, 1728, 1698, 1699])).
% 2.30/1.98 tff(1747,plain,
% 2.30/1.98 (~c1_1(a255)),
% 2.30/1.98 inference(unit_resolution,[status(thm)],[294, 1746])).
% 2.30/1.98 tff(1748,plain,
% 2.30/1.98 (~c0_1(a255)),
% 2.30/1.98 inference(unit_resolution,[status(thm)],[300, 1746])).
% 2.30/1.98 tff(1749,plain,
% 2.30/1.98 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c0_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c0_1(a259)))),
% 2.30/1.98 inference(rewrite,[status(thm)],[])).
% 2.30/1.98 tff(1750,plain,
% 2.30/1.98 ((hskp26 | (~ndr1_0) | c2_1(a259) | c3_1(a259) | (~c0_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261))) <=> (hskp26 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c0_1(a259)))),
% 2.30/1.98 inference(rewrite,[status(thm)],[])).
% 2.30/1.98 tff(1751,plain,
% 2.30/1.98 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a259) | c3_1(a259) | (~c0_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c0_1(a259))))),
% 2.30/1.98 inference(monotonicity,[status(thm)],[1750])).
% 2.30/1.98 tff(1752,plain,
% 2.30/1.98 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a259) | c3_1(a259) | (~c0_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c0_1(a259)))),
% 2.30/1.98 inference(transitivity,[status(thm)],[1751, 1749])).
% 2.30/1.98 tff(1753,plain,
% 2.30/1.98 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a259) | c3_1(a259) | (~c0_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))),
% 2.30/1.98 inference(quant_inst,[status(thm)],[])).
% 2.30/1.98 tff(1754,plain,
% 2.30/1.98 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c0_1(a259))),
% 2.33/1.98 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 2.33/1.98 tff(1755,plain,
% 2.33/1.98 (hskp26 | c3_1(a259) | (~c0_1(a259))),
% 2.33/1.98 inference(unit_resolution,[status(thm)],[1754, 122, 1702, 1701, 857, 1650, 1703])).
% 2.33/1.98 tff(1756,plain,
% 2.33/1.98 (hskp26),
% 2.33/1.98 inference(unit_resolution,[status(thm)],[1755, 1710, 1698])).
% 2.33/1.98 tff(1757,plain,
% 2.33/1.98 (c3_1(a234)),
% 2.33/1.98 inference(unit_resolution,[status(thm)],[66, 1756])).
% 2.33/1.98 tff(1758,plain,
% 2.33/1.98 (c1_1(a234)),
% 2.33/1.98 inference(unit_resolution,[status(thm)],[77, 1756])).
% 2.33/1.98 tff(1759,plain,
% 2.33/1.98 (c0_1(a234)),
% 2.33/1.98 inference(unit_resolution,[status(thm)],[88, 1756])).
% 2.33/1.98 tff(1760,plain,
% 2.33/1.98 (~c2_1(a255)),
% 2.33/1.98 inference(unit_resolution,[status(thm)],[1666, 122, 45, 1759, 1758, 1757, 1748, 1747, 164])).
% 2.33/1.98 tff(1761,plain,
% 2.33/1.98 (~c3_1(a255)),
% 2.33/1.98 inference(unit_resolution,[status(thm)],[288, 1746])).
% 2.33/1.98 tff(1762,plain,
% 2.33/1.98 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c2_1(a255))),
% 2.33/1.98 inference(rewrite,[status(thm)],[])).
% 2.33/1.98 tff(1763,plain,
% 2.33/1.98 ((hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a255) | c0_1(a255) | c2_1(a255)) <=> (hskp9 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c2_1(a255))),
% 2.33/1.98 inference(rewrite,[status(thm)],[])).
% 2.33/1.98 tff(1764,plain,
% 2.33/1.98 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a255) | c0_1(a255) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c2_1(a255)))),
% 2.33/1.98 inference(monotonicity,[status(thm)],[1763])).
% 2.33/1.98 tff(1765,plain,
% 2.33/1.98 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a255) | c0_1(a255) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c2_1(a255))),
% 2.33/1.98 inference(transitivity,[status(thm)],[1764, 1762])).
% 2.33/1.98 tff(1766,plain,
% 2.33/1.98 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a255) | c0_1(a255) | c2_1(a255))),
% 2.33/1.98 inference(quant_inst,[status(thm)],[])).
% 2.33/1.98 tff(1767,plain,
% 2.33/1.98 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c2_1(a255)),
% 2.33/1.98 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 2.33/1.98 tff(1768,plain,
% 2.33/1.98 ($false),
% 2.33/1.98 inference(unit_resolution,[status(thm)],[1767, 122, 23, 1701, 1700, 1748, 1761, 989, 1703, 1760])).
% 2.33/1.98 tff(1769,plain,(c3_1(a259) | hskp9 | (~c2_1(a261)) | (~c3_1(a261)) | hskp5 | c2_1(a259) | (~c1_1(a261))), inference(lemma,lemma(discharge,[]))).
% 2.33/1.98 tff(1770,plain,
% 2.33/1.98 (c3_1(a259)),
% 2.33/1.98 inference(unit_resolution,[status(thm)],[1769, 23, 1328, 1317, 45, 857, 1339])).
% 2.33/1.98 tff(1771,plain,
% 2.33/1.98 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a259) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a259)) | (~c1_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 2.33/1.98 inference(rewrite,[status(thm)],[])).
% 2.33/1.98 tff(1772,plain,
% 2.33/1.98 ((hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231))) <=> (hskp18 | c2_1(a259) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 2.33/1.98 inference(rewrite,[status(thm)],[])).
% 2.33/1.98 tff(1773,plain,
% 2.33/1.98 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a259) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a259)) | (~c1_1(a259))))),
% 2.33/1.98 inference(monotonicity,[status(thm)],[1772])).
% 2.33/1.98 tff(1774,plain,
% 2.33/1.98 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 2.33/1.98 inference(transitivity,[status(thm)],[1773, 1771])).
% 2.33/1.98 tff(1775,plain,
% 2.33/1.98 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))),
% 2.33/1.98 inference(quant_inst,[status(thm)],[])).
% 2.33/1.98 tff(1776,plain,
% 2.33/1.98 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a259)) | (~c1_1(a259))),
% 2.33/1.98 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 2.33/1.98 tff(1777,plain,
% 2.33/1.98 ((~c3_1(a259)) | (~c1_1(a259))),
% 2.33/1.98 inference(unit_resolution,[status(thm)],[1776, 122, 650, 1617, 1616, 857, 1615, 672])).
% 2.33/1.98 tff(1778,plain,
% 2.33/1.98 (~c1_1(a259)),
% 2.33/1.98 inference(unit_resolution,[status(thm)],[1777, 1770])).
% 2.33/1.98 tff(1779,plain,
% 2.33/1.98 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 2.33/1.98 inference(bind,[status(th)],[])).
% 2.33/1.98 tff(1780,plain,
% 2.33/1.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/1.98 inference(quant_intro,[status(thm)],[1779])).
% 2.33/1.98 tff(1781,plain,
% 2.33/1.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/1.98 inference(rewrite,[status(thm)],[])).
% 2.33/1.98 tff(1782,plain,
% 2.33/1.98 (^[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)) | (~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)) | c1_1(V) | c2_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) | c2_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)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_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)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 2.33/1.99 inference(bind,[status(th)],[])).
% 2.33/1.99 tff(1783,plain,
% 2.33/1.99 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/1.99 inference(quant_intro,[status(thm)],[1782])).
% 2.33/1.99 tff(1784,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 2.33/1.99 tff(1785,plain,
% 2.33/1.99 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1784, 1783])).
% 2.33/1.99 tff(1786,plain,
% 2.33/1.99 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1785, 1781])).
% 2.33/1.99 tff(1787,plain,(
% 2.33/1.99 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/1.99 inference(skolemize,[status(sab)],[1786])).
% 2.33/1.99 tff(1788,plain,
% 2.33/1.99 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1787, 1780])).
% 2.33/1.99 tff(1789,plain,
% 2.33/1.99 ((hskp22 | hskp18 | hskp9) <=> (hskp22 | hskp18 | hskp9)),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1790,plain,
% 2.33/1.99 (((hskp18 | hskp9) | hskp22) <=> (hskp22 | hskp18 | hskp9)),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1791,axiom,((hskp18 | hskp9) | hskp22), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 2.33/1.99 tff(1792,plain,
% 2.33/1.99 (hskp22 | hskp18 | hskp9),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 2.33/1.99 tff(1793,plain,
% 2.33/1.99 (hskp22 | hskp18 | hskp9),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1792, 1789])).
% 2.33/1.99 tff(1794,plain,
% 2.33/1.99 (hskp22 | hskp18 | hskp9),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1793, 1789])).
% 2.33/1.99 tff(1795,plain,
% 2.33/1.99 (hskp22 | hskp18 | hskp9),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1794, 1789])).
% 2.33/1.99 tff(1796,plain,
% 2.33/1.99 (hskp22 | hskp18 | hskp9),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1795, 1789])).
% 2.33/1.99 tff(1797,plain,
% 2.33/1.99 (hskp22 | hskp18 | hskp9),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1796, 1789])).
% 2.33/1.99 tff(1798,plain,
% 2.33/1.99 (hskp22 | hskp18 | hskp9),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1797, 1789])).
% 2.33/1.99 tff(1799,plain,
% 2.33/1.99 (hskp22 | hskp18 | hskp9),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1798, 1789])).
% 2.33/1.99 tff(1800,plain,
% 2.33/1.99 (hskp22),
% 2.33/1.99 inference(unit_resolution,[status(thm)],[1799, 23, 650])).
% 2.33/1.99 tff(1801,plain,
% 2.33/1.99 (((~hskp22) | (~c2_1(a271))) <=> ((~hskp22) | (~c2_1(a271)))),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1802,plain,
% 2.33/1.99 (((~c2_1(a271)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a271)))),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1803,axiom,((~c2_1(a271)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 2.33/1.99 tff(1804,plain,
% 2.33/1.99 ((~hskp22) | (~c2_1(a271))),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1803, 1802])).
% 2.33/1.99 tff(1805,plain,
% 2.33/1.99 ((~hskp22) | (~c2_1(a271))),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1804, 1801])).
% 2.33/1.99 tff(1806,plain,
% 2.33/1.99 (~c2_1(a271)),
% 2.33/1.99 inference(unit_resolution,[status(thm)],[1805, 1800])).
% 2.33/1.99 tff(1807,plain,
% 2.33/1.99 (((~hskp22) | (~c1_1(a271))) <=> ((~hskp22) | (~c1_1(a271)))),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1808,plain,
% 2.33/1.99 (((~c1_1(a271)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a271)))),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1809,axiom,((~c1_1(a271)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 2.33/1.99 tff(1810,plain,
% 2.33/1.99 ((~hskp22) | (~c1_1(a271))),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1809, 1808])).
% 2.33/1.99 tff(1811,plain,
% 2.33/1.99 ((~hskp22) | (~c1_1(a271))),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1810, 1807])).
% 2.33/1.99 tff(1812,plain,
% 2.33/1.99 (~c1_1(a271)),
% 2.33/1.99 inference(unit_resolution,[status(thm)],[1811, 1800])).
% 2.33/1.99 tff(1813,plain,
% 2.33/1.99 (((~hskp22) | (~c0_1(a271))) <=> ((~hskp22) | (~c0_1(a271)))),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1814,plain,
% 2.33/1.99 (((~c0_1(a271)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a271)))),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1815,axiom,((~c0_1(a271)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 2.33/1.99 tff(1816,plain,
% 2.33/1.99 ((~hskp22) | (~c0_1(a271))),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1815, 1814])).
% 2.33/1.99 tff(1817,plain,
% 2.33/1.99 ((~hskp22) | (~c0_1(a271))),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1816, 1813])).
% 2.33/1.99 tff(1818,plain,
% 2.33/1.99 (~c0_1(a271)),
% 2.33/1.99 inference(unit_resolution,[status(thm)],[1817, 1800])).
% 2.33/1.99 tff(1819,plain,
% 2.33/1.99 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c0_1(a271) | c1_1(a271) | c2_1(a271) | (~ndr1_0))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a271) | c1_1(a271) | c2_1(a271) | (~ndr1_0))),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1820,plain,
% 2.33/1.99 ((hskp0 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c0_1(a271)) <=> (hskp0 | c0_1(a271) | c1_1(a271) | c2_1(a271) | (~ndr1_0))),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1821,plain,
% 2.33/1.99 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c0_1(a271))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c0_1(a271) | c1_1(a271) | c2_1(a271) | (~ndr1_0)))),
% 2.33/1.99 inference(monotonicity,[status(thm)],[1820])).
% 2.33/1.99 tff(1822,plain,
% 2.33/1.99 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c0_1(a271))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a271) | c1_1(a271) | c2_1(a271) | (~ndr1_0))),
% 2.33/1.99 inference(transitivity,[status(thm)],[1821, 1819])).
% 2.33/1.99 tff(1823,plain,
% 2.33/1.99 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c0_1(a271))),
% 2.33/1.99 inference(quant_inst,[status(thm)],[])).
% 2.33/1.99 tff(1824,plain,
% 2.33/1.99 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a271) | c1_1(a271) | c2_1(a271) | (~ndr1_0)),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1823, 1822])).
% 2.33/1.99 tff(1825,plain,
% 2.33/1.99 (hskp0),
% 2.33/1.99 inference(unit_resolution,[status(thm)],[1824, 122, 1818, 1812, 1806, 1098])).
% 2.33/1.99 tff(1826,plain,
% 2.33/1.99 (~c3_1(a213)),
% 2.33/1.99 inference(unit_resolution,[status(thm)],[810, 1825])).
% 2.33/1.99 tff(1827,plain,
% 2.33/1.99 (~c1_1(a213)),
% 2.33/1.99 inference(unit_resolution,[status(thm)],[816, 1825])).
% 2.33/1.99 tff(1828,plain,
% 2.33/1.99 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a259)) | c1_1(a259))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a259)) | c1_1(a259))),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1829,plain,
% 2.33/1.99 ((hskp5 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a259) | c2_1(a259) | (~c3_1(a259))) <=> (hskp5 | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a259)) | c1_1(a259))),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1830,plain,
% 2.33/1.99 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a259) | c2_1(a259) | (~c3_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a259)) | c1_1(a259)))),
% 2.33/1.99 inference(monotonicity,[status(thm)],[1829])).
% 2.33/1.99 tff(1831,plain,
% 2.33/1.99 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a259) | c2_1(a259) | (~c3_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a259)) | c1_1(a259))),
% 2.33/1.99 inference(transitivity,[status(thm)],[1830, 1828])).
% 2.33/1.99 tff(1832,plain,
% 2.33/1.99 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a259) | c2_1(a259) | (~c3_1(a259)))),
% 2.33/1.99 inference(quant_inst,[status(thm)],[])).
% 2.33/1.99 tff(1833,plain,
% 2.33/1.99 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a259)) | c1_1(a259)),
% 2.33/1.99 inference(modus_ponens,[status(thm)],[1832, 1831])).
% 2.33/1.99 tff(1834,plain,
% 2.33/1.99 (~c0_1(a213)),
% 2.33/1.99 inference(unit_resolution,[status(thm)],[1833, 122, 45, 1770, 857, 1827, 1826, 1788, 1778])).
% 2.33/1.99 tff(1835,plain,
% 2.33/1.99 (c2_1(a213)),
% 2.33/1.99 inference(unit_resolution,[status(thm)],[827, 1825])).
% 2.33/1.99 tff(1836,plain,
% 2.33/1.99 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a259)) | (~c0_1(a259)) | c1_1(a259))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a259)) | (~c0_1(a259)) | c1_1(a259))),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1837,plain,
% 2.33/1.99 ((hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a259) | (~c3_1(a259)) | (~c0_1(a259))) <=> (hskp18 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a259)) | (~c0_1(a259)) | c1_1(a259))),
% 2.33/1.99 inference(rewrite,[status(thm)],[])).
% 2.33/1.99 tff(1838,plain,
% 2.33/1.99 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a259) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a259)) | (~c0_1(a259)) | c1_1(a259)))),
% 2.33/1.99 inference(monotonicity,[status(thm)],[1837])).
% 2.33/1.99 tff(1839,plain,
% 2.33/2.00 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a259) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a259)) | (~c0_1(a259)) | c1_1(a259))),
% 2.33/2.00 inference(transitivity,[status(thm)],[1838, 1836])).
% 2.33/2.00 tff(1840,plain,
% 2.33/2.00 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a259) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.33/2.00 inference(quant_inst,[status(thm)],[])).
% 2.33/2.00 tff(1841,plain,
% 2.33/2.00 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a259)) | (~c0_1(a259)) | c1_1(a259)),
% 2.33/2.00 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 2.33/2.00 tff(1842,plain,
% 2.33/2.00 (~c0_1(a259)),
% 2.33/2.00 inference(unit_resolution,[status(thm)],[1841, 122, 650, 1770, 1507, 1506, 1505, 1387, 1778])).
% 2.33/2.00 tff(1843,plain,
% 2.33/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a259) | c2_1(a259) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a259) | c2_1(a259) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a259)))),
% 2.33/2.00 inference(rewrite,[status(thm)],[])).
% 2.33/2.00 tff(1844,plain,
% 2.33/2.00 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a259) | c2_1(a259) | (~c3_1(a259)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213))) <=> (c0_1(a259) | c2_1(a259) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a259)))),
% 2.33/2.00 inference(rewrite,[status(thm)],[])).
% 2.33/2.00 tff(1845,plain,
% 2.33/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a259) | c2_1(a259) | (~c3_1(a259)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a259) | c2_1(a259) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a259))))),
% 2.33/2.00 inference(monotonicity,[status(thm)],[1844])).
% 2.33/2.00 tff(1846,plain,
% 2.33/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a259) | c2_1(a259) | (~c3_1(a259)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a259) | c2_1(a259) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a259)))),
% 2.33/2.00 inference(transitivity,[status(thm)],[1845, 1843])).
% 2.33/2.00 tff(1847,plain,
% 2.33/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a259) | c2_1(a259) | (~c3_1(a259)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213)))),
% 2.33/2.00 inference(quant_inst,[status(thm)],[])).
% 2.33/2.00 tff(1848,plain,
% 2.33/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a259) | c2_1(a259) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a259))),
% 2.33/2.00 inference(modus_ponens,[status(thm)],[1847, 1846])).
% 2.33/2.00 tff(1849,plain,
% 2.33/2.00 ($false),
% 2.33/2.00 inference(unit_resolution,[status(thm)],[1848, 122, 1339, 1328, 1317, 1842, 1770, 1835, 857, 1827, 1544, 1834])).
% 2.33/2.00 tff(1850,plain,(hskp9 | c2_1(a259) | hskp5 | hskp18 | (~c1_1(a231)) | (~c3_1(a231)) | c0_1(a231)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.00 tff(1851,plain,
% 2.33/2.00 (c2_1(a259)),
% 2.33/2.00 inference(unit_resolution,[status(thm)],[1850, 1697, 45, 650, 1617, 1616, 1615])).
% 2.33/2.00 tff(1852,plain,
% 2.33/2.00 (~hskp21),
% 2.33/2.00 inference(unit_resolution,[status(thm)],[1062, 1851])).
% 2.33/2.00 tff(1853,plain,
% 2.33/2.00 (hskp22),
% 2.33/2.00 inference(unit_resolution,[status(thm)],[1799, 1697, 650])).
% 2.33/2.00 tff(1854,plain,
% 2.33/2.00 (~c0_1(a271)),
% 2.33/2.00 inference(unit_resolution,[status(thm)],[1817, 1853])).
% 2.33/2.00 tff(1855,assumption,(~hskp21), introduced(assumption)).
% 2.33/2.00 tff(1856,plain,
% 2.33/2.00 (~c2_1(a271)),
% 2.33/2.00 inference(unit_resolution,[status(thm)],[1805, 1853])).
% 2.33/2.00 tff(1857,plain,
% 2.33/2.00 (~c1_1(a271)),
% 2.33/2.00 inference(unit_resolution,[status(thm)],[1811, 1853])).
% 2.33/2.00 tff(1858,assumption,(~c2_1(a271)), introduced(assumption)).
% 2.33/2.00 tff(1859,assumption,(~c0_1(a271)), introduced(assumption)).
% 2.33/2.00 tff(1860,assumption,(c2_1(a255)), introduced(assumption)).
% 2.33/2.00 tff(1861,plain,
% 2.33/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a271) | c2_1(a271) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a255)) | (~c3_1(a271)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a271) | c2_1(a271) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a255)) | (~c3_1(a271)))),
% 2.33/2.00 inference(rewrite,[status(thm)],[])).
% 2.33/2.00 tff(1862,plain,
% 2.33/2.00 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255))) <=> (c0_1(a271) | c2_1(a271) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a255)) | (~c3_1(a271)))),
% 2.33/2.00 inference(rewrite,[status(thm)],[])).
% 2.33/2.00 tff(1863,plain,
% 2.33/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a271) | c2_1(a271) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a255)) | (~c3_1(a271))))),
% 2.33/2.00 inference(monotonicity,[status(thm)],[1862])).
% 2.33/2.00 tff(1864,plain,
% 2.33/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a271) | c2_1(a271) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a255)) | (~c3_1(a271)))),
% 2.33/2.00 inference(transitivity,[status(thm)],[1863, 1861])).
% 2.33/2.00 tff(1865,plain,
% 2.33/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))),
% 2.33/2.00 inference(quant_inst,[status(thm)],[])).
% 2.33/2.00 tff(1866,plain,
% 2.33/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a271) | c2_1(a271) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a255)) | (~c3_1(a271))),
% 2.33/2.00 inference(modus_ponens,[status(thm)],[1865, 1864])).
% 2.33/2.00 tff(1867,plain,
% 2.33/2.00 ((~c2_1(a255)) | (~c3_1(a271))),
% 2.33/2.00 inference(unit_resolution,[status(thm)],[1866, 122, 1702, 1701, 1700, 1859, 1858, 1190, 1189, 1544])).
% 2.33/2.00 tff(1868,plain,
% 2.33/2.00 (~c3_1(a271)),
% 2.33/2.00 inference(unit_resolution,[status(thm)],[1867, 1860])).
% 2.33/2.00 tff(1869,plain,
% 2.33/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | c0_1(a231) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | c0_1(a231) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a255)))),
% 2.33/2.00 inference(rewrite,[status(thm)],[])).
% 2.33/2.00 tff(1870,plain,
% 2.33/2.00 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255))) <=> (c0_1(a255) | c1_1(a255) | c0_1(a231) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a255)))),
% 2.33/2.00 inference(rewrite,[status(thm)],[])).
% 2.33/2.00 tff(1871,plain,
% 2.33/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | c0_1(a231) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a255))))),
% 2.33/2.00 inference(monotonicity,[status(thm)],[1870])).
% 2.33/2.00 tff(1872,plain,
% 2.33/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | c0_1(a231) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a255)))),
% 2.33/2.00 inference(transitivity,[status(thm)],[1871, 1869])).
% 2.33/2.00 tff(1873,plain,
% 2.33/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))),
% 2.33/2.00 inference(quant_inst,[status(thm)],[])).
% 2.33/2.00 tff(1874,plain,
% 2.33/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | c0_1(a231) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a255))),
% 2.33/2.00 inference(modus_ponens,[status(thm)],[1873, 1872])).
% 2.33/2.00 tff(1875,plain,
% 2.33/2.00 (c2_1(a231) | (~c2_1(a255))),
% 2.33/2.00 inference(unit_resolution,[status(thm)],[1874, 122, 1702, 1701, 1700, 1616, 1190, 1189, 1615, 1544])).
% 2.33/2.00 tff(1876,plain,
% 2.33/2.00 (c2_1(a231)),
% 2.33/2.00 inference(unit_resolution,[status(thm)],[1875, 1860])).
% 2.33/2.00 tff(1877,plain,
% 2.33/2.00 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271))),
% 2.33/2.01 inference(rewrite,[status(thm)],[])).
% 2.33/2.01 tff(1878,plain,
% 2.33/2.01 ((hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271) | c0_1(a271) | c2_1(a271)) <=> (hskp9 | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271))),
% 2.33/2.01 inference(rewrite,[status(thm)],[])).
% 2.33/2.01 tff(1879,plain,
% 2.33/2.01 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271) | c0_1(a271) | c2_1(a271))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271)))),
% 2.33/2.01 inference(monotonicity,[status(thm)],[1878])).
% 2.33/2.01 tff(1880,plain,
% 2.33/2.01 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271) | c0_1(a271) | c2_1(a271))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271))),
% 2.33/2.01 inference(transitivity,[status(thm)],[1879, 1877])).
% 2.33/2.01 tff(1881,plain,
% 2.33/2.01 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271) | c0_1(a271) | c2_1(a271))),
% 2.33/2.01 inference(quant_inst,[status(thm)],[])).
% 2.33/2.01 tff(1882,plain,
% 2.33/2.01 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271)),
% 2.33/2.01 inference(modus_ponens,[status(thm)],[1881, 1880])).
% 2.33/2.01 tff(1883,plain,
% 2.33/2.01 ($false),
% 2.33/2.01 inference(unit_resolution,[status(thm)],[1882, 122, 23, 1616, 1859, 1858, 1615, 989, 1876, 1868])).
% 2.33/2.01 tff(1884,plain,((~c2_1(a255)) | hskp9 | (~c3_1(a231)) | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a255) | c1_1(a255)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.01 tff(1885,plain,
% 2.33/2.01 (~c2_1(a255)),
% 2.33/2.01 inference(unit_resolution,[status(thm)],[1884, 1190, 1616, 1859, 1858, 1615, 1702, 1701, 1700, 23, 1189])).
% 2.33/2.01 tff(1886,assumption,(~c2_1(a255)), introduced(assumption)).
% 2.33/2.01 tff(1887,assumption,(~c0_1(a261)), introduced(assumption)).
% 2.33/2.01 tff(1888,plain,
% 2.33/2.01 ($false),
% 2.33/2.01 inference(unit_resolution,[status(thm)],[1767, 122, 23, 1701, 1700, 1190, 1207, 989, 1887, 1886])).
% 2.33/2.01 tff(1889,plain,(c3_1(a255) | hskp9 | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a255) | c0_1(a261) | c2_1(a255)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.01 tff(1890,plain,
% 2.33/2.01 (c3_1(a255)),
% 2.33/2.01 inference(unit_resolution,[status(thm)],[1889, 1190, 1701, 1700, 23, 1703, 1885])).
% 2.33/2.01 tff(1891,plain,
% 2.33/2.01 (~hskp19),
% 2.33/2.01 inference(unit_resolution,[status(thm)],[288, 1890])).
% 2.33/2.01 tff(1892,assumption,(~c1_1(a271)), introduced(assumption)).
% 2.33/2.01 tff(1893,plain,
% 2.33/2.01 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | c3_1(a271))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | c3_1(a271))),
% 2.33/2.01 inference(rewrite,[status(thm)],[])).
% 2.33/2.01 tff(1894,plain,
% 2.33/2.01 ((hskp19 | hskp21 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c3_1(a271)) <=> (hskp19 | hskp21 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | c3_1(a271))),
% 2.33/2.01 inference(rewrite,[status(thm)],[])).
% 2.33/2.01 tff(1895,plain,
% 2.33/2.01 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c3_1(a271))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | c3_1(a271)))),
% 2.33/2.01 inference(monotonicity,[status(thm)],[1894])).
% 2.33/2.01 tff(1896,plain,
% 2.33/2.01 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c3_1(a271))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | c3_1(a271))),
% 2.33/2.01 inference(transitivity,[status(thm)],[1895, 1893])).
% 2.33/2.01 tff(1897,plain,
% 2.33/2.01 ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c3_1(a271))),
% 2.33/2.01 inference(quant_inst,[status(thm)],[])).
% 2.33/2.01 tff(1898,plain,
% 2.33/2.01 ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | c3_1(a271)),
% 2.33/2.01 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 2.33/2.01 tff(1899,plain,
% 2.33/2.01 (hskp19 | c3_1(a271)),
% 2.33/2.01 inference(unit_resolution,[status(thm)],[1898, 122, 1855, 1892, 1858, 1738])).
% 2.33/2.01 tff(1900,plain,
% 2.33/2.01 (c3_1(a271)),
% 2.33/2.01 inference(unit_resolution,[status(thm)],[1899, 1891])).
% 2.33/2.01 tff(1901,plain,
% 2.33/2.01 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 2.33/2.01 inference(bind,[status(th)],[])).
% 2.33/2.01 tff(1902,plain,
% 2.33/2.01 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/2.01 inference(quant_intro,[status(thm)],[1901])).
% 2.33/2.01 tff(1903,plain,
% 2.33/2.01 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/2.01 inference(rewrite,[status(thm)],[])).
% 2.33/2.01 tff(1904,plain,
% 2.33/2.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 2.33/2.01 inference(bind,[status(th)],[])).
% 2.33/2.01 tff(1905,plain,
% 2.33/2.01 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/2.01 inference(quant_intro,[status(thm)],[1904])).
% 2.33/2.01 tff(1906,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 2.33/2.01 tff(1907,plain,
% 2.33/2.01 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/2.01 inference(modus_ponens,[status(thm)],[1906, 1905])).
% 2.33/2.01 tff(1908,plain,
% 2.33/2.01 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/2.01 inference(modus_ponens,[status(thm)],[1907, 1903])).
% 2.33/2.01 tff(1909,plain,(
% 2.33/2.01 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/2.01 inference(skolemize,[status(sab)],[1908])).
% 2.33/2.01 tff(1910,plain,
% 2.33/2.01 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.33/2.01 inference(modus_ponens,[status(thm)],[1909, 1902])).
% 2.33/2.01 tff(1911,assumption,(c2_1(a237)), introduced(assumption)).
% 2.33/2.01 tff(1912,plain,
% 2.33/2.01 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | c2_1(a255))),
% 2.33/2.01 inference(rewrite,[status(thm)],[])).
% 2.33/2.01 tff(1913,plain,
% 2.33/2.01 ((hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a255) | c2_1(a255) | (~c3_1(a255))) <=> (hskp5 | c0_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | c2_1(a255))),
% 2.33/2.01 inference(rewrite,[status(thm)],[])).
% 2.33/2.01 tff(1914,plain,
% 2.33/2.01 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a255) | c2_1(a255) | (~c3_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | c2_1(a255)))),
% 2.33/2.01 inference(monotonicity,[status(thm)],[1913])).
% 2.33/2.01 tff(1915,plain,
% 2.33/2.01 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a255) | c2_1(a255) | (~c3_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | c2_1(a255))),
% 2.33/2.01 inference(transitivity,[status(thm)],[1914, 1912])).
% 2.33/2.01 tff(1916,plain,
% 2.33/2.01 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a255) | c2_1(a255) | (~c3_1(a255)))),
% 2.33/2.01 inference(quant_inst,[status(thm)],[])).
% 2.33/2.01 tff(1917,plain,
% 2.33/2.01 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | c2_1(a255)),
% 2.33/2.02 inference(modus_ponens,[status(thm)],[1916, 1915])).
% 2.33/2.02 tff(1918,plain,
% 2.33/2.02 ((~c3_1(a255)) | (~c1_1(a237)) | c2_1(a255)),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1917, 122, 45, 1911, 1190, 179, 1910])).
% 2.33/2.02 tff(1919,plain,
% 2.33/2.02 (~c1_1(a237)),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1918, 1890, 1885])).
% 2.33/2.02 tff(1920,assumption,(c0_1(a237)), introduced(assumption)).
% 2.33/2.02 tff(1921,plain,
% 2.33/2.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a271)))),
% 2.33/2.02 inference(rewrite,[status(thm)],[])).
% 2.33/2.02 tff(1922,plain,
% 2.33/2.02 ((hskp5 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c0_1(a237)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271))) <=> (hskp5 | c1_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a271)))),
% 2.33/2.02 inference(rewrite,[status(thm)],[])).
% 2.33/2.02 tff(1923,plain,
% 2.33/2.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c0_1(a237)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a271))))),
% 2.33/2.02 inference(monotonicity,[status(thm)],[1922])).
% 2.33/2.02 tff(1924,plain,
% 2.33/2.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c0_1(a237)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a271)))),
% 2.33/2.02 inference(transitivity,[status(thm)],[1923, 1921])).
% 2.33/2.02 tff(1925,plain,
% 2.33/2.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c0_1(a237)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271)))),
% 2.33/2.02 inference(quant_inst,[status(thm)],[])).
% 2.33/2.02 tff(1926,plain,
% 2.33/2.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a271))),
% 2.33/2.02 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 2.33/2.02 tff(1927,plain,
% 2.33/2.02 ($false),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1926, 122, 45, 1920, 1892, 1858, 179, 1788, 1919, 1900])).
% 2.33/2.02 tff(1928,plain,(c0_1(a255) | hskp5 | (~c0_1(a237)) | c1_1(a271) | c2_1(a271) | c3_1(a237) | hskp21 | (~c2_1(a237)) | (~c2_1(a261)) | (~c3_1(a261)) | hskp9 | (~c3_1(a231)) | c0_1(a271) | c0_1(a231) | (~c1_1(a261)) | c1_1(a255)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.02 tff(1929,plain,
% 2.33/2.02 (c0_1(a255)),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1928, 1189, 1507, 1857, 1856, 1505, 1855, 1506, 1328, 1317, 1697, 1616, 1854, 1615, 1339, 45])).
% 2.33/2.02 tff(1930,plain,
% 2.33/2.02 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~c0_1(a255)) | c1_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | (~c0_1(a255)) | c1_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.33/2.02 inference(rewrite,[status(thm)],[])).
% 2.33/2.02 tff(1931,plain,
% 2.33/2.02 ((hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a255) | (~c3_1(a255)) | (~c0_1(a255))) <=> (hskp18 | (~c0_1(a255)) | c1_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.33/2.02 inference(rewrite,[status(thm)],[])).
% 2.33/2.02 tff(1932,plain,
% 2.33/2.02 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a255) | (~c3_1(a255)) | (~c0_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~c0_1(a255)) | c1_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237))))),
% 2.33/2.02 inference(monotonicity,[status(thm)],[1931])).
% 2.33/2.02 tff(1933,plain,
% 2.33/2.02 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a255) | (~c3_1(a255)) | (~c0_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | (~c0_1(a255)) | c1_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.33/2.02 inference(transitivity,[status(thm)],[1932, 1930])).
% 2.33/2.02 tff(1934,plain,
% 2.33/2.02 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a255) | (~c3_1(a255)) | (~c0_1(a255)))),
% 2.33/2.02 inference(quant_inst,[status(thm)],[])).
% 2.33/2.02 tff(1935,plain,
% 2.33/2.02 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | (~c0_1(a255)) | c1_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237))),
% 2.33/2.02 inference(modus_ponens,[status(thm)],[1934, 1933])).
% 2.33/2.02 tff(1936,plain,
% 2.33/2.02 ((~c0_1(a255)) | (~c3_1(a255))),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1935, 122, 650, 1507, 1506, 1189, 1505, 1387])).
% 2.33/2.02 tff(1937,plain,
% 2.33/2.02 (~c3_1(a255)),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1936, 1929])).
% 2.33/2.02 tff(1938,plain,
% 2.33/2.02 (~hskp19),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[300, 1929])).
% 2.33/2.02 tff(1939,plain,
% 2.33/2.02 (hskp19 | c3_1(a271)),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1898, 122, 1855, 1857, 1856, 1738])).
% 2.33/2.02 tff(1940,plain,
% 2.33/2.02 (c3_1(a271)),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1939, 1938])).
% 2.33/2.02 tff(1941,plain,
% 2.33/2.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a271) | c2_1(a271) | (~c0_1(a255)) | c1_1(a255) | c3_1(a255) | (~ndr1_0) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a271) | c2_1(a271) | (~c0_1(a255)) | c1_1(a255) | c3_1(a255) | (~ndr1_0) | (~c3_1(a271)))),
% 2.33/2.02 inference(rewrite,[status(thm)],[])).
% 2.33/2.02 tff(1942,plain,
% 2.33/2.02 ((hskp5 | (~ndr1_0) | c1_1(a255) | c3_1(a255) | (~c0_1(a255)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271))) <=> (hskp5 | c1_1(a271) | c2_1(a271) | (~c0_1(a255)) | c1_1(a255) | c3_1(a255) | (~ndr1_0) | (~c3_1(a271)))),
% 2.33/2.02 inference(rewrite,[status(thm)],[])).
% 2.33/2.02 tff(1943,plain,
% 2.33/2.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a255) | c3_1(a255) | (~c0_1(a255)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a271) | c2_1(a271) | (~c0_1(a255)) | c1_1(a255) | c3_1(a255) | (~ndr1_0) | (~c3_1(a271))))),
% 2.33/2.02 inference(monotonicity,[status(thm)],[1942])).
% 2.33/2.02 tff(1944,plain,
% 2.33/2.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a255) | c3_1(a255) | (~c0_1(a255)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a271) | c2_1(a271) | (~c0_1(a255)) | c1_1(a255) | c3_1(a255) | (~ndr1_0) | (~c3_1(a271)))),
% 2.33/2.02 inference(transitivity,[status(thm)],[1943, 1941])).
% 2.33/2.02 tff(1945,plain,
% 2.33/2.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a255) | c3_1(a255) | (~c0_1(a255)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271)))),
% 2.33/2.02 inference(quant_inst,[status(thm)],[])).
% 2.33/2.02 tff(1946,plain,
% 2.33/2.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a271) | c2_1(a271) | (~c0_1(a255)) | c1_1(a255) | c3_1(a255) | (~ndr1_0) | (~c3_1(a271))),
% 2.33/2.02 inference(modus_ponens,[status(thm)],[1945, 1944])).
% 2.33/2.02 tff(1947,plain,
% 2.33/2.02 ((~c0_1(a255)) | c3_1(a255) | (~c3_1(a271))),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1946, 122, 45, 1857, 1856, 1189, 1788])).
% 2.33/2.02 tff(1948,plain,
% 2.33/2.02 ($false),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1947, 1940, 1937, 1929])).
% 2.33/2.02 tff(1949,plain,(c1_1(a255) | hskp5 | hskp21 | hskp18 | (~c3_1(a231)) | c0_1(a231)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.02 tff(1950,plain,
% 2.33/2.02 (c1_1(a255)),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1949, 45, 1852, 650, 1616, 1615])).
% 2.33/2.02 tff(1951,plain,
% 2.33/2.02 (~hskp19),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[294, 1950])).
% 2.33/2.02 tff(1952,plain,
% 2.33/2.02 (hskp19 | c3_1(a271)),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1898, 122, 1852, 1857, 1856, 1738])).
% 2.33/2.02 tff(1953,plain,
% 2.33/2.02 (c3_1(a271)),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1952, 1951])).
% 2.33/2.02 tff(1954,plain,
% 2.33/2.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | (~c3_1(a271)))),
% 2.33/2.02 inference(rewrite,[status(thm)],[])).
% 2.33/2.02 tff(1955,plain,
% 2.33/2.02 ((hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271))) <=> (hskp5 | c0_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | (~c3_1(a271)))),
% 2.33/2.02 inference(rewrite,[status(thm)],[])).
% 2.33/2.02 tff(1956,plain,
% 2.33/2.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | (~c3_1(a271))))),
% 2.33/2.02 inference(monotonicity,[status(thm)],[1955])).
% 2.33/2.02 tff(1957,plain,
% 2.33/2.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | (~c3_1(a271)))),
% 2.33/2.02 inference(transitivity,[status(thm)],[1956, 1954])).
% 2.33/2.02 tff(1958,plain,
% 2.33/2.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)))),
% 2.33/2.02 inference(quant_inst,[status(thm)],[])).
% 2.33/2.02 tff(1959,plain,
% 2.33/2.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | (~c3_1(a271))),
% 2.33/2.02 inference(modus_ponens,[status(thm)],[1958, 1957])).
% 2.33/2.02 tff(1960,plain,
% 2.33/2.02 ((~c1_1(a237)) | (~c3_1(a271))),
% 2.33/2.02 inference(unit_resolution,[status(thm)],[1959, 122, 45, 1506, 1854, 1856, 1505, 1910])).
% 2.33/2.02 tff(1961,plain,
% 2.33/2.02 (~c1_1(a237)),
% 2.33/2.03 inference(unit_resolution,[status(thm)],[1960, 1953])).
% 2.33/2.03 tff(1962,plain,
% 2.33/2.03 ($false),
% 2.33/2.03 inference(unit_resolution,[status(thm)],[1926, 122, 45, 1507, 1857, 1856, 1505, 1788, 1961, 1953])).
% 2.33/2.03 tff(1963,plain,(hskp5 | hskp18 | (~c3_1(a231)) | c0_1(a231) | (~c1_1(a231))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.03 tff(1964,plain,
% 2.33/2.03 ($false),
% 2.33/2.03 inference(unit_resolution,[status(thm)],[1963, 1614, 1613, 650, 1612, 662])).
% 2.33/2.03 tff(1965,plain,((~hskp10) | hskp18), inference(lemma,lemma(discharge,[]))).
% 2.33/2.03 tff(1966,plain,
% 2.33/2.03 (~hskp10),
% 2.33/2.03 inference(unit_resolution,[status(thm)],[1965, 650])).
% 2.33/2.03 tff(1967,plain,
% 2.33/2.03 (~hskp9),
% 2.33/2.03 inference(unit_resolution,[status(thm)],[1696, 1612, 650])).
% 2.33/2.03 tff(1968,plain,
% 2.33/2.03 (hskp22),
% 2.33/2.03 inference(unit_resolution,[status(thm)],[1799, 1967, 650])).
% 2.33/2.03 tff(1969,plain,
% 2.33/2.03 (~c2_1(a271)),
% 2.33/2.03 inference(unit_resolution,[status(thm)],[1805, 1968])).
% 2.33/2.03 tff(1970,plain,
% 2.33/2.03 (~c1_1(a271)),
% 2.33/2.03 inference(unit_resolution,[status(thm)],[1811, 1968])).
% 2.33/2.03 tff(1971,plain,
% 2.33/2.03 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a271)))),
% 2.33/2.03 inference(rewrite,[status(thm)],[])).
% 2.33/2.03 tff(1972,plain,
% 2.33/2.03 ((hskp10 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | (~c3_1(a271)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261))) <=> (hskp10 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a271)))),
% 2.33/2.03 inference(rewrite,[status(thm)],[])).
% 2.33/2.03 tff(1973,plain,
% 2.33/2.03 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | (~c3_1(a271)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a271))))),
% 2.33/2.03 inference(monotonicity,[status(thm)],[1972])).
% 2.33/2.03 tff(1974,plain,
% 2.33/2.03 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | (~c3_1(a271)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a271)))),
% 2.33/2.03 inference(transitivity,[status(thm)],[1973, 1971])).
% 2.33/2.03 tff(1975,plain,
% 2.33/2.03 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | (~c3_1(a271)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))),
% 2.33/2.03 inference(quant_inst,[status(thm)],[])).
% 2.33/2.03 tff(1976,plain,
% 2.33/2.03 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a271))),
% 2.33/2.03 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 2.33/2.03 tff(1977,plain,
% 2.33/2.03 (hskp10 | (~c3_1(a271))),
% 2.33/2.03 inference(unit_resolution,[status(thm)],[1976, 122, 1339, 1317, 1970, 1969, 1404, 1346])).
% 2.33/2.03 tff(1978,plain,
% 2.33/2.03 (~c3_1(a271)),
% 2.33/2.03 inference(unit_resolution,[status(thm)],[1977, 1966])).
% 2.33/2.03 tff(1979,plain,
% 2.33/2.03 (~c0_1(a271)),
% 2.33/2.03 inference(unit_resolution,[status(thm)],[1817, 1968])).
% 2.33/2.03 tff(1980,plain,
% 2.33/2.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a271) | c2_1(a271) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a271))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a271) | c2_1(a271) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a271))),
% 2.38/2.03 inference(rewrite,[status(thm)],[])).
% 2.38/2.03 tff(1981,plain,
% 2.38/2.03 ((hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a271) | c0_1(a271) | c2_1(a271)) <=> (hskp9 | c0_1(a271) | c2_1(a271) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a271))),
% 2.38/2.03 inference(rewrite,[status(thm)],[])).
% 2.38/2.03 tff(1982,plain,
% 2.38/2.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a271) | c0_1(a271) | c2_1(a271))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a271) | c2_1(a271) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a271)))),
% 2.38/2.03 inference(monotonicity,[status(thm)],[1981])).
% 2.38/2.03 tff(1983,plain,
% 2.38/2.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a271) | c0_1(a271) | c2_1(a271))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a271) | c2_1(a271) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a271))),
% 2.38/2.03 inference(transitivity,[status(thm)],[1982, 1980])).
% 2.38/2.03 tff(1984,plain,
% 2.38/2.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a271) | c0_1(a271) | c2_1(a271))),
% 2.38/2.03 inference(quant_inst,[status(thm)],[])).
% 2.38/2.03 tff(1985,plain,
% 2.38/2.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a271) | c2_1(a271) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a271)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 2.38/2.03 tff(1986,plain,
% 2.38/2.03 ($false),
% 2.38/2.03 inference(unit_resolution,[status(thm)],[1985, 122, 1967, 1328, 1317, 1979, 1969, 989, 1346, 1978])).
% 2.38/2.03 tff(1987,plain,(hskp18), inference(lemma,lemma(discharge,[]))).
% 2.38/2.03 tff(1988,plain,
% 2.38/2.03 (((~hskp18) | c2_1(a252)) <=> ((~hskp18) | c2_1(a252))),
% 2.38/2.03 inference(rewrite,[status(thm)],[])).
% 2.38/2.03 tff(1989,axiom,((~hskp18) | c2_1(a252)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 2.38/2.03 tff(1990,plain,
% 2.38/2.03 ((~hskp18) | c2_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 2.38/2.03 tff(1991,plain,
% 2.38/2.03 ((~hskp18) | c2_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[1990, 1988])).
% 2.38/2.03 tff(1992,plain,
% 2.38/2.03 ((~hskp18) | c2_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[1991, 1988])).
% 2.38/2.03 tff(1993,plain,
% 2.38/2.03 ((~hskp18) | c2_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[1992, 1988])).
% 2.38/2.03 tff(1994,plain,
% 2.38/2.03 ((~hskp18) | c2_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[1993, 1988])).
% 2.38/2.03 tff(1995,plain,
% 2.38/2.03 ((~hskp18) | c2_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[1994, 1988])).
% 2.38/2.03 tff(1996,plain,
% 2.38/2.03 ((~hskp18) | c2_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[1995, 1988])).
% 2.38/2.03 tff(1997,plain,
% 2.38/2.03 ((~hskp18) | c2_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[1996, 1988])).
% 2.38/2.03 tff(1998,plain,
% 2.38/2.03 (c2_1(a252)),
% 2.38/2.03 inference(unit_resolution,[status(thm)],[1997, 1987])).
% 2.38/2.03 tff(1999,plain,
% 2.38/2.03 (((~hskp18) | c0_1(a252)) <=> ((~hskp18) | c0_1(a252))),
% 2.38/2.03 inference(rewrite,[status(thm)],[])).
% 2.38/2.03 tff(2000,axiom,((~hskp18) | c0_1(a252)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 2.38/2.03 tff(2001,plain,
% 2.38/2.03 ((~hskp18) | c0_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[2000, 1999])).
% 2.38/2.03 tff(2002,plain,
% 2.38/2.03 ((~hskp18) | c0_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[2001, 1999])).
% 2.38/2.03 tff(2003,plain,
% 2.38/2.03 ((~hskp18) | c0_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[2002, 1999])).
% 2.38/2.03 tff(2004,plain,
% 2.38/2.03 ((~hskp18) | c0_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[2003, 1999])).
% 2.38/2.03 tff(2005,plain,
% 2.38/2.03 ((~hskp18) | c0_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[2004, 1999])).
% 2.38/2.03 tff(2006,plain,
% 2.38/2.03 ((~hskp18) | c0_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[2005, 1999])).
% 2.38/2.03 tff(2007,plain,
% 2.38/2.03 ((~hskp18) | c0_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[2006, 1999])).
% 2.38/2.03 tff(2008,plain,
% 2.38/2.03 ((~hskp18) | c0_1(a252)),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[2007, 1999])).
% 2.38/2.03 tff(2009,plain,
% 2.38/2.03 (c0_1(a252)),
% 2.38/2.03 inference(unit_resolution,[status(thm)],[2008, 1987])).
% 2.38/2.03 tff(2010,plain,
% 2.38/2.03 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.38/2.03 inference(rewrite,[status(thm)],[])).
% 2.38/2.03 tff(2011,plain,
% 2.38/2.03 ((hskp2 | (~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | c0_1(a237)) <=> (hskp2 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.38/2.03 inference(rewrite,[status(thm)],[])).
% 2.38/2.03 tff(2012,plain,
% 2.38/2.03 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | c0_1(a237))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))))),
% 2.38/2.03 inference(monotonicity,[status(thm)],[2011])).
% 2.38/2.03 tff(2013,plain,
% 2.38/2.03 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | c0_1(a237))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.38/2.03 inference(transitivity,[status(thm)],[2012, 2010])).
% 2.38/2.03 tff(2014,plain,
% 2.38/2.03 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | c0_1(a237))),
% 2.38/2.03 inference(quant_inst,[status(thm)],[])).
% 2.38/2.03 tff(2015,plain,
% 2.38/2.03 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[2014, 2013])).
% 2.38/2.03 tff(2016,plain,
% 2.38/2.03 (hskp2 | c0_1(a237) | c1_1(a237) | (~c3_1(a252))),
% 2.38/2.03 inference(unit_resolution,[status(thm)],[2015, 122, 2009, 1998, 179, 649])).
% 2.38/2.03 tff(2017,plain,
% 2.38/2.03 (~c3_1(a252)),
% 2.38/2.03 inference(unit_resolution,[status(thm)],[2016, 639, 619, 90])).
% 2.38/2.03 tff(2018,plain,
% 2.38/2.03 (((~hskp18) | (~c1_1(a252))) <=> ((~hskp18) | (~c1_1(a252)))),
% 2.38/2.03 inference(rewrite,[status(thm)],[])).
% 2.38/2.03 tff(2019,plain,
% 2.38/2.03 (((~c1_1(a252)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a252)))),
% 2.38/2.03 inference(rewrite,[status(thm)],[])).
% 2.38/2.03 tff(2020,axiom,((~c1_1(a252)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 2.38/2.03 tff(2021,plain,
% 2.38/2.03 ((~hskp18) | (~c1_1(a252))),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[2020, 2019])).
% 2.38/2.03 tff(2022,plain,
% 2.38/2.03 ((~hskp18) | (~c1_1(a252))),
% 2.38/2.03 inference(modus_ponens,[status(thm)],[2021, 2018])).
% 2.38/2.03 tff(2023,plain,
% 2.38/2.03 (~c1_1(a252)),
% 2.38/2.03 inference(unit_resolution,[status(thm)],[2022, 1987])).
% 2.38/2.03 tff(2024,plain,
% 2.38/2.03 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)))),
% 2.38/2.03 inference(rewrite,[status(thm)],[])).
% 2.38/2.04 tff(2025,plain,
% 2.38/2.04 ((hskp21 | hskp12 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c2_1(a237))) <=> (hskp21 | hskp12 | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)))),
% 2.38/2.04 inference(rewrite,[status(thm)],[])).
% 2.38/2.04 tff(2026,plain,
% 2.38/2.04 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c2_1(a237)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237))))),
% 2.38/2.04 inference(monotonicity,[status(thm)],[2025])).
% 2.38/2.04 tff(2027,plain,
% 2.38/2.04 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c2_1(a237)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)))),
% 2.38/2.04 inference(transitivity,[status(thm)],[2026, 2024])).
% 2.38/2.04 tff(2028,plain,
% 2.38/2.04 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c2_1(a237)))),
% 2.38/2.04 inference(quant_inst,[status(thm)],[])).
% 2.38/2.04 tff(2029,plain,
% 2.38/2.04 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237))),
% 2.38/2.04 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 2.38/2.04 tff(2030,plain,
% 2.38/2.04 (hskp21 | hskp12 | c1_1(a237) | (~c2_1(a237))),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[2029, 122, 179, 804])).
% 2.38/2.04 tff(2031,plain,
% 2.38/2.04 (hskp21),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[2030, 631, 630, 639])).
% 2.38/2.04 tff(2032,plain,
% 2.38/2.04 (~c2_1(a259)),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[1062, 2031])).
% 2.38/2.04 tff(2033,plain,
% 2.38/2.04 (c3_1(a259)),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[867, 2031])).
% 2.38/2.04 tff(2034,plain,
% 2.38/2.04 (c0_1(a259)),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[855, 2031])).
% 2.38/2.04 tff(2035,plain,
% 2.38/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.38/2.04 inference(rewrite,[status(thm)],[])).
% 2.38/2.04 tff(2036,plain,
% 2.38/2.04 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c2_1(a259) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.38/2.04 inference(rewrite,[status(thm)],[])).
% 2.38/2.04 tff(2037,plain,
% 2.38/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 2.38/2.04 inference(monotonicity,[status(thm)],[2036])).
% 2.38/2.04 tff(2038,plain,
% 2.38/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.38/2.04 inference(transitivity,[status(thm)],[2037, 2035])).
% 2.38/2.04 tff(2039,plain,
% 2.38/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 2.38/2.04 inference(quant_inst,[status(thm)],[])).
% 2.38/2.04 tff(2040,plain,
% 2.38/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 2.38/2.04 inference(modus_ponens,[status(thm)],[2039, 2038])).
% 2.38/2.04 tff(2041,plain,
% 2.38/2.04 ($false),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[2040, 122, 2034, 2033, 2009, 631, 2032, 2023, 179, 22, 2017, 639])).
% 2.38/2.04 tff(2042,plain,(hskp2 | c3_1(a237) | c0_1(a237) | hskp9 | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.38/2.04 tff(2043,plain,
% 2.38/2.04 (hskp2),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[2042, 619, 179, 23, 34])).
% 2.38/2.04 tff(2044,plain,
% 2.38/2.04 (~c1_1(a215)),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[136, 2043])).
% 2.38/2.04 tff(2045,plain,
% 2.38/2.04 (~c0_1(a215)),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[153, 2043])).
% 2.38/2.04 tff(2046,plain,
% 2.38/2.04 (c2_1(a215)),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[147, 2043])).
% 2.38/2.04 tff(2047,plain,
% 2.38/2.04 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a237) | c2_1(a237) | c3_1(a237) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a237) | c2_1(a237) | c3_1(a237) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)))),
% 2.38/2.04 inference(rewrite,[status(thm)],[])).
% 2.38/2.04 tff(2048,plain,
% 2.38/2.04 ((hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a237) | c0_1(a237) | c2_1(a237)) <=> (hskp9 | c0_1(a237) | c2_1(a237) | c3_1(a237) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)))),
% 2.38/2.04 inference(rewrite,[status(thm)],[])).
% 2.38/2.04 tff(2049,plain,
% 2.38/2.04 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a237) | c0_1(a237) | c2_1(a237))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a237) | c2_1(a237) | c3_1(a237) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215))))),
% 2.38/2.04 inference(monotonicity,[status(thm)],[2048])).
% 2.38/2.04 tff(2050,plain,
% 2.38/2.04 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a237) | c0_1(a237) | c2_1(a237))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a237) | c2_1(a237) | c3_1(a237) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)))),
% 2.38/2.04 inference(transitivity,[status(thm)],[2049, 2047])).
% 2.38/2.04 tff(2051,plain,
% 2.38/2.04 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a237) | c0_1(a237) | c2_1(a237))),
% 2.38/2.04 inference(quant_inst,[status(thm)],[])).
% 2.38/2.04 tff(2052,plain,
% 2.38/2.04 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a237) | c2_1(a237) | c3_1(a237) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215))),
% 2.38/2.04 inference(modus_ponens,[status(thm)],[2051, 2050])).
% 2.38/2.04 tff(2053,plain,
% 2.38/2.04 (c2_1(a237) | (~c3_1(a215))),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[2052, 122, 23, 619, 167, 179, 166, 989])).
% 2.38/2.04 tff(2054,plain,
% 2.38/2.04 (~c3_1(a215)),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[2053, 575])).
% 2.38/2.04 tff(2055,plain,
% 2.38/2.04 (hskp21 | c3_1(a215)),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[1263, 122, 630, 167, 165, 804])).
% 2.38/2.04 tff(2056,plain,
% 2.38/2.04 (hskp21),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[2055, 2054])).
% 2.38/2.04 tff(2057,plain,
% 2.38/2.04 (~c2_1(a259)),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[1062, 2056])).
% 2.38/2.04 tff(2058,plain,
% 2.38/2.04 (c3_1(a259)),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[867, 2056])).
% 2.38/2.04 tff(2059,plain,
% 2.38/2.04 (c0_1(a259)),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[855, 2056])).
% 2.38/2.04 tff(2060,plain,
% 2.38/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.38/2.04 inference(rewrite,[status(thm)],[])).
% 2.38/2.04 tff(2061,plain,
% 2.38/2.04 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215))) <=> (c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.38/2.04 inference(rewrite,[status(thm)],[])).
% 2.38/2.04 tff(2062,plain,
% 2.38/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 2.38/2.04 inference(monotonicity,[status(thm)],[2061])).
% 2.38/2.04 tff(2063,plain,
% 2.38/2.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.38/2.04 inference(transitivity,[status(thm)],[2062, 2060])).
% 2.38/2.04 tff(2064,plain,
% 2.38/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))),
% 2.38/2.04 inference(quant_inst,[status(thm)],[])).
% 2.38/2.04 tff(2065,plain,
% 2.38/2.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 2.38/2.04 inference(modus_ponens,[status(thm)],[2064, 2063])).
% 2.38/2.04 tff(2066,plain,
% 2.38/2.04 (~c3_1(a252)),
% 2.38/2.04 inference(unit_resolution,[status(thm)],[2065, 122, 2059, 2058, 2009, 1998, 167, 2057, 166, 165, 931])).
% 2.38/2.04 tff(2067,plain,
% 2.38/2.04 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | c0_1(a237) | c2_1(a237) | c3_1(a237) | (~ndr1_0))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp6 | hskp5 | c0_1(a237) | c2_1(a237) | c3_1(a237) | (~ndr1_0))),
% 2.40/2.05 inference(rewrite,[status(thm)],[])).
% 2.40/2.05 tff(2068,plain,
% 2.40/2.05 ((hskp6 | hskp5 | (~ndr1_0) | c2_1(a237) | c0_1(a237) | c3_1(a237)) <=> (hskp6 | hskp5 | c0_1(a237) | c2_1(a237) | c3_1(a237) | (~ndr1_0))),
% 2.40/2.05 inference(rewrite,[status(thm)],[])).
% 2.40/2.05 tff(2069,plain,
% 2.40/2.05 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a237) | c0_1(a237) | c3_1(a237))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | c0_1(a237) | c2_1(a237) | c3_1(a237) | (~ndr1_0)))),
% 2.40/2.05 inference(monotonicity,[status(thm)],[2068])).
% 2.40/2.05 tff(2070,plain,
% 2.40/2.05 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a237) | c0_1(a237) | c3_1(a237))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp6 | hskp5 | c0_1(a237) | c2_1(a237) | c3_1(a237) | (~ndr1_0))),
% 2.40/2.05 inference(transitivity,[status(thm)],[2069, 2067])).
% 2.40/2.05 tff(2071,plain,
% 2.40/2.05 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a237) | c0_1(a237) | c3_1(a237))),
% 2.40/2.05 inference(quant_inst,[status(thm)],[])).
% 2.40/2.05 tff(2072,plain,
% 2.40/2.05 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp6 | hskp5 | c0_1(a237) | c2_1(a237) | c3_1(a237) | (~ndr1_0)),
% 2.40/2.05 inference(modus_ponens,[status(thm)],[2071, 2070])).
% 2.40/2.05 tff(2073,plain,
% 2.40/2.05 (hskp6 | c0_1(a237) | c2_1(a237)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[2072, 122, 45, 179, 1677])).
% 2.40/2.05 tff(2074,plain,
% 2.40/2.05 (hskp6),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[2073, 575, 619])).
% 2.40/2.05 tff(2075,plain,
% 2.40/2.05 (~c3_1(a220)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[485, 2074])).
% 2.40/2.05 tff(2076,plain,
% 2.40/2.05 (c2_1(a220)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[541, 2074])).
% 2.40/2.05 tff(2077,plain,
% 2.40/2.05 (c1_1(a220)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[530, 2074])).
% 2.40/2.05 tff(2078,plain,
% 2.40/2.05 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a237) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a237) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c1_1(a237)))),
% 2.40/2.05 inference(rewrite,[status(thm)],[])).
% 2.40/2.05 tff(2079,plain,
% 2.40/2.05 ((hskp12 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237))) <=> (hskp12 | c0_1(a237) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c1_1(a237)))),
% 2.40/2.05 inference(rewrite,[status(thm)],[])).
% 2.40/2.05 tff(2080,plain,
% 2.40/2.05 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a237) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c1_1(a237))))),
% 2.40/2.05 inference(monotonicity,[status(thm)],[2079])).
% 2.40/2.05 tff(2081,plain,
% 2.40/2.05 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a237) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c1_1(a237)))),
% 2.40/2.05 inference(transitivity,[status(thm)],[2080, 2078])).
% 2.40/2.05 tff(2082,plain,
% 2.40/2.05 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237)))),
% 2.40/2.05 inference(quant_inst,[status(thm)],[])).
% 2.40/2.05 tff(2083,plain,
% 2.40/2.05 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a237) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c1_1(a237))),
% 2.40/2.05 inference(modus_ponens,[status(thm)],[2082, 2081])).
% 2.40/2.05 tff(2084,plain,
% 2.40/2.05 (~c1_1(a237)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[2083, 122, 630, 619, 2077, 2076, 179, 2075, 44])).
% 2.40/2.05 tff(2085,plain,
% 2.40/2.05 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c0_1(a237) | c2_1(a237) | (~ndr1_0) | c1_1(a237))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a237) | c2_1(a237) | (~ndr1_0) | c1_1(a237))),
% 2.40/2.05 inference(rewrite,[status(thm)],[])).
% 2.40/2.05 tff(2086,plain,
% 2.40/2.05 ((hskp0 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c0_1(a237)) <=> (hskp0 | c0_1(a237) | c2_1(a237) | (~ndr1_0) | c1_1(a237))),
% 2.40/2.05 inference(rewrite,[status(thm)],[])).
% 2.40/2.05 tff(2087,plain,
% 2.40/2.05 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c0_1(a237))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c0_1(a237) | c2_1(a237) | (~ndr1_0) | c1_1(a237)))),
% 2.40/2.05 inference(monotonicity,[status(thm)],[2086])).
% 2.40/2.05 tff(2088,plain,
% 2.40/2.05 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c0_1(a237))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a237) | c2_1(a237) | (~ndr1_0) | c1_1(a237))),
% 2.40/2.05 inference(transitivity,[status(thm)],[2087, 2085])).
% 2.40/2.05 tff(2089,plain,
% 2.40/2.05 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c0_1(a237))),
% 2.40/2.05 inference(quant_inst,[status(thm)],[])).
% 2.40/2.05 tff(2090,plain,
% 2.40/2.05 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a237) | c2_1(a237) | (~ndr1_0) | c1_1(a237)),
% 2.40/2.05 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 2.40/2.05 tff(2091,plain,
% 2.40/2.05 (hskp0 | c2_1(a237) | c1_1(a237)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[2090, 122, 619, 1098])).
% 2.40/2.05 tff(2092,plain,
% 2.40/2.05 (hskp0),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[2091, 2084, 575])).
% 2.40/2.05 tff(2093,plain,
% 2.40/2.05 (~c3_1(a213)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[810, 2092])).
% 2.40/2.05 tff(2094,plain,
% 2.40/2.05 (~c1_1(a213)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[816, 2092])).
% 2.40/2.05 tff(2095,plain,
% 2.40/2.05 (c2_1(a213)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[827, 2092])).
% 2.40/2.05 tff(2096,plain,
% 2.40/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.05 inference(rewrite,[status(thm)],[])).
% 2.40/2.05 tff(2097,plain,
% 2.40/2.05 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c2_1(a259) | c1_1(a252) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.05 inference(rewrite,[status(thm)],[])).
% 2.40/2.05 tff(2098,plain,
% 2.40/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 2.40/2.05 inference(monotonicity,[status(thm)],[2097])).
% 2.40/2.05 tff(2099,plain,
% 2.40/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.05 inference(transitivity,[status(thm)],[2098, 2096])).
% 2.40/2.05 tff(2100,plain,
% 2.40/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 2.40/2.05 inference(quant_inst,[status(thm)],[])).
% 2.40/2.05 tff(2101,plain,
% 2.40/2.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 2.40/2.05 inference(modus_ponens,[status(thm)],[2100, 2099])).
% 2.40/2.05 tff(2102,plain,
% 2.40/2.05 ($false),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[2101, 122, 2059, 2058, 2009, 2095, 2057, 2023, 2094, 2093, 22, 2066])).
% 2.40/2.05 tff(2103,plain,(c2_1(a237) | c0_1(a237) | c3_1(a237) | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | hskp9 | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.40/2.05 tff(2104,plain,
% 2.40/2.05 (c2_1(a237)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[2103, 619, 179, 2046, 2045, 2044, 23, 45])).
% 2.40/2.05 tff(2105,plain,
% 2.40/2.05 (~c1_1(a237)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[638, 2104, 619, 630])).
% 2.40/2.05 tff(2106,plain,
% 2.40/2.05 (hskp21),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[2030, 2104, 630, 2105])).
% 2.40/2.05 tff(2107,plain,
% 2.40/2.05 (~c2_1(a259)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[1062, 2106])).
% 2.40/2.05 tff(2108,plain,
% 2.40/2.05 (c3_1(a259)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[867, 2106])).
% 2.40/2.05 tff(2109,plain,
% 2.40/2.05 (c0_1(a259)),
% 2.40/2.05 inference(unit_resolution,[status(thm)],[855, 2106])).
% 2.40/2.05 tff(2110,plain,
% 2.40/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a237) | c2_1(a259) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a237) | c2_1(a259) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.05 inference(rewrite,[status(thm)],[])).
% 2.40/2.05 tff(2111,plain,
% 2.40/2.05 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a237) | c1_1(a237) | (~c2_1(a237))) <=> (c0_1(a237) | c2_1(a259) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.05 inference(rewrite,[status(thm)],[])).
% 2.40/2.05 tff(2112,plain,
% 2.40/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a237) | c1_1(a237) | (~c2_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a237) | c2_1(a259) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 2.40/2.05 inference(monotonicity,[status(thm)],[2111])).
% 2.40/2.05 tff(2113,plain,
% 2.40/2.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a237) | c1_1(a237) | (~c2_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a237) | c2_1(a259) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.06 inference(transitivity,[status(thm)],[2112, 2110])).
% 2.40/2.06 tff(2114,plain,
% 2.40/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a237) | c1_1(a237) | (~c2_1(a237)))),
% 2.40/2.06 inference(quant_inst,[status(thm)],[])).
% 2.40/2.06 tff(2115,plain,
% 2.40/2.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a237) | c2_1(a259) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 2.40/2.06 inference(modus_ponens,[status(thm)],[2114, 2113])).
% 2.40/2.06 tff(2116,plain,
% 2.40/2.06 (~c3_1(a252)),
% 2.40/2.06 inference(unit_resolution,[status(thm)],[2115, 122, 2109, 2108, 2009, 1998, 619, 2104, 2107, 931, 2105])).
% 2.40/2.06 tff(2117,plain,
% 2.40/2.06 ($false),
% 2.40/2.06 inference(unit_resolution,[status(thm)],[2040, 122, 2109, 2108, 2009, 2104, 2107, 2023, 179, 22, 2116, 2105])).
% 2.40/2.06 tff(2118,plain,(c0_1(a237) | c3_1(a237) | hskp9 | hskp5 | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.40/2.06 tff(2119,plain,
% 2.40/2.06 (c0_1(a237)),
% 2.40/2.06 inference(unit_resolution,[status(thm)],[2118, 179, 23, 45, 34])).
% 2.40/2.06 tff(2120,plain,
% 2.40/2.06 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp5 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp5 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)))),
% 2.40/2.06 inference(rewrite,[status(thm)],[])).
% 2.40/2.06 tff(2121,plain,
% 2.40/2.06 ((hskp5 | (~ndr1_0) | c2_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a237) | c2_1(a237) | (~c0_1(a237))) <=> (hskp5 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)))),
% 2.40/2.06 inference(rewrite,[status(thm)],[])).
% 2.40/2.06 tff(2122,plain,
% 2.40/2.06 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a237) | c2_1(a237) | (~c0_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp5 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237))))),
% 2.40/2.06 inference(monotonicity,[status(thm)],[2121])).
% 2.40/2.06 tff(2123,plain,
% 2.40/2.06 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a237) | c2_1(a237) | (~c0_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp5 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)))),
% 2.40/2.06 inference(transitivity,[status(thm)],[2122, 2120])).
% 2.40/2.06 tff(2124,plain,
% 2.40/2.06 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a237) | c2_1(a237) | (~c0_1(a237)))),
% 2.40/2.06 inference(quant_inst,[status(thm)],[])).
% 2.40/2.06 tff(2125,plain,
% 2.40/2.06 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp5 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237))),
% 2.40/2.06 inference(modus_ponens,[status(thm)],[2124, 2123])).
% 2.40/2.06 tff(2126,plain,
% 2.40/2.06 (~c1_1(a237)),
% 2.40/2.06 inference(unit_resolution,[status(thm)],[2125, 122, 45, 2119, 575, 179, 618])).
% 2.40/2.06 tff(2127,plain,
% 2.40/2.06 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)))),
% 2.40/2.06 inference(rewrite,[status(thm)],[])).
% 2.40/2.06 tff(2128,plain,
% 2.40/2.06 ((hskp17 | hskp12 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | (~c0_1(a237))) <=> (hskp17 | hskp12 | c2_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)))),
% 2.40/2.06 inference(rewrite,[status(thm)],[])).
% 2.40/2.06 tff(2129,plain,
% 2.40/2.06 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237))))),
% 2.40/2.06 inference(monotonicity,[status(thm)],[2128])).
% 2.40/2.06 tff(2130,plain,
% 2.40/2.06 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)))),
% 2.40/2.06 inference(transitivity,[status(thm)],[2129, 2127])).
% 2.40/2.06 tff(2131,plain,
% 2.40/2.06 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | (~c0_1(a237)))),
% 2.40/2.06 inference(quant_inst,[status(thm)],[])).
% 2.40/2.06 tff(2132,plain,
% 2.40/2.06 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237))),
% 2.40/2.06 inference(modus_ponens,[status(thm)],[2131, 2130])).
% 2.40/2.06 tff(2133,plain,
% 2.40/2.06 (hskp17 | hskp12 | c2_1(a237) | c1_1(a237)),
% 2.40/2.06 inference(unit_resolution,[status(thm)],[2132, 122, 2119, 1427])).
% 2.40/2.06 tff(2134,plain,
% 2.40/2.06 (hskp17),
% 2.40/2.06 inference(unit_resolution,[status(thm)],[2133, 2126, 575, 608])).
% 2.40/2.06 tff(2135,plain,
% 2.40/2.06 (c3_1(a248)),
% 2.40/2.06 inference(unit_resolution,[status(thm)],[700, 2134])).
% 2.40/2.06 tff(2136,plain,
% 2.40/2.06 (c1_1(a248)),
% 2.40/2.06 inference(unit_resolution,[status(thm)],[683, 2134])).
% 2.40/2.06 tff(2137,plain,
% 2.40/2.06 (~c0_1(a248)),
% 2.40/2.06 inference(unit_resolution,[status(thm)],[731, 122, 45, 2136, 2135, 597, 596, 595, 164])).
% 2.40/2.06 tff(2138,plain,
% 2.40/2.06 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a252) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a252)) | (~c2_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a252) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a252)) | (~c2_1(a252)))),
% 2.40/2.06 inference(rewrite,[status(thm)],[])).
% 2.40/2.06 tff(2139,plain,
% 2.40/2.06 ((hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248))) <=> (hskp9 | c1_1(a252) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a252)) | (~c2_1(a252)))),
% 2.40/2.06 inference(rewrite,[status(thm)],[])).
% 2.40/2.06 tff(2140,plain,
% 2.40/2.06 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a252) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a252)) | (~c2_1(a252))))),
% 2.40/2.06 inference(monotonicity,[status(thm)],[2139])).
% 2.40/2.06 tff(2141,plain,
% 2.40/2.06 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a252) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a252)) | (~c2_1(a252)))),
% 2.40/2.07 inference(transitivity,[status(thm)],[2140, 2138])).
% 2.40/2.07 tff(2142,plain,
% 2.40/2.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))),
% 2.40/2.07 inference(quant_inst,[status(thm)],[])).
% 2.40/2.07 tff(2143,plain,
% 2.40/2.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a252) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a252)) | (~c2_1(a252))),
% 2.40/2.07 inference(modus_ponens,[status(thm)],[2142, 2141])).
% 2.40/2.07 tff(2144,plain,
% 2.40/2.07 (~c3_1(a252)),
% 2.40/2.07 inference(unit_resolution,[status(thm)],[2143, 122, 23, 1998, 2136, 2135, 2023, 445, 2137])).
% 2.40/2.07 tff(2145,plain,
% 2.40/2.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))),
% 2.40/2.07 inference(rewrite,[status(thm)],[])).
% 2.40/2.07 tff(2146,plain,
% 2.40/2.07 ((hskp9 | (~ndr1_0) | c1_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248))) <=> (hskp9 | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))),
% 2.40/2.07 inference(rewrite,[status(thm)],[])).
% 2.40/2.07 tff(2147,plain,
% 2.40/2.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248))))),
% 2.40/2.07 inference(monotonicity,[status(thm)],[2146])).
% 2.40/2.07 tff(2148,plain,
% 2.40/2.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))),
% 2.40/2.07 inference(transitivity,[status(thm)],[2147, 2145])).
% 2.40/2.07 tff(2149,plain,
% 2.40/2.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))),
% 2.40/2.07 inference(quant_inst,[status(thm)],[])).
% 2.40/2.07 tff(2150,plain,
% 2.40/2.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248))),
% 2.40/2.07 inference(modus_ponens,[status(thm)],[2149, 2148])).
% 2.40/2.07 tff(2151,plain,
% 2.40/2.07 (~c3_1(a215)),
% 2.40/2.07 inference(unit_resolution,[status(thm)],[2150, 122, 23, 2136, 2135, 597, 595, 445, 2137])).
% 2.40/2.07 tff(2152,plain,
% 2.40/2.07 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c2_1(a252)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c2_1(a252)))),
% 2.40/2.07 inference(rewrite,[status(thm)],[])).
% 2.40/2.07 tff(2153,plain,
% 2.40/2.07 ((hskp21 | hskp12 | (~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c2_1(a252))) <=> (hskp21 | hskp12 | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c2_1(a252)))),
% 2.40/2.07 inference(rewrite,[status(thm)],[])).
% 2.40/2.07 tff(2154,plain,
% 2.40/2.07 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c2_1(a252)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c2_1(a252))))),
% 2.40/2.07 inference(monotonicity,[status(thm)],[2153])).
% 2.40/2.07 tff(2155,plain,
% 2.40/2.07 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c2_1(a252)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c2_1(a252)))),
% 2.40/2.07 inference(transitivity,[status(thm)],[2154, 2152])).
% 2.40/2.07 tff(2156,plain,
% 2.40/2.07 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c2_1(a252)))),
% 2.40/2.07 inference(quant_inst,[status(thm)],[])).
% 2.40/2.07 tff(2157,plain,
% 2.40/2.07 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c2_1(a252))),
% 2.40/2.07 inference(modus_ponens,[status(thm)],[2156, 2155])).
% 2.40/2.07 tff(2158,plain,
% 2.40/2.07 (hskp21 | hskp12 | c3_1(a252)),
% 2.40/2.07 inference(unit_resolution,[status(thm)],[2157, 122, 1998, 2023, 804])).
% 2.40/2.07 tff(2159,plain,
% 2.40/2.07 (hskp21),
% 2.40/2.07 inference(unit_resolution,[status(thm)],[2158, 2144, 608])).
% 2.40/2.07 tff(2160,plain,
% 2.40/2.07 (~c2_1(a259)),
% 2.40/2.07 inference(unit_resolution,[status(thm)],[1062, 2159])).
% 2.40/2.07 tff(2161,plain,
% 2.40/2.07 (c3_1(a259)),
% 2.40/2.07 inference(unit_resolution,[status(thm)],[867, 2159])).
% 2.40/2.07 tff(2162,plain,
% 2.40/2.07 (c0_1(a259)),
% 2.40/2.07 inference(unit_resolution,[status(thm)],[855, 2159])).
% 2.40/2.07 tff(2163,plain,
% 2.40/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.07 inference(rewrite,[status(thm)],[])).
% 2.40/2.07 tff(2164,plain,
% 2.40/2.07 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c2_1(a259) | c1_1(a252) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.07 inference(rewrite,[status(thm)],[])).
% 2.40/2.07 tff(2165,plain,
% 2.40/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 2.40/2.07 inference(monotonicity,[status(thm)],[2164])).
% 2.40/2.07 tff(2166,plain,
% 2.40/2.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.07 inference(transitivity,[status(thm)],[2165, 2163])).
% 2.40/2.07 tff(2167,plain,
% 2.40/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 2.40/2.07 inference(quant_inst,[status(thm)],[])).
% 2.40/2.07 tff(2168,plain,
% 2.40/2.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 2.40/2.07 inference(modus_ponens,[status(thm)],[2167, 2166])).
% 2.40/2.07 tff(2169,plain,
% 2.40/2.07 ($false),
% 2.40/2.07 inference(unit_resolution,[status(thm)],[2168, 122, 2162, 2161, 2009, 597, 2160, 2023, 595, 22, 2151, 2144])).
% 2.40/2.07 tff(2170,plain,(c2_1(a237) | hskp9 | hskp5 | c3_1(a237) | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.40/2.07 tff(2171,plain,
% 2.40/2.07 (c2_1(a237)),
% 2.40/2.07 inference(unit_resolution,[status(thm)],[2170, 179, 45, 23, 34])).
% 2.40/2.07 tff(2172,plain,
% 2.40/2.07 (c1_1(a237)),
% 2.40/2.07 inference(unit_resolution,[status(thm)],[2030, 1855, 1911, 574])).
% 2.40/2.07 tff(2173,plain,
% 2.40/2.07 (c3_1(a252)),
% 2.40/2.07 inference(unit_resolution,[status(thm)],[2158, 1855, 574])).
% 2.40/2.07 tff(2174,plain,
% 2.40/2.07 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))))),
% 2.40/2.07 inference(bind,[status(th)],[])).
% 2.40/2.07 tff(2175,plain,
% 2.40/2.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.40/2.07 inference(quant_intro,[status(thm)],[2174])).
% 2.40/2.07 tff(2176,plain,
% 2.40/2.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.40/2.07 inference(rewrite,[status(thm)],[])).
% 2.40/2.07 tff(2177,plain,
% 2.40/2.07 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))))),
% 2.40/2.07 inference(bind,[status(th)],[])).
% 2.40/2.07 tff(2178,plain,
% 2.40/2.07 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.40/2.07 inference(quant_intro,[status(thm)],[2177])).
% 2.40/2.07 tff(2179,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 2.40/2.07 tff(2180,plain,
% 2.40/2.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.40/2.07 inference(modus_ponens,[status(thm)],[2179, 2178])).
% 2.40/2.07 tff(2181,plain,
% 2.40/2.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.40/2.07 inference(modus_ponens,[status(thm)],[2180, 2176])).
% 2.40/2.07 tff(2182,plain,(
% 2.40/2.07 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.40/2.07 inference(skolemize,[status(sab)],[2181])).
% 2.40/2.07 tff(2183,plain,
% 2.40/2.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 2.40/2.07 inference(modus_ponens,[status(thm)],[2182, 2175])).
% 2.40/2.08 tff(2184,plain,
% 2.40/2.08 (^[U: $i] : refl((hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.40/2.08 inference(bind,[status(th)],[])).
% 2.40/2.08 tff(2185,plain,
% 2.40/2.08 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.08 inference(quant_intro,[status(thm)],[2184])).
% 2.40/2.08 tff(2186,plain,
% 2.40/2.08 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.08 inference(rewrite,[status(thm)],[])).
% 2.40/2.08 tff(2187,plain,
% 2.40/2.08 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23) <=> ((hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23) <=> (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.40/2.08 inference(bind,[status(th)],[])).
% 2.40/2.08 tff(2188,plain,
% 2.40/2.08 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23) <=> ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.08 inference(quant_intro,[status(thm)],[2187])).
% 2.40/2.08 tff(2189,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 2.40/2.08 tff(2190,plain,
% 2.40/2.08 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2189, 2188])).
% 2.40/2.08 tff(2191,plain,
% 2.40/2.08 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2190, 2186])).
% 2.40/2.08 tff(2192,plain,(
% 2.40/2.08 ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.08 inference(skolemize,[status(sab)],[2191])).
% 2.40/2.08 tff(2193,plain,
% 2.40/2.08 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2192, 2185])).
% 2.40/2.08 tff(2194,plain,
% 2.40/2.08 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c0_1(a252)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c0_1(a252)))),
% 2.40/2.08 inference(rewrite,[status(thm)],[])).
% 2.40/2.08 tff(2195,plain,
% 2.40/2.08 ((hskp26 | hskp23 | (~ndr1_0) | c1_1(a252) | (~c3_1(a252)) | (~c0_1(a252))) <=> (hskp26 | hskp23 | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c0_1(a252)))),
% 2.40/2.08 inference(rewrite,[status(thm)],[])).
% 2.40/2.08 tff(2196,plain,
% 2.40/2.08 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a252) | (~c3_1(a252)) | (~c0_1(a252)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c0_1(a252))))),
% 2.40/2.08 inference(monotonicity,[status(thm)],[2195])).
% 2.40/2.08 tff(2197,plain,
% 2.40/2.08 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a252) | (~c3_1(a252)) | (~c0_1(a252)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c0_1(a252)))),
% 2.40/2.08 inference(transitivity,[status(thm)],[2196, 2194])).
% 2.40/2.08 tff(2198,plain,
% 2.40/2.08 ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a252) | (~c3_1(a252)) | (~c0_1(a252)))),
% 2.40/2.08 inference(quant_inst,[status(thm)],[])).
% 2.40/2.08 tff(2199,plain,
% 2.40/2.08 ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c0_1(a252))),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2198, 2197])).
% 2.40/2.08 tff(2200,plain,
% 2.40/2.08 (hskp26 | hskp23 | (~c3_1(a252))),
% 2.40/2.08 inference(unit_resolution,[status(thm)],[2199, 122, 2009, 2023, 2193])).
% 2.40/2.08 tff(2201,plain,
% 2.40/2.08 (hskp23),
% 2.40/2.08 inference(unit_resolution,[status(thm)],[2200, 2173, 1])).
% 2.40/2.08 tff(2202,plain,
% 2.40/2.08 (((~hskp23) | (~c3_1(a274))) <=> ((~hskp23) | (~c3_1(a274)))),
% 2.40/2.08 inference(rewrite,[status(thm)],[])).
% 2.40/2.08 tff(2203,plain,
% 2.40/2.08 (((~c3_1(a274)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a274)))),
% 2.40/2.08 inference(rewrite,[status(thm)],[])).
% 2.40/2.08 tff(2204,axiom,((~c3_1(a274)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 2.40/2.08 tff(2205,plain,
% 2.40/2.08 ((~hskp23) | (~c3_1(a274))),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2204, 2203])).
% 2.40/2.08 tff(2206,plain,
% 2.40/2.08 ((~hskp23) | (~c3_1(a274))),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2205, 2202])).
% 2.40/2.08 tff(2207,plain,
% 2.40/2.08 (~c3_1(a274)),
% 2.40/2.08 inference(unit_resolution,[status(thm)],[2206, 2201])).
% 2.40/2.08 tff(2208,plain,
% 2.40/2.08 (((~hskp23) | c1_1(a274)) <=> ((~hskp23) | c1_1(a274))),
% 2.40/2.08 inference(rewrite,[status(thm)],[])).
% 2.40/2.08 tff(2209,axiom,((~hskp23) | c1_1(a274)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 2.40/2.08 tff(2210,plain,
% 2.40/2.08 ((~hskp23) | c1_1(a274)),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2209, 2208])).
% 2.40/2.08 tff(2211,plain,
% 2.40/2.08 ((~hskp23) | c1_1(a274)),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2210, 2208])).
% 2.40/2.08 tff(2212,plain,
% 2.40/2.08 ((~hskp23) | c1_1(a274)),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2211, 2208])).
% 2.40/2.08 tff(2213,plain,
% 2.40/2.08 ((~hskp23) | c1_1(a274)),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2212, 2208])).
% 2.40/2.08 tff(2214,plain,
% 2.40/2.08 ((~hskp23) | c1_1(a274)),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2213, 2208])).
% 2.40/2.08 tff(2215,plain,
% 2.40/2.08 ((~hskp23) | c1_1(a274)),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2214, 2208])).
% 2.40/2.08 tff(2216,plain,
% 2.40/2.08 ((~hskp23) | c1_1(a274)),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2215, 2208])).
% 2.40/2.08 tff(2217,plain,
% 2.40/2.08 ((~hskp23) | c1_1(a274)),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2216, 2208])).
% 2.40/2.08 tff(2218,plain,
% 2.40/2.08 (c1_1(a274)),
% 2.40/2.08 inference(unit_resolution,[status(thm)],[2217, 2201])).
% 2.40/2.08 tff(2219,plain,
% 2.40/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | c2_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | c2_1(a274) | (~c1_1(a274)))),
% 2.40/2.08 inference(rewrite,[status(thm)],[])).
% 2.40/2.08 tff(2220,plain,
% 2.40/2.08 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c2_1(a274) | (~c1_1(a274))) <=> (c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | c2_1(a274) | (~c1_1(a274)))),
% 2.40/2.08 inference(rewrite,[status(thm)],[])).
% 2.40/2.08 tff(2221,plain,
% 2.40/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c2_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | c2_1(a274) | (~c1_1(a274))))),
% 2.40/2.08 inference(monotonicity,[status(thm)],[2220])).
% 2.40/2.08 tff(2222,plain,
% 2.40/2.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c2_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | c2_1(a274) | (~c1_1(a274)))),
% 2.40/2.08 inference(transitivity,[status(thm)],[2221, 2219])).
% 2.40/2.08 tff(2223,plain,
% 2.40/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c2_1(a274) | (~c1_1(a274)))),
% 2.40/2.08 inference(quant_inst,[status(thm)],[])).
% 2.40/2.08 tff(2224,plain,
% 2.40/2.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | c2_1(a274) | (~c1_1(a274))),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2223, 2222])).
% 2.40/2.08 tff(2225,plain,
% 2.40/2.08 (c2_1(a274)),
% 2.40/2.08 inference(unit_resolution,[status(thm)],[2224, 122, 2218, 2009, 1998, 1920, 2207, 179, 2183, 2173, 2172])).
% 2.40/2.08 tff(2226,plain,
% 2.40/2.08 (((~hskp23) | (~c0_1(a274))) <=> ((~hskp23) | (~c0_1(a274)))),
% 2.40/2.08 inference(rewrite,[status(thm)],[])).
% 2.40/2.08 tff(2227,plain,
% 2.40/2.08 (((~c0_1(a274)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a274)))),
% 2.40/2.08 inference(rewrite,[status(thm)],[])).
% 2.40/2.08 tff(2228,axiom,((~c0_1(a274)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 2.40/2.08 tff(2229,plain,
% 2.40/2.08 ((~hskp23) | (~c0_1(a274))),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2228, 2227])).
% 2.40/2.08 tff(2230,plain,
% 2.40/2.08 ((~hskp23) | (~c0_1(a274))),
% 2.40/2.08 inference(modus_ponens,[status(thm)],[2229, 2226])).
% 2.40/2.08 tff(2231,plain,
% 2.40/2.08 (~c0_1(a274)),
% 2.40/2.08 inference(unit_resolution,[status(thm)],[2230, 2201])).
% 2.40/2.08 tff(2232,plain,
% 2.40/2.08 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a274) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a274) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)))),
% 2.40/2.08 inference(rewrite,[status(thm)],[])).
% 2.40/2.08 tff(2233,plain,
% 2.40/2.08 ((hskp12 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274))) <=> (hskp12 | c0_1(a274) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)))),
% 2.40/2.08 inference(rewrite,[status(thm)],[])).
% 2.40/2.08 tff(2234,plain,
% 2.40/2.08 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a274) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274))))),
% 2.40/2.08 inference(monotonicity,[status(thm)],[2233])).
% 2.40/2.08 tff(2235,plain,
% 2.40/2.08 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a274) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)))),
% 2.40/2.09 inference(transitivity,[status(thm)],[2234, 2232])).
% 2.40/2.09 tff(2236,plain,
% 2.40/2.09 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))),
% 2.40/2.09 inference(quant_inst,[status(thm)],[])).
% 2.40/2.09 tff(2237,plain,
% 2.40/2.09 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a274) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274))),
% 2.40/2.09 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 2.40/2.09 tff(2238,plain,
% 2.40/2.09 ($false),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[2237, 122, 574, 2218, 2231, 2207, 44, 2225])).
% 2.40/2.09 tff(2239,plain,(hskp21 | hskp12 | (~c0_1(a237)) | c3_1(a237) | hskp26 | (~c2_1(a237))), inference(lemma,lemma(discharge,[]))).
% 2.40/2.09 tff(2240,plain,
% 2.40/2.09 (hskp21),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[2239, 576, 1920, 179, 574, 1911])).
% 2.40/2.09 tff(2241,plain,
% 2.40/2.09 (c3_1(a259)),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[867, 2240])).
% 2.40/2.09 tff(2242,plain,
% 2.40/2.09 (c0_1(a259)),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[855, 2240])).
% 2.40/2.09 tff(2243,plain,
% 2.40/2.09 (^[U: $i] : refl((hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.40/2.09 inference(bind,[status(th)],[])).
% 2.40/2.09 tff(2244,plain,
% 2.40/2.09 (![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.09 inference(quant_intro,[status(thm)],[2243])).
% 2.40/2.09 tff(2245,plain,
% 2.40/2.09 (![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.09 inference(rewrite,[status(thm)],[])).
% 2.40/2.09 tff(2246,plain,
% 2.40/2.09 (^[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)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp27) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp27))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp27) <=> (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.40/2.09 inference(bind,[status(th)],[])).
% 2.40/2.09 tff(2247,plain,
% 2.40/2.09 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp27) <=> ![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.09 inference(quant_intro,[status(thm)],[2246])).
% 2.40/2.09 tff(2248,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 2.40/2.09 tff(2249,plain,
% 2.40/2.09 (![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.09 inference(modus_ponens,[status(thm)],[2248, 2247])).
% 2.40/2.09 tff(2250,plain,
% 2.40/2.09 (![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.09 inference(modus_ponens,[status(thm)],[2249, 2245])).
% 2.40/2.09 tff(2251,plain,(
% 2.40/2.09 ![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.09 inference(skolemize,[status(sab)],[2250])).
% 2.40/2.09 tff(2252,plain,
% 2.40/2.09 (![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.40/2.09 inference(modus_ponens,[status(thm)],[2251, 2244])).
% 2.40/2.09 tff(2253,plain,
% 2.40/2.09 (((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp27 | c2_1(a259) | (~ndr1_0) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp3 | hskp27 | c2_1(a259) | (~ndr1_0) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.09 inference(rewrite,[status(thm)],[])).
% 2.40/2.09 tff(2254,plain,
% 2.40/2.09 ((hskp3 | hskp27 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259))) <=> (hskp3 | hskp27 | c2_1(a259) | (~ndr1_0) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.09 inference(rewrite,[status(thm)],[])).
% 2.40/2.09 tff(2255,plain,
% 2.40/2.09 (((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp27 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp27 | c2_1(a259) | (~ndr1_0) | (~c3_1(a259)) | (~c0_1(a259))))),
% 2.40/2.09 inference(monotonicity,[status(thm)],[2254])).
% 2.40/2.09 tff(2256,plain,
% 2.40/2.09 (((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp27 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp3 | hskp27 | c2_1(a259) | (~ndr1_0) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.09 inference(transitivity,[status(thm)],[2255, 2253])).
% 2.40/2.09 tff(2257,plain,
% 2.40/2.09 ((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp27 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.09 inference(quant_inst,[status(thm)],[])).
% 2.40/2.09 tff(2258,plain,
% 2.40/2.09 ((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp3 | hskp27 | c2_1(a259) | (~ndr1_0) | (~c3_1(a259)) | (~c0_1(a259))),
% 2.40/2.09 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 2.40/2.09 tff(2259,plain,
% 2.40/2.09 (hskp3 | (~c3_1(a259)) | (~c0_1(a259))),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[2258, 122, 34, 857, 2252])).
% 2.40/2.09 tff(2260,plain,
% 2.40/2.09 (hskp3),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[2259, 2242, 2241])).
% 2.40/2.09 tff(2261,plain,
% 2.40/2.09 (c1_1(a216)),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[228, 2260])).
% 2.40/2.09 tff(2262,plain,
% 2.40/2.09 (c0_1(a216)),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[239, 2260])).
% 2.40/2.09 tff(2263,plain,
% 2.40/2.09 (~c3_1(a216)),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[246, 122, 34, 90, 2262, 2261, 56])).
% 2.40/2.09 tff(2264,plain,
% 2.40/2.09 (~c2_1(a216)),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[262, 2260])).
% 2.40/2.09 tff(2265,plain,
% 2.40/2.09 ($false),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[269, 122, 576, 23, 2261, 2264, 257, 2263])).
% 2.40/2.09 tff(2266,plain,(hskp2 | hskp9 | hskp27 | c2_1(a259) | (~c0_1(a237)) | c3_1(a237) | hskp12 | (~c2_1(a237))), inference(lemma,lemma(discharge,[]))).
% 2.40/2.09 tff(2267,plain,
% 2.40/2.09 (hskp2),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[2266, 857, 34, 23, 2119, 179, 574, 2171])).
% 2.40/2.09 tff(2268,plain,
% 2.40/2.09 (~c1_1(a215)),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[136, 2267])).
% 2.40/2.09 tff(2269,plain,
% 2.40/2.09 (~c0_1(a215)),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[153, 2267])).
% 2.40/2.09 tff(2270,plain,
% 2.40/2.09 (c2_1(a215)),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[147, 2267])).
% 2.40/2.09 tff(2271,plain,
% 2.40/2.09 (~hskp26),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[175, 2270, 45, 2269, 2268])).
% 2.40/2.09 tff(2272,plain,
% 2.40/2.09 (hskp21),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[2239, 2271, 2119, 179, 574, 2171])).
% 2.40/2.09 tff(2273,plain,
% 2.40/2.09 (c0_1(a259)),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[855, 2272])).
% 2.40/2.09 tff(2274,plain,
% 2.40/2.09 (c3_1(a259)),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[867, 2272])).
% 2.40/2.09 tff(2275,plain,
% 2.40/2.09 ((~c3_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[2065, 122, 2009, 1998, 2270, 857, 2269, 2268, 931])).
% 2.40/2.09 tff(2276,plain,
% 2.40/2.09 (~c3_1(a252)),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[2275, 2274, 2273])).
% 2.40/2.09 tff(2277,plain,
% 2.40/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.09 inference(rewrite,[status(thm)],[])).
% 2.40/2.09 tff(2278,plain,
% 2.40/2.09 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c2_1(a259) | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.09 inference(rewrite,[status(thm)],[])).
% 2.40/2.09 tff(2279,plain,
% 2.40/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 2.40/2.09 inference(monotonicity,[status(thm)],[2278])).
% 2.40/2.09 tff(2280,plain,
% 2.40/2.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 2.40/2.09 inference(transitivity,[status(thm)],[2279, 2277])).
% 2.40/2.09 tff(2281,plain,
% 2.40/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 2.40/2.09 inference(quant_inst,[status(thm)],[])).
% 2.40/2.09 tff(2282,plain,
% 2.40/2.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 2.40/2.09 inference(modus_ponens,[status(thm)],[2281, 2280])).
% 2.40/2.09 tff(2283,plain,
% 2.40/2.09 ($false),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[2282, 122, 2273, 2274, 2009, 1998, 857, 2023, 22, 2276])).
% 2.40/2.09 tff(2284,plain,(c2_1(a259) | c3_1(a237) | hskp12 | hskp5 | hskp27 | hskp9), inference(lemma,lemma(discharge,[]))).
% 2.40/2.09 tff(2285,plain,
% 2.40/2.09 (c2_1(a259)),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[2284, 574, 179, 45, 34, 23])).
% 2.40/2.09 tff(2286,plain,
% 2.40/2.09 (hskp21),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[2239, 574, 178, 179, 2119, 2171])).
% 2.40/2.09 tff(2287,plain,
% 2.40/2.09 ($false),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[1062, 2286, 2285])).
% 2.40/2.09 tff(2288,plain,(hskp12 | c3_1(a237) | hskp5 | hskp27 | hskp9), inference(lemma,lemma(discharge,[]))).
% 2.40/2.09 tff(2289,plain,
% 2.40/2.09 (hskp12),
% 2.40/2.09 inference(unit_resolution,[status(thm)],[2288, 179, 45, 34, 23])).
% 2.40/2.09 tff(2290,plain,
% 2.40/2.09 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c2_1(a252)) | (~c1_1(a320)) | (~c3_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c2_1(a252)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 2.40/2.10 inference(rewrite,[status(thm)],[])).
% 2.40/2.10 tff(2291,plain,
% 2.40/2.10 ((hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a320) | (~c1_1(a320)) | (~c3_1(a320))) <=> (hskp9 | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c2_1(a252)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 2.40/2.10 inference(rewrite,[status(thm)],[])).
% 2.40/2.10 tff(2292,plain,
% 2.40/2.10 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a320) | (~c1_1(a320)) | (~c3_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c2_1(a252)) | (~c1_1(a320)) | (~c3_1(a320))))),
% 2.40/2.10 inference(monotonicity,[status(thm)],[2291])).
% 2.40/2.10 tff(2293,plain,
% 2.40/2.10 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a320) | (~c1_1(a320)) | (~c3_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c2_1(a252)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 2.40/2.10 inference(transitivity,[status(thm)],[2292, 2290])).
% 2.40/2.10 tff(2294,plain,
% 2.40/2.10 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a320) | (~c1_1(a320)) | (~c3_1(a320)))),
% 2.40/2.10 inference(quant_inst,[status(thm)],[])).
% 2.40/2.10 tff(2295,plain,
% 2.40/2.10 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c2_1(a252)) | (~c1_1(a320)) | (~c3_1(a320))),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2294, 2293])).
% 2.40/2.10 tff(2296,plain,
% 2.40/2.10 (~c3_1(a252)),
% 2.40/2.10 inference(unit_resolution,[status(thm)],[2295, 122, 23, 356, 1998, 386, 2023, 445, 543])).
% 2.40/2.10 tff(2297,plain,
% 2.40/2.10 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))))),
% 2.40/2.10 inference(bind,[status(th)],[])).
% 2.40/2.10 tff(2298,plain,
% 2.40/2.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 2.40/2.10 inference(quant_intro,[status(thm)],[2297])).
% 2.40/2.10 tff(2299,plain,
% 2.40/2.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 2.40/2.10 inference(rewrite,[status(thm)],[])).
% 2.40/2.10 tff(2300,plain,
% 2.40/2.10 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))))),
% 2.40/2.10 inference(bind,[status(th)],[])).
% 2.40/2.10 tff(2301,plain,
% 2.40/2.10 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 2.40/2.10 inference(quant_intro,[status(thm)],[2300])).
% 2.40/2.10 tff(2302,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 2.40/2.10 tff(2303,plain,
% 2.40/2.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2302, 2301])).
% 2.40/2.10 tff(2304,plain,
% 2.40/2.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2303, 2299])).
% 2.40/2.10 tff(2305,plain,(
% 2.40/2.10 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 2.40/2.10 inference(skolemize,[status(sab)],[2304])).
% 2.40/2.10 tff(2306,plain,
% 2.40/2.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2305, 2298])).
% 2.40/2.10 tff(2307,plain,
% 2.40/2.10 (^[U: $i] : refl((hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 2.40/2.10 inference(bind,[status(th)],[])).
% 2.40/2.10 tff(2308,plain,
% 2.40/2.10 (![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.40/2.10 inference(quant_intro,[status(thm)],[2307])).
% 2.40/2.10 tff(2309,plain,
% 2.40/2.10 (![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.40/2.10 inference(rewrite,[status(thm)],[])).
% 2.40/2.10 tff(2310,plain,
% 2.40/2.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp26))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp29) <=> ((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp29))), rewrite(((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp29) <=> (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp29) <=> (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 2.40/2.10 inference(bind,[status(th)],[])).
% 2.40/2.10 tff(2311,plain,
% 2.40/2.10 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp29) <=> ![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.40/2.10 inference(quant_intro,[status(thm)],[2310])).
% 2.40/2.10 tff(2312,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 2.40/2.10 tff(2313,plain,
% 2.40/2.10 (![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2312, 2311])).
% 2.40/2.10 tff(2314,plain,
% 2.40/2.10 (![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2313, 2309])).
% 2.40/2.10 tff(2315,plain,(
% 2.40/2.10 ![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.40/2.10 inference(skolemize,[status(sab)],[2314])).
% 2.40/2.10 tff(2316,plain,
% 2.40/2.10 (![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2315, 2308])).
% 2.40/2.10 tff(2317,plain,
% 2.40/2.10 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 2.40/2.10 inference(rewrite,[status(thm)],[])).
% 2.40/2.10 tff(2318,plain,
% 2.40/2.10 ((hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320))) <=> (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 2.40/2.10 inference(rewrite,[status(thm)],[])).
% 2.40/2.10 tff(2319,plain,
% 2.40/2.10 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320))))),
% 2.40/2.10 inference(monotonicity,[status(thm)],[2318])).
% 2.40/2.10 tff(2320,plain,
% 2.40/2.10 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 2.40/2.10 inference(transitivity,[status(thm)],[2319, 2317])).
% 2.40/2.10 tff(2321,plain,
% 2.40/2.10 ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)))),
% 2.40/2.10 inference(quant_inst,[status(thm)],[])).
% 2.40/2.10 tff(2322,plain,
% 2.40/2.10 ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320))),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2321, 2320])).
% 2.40/2.10 tff(2323,plain,
% 2.40/2.10 (hskp29),
% 2.40/2.10 inference(unit_resolution,[status(thm)],[2322, 122, 1, 367, 356, 2316, 543])).
% 2.40/2.10 tff(2324,plain,
% 2.40/2.10 (((~hskp29) | c3_1(a296)) <=> ((~hskp29) | c3_1(a296))),
% 2.40/2.10 inference(rewrite,[status(thm)],[])).
% 2.40/2.10 tff(2325,axiom,((~hskp29) | c3_1(a296)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 2.40/2.10 tff(2326,plain,
% 2.40/2.10 ((~hskp29) | c3_1(a296)),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2325, 2324])).
% 2.40/2.10 tff(2327,plain,
% 2.40/2.10 ((~hskp29) | c3_1(a296)),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2326, 2324])).
% 2.40/2.10 tff(2328,plain,
% 2.40/2.10 ((~hskp29) | c3_1(a296)),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2327, 2324])).
% 2.40/2.10 tff(2329,plain,
% 2.40/2.10 ((~hskp29) | c3_1(a296)),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2328, 2324])).
% 2.40/2.10 tff(2330,plain,
% 2.40/2.10 ((~hskp29) | c3_1(a296)),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2329, 2324])).
% 2.40/2.10 tff(2331,plain,
% 2.40/2.10 ((~hskp29) | c3_1(a296)),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2330, 2324])).
% 2.40/2.10 tff(2332,plain,
% 2.40/2.10 ((~hskp29) | c3_1(a296)),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2331, 2324])).
% 2.40/2.10 tff(2333,plain,
% 2.40/2.10 ((~hskp29) | c3_1(a296)),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2332, 2324])).
% 2.40/2.10 tff(2334,plain,
% 2.40/2.10 (c3_1(a296)),
% 2.40/2.10 inference(unit_resolution,[status(thm)],[2333, 2323])).
% 2.40/2.10 tff(2335,plain,
% 2.40/2.10 (((~hskp29) | c2_1(a296)) <=> ((~hskp29) | c2_1(a296))),
% 2.40/2.10 inference(rewrite,[status(thm)],[])).
% 2.40/2.10 tff(2336,axiom,((~hskp29) | c2_1(a296)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 2.40/2.10 tff(2337,plain,
% 2.40/2.10 ((~hskp29) | c2_1(a296)),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2336, 2335])).
% 2.40/2.10 tff(2338,plain,
% 2.40/2.10 ((~hskp29) | c2_1(a296)),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2337, 2335])).
% 2.40/2.10 tff(2339,plain,
% 2.40/2.10 ((~hskp29) | c2_1(a296)),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2338, 2335])).
% 2.40/2.10 tff(2340,plain,
% 2.40/2.10 ((~hskp29) | c2_1(a296)),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2339, 2335])).
% 2.40/2.10 tff(2341,plain,
% 2.40/2.10 ((~hskp29) | c2_1(a296)),
% 2.40/2.10 inference(modus_ponens,[status(thm)],[2340, 2335])).
% 2.40/2.10 tff(2342,plain,
% 2.40/2.10 ((~hskp29) | c2_1(a296)),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2341, 2335])).
% 2.40/2.11 tff(2343,plain,
% 2.40/2.11 ((~hskp29) | c2_1(a296)),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2342, 2335])).
% 2.40/2.11 tff(2344,plain,
% 2.40/2.11 ((~hskp29) | c2_1(a296)),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2343, 2335])).
% 2.40/2.11 tff(2345,plain,
% 2.40/2.11 (c2_1(a296)),
% 2.40/2.11 inference(unit_resolution,[status(thm)],[2344, 2323])).
% 2.40/2.11 tff(2346,plain,
% 2.40/2.11 (((~hskp29) | c0_1(a296)) <=> ((~hskp29) | c0_1(a296))),
% 2.40/2.11 inference(rewrite,[status(thm)],[])).
% 2.40/2.11 tff(2347,axiom,((~hskp29) | c0_1(a296)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 2.40/2.11 tff(2348,plain,
% 2.40/2.11 ((~hskp29) | c0_1(a296)),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2347, 2346])).
% 2.40/2.11 tff(2349,plain,
% 2.40/2.11 ((~hskp29) | c0_1(a296)),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2348, 2346])).
% 2.40/2.11 tff(2350,plain,
% 2.40/2.11 ((~hskp29) | c0_1(a296)),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2349, 2346])).
% 2.40/2.11 tff(2351,plain,
% 2.40/2.11 ((~hskp29) | c0_1(a296)),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2350, 2346])).
% 2.40/2.11 tff(2352,plain,
% 2.40/2.11 ((~hskp29) | c0_1(a296)),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2351, 2346])).
% 2.40/2.11 tff(2353,plain,
% 2.40/2.11 ((~hskp29) | c0_1(a296)),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2352, 2346])).
% 2.40/2.11 tff(2354,plain,
% 2.40/2.11 ((~hskp29) | c0_1(a296)),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2353, 2346])).
% 2.40/2.11 tff(2355,plain,
% 2.40/2.11 ((~hskp29) | c0_1(a296)),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2354, 2346])).
% 2.40/2.11 tff(2356,plain,
% 2.40/2.11 (c0_1(a296)),
% 2.40/2.11 inference(unit_resolution,[status(thm)],[2355, 2323])).
% 2.40/2.11 tff(2357,plain,
% 2.40/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | (~c2_1(a252)) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | (~c2_1(a252)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.40/2.11 inference(rewrite,[status(thm)],[])).
% 2.40/2.11 tff(2358,plain,
% 2.40/2.11 (((~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c0_1(a320) | (~c2_1(a320)) | (~c3_1(a320))) <=> (c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | (~c2_1(a252)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.40/2.11 inference(rewrite,[status(thm)],[])).
% 2.40/2.11 tff(2359,plain,
% 2.40/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c0_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | (~c2_1(a252)) | (~c2_1(a320)) | (~c3_1(a320))))),
% 2.40/2.11 inference(monotonicity,[status(thm)],[2358])).
% 2.40/2.11 tff(2360,plain,
% 2.40/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c0_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | (~c2_1(a252)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.40/2.11 inference(transitivity,[status(thm)],[2359, 2357])).
% 2.40/2.11 tff(2361,plain,
% 2.40/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c0_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))),
% 2.40/2.11 inference(quant_inst,[status(thm)],[])).
% 2.40/2.11 tff(2362,plain,
% 2.40/2.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | (~c2_1(a252)) | (~c2_1(a320)) | (~c3_1(a320))),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2361, 2360])).
% 2.40/2.11 tff(2363,plain,
% 2.40/2.11 ($false),
% 2.40/2.11 inference(unit_resolution,[status(thm)],[2362, 122, 2356, 2345, 2334, 367, 356, 1998, 386, 2023, 2306, 2296])).
% 2.40/2.11 tff(2364,plain,(hskp19 | hskp9 | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.40/2.11 tff(2365,plain,
% 2.40/2.11 (hskp19),
% 2.40/2.11 inference(unit_resolution,[status(thm)],[2364, 1, 23])).
% 2.40/2.11 tff(2366,plain,
% 2.40/2.11 (~c0_1(a255)),
% 2.40/2.11 inference(unit_resolution,[status(thm)],[300, 2365])).
% 2.40/2.11 tff(2367,plain,
% 2.40/2.11 (~c3_1(a255)),
% 2.40/2.11 inference(unit_resolution,[status(thm)],[288, 2365])).
% 2.40/2.11 tff(2368,plain,
% 2.40/2.11 (~c1_1(a255)),
% 2.40/2.11 inference(unit_resolution,[status(thm)],[294, 2365])).
% 2.40/2.11 tff(2369,assumption,(~hskp6), introduced(assumption)).
% 2.40/2.11 tff(2370,plain,
% 2.40/2.11 (hskp6 | c2_1(a255)),
% 2.40/2.11 inference(unit_resolution,[status(thm)],[1684, 122, 45, 1190, 1207, 1677])).
% 2.40/2.11 tff(2371,plain,
% 2.40/2.11 (c2_1(a255)),
% 2.40/2.11 inference(unit_resolution,[status(thm)],[2370, 2369])).
% 2.40/2.11 tff(2372,plain,
% 2.40/2.11 (^[U: $i] : refl((hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 2.40/2.11 inference(bind,[status(th)],[])).
% 2.40/2.11 tff(2373,plain,
% 2.40/2.11 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.40/2.11 inference(quant_intro,[status(thm)],[2372])).
% 2.40/2.11 tff(2374,plain,
% 2.40/2.11 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.40/2.11 inference(rewrite,[status(thm)],[])).
% 2.40/2.11 tff(2375,plain,
% 2.40/2.11 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp6) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6) <=> (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp6) <=> (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 2.40/2.11 inference(bind,[status(th)],[])).
% 2.40/2.11 tff(2376,plain,
% 2.40/2.11 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp6) <=> ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.40/2.11 inference(quant_intro,[status(thm)],[2375])).
% 2.40/2.11 tff(2377,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 2.40/2.11 tff(2378,plain,
% 2.40/2.11 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2377, 2376])).
% 2.40/2.11 tff(2379,plain,
% 2.40/2.11 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2378, 2374])).
% 2.40/2.11 tff(2380,plain,(
% 2.40/2.11 ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.40/2.11 inference(skolemize,[status(sab)],[2379])).
% 2.40/2.11 tff(2381,plain,
% 2.40/2.11 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2380, 2373])).
% 2.40/2.11 tff(2382,plain,
% 2.40/2.11 (((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp6 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)))) <=> ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp6 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)))),
% 2.40/2.11 inference(rewrite,[status(thm)],[])).
% 2.40/2.11 tff(2383,plain,
% 2.40/2.11 ((hskp3 | hskp6 | (~ndr1_0) | c1_1(a215) | c0_1(a215) | (~c2_1(a215))) <=> (hskp3 | hskp6 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)))),
% 2.40/2.11 inference(rewrite,[status(thm)],[])).
% 2.40/2.11 tff(2384,plain,
% 2.40/2.11 (((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp6 | (~ndr1_0) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp6 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215))))),
% 2.40/2.11 inference(monotonicity,[status(thm)],[2383])).
% 2.40/2.11 tff(2385,plain,
% 2.40/2.11 (((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp6 | (~ndr1_0) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp6 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)))),
% 2.40/2.11 inference(transitivity,[status(thm)],[2384, 2382])).
% 2.40/2.11 tff(2386,plain,
% 2.40/2.11 ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp6 | (~ndr1_0) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))),
% 2.40/2.11 inference(quant_inst,[status(thm)],[])).
% 2.40/2.11 tff(2387,plain,
% 2.40/2.11 ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp6 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215))),
% 2.40/2.11 inference(modus_ponens,[status(thm)],[2386, 2385])).
% 2.40/2.11 tff(2388,plain,
% 2.40/2.11 (hskp3 | hskp6),
% 2.40/2.11 inference(unit_resolution,[status(thm)],[2387, 122, 167, 166, 165, 2381])).
% 2.40/2.11 tff(2389,plain,
% 2.40/2.11 (hskp3),
% 2.40/2.11 inference(unit_resolution,[status(thm)],[2388, 2369])).
% 2.40/2.11 tff(2390,plain,
% 2.40/2.11 (~c2_1(a216)),
% 2.40/2.11 inference(unit_resolution,[status(thm)],[262, 2389])).
% 2.40/2.11 tff(2391,plain,
% 2.40/2.11 (c0_1(a216)),
% 2.40/2.11 inference(unit_resolution,[status(thm)],[239, 2389])).
% 2.40/2.11 tff(2392,plain,
% 2.40/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a255) | c3_1(a255) | c1_1(a252) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c1_1(a252) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a255)))),
% 2.40/2.11 inference(rewrite,[status(thm)],[])).
% 2.40/2.11 tff(2393,plain,
% 2.40/2.11 (((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c1_1(a255) | c3_1(a255) | c1_1(a252) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a255)))),
% 2.40/2.11 inference(rewrite,[status(thm)],[])).
% 2.40/2.11 tff(2394,plain,
% 2.40/2.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a255) | c3_1(a255) | c1_1(a252) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a255))))),
% 2.46/2.12 inference(monotonicity,[status(thm)],[2393])).
% 2.46/2.12 tff(2395,plain,
% 2.46/2.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c1_1(a252) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a255)))),
% 2.46/2.12 inference(transitivity,[status(thm)],[2394, 2392])).
% 2.46/2.12 tff(2396,plain,
% 2.46/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 2.46/2.12 inference(quant_inst,[status(thm)],[])).
% 2.46/2.12 tff(2397,plain,
% 2.46/2.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c1_1(a252) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a255))),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2396, 2395])).
% 2.46/2.12 tff(2398,plain,
% 2.46/2.12 (~c3_1(a216)),
% 2.46/2.12 inference(unit_resolution,[status(thm)],[2397, 122, 2009, 2391, 1189, 1207, 2023, 2390, 22, 2371, 12])).
% 2.46/2.12 tff(2399,assumption,(~hskp7), introduced(assumption)).
% 2.46/2.12 tff(2400,plain,
% 2.46/2.12 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 2.46/2.12 inference(bind,[status(th)],[])).
% 2.46/2.12 tff(2401,plain,
% 2.46/2.12 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.46/2.12 inference(quant_intro,[status(thm)],[2400])).
% 2.46/2.12 tff(2402,plain,
% 2.46/2.12 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.46/2.12 inference(rewrite,[status(thm)],[])).
% 2.46/2.12 tff(2403,plain,
% 2.46/2.12 (^[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)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp6) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp6))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp6) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 2.46/2.12 inference(bind,[status(th)],[])).
% 2.46/2.12 tff(2404,plain,
% 2.46/2.12 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp6) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.46/2.12 inference(quant_intro,[status(thm)],[2403])).
% 2.46/2.12 tff(2405,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 2.46/2.12 tff(2406,plain,
% 2.46/2.12 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2405, 2404])).
% 2.46/2.12 tff(2407,plain,
% 2.46/2.12 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2406, 2402])).
% 2.46/2.12 tff(2408,plain,(
% 2.46/2.12 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.46/2.12 inference(skolemize,[status(sab)],[2407])).
% 2.46/2.12 tff(2409,plain,
% 2.46/2.12 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2408, 2401])).
% 2.46/2.12 tff(2410,plain,
% 2.46/2.12 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp6 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | hskp6 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.46/2.12 inference(rewrite,[status(thm)],[])).
% 2.46/2.12 tff(2411,plain,
% 2.46/2.12 ((hskp7 | hskp6 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237))) <=> (hskp7 | hskp6 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.46/2.12 inference(rewrite,[status(thm)],[])).
% 2.46/2.12 tff(2412,plain,
% 2.46/2.12 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp6 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237))))),
% 2.46/2.12 inference(monotonicity,[status(thm)],[2411])).
% 2.46/2.12 tff(2413,plain,
% 2.46/2.12 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | hskp6 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.46/2.12 inference(transitivity,[status(thm)],[2412, 2410])).
% 2.46/2.12 tff(2414,plain,
% 2.46/2.12 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.46/2.12 inference(quant_inst,[status(thm)],[])).
% 2.46/2.12 tff(2415,plain,
% 2.46/2.12 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | hskp6 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237))),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 2.46/2.12 tff(2416,plain,
% 2.46/2.12 (hskp7 | (~c2_1(a237)) | (~c0_1(a237))),
% 2.46/2.12 inference(unit_resolution,[status(thm)],[2415, 122, 2369, 179, 2409])).
% 2.46/2.12 tff(2417,plain,
% 2.46/2.12 ($false),
% 2.46/2.12 inference(unit_resolution,[status(thm)],[2416, 764, 765, 2399])).
% 2.46/2.12 tff(2418,plain,((~hskp12) | hskp7 | hskp6 | c3_1(a237)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.12 tff(2419,plain,
% 2.46/2.12 (hskp7),
% 2.46/2.12 inference(unit_resolution,[status(thm)],[2418, 2369, 757, 179])).
% 2.46/2.12 tff(2420,plain,
% 2.46/2.12 (((~hskp7) | (~c0_1(a223))) <=> ((~hskp7) | (~c0_1(a223)))),
% 2.46/2.12 inference(rewrite,[status(thm)],[])).
% 2.46/2.12 tff(2421,plain,
% 2.46/2.12 (((~c0_1(a223)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a223)))),
% 2.46/2.12 inference(rewrite,[status(thm)],[])).
% 2.46/2.12 tff(2422,axiom,((~c0_1(a223)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 2.46/2.12 tff(2423,plain,
% 2.46/2.12 ((~hskp7) | (~c0_1(a223))),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 2.46/2.12 tff(2424,plain,
% 2.46/2.12 ((~hskp7) | (~c0_1(a223))),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2423, 2420])).
% 2.46/2.12 tff(2425,plain,
% 2.46/2.12 (~c0_1(a223)),
% 2.46/2.12 inference(unit_resolution,[status(thm)],[2424, 2419])).
% 2.46/2.12 tff(2426,plain,
% 2.46/2.12 (((~hskp7) | c2_1(a223)) <=> ((~hskp7) | c2_1(a223))),
% 2.46/2.12 inference(rewrite,[status(thm)],[])).
% 2.46/2.12 tff(2427,axiom,((~hskp7) | c2_1(a223)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 2.46/2.12 tff(2428,plain,
% 2.46/2.12 ((~hskp7) | c2_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2427, 2426])).
% 2.46/2.12 tff(2429,plain,
% 2.46/2.12 ((~hskp7) | c2_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2428, 2426])).
% 2.46/2.12 tff(2430,plain,
% 2.46/2.12 ((~hskp7) | c2_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2429, 2426])).
% 2.46/2.12 tff(2431,plain,
% 2.46/2.12 ((~hskp7) | c2_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2430, 2426])).
% 2.46/2.12 tff(2432,plain,
% 2.46/2.12 ((~hskp7) | c2_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2431, 2426])).
% 2.46/2.12 tff(2433,plain,
% 2.46/2.12 ((~hskp7) | c2_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2432, 2426])).
% 2.46/2.12 tff(2434,plain,
% 2.46/2.12 ((~hskp7) | c2_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2433, 2426])).
% 2.46/2.12 tff(2435,plain,
% 2.46/2.12 ((~hskp7) | c2_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2434, 2426])).
% 2.46/2.12 tff(2436,plain,
% 2.46/2.12 (c2_1(a223)),
% 2.46/2.12 inference(unit_resolution,[status(thm)],[2435, 2419])).
% 2.46/2.12 tff(2437,plain,
% 2.46/2.12 (((~hskp7) | c1_1(a223)) <=> ((~hskp7) | c1_1(a223))),
% 2.46/2.12 inference(rewrite,[status(thm)],[])).
% 2.46/2.12 tff(2438,axiom,((~hskp7) | c1_1(a223)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 2.46/2.12 tff(2439,plain,
% 2.46/2.12 ((~hskp7) | c1_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2438, 2437])).
% 2.46/2.12 tff(2440,plain,
% 2.46/2.12 ((~hskp7) | c1_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2439, 2437])).
% 2.46/2.12 tff(2441,plain,
% 2.46/2.12 ((~hskp7) | c1_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2440, 2437])).
% 2.46/2.12 tff(2442,plain,
% 2.46/2.12 ((~hskp7) | c1_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2441, 2437])).
% 2.46/2.12 tff(2443,plain,
% 2.46/2.12 ((~hskp7) | c1_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2442, 2437])).
% 2.46/2.12 tff(2444,plain,
% 2.46/2.12 ((~hskp7) | c1_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2443, 2437])).
% 2.46/2.12 tff(2445,plain,
% 2.46/2.12 ((~hskp7) | c1_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2444, 2437])).
% 2.46/2.12 tff(2446,plain,
% 2.46/2.12 ((~hskp7) | c1_1(a223)),
% 2.46/2.12 inference(modus_ponens,[status(thm)],[2445, 2437])).
% 2.46/2.12 tff(2447,plain,
% 2.46/2.12 (c1_1(a223)),
% 2.46/2.12 inference(unit_resolution,[status(thm)],[2446, 2419])).
% 2.46/2.12 tff(2448,plain,
% 2.46/2.12 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a223) | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c0_1(a216)) | (~c2_1(a223)) | (~c1_1(a223)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a223) | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c0_1(a216)) | (~c2_1(a223)) | (~c1_1(a223)))),
% 2.46/2.12 inference(rewrite,[status(thm)],[])).
% 2.46/2.12 tff(2449,plain,
% 2.46/2.12 ((hskp26 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c0_1(a216)) | c0_1(a223) | (~c1_1(a223)) | (~c2_1(a223))) <=> (hskp26 | c0_1(a223) | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c0_1(a216)) | (~c2_1(a223)) | (~c1_1(a223)))),
% 2.46/2.12 inference(rewrite,[status(thm)],[])).
% 2.46/2.12 tff(2450,plain,
% 2.46/2.12 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c0_1(a216)) | c0_1(a223) | (~c1_1(a223)) | (~c2_1(a223)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a223) | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c0_1(a216)) | (~c2_1(a223)) | (~c1_1(a223))))),
% 2.46/2.12 inference(monotonicity,[status(thm)],[2449])).
% 2.46/2.12 tff(2451,plain,
% 2.46/2.12 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c0_1(a216)) | c0_1(a223) | (~c1_1(a223)) | (~c2_1(a223)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a223) | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c0_1(a216)) | (~c2_1(a223)) | (~c1_1(a223)))),
% 2.46/2.12 inference(transitivity,[status(thm)],[2450, 2448])).
% 2.46/2.12 tff(2452,plain,
% 2.46/2.12 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c0_1(a216)) | c0_1(a223) | (~c1_1(a223)) | (~c2_1(a223)))),
% 2.46/2.12 inference(quant_inst,[status(thm)],[])).
% 2.46/2.12 tff(2453,plain,
% 2.46/2.12 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a223) | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c0_1(a216)) | (~c2_1(a223)) | (~c1_1(a223))),
% 2.46/2.13 inference(modus_ponens,[status(thm)],[2452, 2451])).
% 2.46/2.13 tff(2454,plain,
% 2.46/2.13 ($false),
% 2.46/2.13 inference(unit_resolution,[status(thm)],[2453, 122, 1, 2447, 2436, 2391, 2425, 2390, 1650, 2398])).
% 2.46/2.13 tff(2455,plain,(hskp6 | hskp26 | c1_1(a255) | c3_1(a255) | c3_1(a252) | hskp5 | c0_1(a255) | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | (~hskp12) | c3_1(a237)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.13 tff(2456,plain,
% 2.46/2.13 (hskp6),
% 2.46/2.13 inference(unit_resolution,[status(thm)],[2455, 12, 2368, 2367, 1, 45, 2366, 167, 166, 165, 757, 179])).
% 2.46/2.13 tff(2457,plain,
% 2.46/2.13 (~c3_1(a220)),
% 2.46/2.13 inference(unit_resolution,[status(thm)],[485, 2456])).
% 2.46/2.13 tff(2458,assumption,(~hskp10), introduced(assumption)).
% 2.46/2.13 tff(2459,plain,
% 2.46/2.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a255) | c3_1(a255) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a255) | c3_1(a255) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a255)))),
% 2.46/2.13 inference(rewrite,[status(thm)],[])).
% 2.46/2.13 tff(2460,plain,
% 2.46/2.13 ((hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a255) | c0_1(a255) | (~c2_1(a255))) <=> (hskp10 | c0_1(a255) | c3_1(a255) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a255)))),
% 2.46/2.13 inference(rewrite,[status(thm)],[])).
% 2.46/2.13 tff(2461,plain,
% 2.46/2.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a255) | c0_1(a255) | (~c2_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a255) | c3_1(a255) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a255))))),
% 2.46/2.13 inference(monotonicity,[status(thm)],[2460])).
% 2.46/2.13 tff(2462,plain,
% 2.46/2.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a255) | c0_1(a255) | (~c2_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a255) | c3_1(a255) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a255)))),
% 2.46/2.13 inference(transitivity,[status(thm)],[2461, 2459])).
% 2.46/2.13 tff(2463,plain,
% 2.46/2.13 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a255) | c0_1(a255) | (~c2_1(a255)))),
% 2.46/2.13 inference(quant_inst,[status(thm)],[])).
% 2.46/2.13 tff(2464,plain,
% 2.46/2.13 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a255) | c3_1(a255) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a255))),
% 2.46/2.13 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 2.46/2.13 tff(2465,plain,
% 2.46/2.13 (hskp10 | (~c2_1(a255))),
% 2.46/2.13 inference(unit_resolution,[status(thm)],[2464, 122, 2009, 1998, 1190, 1207, 2023, 11])).
% 2.46/2.13 tff(2466,plain,
% 2.46/2.13 (~c2_1(a255)),
% 2.46/2.13 inference(unit_resolution,[status(thm)],[2465, 2458])).
% 2.46/2.13 tff(2467,plain,
% 2.46/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a255) | c3_1(a255) | c1_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a255) | c3_1(a255) | c1_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))),
% 2.46/2.13 inference(rewrite,[status(thm)],[])).
% 2.46/2.13 tff(2468,plain,
% 2.46/2.13 (((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a215) | c0_1(a215) | (~c3_1(a215)) | c3_1(a255) | c2_1(a255) | c0_1(a255)) <=> (c0_1(a255) | c3_1(a255) | c1_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))),
% 2.46/2.13 inference(rewrite,[status(thm)],[])).
% 2.46/2.13 tff(2469,plain,
% 2.46/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a215) | c0_1(a215) | (~c3_1(a215)) | c3_1(a255) | c2_1(a255) | c0_1(a255))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a255) | c3_1(a255) | c1_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255)))),
% 2.46/2.13 inference(monotonicity,[status(thm)],[2468])).
% 2.46/2.13 tff(2470,plain,
% 2.46/2.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a215) | c0_1(a215) | (~c3_1(a215)) | c3_1(a255) | c2_1(a255) | c0_1(a255))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a255) | c3_1(a255) | c1_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))),
% 2.46/2.13 inference(transitivity,[status(thm)],[2469, 2467])).
% 2.46/2.13 tff(2471,plain,
% 2.46/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a215) | c0_1(a215) | (~c3_1(a215)) | c3_1(a255) | c2_1(a255) | c0_1(a255))),
% 2.46/2.13 inference(quant_inst,[status(thm)],[])).
% 2.46/2.13 tff(2472,plain,
% 2.46/2.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a255) | c3_1(a255) | c1_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255)),
% 2.46/2.13 inference(modus_ponens,[status(thm)],[2471, 2470])).
% 2.46/2.13 tff(2473,plain,
% 2.46/2.13 ((~c3_1(a215)) | c3_1(a252) | c2_1(a255)),
% 2.46/2.13 inference(unit_resolution,[status(thm)],[2472, 122, 2009, 1190, 1207, 2023, 166, 165, 1524])).
% 2.46/2.13 tff(2474,plain,
% 2.46/2.13 (~c3_1(a215)),
% 2.46/2.13 inference(unit_resolution,[status(thm)],[2473, 2466, 12])).
% 2.46/2.13 tff(2475,plain,
% 2.46/2.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a252) | c0_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a252) | c0_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.46/2.13 inference(rewrite,[status(thm)],[])).
% 2.46/2.13 tff(2476,plain,
% 2.46/2.13 ((hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215))) <=> (hskp10 | c1_1(a252) | c0_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.46/2.13 inference(rewrite,[status(thm)],[])).
% 2.46/2.13 tff(2477,plain,
% 2.46/2.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a252) | c0_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a252)) | (~c2_1(a252))))),
% 2.46/2.13 inference(monotonicity,[status(thm)],[2476])).
% 2.46/2.13 tff(2478,plain,
% 2.46/2.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a252) | c0_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.46/2.13 inference(transitivity,[status(thm)],[2477, 2475])).
% 2.46/2.13 tff(2479,plain,
% 2.46/2.13 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)))),
% 2.46/2.13 inference(quant_inst,[status(thm)],[])).
% 2.46/2.13 tff(2480,plain,
% 2.46/2.13 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a252) | c0_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a252)) | (~c2_1(a252))),
% 2.46/2.13 inference(modus_ponens,[status(thm)],[2479, 2478])).
% 2.46/2.13 tff(2481,plain,
% 2.46/2.13 ($false),
% 2.46/2.13 inference(unit_resolution,[status(thm)],[2480, 122, 2458, 2009, 1998, 167, 2023, 166, 11, 2474])).
% 2.46/2.13 tff(2482,plain,(hskp10 | (~c2_1(a215)) | c0_1(a215) | c3_1(a252) | c0_1(a255) | c3_1(a255) | c1_1(a215)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.13 tff(2483,plain,
% 2.46/2.13 (hskp10),
% 2.46/2.13 inference(unit_resolution,[status(thm)],[2482, 12, 166, 167, 2366, 2367, 165])).
% 2.46/2.13 tff(2484,plain,
% 2.46/2.13 (~c0_1(a231)),
% 2.46/2.13 inference(unit_resolution,[status(thm)],[1416, 2483])).
% 2.46/2.13 tff(2485,plain,
% 2.46/2.13 (c2_1(a220)),
% 2.46/2.13 inference(unit_resolution,[status(thm)],[541, 2456])).
% 2.46/2.13 tff(2486,plain,
% 2.46/2.13 (c1_1(a220)),
% 2.46/2.13 inference(unit_resolution,[status(thm)],[530, 2456])).
% 2.46/2.13 tff(2487,plain,
% 2.46/2.13 (c3_1(a231)),
% 2.46/2.13 inference(unit_resolution,[status(thm)],[1446, 2483])).
% 2.46/2.13 tff(2488,plain,
% 2.46/2.13 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a231) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | c2_1(a231) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a231) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | c2_1(a231) | (~c3_1(a231)))),
% 2.46/2.13 inference(rewrite,[status(thm)],[])).
% 2.46/2.13 tff(2489,plain,
% 2.46/2.13 ((hskp5 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231))) <=> (hskp5 | c0_1(a231) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | c2_1(a231) | (~c3_1(a231)))),
% 2.46/2.13 inference(rewrite,[status(thm)],[])).
% 2.46/2.13 tff(2490,plain,
% 2.46/2.13 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a231) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | c2_1(a231) | (~c3_1(a231))))),
% 2.46/2.13 inference(monotonicity,[status(thm)],[2489])).
% 2.46/2.13 tff(2491,plain,
% 2.46/2.13 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a231) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | c2_1(a231) | (~c3_1(a231)))),
% 2.46/2.13 inference(transitivity,[status(thm)],[2490, 2488])).
% 2.46/2.13 tff(2492,plain,
% 2.46/2.13 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)))),
% 2.46/2.13 inference(quant_inst,[status(thm)],[])).
% 2.46/2.13 tff(2493,plain,
% 2.46/2.13 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a231) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | c2_1(a231) | (~c3_1(a231))),
% 2.46/2.13 inference(modus_ponens,[status(thm)],[2492, 2491])).
% 2.46/2.13 tff(2494,plain,
% 2.46/2.13 (c2_1(a231)),
% 2.46/2.14 inference(unit_resolution,[status(thm)],[2493, 122, 45, 2487, 2486, 2485, 2484, 2457, 1910])).
% 2.46/2.14 tff(2495,plain,
% 2.46/2.14 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a255) | c3_1(a255) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a255) | c3_1(a255) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c2_1(a255))),
% 2.46/2.14 inference(rewrite,[status(thm)],[])).
% 2.46/2.14 tff(2496,plain,
% 2.46/2.14 ((hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a255) | c0_1(a255) | c2_1(a255)) <=> (hskp9 | c0_1(a255) | c3_1(a255) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c2_1(a255))),
% 2.46/2.14 inference(rewrite,[status(thm)],[])).
% 2.46/2.14 tff(2497,plain,
% 2.46/2.14 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a255) | c0_1(a255) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a255) | c3_1(a255) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c2_1(a255)))),
% 2.46/2.14 inference(monotonicity,[status(thm)],[2496])).
% 2.46/2.14 tff(2498,plain,
% 2.46/2.14 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a255) | c0_1(a255) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a255) | c3_1(a255) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c2_1(a255))),
% 2.46/2.14 inference(transitivity,[status(thm)],[2497, 2495])).
% 2.46/2.14 tff(2499,plain,
% 2.46/2.14 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a255) | c0_1(a255) | c2_1(a255))),
% 2.46/2.14 inference(quant_inst,[status(thm)],[])).
% 2.46/2.14 tff(2500,plain,
% 2.46/2.14 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a255) | c3_1(a255) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c2_1(a255)),
% 2.46/2.14 inference(modus_ponens,[status(thm)],[2499, 2498])).
% 2.46/2.14 tff(2501,plain,
% 2.46/2.14 ((~c2_1(a231)) | c2_1(a255)),
% 2.46/2.14 inference(unit_resolution,[status(thm)],[2500, 122, 23, 2487, 2366, 2367, 2484, 989])).
% 2.46/2.14 tff(2502,plain,
% 2.46/2.14 (c2_1(a255)),
% 2.46/2.14 inference(unit_resolution,[status(thm)],[2501, 2494])).
% 2.46/2.14 tff(2503,plain,
% 2.46/2.14 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 2.46/2.14 inference(bind,[status(th)],[])).
% 2.46/2.14 tff(2504,plain,
% 2.46/2.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.46/2.14 inference(quant_intro,[status(thm)],[2503])).
% 2.46/2.14 tff(2505,plain,
% 2.46/2.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.46/2.14 inference(rewrite,[status(thm)],[])).
% 2.46/2.14 tff(2506,plain,
% 2.46/2.14 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 2.46/2.14 inference(bind,[status(th)],[])).
% 2.46/2.14 tff(2507,plain,
% 2.46/2.14 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.46/2.14 inference(quant_intro,[status(thm)],[2506])).
% 2.46/2.14 tff(2508,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 2.46/2.14 tff(2509,plain,
% 2.46/2.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.46/2.14 inference(modus_ponens,[status(thm)],[2508, 2507])).
% 2.46/2.14 tff(2510,plain,
% 2.46/2.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.46/2.14 inference(modus_ponens,[status(thm)],[2509, 2505])).
% 2.46/2.14 tff(2511,plain,(
% 2.46/2.14 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.46/2.14 inference(skolemize,[status(sab)],[2510])).
% 2.46/2.14 tff(2512,plain,
% 2.46/2.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 2.46/2.14 inference(modus_ponens,[status(thm)],[2511, 2504])).
% 2.46/2.14 tff(2513,plain,
% 2.46/2.14 (c1_1(a231)),
% 2.46/2.14 inference(unit_resolution,[status(thm)],[661, 2483])).
% 2.46/2.14 tff(2514,plain,
% 2.46/2.14 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)))),
% 2.46/2.14 inference(rewrite,[status(thm)],[])).
% 2.46/2.14 tff(2515,plain,
% 2.46/2.14 ((hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231))) <=> (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)))),
% 2.46/2.14 inference(rewrite,[status(thm)],[])).
% 2.46/2.14 tff(2516,plain,
% 2.46/2.14 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231))))),
% 2.46/2.14 inference(monotonicity,[status(thm)],[2515])).
% 2.46/2.14 tff(2517,plain,
% 2.46/2.14 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)))),
% 2.46/2.14 inference(transitivity,[status(thm)],[2516, 2514])).
% 2.46/2.14 tff(2518,plain,
% 2.46/2.14 ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)))),
% 2.46/2.14 inference(quant_inst,[status(thm)],[])).
% 2.46/2.14 tff(2519,plain,
% 2.46/2.14 ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231))),
% 2.46/2.14 inference(modus_ponens,[status(thm)],[2518, 2517])).
% 2.46/2.14 tff(2520,plain,
% 2.46/2.14 (hskp29 | (~c2_1(a231))),
% 2.46/2.14 inference(unit_resolution,[status(thm)],[2519, 122, 1, 2513, 2487, 2316])).
% 2.46/2.14 tff(2521,plain,
% 2.46/2.14 (hskp29),
% 2.46/2.14 inference(unit_resolution,[status(thm)],[2520, 2494])).
% 2.46/2.14 tff(2522,plain,
% 2.46/2.14 (c3_1(a296)),
% 2.46/2.14 inference(unit_resolution,[status(thm)],[2333, 2521])).
% 2.46/2.14 tff(2523,plain,
% 2.46/2.14 (c2_1(a296)),
% 2.46/2.14 inference(unit_resolution,[status(thm)],[2344, 2521])).
% 2.46/2.14 tff(2524,plain,
% 2.46/2.14 (c0_1(a296)),
% 2.46/2.14 inference(unit_resolution,[status(thm)],[2355, 2521])).
% 2.46/2.14 tff(2525,plain,
% 2.46/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)) | (~c2_1(a255)))),
% 2.46/2.14 inference(rewrite,[status(thm)],[])).
% 2.46/2.14 tff(2526,plain,
% 2.46/2.14 (((~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255))) <=> (c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)) | (~c2_1(a255)))),
% 2.46/2.14 inference(rewrite,[status(thm)],[])).
% 2.46/2.14 tff(2527,plain,
% 2.46/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)) | (~c2_1(a255))))),
% 2.46/2.14 inference(monotonicity,[status(thm)],[2526])).
% 2.46/2.14 tff(2528,plain,
% 2.46/2.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)) | (~c2_1(a255)))),
% 2.46/2.14 inference(transitivity,[status(thm)],[2527, 2525])).
% 2.46/2.14 tff(2529,plain,
% 2.46/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))),
% 2.46/2.14 inference(quant_inst,[status(thm)],[])).
% 2.46/2.14 tff(2530,plain,
% 2.46/2.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)) | (~c2_1(a255))),
% 2.46/2.14 inference(modus_ponens,[status(thm)],[2529, 2528])).
% 2.46/2.14 tff(2531,plain,
% 2.46/2.14 ($false),
% 2.46/2.14 inference(unit_resolution,[status(thm)],[2530, 122, 2524, 2523, 2522, 2513, 2487, 2366, 2368, 2512, 2502, 2494])).
% 2.46/2.14 tff(2532,plain,(c3_1(a252) | hskp9 | hskp26 | hskp5 | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | (~hskp12) | c3_1(a237)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.14 tff(2533,plain,
% 2.46/2.14 (c3_1(a252)),
% 2.46/2.14 inference(unit_resolution,[status(thm)],[2532, 2289, 178, 45, 573, 572, 571, 23, 179])).
% 2.46/2.14 tff(2534,plain,
% 2.46/2.14 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 2.46/2.14 inference(bind,[status(th)],[])).
% 2.46/2.14 tff(2535,plain,
% 2.46/2.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.46/2.15 inference(quant_intro,[status(thm)],[2534])).
% 2.46/2.15 tff(2536,plain,
% 2.46/2.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.46/2.15 inference(rewrite,[status(thm)],[])).
% 2.46/2.15 tff(2537,plain,
% 2.46/2.15 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 2.46/2.15 inference(bind,[status(th)],[])).
% 2.46/2.15 tff(2538,plain,
% 2.46/2.15 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.46/2.15 inference(quant_intro,[status(thm)],[2537])).
% 2.46/2.15 tff(2539,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 2.46/2.15 tff(2540,plain,
% 2.46/2.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.46/2.15 inference(modus_ponens,[status(thm)],[2539, 2538])).
% 2.46/2.15 tff(2541,plain,
% 2.46/2.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.46/2.15 inference(modus_ponens,[status(thm)],[2540, 2536])).
% 2.46/2.15 tff(2542,plain,(
% 2.46/2.15 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.46/2.15 inference(skolemize,[status(sab)],[2541])).
% 2.46/2.15 tff(2543,plain,
% 2.46/2.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.46/2.15 inference(modus_ponens,[status(thm)],[2542, 2535])).
% 2.46/2.15 tff(2544,plain,
% 2.46/2.15 (hskp23),
% 2.46/2.15 inference(unit_resolution,[status(thm)],[2200, 2533, 178])).
% 2.46/2.15 tff(2545,plain,
% 2.46/2.15 (~c3_1(a274)),
% 2.46/2.15 inference(unit_resolution,[status(thm)],[2206, 2544])).
% 2.46/2.15 tff(2546,plain,
% 2.46/2.15 (~c0_1(a274)),
% 2.46/2.15 inference(unit_resolution,[status(thm)],[2230, 2544])).
% 2.46/2.15 tff(2547,plain,
% 2.46/2.15 (c1_1(a274)),
% 2.46/2.15 inference(unit_resolution,[status(thm)],[2217, 2544])).
% 2.46/2.15 tff(2548,plain,
% 2.46/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 2.46/2.15 inference(rewrite,[status(thm)],[])).
% 2.46/2.15 tff(2549,plain,
% 2.46/2.15 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274))) <=> (c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 2.46/2.15 inference(rewrite,[status(thm)],[])).
% 2.46/2.15 tff(2550,plain,
% 2.46/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274))))),
% 2.46/2.15 inference(monotonicity,[status(thm)],[2549])).
% 2.46/2.15 tff(2551,plain,
% 2.46/2.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 2.46/2.15 inference(transitivity,[status(thm)],[2550, 2548])).
% 2.46/2.15 tff(2552,plain,
% 2.46/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))),
% 2.46/2.15 inference(quant_inst,[status(thm)],[])).
% 2.46/2.15 tff(2553,plain,
% 2.46/2.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274))),
% 2.46/2.15 inference(modus_ponens,[status(thm)],[2552, 2551])).
% 2.46/2.15 tff(2554,plain,
% 2.46/2.15 (c1_1(a237)),
% 2.46/2.15 inference(unit_resolution,[status(thm)],[2553, 122, 2547, 2009, 1998, 2119, 2546, 2545, 179, 2543, 2533])).
% 2.46/2.15 tff(2555,plain,
% 2.46/2.15 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)))),
% 2.46/2.15 inference(rewrite,[status(thm)],[])).
% 2.46/2.15 tff(2556,plain,
% 2.46/2.15 ((hskp26 | hskp9 | (~ndr1_0) | c2_1(a274) | c3_1(a274) | (~c1_1(a274))) <=> (hskp26 | hskp9 | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)))),
% 2.46/2.15 inference(rewrite,[status(thm)],[])).
% 2.46/2.15 tff(2557,plain,
% 2.46/2.15 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a274) | c3_1(a274) | (~c1_1(a274)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274))))),
% 2.46/2.15 inference(monotonicity,[status(thm)],[2556])).
% 2.46/2.15 tff(2558,plain,
% 2.46/2.15 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a274) | c3_1(a274) | (~c1_1(a274)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)))),
% 2.46/2.15 inference(transitivity,[status(thm)],[2557, 2555])).
% 2.46/2.15 tff(2559,plain,
% 2.46/2.15 ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a274) | c3_1(a274) | (~c1_1(a274)))),
% 2.46/2.15 inference(quant_inst,[status(thm)],[])).
% 2.46/2.15 tff(2560,plain,
% 2.46/2.15 ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274))),
% 2.46/2.15 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 2.46/2.15 tff(2561,plain,
% 2.46/2.15 (c2_1(a274)),
% 2.46/2.15 inference(unit_resolution,[status(thm)],[2560, 122, 178, 23, 2547, 2545, 257])).
% 2.46/2.15 tff(2562,plain,
% 2.46/2.15 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 2.46/2.15 inference(bind,[status(th)],[])).
% 2.46/2.15 tff(2563,plain,
% 2.46/2.15 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.46/2.15 inference(quant_intro,[status(thm)],[2562])).
% 2.46/2.15 tff(2564,plain,
% 2.46/2.15 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.46/2.15 inference(rewrite,[status(thm)],[])).
% 2.46/2.15 tff(2565,plain,
% 2.46/2.15 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_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))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_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))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_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))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_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))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~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))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 2.46/2.15 inference(bind,[status(th)],[])).
% 2.46/2.15 tff(2566,plain,
% 2.46/2.15 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.46/2.15 inference(quant_intro,[status(thm)],[2565])).
% 2.46/2.15 tff(2567,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 2.46/2.15 tff(2568,plain,
% 2.46/2.15 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.46/2.15 inference(modus_ponens,[status(thm)],[2567, 2566])).
% 2.46/2.15 tff(2569,plain,
% 2.46/2.15 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.46/2.15 inference(modus_ponens,[status(thm)],[2568, 2564])).
% 2.46/2.15 tff(2570,plain,(
% 2.46/2.15 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.46/2.15 inference(skolemize,[status(sab)],[2569])).
% 2.46/2.15 tff(2571,plain,
% 2.46/2.16 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.46/2.16 inference(modus_ponens,[status(thm)],[2570, 2563])).
% 2.46/2.16 tff(2572,plain,
% 2.46/2.16 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a274)))),
% 2.46/2.16 inference(rewrite,[status(thm)],[])).
% 2.46/2.16 tff(2573,plain,
% 2.46/2.16 ((hskp14 | (~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274))) <=> (hskp14 | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a274)))),
% 2.46/2.16 inference(rewrite,[status(thm)],[])).
% 2.46/2.16 tff(2574,plain,
% 2.46/2.16 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a274))))),
% 2.46/2.16 inference(monotonicity,[status(thm)],[2573])).
% 2.46/2.16 tff(2575,plain,
% 2.46/2.16 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a274)))),
% 2.46/2.16 inference(transitivity,[status(thm)],[2574, 2572])).
% 2.46/2.16 tff(2576,plain,
% 2.46/2.16 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274)))),
% 2.46/2.16 inference(quant_inst,[status(thm)],[])).
% 2.46/2.16 tff(2577,plain,
% 2.46/2.16 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a274))),
% 2.46/2.16 inference(modus_ponens,[status(thm)],[2576, 2575])).
% 2.46/2.16 tff(2578,plain,
% 2.46/2.16 (hskp14 | (~c2_1(a274))),
% 2.46/2.16 inference(unit_resolution,[status(thm)],[2577, 122, 2119, 2546, 2545, 179, 2571, 2554])).
% 2.46/2.16 tff(2579,plain,
% 2.46/2.16 (hskp14),
% 2.46/2.16 inference(unit_resolution,[status(thm)],[2578, 2561])).
% 2.46/2.16 tff(2580,plain,
% 2.46/2.16 (((~hskp14) | (~c1_1(a241))) <=> ((~hskp14) | (~c1_1(a241)))),
% 2.46/2.16 inference(rewrite,[status(thm)],[])).
% 2.46/2.16 tff(2581,plain,
% 2.46/2.16 (((~c1_1(a241)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a241)))),
% 2.46/2.16 inference(rewrite,[status(thm)],[])).
% 2.46/2.16 tff(2582,axiom,((~c1_1(a241)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 2.46/2.16 tff(2583,plain,
% 2.46/2.16 ((~hskp14) | (~c1_1(a241))),
% 2.46/2.16 inference(modus_ponens,[status(thm)],[2582, 2581])).
% 2.46/2.16 tff(2584,plain,
% 2.46/2.16 ((~hskp14) | (~c1_1(a241))),
% 2.46/2.16 inference(modus_ponens,[status(thm)],[2583, 2580])).
% 2.46/2.16 tff(2585,plain,
% 2.46/2.16 (~c1_1(a241)),
% 2.46/2.16 inference(unit_resolution,[status(thm)],[2584, 2579])).
% 2.46/2.16 tff(2586,plain,
% 2.46/2.16 (((~hskp14) | c3_1(a241)) <=> ((~hskp14) | c3_1(a241))),
% 2.46/2.16 inference(rewrite,[status(thm)],[])).
% 2.46/2.16 tff(2587,axiom,((~hskp14) | c3_1(a241)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 2.46/2.16 tff(2588,plain,
% 2.46/2.16 ((~hskp14) | c3_1(a241)),
% 2.46/2.16 inference(modus_ponens,[status(thm)],[2587, 2586])).
% 2.46/2.16 tff(2589,plain,
% 2.46/2.16 ((~hskp14) | c3_1(a241)),
% 2.46/2.16 inference(modus_ponens,[status(thm)],[2588, 2586])).
% 2.46/2.16 tff(2590,plain,
% 2.46/2.16 ((~hskp14) | c3_1(a241)),
% 2.46/2.16 inference(modus_ponens,[status(thm)],[2589, 2586])).
% 2.46/2.16 tff(2591,plain,
% 2.46/2.16 ((~hskp14) | c3_1(a241)),
% 2.46/2.16 inference(modus_ponens,[status(thm)],[2590, 2586])).
% 2.46/2.16 tff(2592,plain,
% 2.46/2.16 ((~hskp14) | c3_1(a241)),
% 2.46/2.16 inference(modus_ponens,[status(thm)],[2591, 2586])).
% 2.46/2.16 tff(2593,plain,
% 2.46/2.16 ((~hskp14) | c3_1(a241)),
% 2.46/2.16 inference(modus_ponens,[status(thm)],[2592, 2586])).
% 2.46/2.16 tff(2594,plain,
% 2.46/2.16 ((~hskp14) | c3_1(a241)),
% 2.46/2.16 inference(modus_ponens,[status(thm)],[2593, 2586])).
% 2.46/2.16 tff(2595,plain,
% 2.46/2.16 ((~hskp14) | c3_1(a241)),
% 2.46/2.16 inference(modus_ponens,[status(thm)],[2594, 2586])).
% 2.46/2.16 tff(2596,plain,
% 2.46/2.16 (c3_1(a241)),
% 2.46/2.16 inference(unit_resolution,[status(thm)],[2595, 2579])).
% 2.46/2.16 tff(2597,plain,
% 2.46/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a241) | c3_1(a237) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a241) | (~c3_1(a241)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a241) | c3_1(a237) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a241) | (~c3_1(a241)))),
% 2.46/2.16 inference(rewrite,[status(thm)],[])).
% 2.46/2.16 tff(2598,plain,
% 2.46/2.16 (((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a241) | c2_1(a241) | (~c3_1(a241)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215))) <=> (c1_1(a241) | c3_1(a237) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a241) | (~c3_1(a241)))),
% 2.46/2.16 inference(rewrite,[status(thm)],[])).
% 2.46/2.16 tff(2599,plain,
% 2.46/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a241) | c2_1(a241) | (~c3_1(a241)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a241) | c3_1(a237) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a241) | (~c3_1(a241))))),
% 2.46/2.16 inference(monotonicity,[status(thm)],[2598])).
% 2.46/2.16 tff(2600,plain,
% 2.46/2.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a241) | c2_1(a241) | (~c3_1(a241)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a241) | c3_1(a237) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a241) | (~c3_1(a241)))),
% 2.46/2.16 inference(transitivity,[status(thm)],[2599, 2597])).
% 2.46/2.16 tff(2601,plain,
% 2.46/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a241) | c2_1(a241) | (~c3_1(a241)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))),
% 2.46/2.16 inference(quant_inst,[status(thm)],[])).
% 2.46/2.16 tff(2602,plain,
% 2.46/2.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a241) | c3_1(a237) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a241) | (~c3_1(a241))),
% 2.46/2.16 inference(modus_ponens,[status(thm)],[2601, 2600])).
% 2.46/2.16 tff(2603,plain,
% 2.46/2.16 (c2_1(a241)),
% 2.46/2.16 inference(unit_resolution,[status(thm)],[2602, 122, 2596, 2119, 573, 2585, 179, 572, 571, 782, 2554])).
% 2.46/2.16 tff(2604,plain,
% 2.46/2.16 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a274)))),
% 2.51/2.17 inference(rewrite,[status(thm)],[])).
% 2.51/2.17 tff(2605,plain,
% 2.51/2.17 ((hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274))) <=> (hskp10 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a274)))),
% 2.51/2.17 inference(rewrite,[status(thm)],[])).
% 2.51/2.17 tff(2606,plain,
% 2.51/2.17 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a274))))),
% 2.51/2.17 inference(monotonicity,[status(thm)],[2605])).
% 2.51/2.17 tff(2607,plain,
% 2.51/2.17 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a274)))),
% 2.51/2.17 inference(transitivity,[status(thm)],[2606, 2604])).
% 2.51/2.17 tff(2608,plain,
% 2.51/2.17 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274)))),
% 2.51/2.17 inference(quant_inst,[status(thm)],[])).
% 2.51/2.17 tff(2609,plain,
% 2.51/2.17 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a274))),
% 2.51/2.17 inference(modus_ponens,[status(thm)],[2608, 2607])).
% 2.51/2.17 tff(2610,plain,
% 2.51/2.17 (hskp10 | (~c2_1(a274))),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2609, 122, 2009, 1998, 2546, 2545, 2023, 11])).
% 2.51/2.17 tff(2611,plain,
% 2.51/2.17 (hskp10),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2610, 2561])).
% 2.51/2.17 tff(2612,plain,
% 2.51/2.17 (~c0_1(a231)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[1416, 2611])).
% 2.51/2.17 tff(2613,plain,
% 2.51/2.17 (c3_1(a231)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[1446, 2611])).
% 2.51/2.17 tff(2614,plain,
% 2.51/2.17 (c1_1(a231)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[661, 2611])).
% 2.51/2.17 tff(2615,plain,
% 2.51/2.17 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a241) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a241)) | (~c2_1(a241)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a241) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a241)) | (~c2_1(a241)))),
% 2.51/2.17 inference(rewrite,[status(thm)],[])).
% 2.51/2.17 tff(2616,plain,
% 2.51/2.17 ((hskp9 | (~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c3_1(a241)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231))) <=> (hskp9 | c1_1(a241) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a241)) | (~c2_1(a241)))),
% 2.51/2.17 inference(rewrite,[status(thm)],[])).
% 2.51/2.17 tff(2617,plain,
% 2.51/2.17 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c3_1(a241)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a241) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a241)) | (~c2_1(a241))))),
% 2.51/2.17 inference(monotonicity,[status(thm)],[2616])).
% 2.51/2.17 tff(2618,plain,
% 2.51/2.17 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c3_1(a241)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a241) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a241)) | (~c2_1(a241)))),
% 2.51/2.17 inference(transitivity,[status(thm)],[2617, 2615])).
% 2.51/2.17 tff(2619,plain,
% 2.51/2.17 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c3_1(a241)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))),
% 2.51/2.17 inference(quant_inst,[status(thm)],[])).
% 2.51/2.17 tff(2620,plain,
% 2.51/2.17 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a241) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a241)) | (~c2_1(a241))),
% 2.51/2.17 inference(modus_ponens,[status(thm)],[2619, 2618])).
% 2.51/2.17 tff(2621,plain,
% 2.51/2.17 ($false),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2620, 122, 23, 2596, 2614, 2613, 2585, 2612, 445, 2603])).
% 2.51/2.17 tff(2622,plain,(c3_1(a237) | hskp9 | hskp5 | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.51/2.17 tff(2623,plain,
% 2.51/2.17 (c3_1(a237)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2622, 45, 23, 34])).
% 2.51/2.17 tff(2624,plain,
% 2.51/2.17 (~hskp12),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[762, 2623])).
% 2.51/2.17 tff(2625,plain,
% 2.51/2.17 (hskp21),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2158, 12, 574])).
% 2.51/2.17 tff(2626,plain,
% 2.51/2.17 (~c2_1(a259)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[1062, 2625])).
% 2.51/2.17 tff(2627,plain,
% 2.51/2.17 (c3_1(a259)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[867, 2625])).
% 2.51/2.17 tff(2628,plain,
% 2.51/2.17 (c0_1(a259)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[855, 2625])).
% 2.51/2.17 tff(2629,plain,
% 2.51/2.17 ($false),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2282, 122, 2628, 2627, 2009, 1998, 2626, 2023, 22, 12])).
% 2.51/2.17 tff(2630,plain,(c3_1(a252) | hskp12), inference(lemma,lemma(discharge,[]))).
% 2.51/2.17 tff(2631,plain,
% 2.51/2.17 (c3_1(a252)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2630, 2624])).
% 2.51/2.17 tff(2632,plain,
% 2.51/2.17 (hskp23),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2200, 2631, 178])).
% 2.51/2.17 tff(2633,plain,
% 2.51/2.17 (~c3_1(a274)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2206, 2632])).
% 2.51/2.17 tff(2634,plain,
% 2.51/2.17 (~c0_1(a274)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2230, 2632])).
% 2.51/2.17 tff(2635,plain,
% 2.51/2.17 (c1_1(a274)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2217, 2632])).
% 2.51/2.17 tff(2636,plain,
% 2.51/2.17 (~c2_1(a274)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2237, 122, 2624, 2635, 2634, 2633, 44])).
% 2.51/2.17 tff(2637,plain,
% 2.51/2.17 ($false),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2560, 122, 178, 23, 2635, 2633, 257, 2636])).
% 2.51/2.17 tff(2638,plain,(hskp5 | hskp9 | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.51/2.17 tff(2639,plain,
% 2.51/2.17 (hskp5),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[2638, 34, 23])).
% 2.51/2.17 tff(2640,plain,
% 2.51/2.17 (~c1_1(a218)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[743, 2639])).
% 2.51/2.17 tff(2641,plain,
% 2.51/2.17 (hskp2),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[569, 1, 34, 23])).
% 2.51/2.17 tff(2642,plain,
% 2.51/2.17 (~c1_1(a215)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[136, 2641])).
% 2.51/2.17 tff(2643,plain,
% 2.51/2.17 (~c0_1(a215)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[153, 2641])).
% 2.51/2.17 tff(2644,plain,
% 2.51/2.17 (c2_1(a215)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[147, 2641])).
% 2.51/2.17 tff(2645,plain,
% 2.51/2.17 (~c2_1(a218)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[737, 2639])).
% 2.51/2.17 tff(2646,plain,
% 2.51/2.17 (c3_1(a218)),
% 2.51/2.17 inference(unit_resolution,[status(thm)],[754, 2639])).
% 2.51/2.17 tff(2647,plain,
% 2.51/2.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.17 inference(rewrite,[status(thm)],[])).
% 2.51/2.18 tff(2648,plain,
% 2.51/2.18 (((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c1_1(a252) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.18 inference(rewrite,[status(thm)],[])).
% 2.51/2.18 tff(2649,plain,
% 2.51/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252))))),
% 2.51/2.18 inference(monotonicity,[status(thm)],[2648])).
% 2.51/2.18 tff(2650,plain,
% 2.51/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.18 inference(transitivity,[status(thm)],[2649, 2647])).
% 2.51/2.18 tff(2651,plain,
% 2.51/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 2.51/2.18 inference(quant_inst,[status(thm)],[])).
% 2.51/2.18 tff(2652,plain,
% 2.51/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252))),
% 2.51/2.18 inference(modus_ponens,[status(thm)],[2651, 2650])).
% 2.51/2.18 tff(2653,plain,
% 2.51/2.18 (~c0_1(a218)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[2652, 122, 2009, 1998, 785, 2023, 783, 22, 12])).
% 2.51/2.18 tff(2654,plain,
% 2.51/2.18 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 2.51/2.18 inference(bind,[status(th)],[])).
% 2.51/2.18 tff(2655,plain,
% 2.51/2.18 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.51/2.18 inference(quant_intro,[status(thm)],[2654])).
% 2.51/2.18 tff(2656,plain,
% 2.51/2.18 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.51/2.18 inference(rewrite,[status(thm)],[])).
% 2.51/2.18 tff(2657,plain,
% 2.51/2.18 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp26) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp26))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 2.51/2.18 inference(bind,[status(th)],[])).
% 2.51/2.18 tff(2658,plain,
% 2.51/2.18 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.51/2.18 inference(quant_intro,[status(thm)],[2657])).
% 2.51/2.18 tff(2659,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 2.51/2.18 tff(2660,plain,
% 2.51/2.18 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.51/2.18 inference(modus_ponens,[status(thm)],[2659, 2658])).
% 2.51/2.18 tff(2661,plain,
% 2.51/2.18 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.51/2.18 inference(modus_ponens,[status(thm)],[2660, 2656])).
% 2.51/2.18 tff(2662,plain,(
% 2.51/2.18 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.51/2.18 inference(skolemize,[status(sab)],[2661])).
% 2.51/2.18 tff(2663,plain,
% 2.51/2.18 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.51/2.18 inference(modus_ponens,[status(thm)],[2662, 2655])).
% 2.51/2.18 tff(2664,plain,
% 2.51/2.18 (hskp12),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[2630, 12])).
% 2.51/2.18 tff(2665,plain,
% 2.51/2.18 (~c3_1(a237)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[762, 2664])).
% 2.51/2.18 tff(2666,plain,
% 2.51/2.18 (c0_1(a237)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[629, 2664])).
% 2.51/2.18 tff(2667,plain,
% 2.51/2.18 (~c1_1(a237)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[791, 122, 2666, 785, 167, 2665, 784, 783, 166, 165, 782])).
% 2.51/2.18 tff(2668,plain,
% 2.51/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a255) | c3_1(a255) | c1_1(a252) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a255) | c3_1(a255) | c1_1(a252) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))),
% 2.51/2.18 inference(rewrite,[status(thm)],[])).
% 2.51/2.18 tff(2669,plain,
% 2.51/2.18 (((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a255) | c2_1(a255) | c0_1(a255)) <=> (c0_1(a255) | c3_1(a255) | c1_1(a252) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))),
% 2.51/2.18 inference(rewrite,[status(thm)],[])).
% 2.51/2.18 tff(2670,plain,
% 2.51/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a255) | c2_1(a255) | c0_1(a255))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a255) | c3_1(a255) | c1_1(a252) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255)))),
% 2.51/2.18 inference(monotonicity,[status(thm)],[2669])).
% 2.51/2.18 tff(2671,plain,
% 2.51/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a255) | c2_1(a255) | c0_1(a255))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a255) | c3_1(a255) | c1_1(a252) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))),
% 2.51/2.18 inference(transitivity,[status(thm)],[2670, 2668])).
% 2.51/2.18 tff(2672,plain,
% 2.51/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a255) | c2_1(a255) | c0_1(a255))),
% 2.51/2.18 inference(quant_inst,[status(thm)],[])).
% 2.51/2.18 tff(2673,plain,
% 2.51/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a255) | c3_1(a255) | c1_1(a252) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255)),
% 2.51/2.18 inference(modus_ponens,[status(thm)],[2672, 2671])).
% 2.51/2.18 tff(2674,plain,
% 2.51/2.18 (c0_1(a218) | c3_1(a252) | c2_1(a255)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[2673, 122, 2009, 785, 1190, 1207, 2023, 784, 1524])).
% 2.51/2.18 tff(2675,plain,
% 2.51/2.18 (c2_1(a255)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[2674, 2653, 12])).
% 2.51/2.18 tff(2676,assumption,(~c1_1(a237)), introduced(assumption)).
% 2.51/2.18 tff(2677,plain,
% 2.51/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a255) | c3_1(a255) | c3_1(a237) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c1_1(a237) | (~c0_1(a237)) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c3_1(a237) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c1_1(a237) | (~c0_1(a237)) | (~c2_1(a255)))),
% 2.51/2.18 inference(rewrite,[status(thm)],[])).
% 2.51/2.18 tff(2678,plain,
% 2.51/2.18 (((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237))) <=> (c1_1(a255) | c3_1(a255) | c3_1(a237) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c1_1(a237) | (~c0_1(a237)) | (~c2_1(a255)))),
% 2.51/2.18 inference(rewrite,[status(thm)],[])).
% 2.51/2.18 tff(2679,plain,
% 2.51/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a255) | c3_1(a255) | c3_1(a237) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c1_1(a237) | (~c0_1(a237)) | (~c2_1(a255))))),
% 2.51/2.18 inference(monotonicity,[status(thm)],[2678])).
% 2.51/2.18 tff(2680,plain,
% 2.51/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c3_1(a237) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c1_1(a237) | (~c0_1(a237)) | (~c2_1(a255)))),
% 2.51/2.18 inference(transitivity,[status(thm)],[2679, 2677])).
% 2.51/2.18 tff(2681,plain,
% 2.51/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))),
% 2.51/2.18 inference(quant_inst,[status(thm)],[])).
% 2.51/2.18 tff(2682,plain,
% 2.51/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c3_1(a237) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c1_1(a237) | (~c0_1(a237)) | (~c2_1(a255))),
% 2.51/2.18 inference(modus_ponens,[status(thm)],[2681, 2680])).
% 2.51/2.18 tff(2683,plain,
% 2.51/2.18 (~c3_1(a216)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[2682, 122, 765, 2391, 1189, 1207, 763, 2390, 22, 1860, 2676])).
% 2.51/2.18 tff(2684,plain,
% 2.51/2.18 (hskp7),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[2418, 2369, 757, 763])).
% 2.51/2.18 tff(2685,plain,
% 2.51/2.18 (~c0_1(a223)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[2424, 2684])).
% 2.51/2.18 tff(2686,plain,
% 2.51/2.18 (c2_1(a223)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[2435, 2684])).
% 2.51/2.18 tff(2687,plain,
% 2.51/2.18 (c1_1(a223)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[2446, 2684])).
% 2.51/2.18 tff(2688,plain,
% 2.51/2.18 ($false),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[2453, 122, 1, 2687, 2686, 2391, 2685, 2390, 1650, 2683])).
% 2.51/2.18 tff(2689,plain,(hskp6 | hskp26 | c1_1(a255) | c3_1(a255) | (~c2_1(a255)) | c1_1(a237) | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | (~hskp12)), inference(lemma,lemma(discharge,[]))).
% 2.51/2.18 tff(2690,plain,
% 2.51/2.18 (hskp6),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[2689, 2675, 1189, 1207, 1, 2667, 167, 166, 165, 2664])).
% 2.51/2.18 tff(2691,plain,
% 2.51/2.18 (~c3_1(a220)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[485, 2690])).
% 2.51/2.18 tff(2692,plain,
% 2.51/2.18 (c2_1(a220)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[541, 2690])).
% 2.51/2.18 tff(2693,plain,
% 2.51/2.18 (c1_1(a220)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[530, 2690])).
% 2.51/2.18 tff(2694,plain,
% 2.51/2.18 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a220) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a220)) | (~c1_1(a220)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a220) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a220)) | (~c1_1(a220)))),
% 2.51/2.18 inference(rewrite,[status(thm)],[])).
% 2.51/2.18 tff(2695,plain,
% 2.51/2.18 ((hskp26 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218))) <=> (hskp26 | c3_1(a220) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a220)) | (~c1_1(a220)))),
% 2.51/2.18 inference(rewrite,[status(thm)],[])).
% 2.51/2.18 tff(2696,plain,
% 2.51/2.18 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a220) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a220)) | (~c1_1(a220))))),
% 2.51/2.18 inference(monotonicity,[status(thm)],[2695])).
% 2.51/2.18 tff(2697,plain,
% 2.51/2.18 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a220) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a220)) | (~c1_1(a220)))),
% 2.51/2.18 inference(transitivity,[status(thm)],[2696, 2694])).
% 2.51/2.18 tff(2698,plain,
% 2.51/2.18 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)))),
% 2.51/2.18 inference(quant_inst,[status(thm)],[])).
% 2.51/2.18 tff(2699,plain,
% 2.51/2.18 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a220) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a220)) | (~c1_1(a220))),
% 2.51/2.18 inference(modus_ponens,[status(thm)],[2698, 2697])).
% 2.51/2.18 tff(2700,plain,
% 2.51/2.18 ($false),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[2699, 122, 1, 2693, 2692, 785, 2691, 783, 2663, 2653])).
% 2.51/2.18 tff(2701,plain,(c3_1(a252) | hskp26 | (~c3_1(a218)) | c2_1(a218) | c1_1(a255) | c3_1(a255) | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | c0_1(a255) | c1_1(a218)), inference(lemma,lemma(discharge,[]))).
% 2.51/2.18 tff(2702,plain,
% 2.51/2.18 (c3_1(a252)),
% 2.51/2.18 inference(unit_resolution,[status(thm)],[2701, 1, 2646, 2645, 2368, 2367, 2644, 2643, 2642, 2366, 2640])).
% 2.51/2.18 tff(2703,plain,
% 2.51/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.18 inference(rewrite,[status(thm)],[])).
% 2.51/2.18 tff(2704,plain,
% 2.51/2.18 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215))) <=> (c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.18 inference(rewrite,[status(thm)],[])).
% 2.51/2.18 tff(2705,plain,
% 2.51/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))))),
% 2.51/2.18 inference(monotonicity,[status(thm)],[2704])).
% 2.51/2.18 tff(2706,plain,
% 2.51/2.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.18 inference(transitivity,[status(thm)],[2705, 2703])).
% 2.51/2.18 tff(2707,plain,
% 2.51/2.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))),
% 2.51/2.19 inference(quant_inst,[status(thm)],[])).
% 2.51/2.19 tff(2708,plain,
% 2.51/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))),
% 2.51/2.19 inference(modus_ponens,[status(thm)],[2707, 2706])).
% 2.51/2.19 tff(2709,plain,
% 2.51/2.19 ((~c0_1(a218)) | (~c3_1(a252))),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2708, 122, 2009, 1998, 2646, 2644, 2645, 2643, 2642, 931])).
% 2.51/2.19 tff(2710,plain,
% 2.51/2.19 (~c0_1(a218)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2709, 2702])).
% 2.51/2.19 tff(2711,plain,
% 2.51/2.19 (hskp23),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2200, 2702, 1])).
% 2.51/2.19 tff(2712,plain,
% 2.51/2.19 (~c3_1(a274)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2206, 2711])).
% 2.51/2.19 tff(2713,plain,
% 2.51/2.19 (c1_1(a274)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2217, 2711])).
% 2.51/2.19 tff(2714,plain,
% 2.51/2.19 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a274) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a274)) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a274) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a274)) | (~c1_1(a274)))),
% 2.51/2.19 inference(rewrite,[status(thm)],[])).
% 2.51/2.19 tff(2715,plain,
% 2.51/2.19 ((hskp26 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218))) <=> (hskp26 | c3_1(a274) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a274)) | (~c1_1(a274)))),
% 2.51/2.19 inference(rewrite,[status(thm)],[])).
% 2.51/2.19 tff(2716,plain,
% 2.51/2.19 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a274) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a274)) | (~c1_1(a274))))),
% 2.51/2.19 inference(monotonicity,[status(thm)],[2715])).
% 2.51/2.19 tff(2717,plain,
% 2.51/2.19 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a274) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a274)) | (~c1_1(a274)))),
% 2.51/2.19 inference(transitivity,[status(thm)],[2716, 2714])).
% 2.51/2.19 tff(2718,plain,
% 2.51/2.19 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)))),
% 2.51/2.19 inference(quant_inst,[status(thm)],[])).
% 2.51/2.19 tff(2719,plain,
% 2.51/2.19 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a274) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a274)) | (~c1_1(a274))),
% 2.51/2.19 inference(modus_ponens,[status(thm)],[2718, 2717])).
% 2.51/2.19 tff(2720,plain,
% 2.51/2.19 (~c2_1(a274)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2719, 122, 1, 2713, 2646, 2712, 2645, 2663, 2710])).
% 2.51/2.19 tff(2721,plain,
% 2.51/2.19 ($false),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2560, 122, 1, 23, 2713, 2712, 257, 2720])).
% 2.51/2.19 tff(2722,plain,(hskp26 | hskp9 | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.51/2.19 tff(2723,plain,
% 2.51/2.19 (hskp26),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2722, 34, 23])).
% 2.51/2.19 tff(2724,plain,
% 2.51/2.19 (c3_1(a234)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[66, 2723])).
% 2.51/2.19 tff(2725,plain,
% 2.51/2.19 (c1_1(a234)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[77, 2723])).
% 2.51/2.19 tff(2726,plain,
% 2.51/2.19 (c0_1(a234)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[88, 2723])).
% 2.51/2.19 tff(2727,assumption,(c2_1(a234)), introduced(assumption)).
% 2.51/2.19 tff(2728,assumption,(c3_1(a234)), introduced(assumption)).
% 2.51/2.19 tff(2729,assumption,(c1_1(a234)), introduced(assumption)).
% 2.51/2.19 tff(2730,assumption,(c0_1(a234)), introduced(assumption)).
% 2.51/2.19 tff(2731,plain,
% 2.51/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a234)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a234)))),
% 2.51/2.19 inference(rewrite,[status(thm)],[])).
% 2.51/2.19 tff(2732,plain,
% 2.51/2.19 (((~ndr1_0) | (~c2_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c3_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c1_1(a234))) <=> ((~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a234)))),
% 2.51/2.19 inference(rewrite,[status(thm)],[])).
% 2.51/2.19 tff(2733,plain,
% 2.51/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c3_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c1_1(a234)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a234))))),
% 2.51/2.19 inference(monotonicity,[status(thm)],[2732])).
% 2.51/2.19 tff(2734,plain,
% 2.51/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c3_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c1_1(a234)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a234)))),
% 2.51/2.19 inference(transitivity,[status(thm)],[2733, 2731])).
% 2.51/2.19 tff(2735,plain,
% 2.51/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c3_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c1_1(a234)))),
% 2.51/2.19 inference(quant_inst,[status(thm)],[])).
% 2.51/2.19 tff(2736,plain,
% 2.51/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a234))),
% 2.51/2.19 inference(modus_ponens,[status(thm)],[2735, 2734])).
% 2.51/2.19 tff(2737,plain,
% 2.51/2.19 ($false),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2736, 122, 2730, 2729, 2728, 33, 2727])).
% 2.51/2.19 tff(2738,plain,((~c2_1(a234)) | (~c0_1(a234)) | (~c1_1(a234)) | (~c3_1(a234))), inference(lemma,lemma(discharge,[]))).
% 2.51/2.19 tff(2739,plain,
% 2.51/2.19 (~c2_1(a234)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2738, 2726, 2725, 2724])).
% 2.51/2.19 tff(2740,plain,
% 2.51/2.19 (hskp2),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[130, 2723, 34])).
% 2.51/2.19 tff(2741,plain,
% 2.51/2.19 (~c1_1(a215)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[136, 2740])).
% 2.51/2.19 tff(2742,plain,
% 2.51/2.19 (~c0_1(a215)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[153, 2740])).
% 2.51/2.19 tff(2743,plain,
% 2.51/2.19 (c2_1(a215)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[147, 2740])).
% 2.51/2.19 tff(2744,plain,
% 2.51/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.19 inference(rewrite,[status(thm)],[])).
% 2.51/2.19 tff(2745,plain,
% 2.51/2.19 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215))) <=> (c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.19 inference(rewrite,[status(thm)],[])).
% 2.51/2.19 tff(2746,plain,
% 2.51/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))))),
% 2.51/2.19 inference(monotonicity,[status(thm)],[2745])).
% 2.51/2.19 tff(2747,plain,
% 2.51/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.19 inference(transitivity,[status(thm)],[2746, 2744])).
% 2.51/2.19 tff(2748,plain,
% 2.51/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))),
% 2.51/2.19 inference(quant_inst,[status(thm)],[])).
% 2.51/2.19 tff(2749,plain,
% 2.51/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))),
% 2.51/2.19 inference(modus_ponens,[status(thm)],[2748, 2747])).
% 2.51/2.19 tff(2750,plain,
% 2.51/2.19 (~c3_1(a252)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2749, 122, 2726, 2724, 2009, 1998, 2743, 2742, 2741, 931, 2739])).
% 2.51/2.19 tff(2751,plain,
% 2.51/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.19 inference(rewrite,[status(thm)],[])).
% 2.51/2.19 tff(2752,plain,
% 2.51/2.19 (((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.19 inference(rewrite,[status(thm)],[])).
% 2.51/2.19 tff(2753,plain,
% 2.51/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252))))),
% 2.51/2.19 inference(monotonicity,[status(thm)],[2752])).
% 2.51/2.19 tff(2754,plain,
% 2.51/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.19 inference(transitivity,[status(thm)],[2753, 2751])).
% 2.51/2.19 tff(2755,plain,
% 2.51/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 2.51/2.19 inference(quant_inst,[status(thm)],[])).
% 2.51/2.19 tff(2756,plain,
% 2.51/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252))),
% 2.51/2.19 inference(modus_ponens,[status(thm)],[2755, 2754])).
% 2.51/2.19 tff(2757,plain,
% 2.51/2.19 ($false),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2756, 122, 2726, 2724, 2009, 1998, 2023, 22, 2750, 2739])).
% 2.51/2.19 tff(2758,plain,(hskp27 | hskp9), inference(lemma,lemma(discharge,[]))).
% 2.51/2.19 tff(2759,plain,
% 2.51/2.19 (hskp27),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2758, 23])).
% 2.51/2.19 tff(2760,plain,
% 2.51/2.19 (c3_1(a261)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[1316, 2759])).
% 2.51/2.19 tff(2761,plain,
% 2.51/2.19 (c2_1(a261)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[1327, 2759])).
% 2.51/2.19 tff(2762,plain,
% 2.51/2.19 (c1_1(a261)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[1338, 2759])).
% 2.51/2.19 tff(2763,plain,
% 2.51/2.19 (~c0_1(a261)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[1345, 122, 2762, 2761, 2760, 33])).
% 2.51/2.19 tff(2764,plain,
% 2.51/2.19 (c2_1(a255)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[1889, 2367, 2761, 2760, 2366, 2763, 23])).
% 2.51/2.19 tff(2765,plain,
% 2.51/2.19 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)))),
% 2.51/2.19 inference(rewrite,[status(thm)],[])).
% 2.51/2.19 tff(2766,plain,
% 2.51/2.19 ((hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261))) <=> (hskp29 | hskp26 | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)))),
% 2.51/2.19 inference(rewrite,[status(thm)],[])).
% 2.51/2.19 tff(2767,plain,
% 2.51/2.19 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261))))),
% 2.51/2.19 inference(monotonicity,[status(thm)],[2766])).
% 2.51/2.19 tff(2768,plain,
% 2.51/2.19 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)))),
% 2.51/2.19 inference(transitivity,[status(thm)],[2767, 2765])).
% 2.51/2.19 tff(2769,plain,
% 2.51/2.19 ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)))),
% 2.51/2.19 inference(quant_inst,[status(thm)],[])).
% 2.51/2.19 tff(2770,plain,
% 2.51/2.19 ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261))),
% 2.51/2.19 inference(modus_ponens,[status(thm)],[2769, 2768])).
% 2.51/2.19 tff(2771,plain,
% 2.51/2.19 (hskp29 | hskp26),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2770, 122, 2762, 2761, 2760, 2316])).
% 2.51/2.19 tff(2772,plain,
% 2.51/2.19 (hskp29),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2771, 1])).
% 2.51/2.19 tff(2773,plain,
% 2.51/2.19 (c3_1(a296)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2333, 2772])).
% 2.51/2.19 tff(2774,plain,
% 2.51/2.19 (c2_1(a296)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2344, 2772])).
% 2.51/2.19 tff(2775,plain,
% 2.51/2.19 (c0_1(a296)),
% 2.51/2.19 inference(unit_resolution,[status(thm)],[2355, 2772])).
% 2.51/2.19 tff(2776,plain,
% 2.51/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a255)))),
% 2.51/2.19 inference(rewrite,[status(thm)],[])).
% 2.51/2.19 tff(2777,plain,
% 2.51/2.19 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255))) <=> (c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a255)))),
% 2.51/2.19 inference(rewrite,[status(thm)],[])).
% 2.51/2.19 tff(2778,plain,
% 2.51/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a255))))),
% 2.51/2.19 inference(monotonicity,[status(thm)],[2777])).
% 2.51/2.19 tff(2779,plain,
% 2.51/2.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a255)))),
% 2.51/2.19 inference(transitivity,[status(thm)],[2778, 2776])).
% 2.51/2.19 tff(2780,plain,
% 2.51/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))),
% 2.51/2.19 inference(quant_inst,[status(thm)],[])).
% 2.51/2.19 tff(2781,plain,
% 2.51/2.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a255))),
% 2.51/2.20 inference(modus_ponens,[status(thm)],[2780, 2779])).
% 2.51/2.20 tff(2782,plain,
% 2.51/2.20 ($false),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[2781, 122, 2775, 2774, 2773, 2762, 2761, 2760, 2366, 2368, 2512, 2764])).
% 2.51/2.20 tff(2783,plain,(hskp26 | hskp9), inference(lemma,lemma(discharge,[]))).
% 2.51/2.20 tff(2784,plain,
% 2.51/2.20 (hskp26),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[2783, 23])).
% 2.51/2.20 tff(2785,plain,
% 2.51/2.20 (c0_1(a234)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[88, 2784])).
% 2.51/2.20 tff(2786,plain,
% 2.51/2.20 (c1_1(a234)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[77, 2784])).
% 2.51/2.20 tff(2787,plain,
% 2.51/2.20 (c3_1(a234)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[66, 2784])).
% 2.51/2.20 tff(2788,plain,
% 2.51/2.20 (~c2_1(a234)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[2738, 2787, 2786, 2785])).
% 2.51/2.20 tff(2789,plain,
% 2.51/2.20 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a252) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a252)) | (~c2_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a252) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a252)) | (~c2_1(a252)))),
% 2.51/2.20 inference(rewrite,[status(thm)],[])).
% 2.51/2.20 tff(2790,plain,
% 2.51/2.20 ((hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261))) <=> (hskp9 | c1_1(a252) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a252)) | (~c2_1(a252)))),
% 2.51/2.20 inference(rewrite,[status(thm)],[])).
% 2.51/2.20 tff(2791,plain,
% 2.51/2.20 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a252) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a252)) | (~c2_1(a252))))),
% 2.51/2.20 inference(monotonicity,[status(thm)],[2790])).
% 2.51/2.20 tff(2792,plain,
% 2.51/2.20 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a252) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a252)) | (~c2_1(a252)))),
% 2.51/2.20 inference(transitivity,[status(thm)],[2791, 2789])).
% 2.51/2.20 tff(2793,plain,
% 2.51/2.20 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))),
% 2.51/2.20 inference(quant_inst,[status(thm)],[])).
% 2.51/2.20 tff(2794,plain,
% 2.51/2.20 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a252) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a252)) | (~c2_1(a252))),
% 2.51/2.20 inference(modus_ponens,[status(thm)],[2793, 2792])).
% 2.51/2.20 tff(2795,plain,
% 2.51/2.20 (~c3_1(a252)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[2794, 122, 23, 2762, 2760, 1998, 2023, 445, 2763])).
% 2.51/2.20 tff(2796,plain,
% 2.51/2.20 (hskp12),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[2630, 2795])).
% 2.51/2.20 tff(2797,plain,
% 2.51/2.20 (~c3_1(a237)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[762, 2796])).
% 2.51/2.20 tff(2798,plain,
% 2.51/2.20 (c2_1(a237)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[607, 2796])).
% 2.51/2.20 tff(2799,plain,
% 2.51/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | c3_1(a237) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a252) | (~c0_1(a252)))),
% 2.51/2.20 inference(rewrite,[status(thm)],[])).
% 2.51/2.20 tff(2800,plain,
% 2.51/2.20 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c1_1(a252) | c3_1(a237) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a252) | (~c0_1(a252)))),
% 2.51/2.20 inference(rewrite,[status(thm)],[])).
% 2.51/2.20 tff(2801,plain,
% 2.51/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | c3_1(a237) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a252) | (~c0_1(a252))))),
% 2.51/2.20 inference(monotonicity,[status(thm)],[2800])).
% 2.51/2.20 tff(2802,plain,
% 2.51/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a252) | (~c0_1(a252)))),
% 2.51/2.20 inference(transitivity,[status(thm)],[2801, 2799])).
% 2.51/2.20 tff(2803,plain,
% 2.51/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 2.51/2.20 inference(quant_inst,[status(thm)],[])).
% 2.51/2.20 tff(2804,plain,
% 2.51/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a252) | (~c0_1(a252))),
% 2.51/2.20 inference(modus_ponens,[status(thm)],[2803, 2802])).
% 2.51/2.20 tff(2805,plain,
% 2.51/2.20 (~c1_1(a237)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[2804, 122, 2762, 2761, 2760, 2009, 2798, 2023, 2797, 553, 2795])).
% 2.51/2.20 tff(2806,plain,
% 2.51/2.20 (c0_1(a237)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[629, 2796])).
% 2.51/2.20 tff(2807,plain,
% 2.51/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.51/2.20 inference(rewrite,[status(thm)],[])).
% 2.51/2.20 tff(2808,plain,
% 2.51/2.20 (((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237))) <=> (c3_1(a237) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.51/2.20 inference(rewrite,[status(thm)],[])).
% 2.51/2.20 tff(2809,plain,
% 2.51/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237))))),
% 2.51/2.20 inference(monotonicity,[status(thm)],[2808])).
% 2.51/2.20 tff(2810,plain,
% 2.51/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 2.51/2.20 inference(transitivity,[status(thm)],[2809, 2807])).
% 2.51/2.20 tff(2811,plain,
% 2.51/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))),
% 2.51/2.20 inference(quant_inst,[status(thm)],[])).
% 2.51/2.20 tff(2812,plain,
% 2.51/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237))),
% 2.51/2.20 inference(modus_ponens,[status(thm)],[2811, 2810])).
% 2.51/2.20 tff(2813,plain,
% 2.51/2.20 ($false),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[2812, 122, 2785, 2787, 2806, 2798, 2797, 22, 2805, 2788])).
% 2.51/2.20 tff(2814,plain,(hskp9), inference(lemma,lemma(discharge,[]))).
% 2.51/2.20 tff(2815,plain,
% 2.51/2.20 (~c2_1(a226)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[893, 2814])).
% 2.51/2.20 tff(2816,plain,
% 2.51/2.20 (c0_1(a226)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[910, 2814])).
% 2.51/2.20 tff(2817,plain,
% 2.51/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | c2_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c2_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.20 inference(rewrite,[status(thm)],[])).
% 2.51/2.20 tff(2818,plain,
% 2.51/2.20 (((~ndr1_0) | c2_1(a226) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c1_1(a252) | c2_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.20 inference(rewrite,[status(thm)],[])).
% 2.51/2.20 tff(2819,plain,
% 2.51/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a226) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | c2_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252))))),
% 2.51/2.20 inference(monotonicity,[status(thm)],[2818])).
% 2.51/2.20 tff(2820,plain,
% 2.51/2.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a226) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c2_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.20 inference(transitivity,[status(thm)],[2819, 2817])).
% 2.51/2.20 tff(2821,plain,
% 2.51/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a226) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 2.51/2.20 inference(quant_inst,[status(thm)],[])).
% 2.51/2.20 tff(2822,plain,
% 2.51/2.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c2_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252))),
% 2.51/2.20 inference(modus_ponens,[status(thm)],[2821, 2820])).
% 2.51/2.20 tff(2823,plain,
% 2.51/2.20 (~c3_1(a226)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[2822, 122, 2009, 1998, 2816, 2023, 2815, 22, 12])).
% 2.51/2.20 tff(2824,plain,
% 2.51/2.20 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 2.51/2.20 inference(bind,[status(th)],[])).
% 2.51/2.20 tff(2825,plain,
% 2.51/2.20 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.51/2.20 inference(quant_intro,[status(thm)],[2824])).
% 2.51/2.20 tff(2826,plain,
% 2.51/2.20 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.51/2.20 inference(rewrite,[status(thm)],[])).
% 2.51/2.20 tff(2827,plain,
% 2.51/2.20 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 2.51/2.20 inference(bind,[status(th)],[])).
% 2.51/2.20 tff(2828,plain,
% 2.51/2.20 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.51/2.20 inference(quant_intro,[status(thm)],[2827])).
% 2.51/2.20 tff(2829,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 2.51/2.20 tff(2830,plain,
% 2.51/2.20 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.51/2.20 inference(modus_ponens,[status(thm)],[2829, 2828])).
% 2.51/2.20 tff(2831,plain,
% 2.51/2.20 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.51/2.20 inference(modus_ponens,[status(thm)],[2830, 2826])).
% 2.51/2.20 tff(2832,plain,(
% 2.51/2.20 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.51/2.20 inference(skolemize,[status(sab)],[2831])).
% 2.51/2.20 tff(2833,plain,
% 2.51/2.20 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 2.51/2.20 inference(modus_ponens,[status(thm)],[2832, 2825])).
% 2.51/2.20 tff(2834,assumption,(hskp21), introduced(assumption)).
% 2.51/2.20 tff(2835,plain,
% 2.51/2.20 (~c2_1(a259)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[1062, 2834])).
% 2.51/2.20 tff(2836,plain,
% 2.51/2.20 (c3_1(a259)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[867, 2834])).
% 2.51/2.20 tff(2837,plain,
% 2.51/2.20 (c0_1(a259)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[855, 2834])).
% 2.51/2.20 tff(2838,plain,
% 2.51/2.20 ($false),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[2282, 122, 2837, 2836, 2009, 1998, 2835, 2023, 22, 12])).
% 2.51/2.20 tff(2839,plain,((~hskp21) | c3_1(a252)), inference(lemma,lemma(discharge,[]))).
% 2.51/2.20 tff(2840,plain,
% 2.51/2.20 (~hskp21),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[2839, 12])).
% 2.51/2.20 tff(2841,plain,
% 2.51/2.20 (~c1_1(a226)),
% 2.51/2.20 inference(unit_resolution,[status(thm)],[899, 2814])).
% 2.51/2.20 tff(2842,plain,
% 2.51/2.20 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | c3_1(a226))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | c3_1(a226))),
% 2.51/2.20 inference(rewrite,[status(thm)],[])).
% 2.51/2.20 tff(2843,plain,
% 2.51/2.20 ((hskp19 | hskp21 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | c3_1(a226)) <=> (hskp19 | hskp21 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | c3_1(a226))),
% 2.51/2.20 inference(rewrite,[status(thm)],[])).
% 2.51/2.20 tff(2844,plain,
% 2.51/2.20 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | c3_1(a226))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | c3_1(a226)))),
% 2.51/2.20 inference(monotonicity,[status(thm)],[2843])).
% 2.51/2.20 tff(2845,plain,
% 2.51/2.20 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | c3_1(a226))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | c3_1(a226))),
% 2.51/2.20 inference(transitivity,[status(thm)],[2844, 2842])).
% 2.51/2.20 tff(2846,plain,
% 2.51/2.20 ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | c3_1(a226))),
% 2.51/2.20 inference(quant_inst,[status(thm)],[])).
% 2.51/2.20 tff(2847,plain,
% 2.51/2.20 ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | c3_1(a226)),
% 2.51/2.20 inference(modus_ponens,[status(thm)],[2846, 2845])).
% 2.51/2.20 tff(2848,plain,
% 2.51/2.21 (hskp19 | hskp21 | c3_1(a226)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2847, 122, 2841, 2815, 1738])).
% 2.51/2.21 tff(2849,plain,
% 2.51/2.21 (hskp19),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2848, 2840, 2823])).
% 2.51/2.21 tff(2850,plain,
% 2.51/2.21 (~c3_1(a255)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[288, 2849])).
% 2.51/2.21 tff(2851,plain,
% 2.51/2.21 (~c1_1(a255)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[294, 2849])).
% 2.51/2.21 tff(2852,plain,
% 2.51/2.21 (~c0_1(a255)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[300, 2849])).
% 2.51/2.21 tff(2853,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a255) | c1_1(a255) | c3_1(a255) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a255) | c1_1(a255) | c3_1(a255) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2854,plain,
% 2.51/2.21 ((hskp1 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c3_1(a255) | c1_1(a255) | c0_1(a255)) <=> (hskp1 | c0_1(a255) | c1_1(a255) | c3_1(a255) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2855,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c3_1(a255) | c1_1(a255) | c0_1(a255))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a255) | c1_1(a255) | c3_1(a255) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226))))),
% 2.51/2.21 inference(monotonicity,[status(thm)],[2854])).
% 2.51/2.21 tff(2856,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c3_1(a255) | c1_1(a255) | c0_1(a255))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a255) | c1_1(a255) | c3_1(a255) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)))),
% 2.51/2.21 inference(transitivity,[status(thm)],[2855, 2853])).
% 2.51/2.21 tff(2857,plain,
% 2.51/2.21 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c3_1(a255) | c1_1(a255) | c0_1(a255))),
% 2.51/2.21 inference(quant_inst,[status(thm)],[])).
% 2.51/2.21 tff(2858,plain,
% 2.51/2.21 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a255) | c1_1(a255) | c3_1(a255) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226))),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2857, 2856])).
% 2.51/2.21 tff(2859,plain,
% 2.51/2.21 (hskp1),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2858, 122, 2816, 2852, 2851, 2850, 2815, 2833, 2823])).
% 2.51/2.21 tff(2860,plain,
% 2.51/2.21 (~c3_1(a214)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[1087, 2859])).
% 2.51/2.21 tff(2861,plain,
% 2.51/2.21 (~c0_1(a214)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[1150, 2859])).
% 2.51/2.21 tff(2862,plain,
% 2.51/2.21 (c2_1(a214)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[1136, 2859])).
% 2.51/2.21 tff(2863,plain,
% 2.51/2.21 (c2_1(a237)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[607, 2664])).
% 2.51/2.21 tff(2864,assumption,(~c3_1(a226)), introduced(assumption)).
% 2.51/2.21 tff(2865,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a231) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a231)) | (~c1_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a231) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a231)) | (~c1_1(a231)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2866,plain,
% 2.51/2.21 ((hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a231) | (~c1_1(a231)) | (~c2_1(a231))) <=> (hskp26 | c0_1(a231) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a231)) | (~c1_1(a231)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2867,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a231) | (~c1_1(a231)) | (~c2_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a231) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a231)) | (~c1_1(a231))))),
% 2.51/2.21 inference(monotonicity,[status(thm)],[2866])).
% 2.51/2.21 tff(2868,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a231) | (~c1_1(a231)) | (~c2_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a231) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a231)) | (~c1_1(a231)))),
% 2.51/2.21 inference(transitivity,[status(thm)],[2867, 2865])).
% 2.51/2.21 tff(2869,plain,
% 2.51/2.21 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a231) | (~c1_1(a231)) | (~c2_1(a231)))),
% 2.51/2.21 inference(quant_inst,[status(thm)],[])).
% 2.51/2.21 tff(2870,plain,
% 2.51/2.21 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a231) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a231)) | (~c1_1(a231))),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2869, 2868])).
% 2.51/2.21 tff(2871,plain,
% 2.51/2.21 (~c2_1(a231)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2870, 122, 1, 662, 2816, 1614, 2815, 1650, 2864])).
% 2.51/2.21 tff(2872,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a237) | c0_1(a231) | (~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a237)) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a237) | c0_1(a231) | (~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a237)) | (~c1_1(a237)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2873,plain,
% 2.51/2.21 ((hskp26 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231))) <=> (hskp26 | c3_1(a237) | c0_1(a231) | (~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a237)) | (~c1_1(a237)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2874,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a237) | c0_1(a231) | (~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a237)) | (~c1_1(a237))))),
% 2.51/2.21 inference(monotonicity,[status(thm)],[2873])).
% 2.51/2.21 tff(2875,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a237) | c0_1(a231) | (~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a237)) | (~c1_1(a237)))),
% 2.51/2.21 inference(transitivity,[status(thm)],[2874, 2872])).
% 2.51/2.21 tff(2876,plain,
% 2.51/2.21 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)))),
% 2.51/2.21 inference(quant_inst,[status(thm)],[])).
% 2.51/2.21 tff(2877,plain,
% 2.51/2.21 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a237) | c0_1(a231) | (~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a237)) | (~c1_1(a237))),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2876, 2875])).
% 2.51/2.21 tff(2878,plain,
% 2.51/2.21 (~c1_1(a237)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2877, 122, 1, 1911, 1613, 179, 1614, 2663, 2871])).
% 2.51/2.21 tff(2879,plain,
% 2.51/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)) | c2_1(a231) | (~c1_1(a231)) | (~c3_1(a231)) | c1_1(a237) | (~c2_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)) | c2_1(a231) | (~c1_1(a231)) | (~c3_1(a231)) | c1_1(a237) | (~c2_1(a237)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2880,plain,
% 2.51/2.21 (((~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c1_1(a231)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226))) <=> (c3_1(a237) | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)) | c2_1(a231) | (~c1_1(a231)) | (~c3_1(a231)) | c1_1(a237) | (~c2_1(a237)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2881,plain,
% 2.51/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c1_1(a231)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)) | c2_1(a231) | (~c1_1(a231)) | (~c3_1(a231)) | c1_1(a237) | (~c2_1(a237))))),
% 2.51/2.21 inference(monotonicity,[status(thm)],[2880])).
% 2.51/2.21 tff(2882,plain,
% 2.51/2.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c1_1(a231)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)) | c2_1(a231) | (~c1_1(a231)) | (~c3_1(a231)) | c1_1(a237) | (~c2_1(a237)))),
% 2.51/2.21 inference(transitivity,[status(thm)],[2881, 2879])).
% 2.51/2.21 tff(2883,plain,
% 2.51/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c1_1(a231)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))),
% 2.51/2.21 inference(quant_inst,[status(thm)],[])).
% 2.51/2.21 tff(2884,plain,
% 2.51/2.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)) | c2_1(a231) | (~c1_1(a231)) | (~c3_1(a231)) | c1_1(a237) | (~c2_1(a237))),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2883, 2882])).
% 2.51/2.21 tff(2885,plain,
% 2.51/2.21 ($false),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2884, 122, 1911, 662, 1613, 2816, 179, 2841, 2815, 878, 2878, 2871])).
% 2.51/2.21 tff(2886,plain,((~hskp10) | (~c2_1(a237)) | c3_1(a237) | hskp26 | c3_1(a226)), inference(lemma,lemma(discharge,[]))).
% 2.51/2.21 tff(2887,plain,
% 2.51/2.21 (~hskp10),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2886, 2863, 2665, 1, 2823])).
% 2.51/2.21 tff(2888,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a252) | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c2_1(a214)) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a252) | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c2_1(a214)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2889,plain,
% 2.51/2.21 ((hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a214) | c0_1(a214) | (~c2_1(a214))) <=> (hskp10 | c1_1(a252) | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c2_1(a214)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2890,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a252) | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c2_1(a214)) | (~c0_1(a252)) | (~c2_1(a252))))),
% 2.51/2.21 inference(monotonicity,[status(thm)],[2889])).
% 2.51/2.21 tff(2891,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a252) | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c2_1(a214)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.21 inference(transitivity,[status(thm)],[2890, 2888])).
% 2.51/2.21 tff(2892,plain,
% 2.51/2.21 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)))),
% 2.51/2.21 inference(quant_inst,[status(thm)],[])).
% 2.51/2.21 tff(2893,plain,
% 2.51/2.21 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a252) | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c2_1(a214)) | (~c0_1(a252)) | (~c2_1(a252))),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2892, 2891])).
% 2.51/2.21 tff(2894,plain,
% 2.51/2.21 ($false),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2893, 122, 2887, 2009, 1998, 2862, 2023, 2861, 2860, 11])).
% 2.51/2.21 tff(2895,plain,(c3_1(a252) | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.51/2.21 tff(2896,plain,
% 2.51/2.21 (c3_1(a252)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2895, 1])).
% 2.51/2.21 tff(2897,plain,
% 2.51/2.21 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 2.51/2.21 inference(bind,[status(th)],[])).
% 2.51/2.21 tff(2898,plain,
% 2.51/2.21 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.51/2.21 inference(quant_intro,[status(thm)],[2897])).
% 2.51/2.21 tff(2899,plain,
% 2.51/2.21 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2900,plain,
% 2.51/2.21 (^[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)) | (~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))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 2.51/2.21 inference(bind,[status(th)],[])).
% 2.51/2.21 tff(2901,plain,
% 2.51/2.21 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.51/2.21 inference(quant_intro,[status(thm)],[2900])).
% 2.51/2.21 tff(2902,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 2.51/2.21 tff(2903,plain,
% 2.51/2.21 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2902, 2901])).
% 2.51/2.21 tff(2904,plain,
% 2.51/2.21 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2903, 2899])).
% 2.51/2.21 tff(2905,plain,(
% 2.51/2.21 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.51/2.21 inference(skolemize,[status(sab)],[2904])).
% 2.51/2.21 tff(2906,plain,
% 2.51/2.21 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2905, 2898])).
% 2.51/2.21 tff(2907,plain,
% 2.51/2.21 (hskp23),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2200, 2896, 1])).
% 2.51/2.21 tff(2908,plain,
% 2.51/2.21 (~c3_1(a274)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2206, 2907])).
% 2.51/2.21 tff(2909,plain,
% 2.51/2.21 (~c0_1(a274)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2230, 2907])).
% 2.51/2.21 tff(2910,plain,
% 2.51/2.21 (c1_1(a274)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2217, 2907])).
% 2.51/2.21 tff(2911,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2912,plain,
% 2.51/2.21 ((hskp11 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274))) <=> (hskp11 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2913,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274))))),
% 2.51/2.21 inference(monotonicity,[status(thm)],[2912])).
% 2.51/2.21 tff(2914,plain,
% 2.51/2.21 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 2.51/2.21 inference(transitivity,[status(thm)],[2913, 2911])).
% 2.51/2.21 tff(2915,plain,
% 2.51/2.21 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))),
% 2.51/2.21 inference(quant_inst,[status(thm)],[])).
% 2.51/2.21 tff(2916,plain,
% 2.51/2.21 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274))),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2915, 2914])).
% 2.51/2.21 tff(2917,plain,
% 2.51/2.21 (hskp11),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2916, 122, 2910, 2009, 1998, 2909, 2908, 2023, 2906])).
% 2.51/2.21 tff(2918,plain,
% 2.51/2.21 (((~hskp11) | (~c3_1(a236))) <=> ((~hskp11) | (~c3_1(a236)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2919,plain,
% 2.51/2.21 (((~c3_1(a236)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a236)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2920,axiom,((~c3_1(a236)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 2.51/2.21 tff(2921,plain,
% 2.51/2.21 ((~hskp11) | (~c3_1(a236))),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2920, 2919])).
% 2.51/2.21 tff(2922,plain,
% 2.51/2.21 ((~hskp11) | (~c3_1(a236))),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2921, 2918])).
% 2.51/2.21 tff(2923,plain,
% 2.51/2.21 (~c3_1(a236)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2922, 2917])).
% 2.51/2.21 tff(2924,plain,
% 2.51/2.21 (((~hskp11) | (~c2_1(a236))) <=> ((~hskp11) | (~c2_1(a236)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2925,plain,
% 2.51/2.21 (((~c2_1(a236)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a236)))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2926,axiom,((~c2_1(a236)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 2.51/2.21 tff(2927,plain,
% 2.51/2.21 ((~hskp11) | (~c2_1(a236))),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2926, 2925])).
% 2.51/2.21 tff(2928,plain,
% 2.51/2.21 ((~hskp11) | (~c2_1(a236))),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2927, 2924])).
% 2.51/2.21 tff(2929,plain,
% 2.51/2.21 (~c2_1(a236)),
% 2.51/2.21 inference(unit_resolution,[status(thm)],[2928, 2917])).
% 2.51/2.21 tff(2930,plain,
% 2.51/2.21 (((~hskp11) | c0_1(a236)) <=> ((~hskp11) | c0_1(a236))),
% 2.51/2.21 inference(rewrite,[status(thm)],[])).
% 2.51/2.21 tff(2931,axiom,((~hskp11) | c0_1(a236)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 2.51/2.21 tff(2932,plain,
% 2.51/2.21 ((~hskp11) | c0_1(a236)),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2931, 2930])).
% 2.51/2.21 tff(2933,plain,
% 2.51/2.21 ((~hskp11) | c0_1(a236)),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2932, 2930])).
% 2.51/2.21 tff(2934,plain,
% 2.51/2.21 ((~hskp11) | c0_1(a236)),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2933, 2930])).
% 2.51/2.21 tff(2935,plain,
% 2.51/2.21 ((~hskp11) | c0_1(a236)),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2934, 2930])).
% 2.51/2.21 tff(2936,plain,
% 2.51/2.21 ((~hskp11) | c0_1(a236)),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2935, 2930])).
% 2.51/2.21 tff(2937,plain,
% 2.51/2.21 ((~hskp11) | c0_1(a236)),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2936, 2930])).
% 2.51/2.21 tff(2938,plain,
% 2.51/2.21 ((~hskp11) | c0_1(a236)),
% 2.51/2.21 inference(modus_ponens,[status(thm)],[2937, 2930])).
% 2.51/2.22 tff(2939,plain,
% 2.51/2.22 ((~hskp11) | c0_1(a236)),
% 2.51/2.22 inference(modus_ponens,[status(thm)],[2938, 2930])).
% 2.51/2.22 tff(2940,plain,
% 2.51/2.22 (c0_1(a236)),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[2939, 2917])).
% 2.51/2.22 tff(2941,plain,
% 2.51/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c0_1(a236)) | (~c1_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c0_1(a236)) | (~c1_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.22 inference(rewrite,[status(thm)],[])).
% 2.51/2.22 tff(2942,plain,
% 2.51/2.22 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | (~c1_1(a236)) | (~c0_1(a236)) | c3_1(a236) | c2_1(a236) | (~c1_1(a236))) <=> (c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c0_1(a236)) | (~c1_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.22 inference(rewrite,[status(thm)],[])).
% 2.51/2.22 tff(2943,plain,
% 2.51/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | (~c1_1(a236)) | (~c0_1(a236)) | c3_1(a236) | c2_1(a236) | (~c1_1(a236)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c0_1(a236)) | (~c1_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))))),
% 2.51/2.22 inference(monotonicity,[status(thm)],[2942])).
% 2.51/2.22 tff(2944,plain,
% 2.51/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | (~c1_1(a236)) | (~c0_1(a236)) | c3_1(a236) | c2_1(a236) | (~c1_1(a236)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c0_1(a236)) | (~c1_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.22 inference(transitivity,[status(thm)],[2943, 2941])).
% 2.51/2.22 tff(2945,plain,
% 2.51/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | (~c1_1(a236)) | (~c0_1(a236)) | c3_1(a236) | c2_1(a236) | (~c1_1(a236)))),
% 2.51/2.22 inference(quant_inst,[status(thm)],[])).
% 2.51/2.22 tff(2946,plain,
% 2.51/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c0_1(a236)) | (~c1_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))),
% 2.51/2.22 inference(modus_ponens,[status(thm)],[2945, 2944])).
% 2.51/2.22 tff(2947,plain,
% 2.51/2.22 (~c1_1(a236)),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[2946, 122, 2009, 1998, 2940, 2929, 2923, 2183, 2896])).
% 2.51/2.22 tff(2948,plain,
% 2.51/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a274) | c3_1(a274) | c3_1(a236) | (~ndr1_0) | c1_1(a236) | (~c0_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a274) | c3_1(a274) | c3_1(a236) | (~ndr1_0) | c1_1(a236) | (~c0_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 2.51/2.22 inference(rewrite,[status(thm)],[])).
% 2.51/2.22 tff(2949,plain,
% 2.51/2.22 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | c1_1(a236) | (~c0_1(a236)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274))) <=> (c0_1(a274) | c3_1(a274) | c3_1(a236) | (~ndr1_0) | c1_1(a236) | (~c0_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 2.51/2.22 inference(rewrite,[status(thm)],[])).
% 2.51/2.22 tff(2950,plain,
% 2.51/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | c1_1(a236) | (~c0_1(a236)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a274) | c3_1(a274) | c3_1(a236) | (~ndr1_0) | c1_1(a236) | (~c0_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274))))),
% 2.51/2.22 inference(monotonicity,[status(thm)],[2949])).
% 2.51/2.22 tff(2951,plain,
% 2.51/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | c1_1(a236) | (~c0_1(a236)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a274) | c3_1(a274) | c3_1(a236) | (~ndr1_0) | c1_1(a236) | (~c0_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 2.51/2.22 inference(transitivity,[status(thm)],[2950, 2948])).
% 2.51/2.22 tff(2952,plain,
% 2.51/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | c1_1(a236) | (~c0_1(a236)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))),
% 2.51/2.22 inference(quant_inst,[status(thm)],[])).
% 2.51/2.22 tff(2953,plain,
% 2.51/2.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a274) | c3_1(a274) | c3_1(a236) | (~ndr1_0) | c1_1(a236) | (~c0_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274))),
% 2.51/2.22 inference(modus_ponens,[status(thm)],[2952, 2951])).
% 2.51/2.22 tff(2954,plain,
% 2.51/2.22 ($false),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[2953, 122, 2910, 2009, 1998, 2940, 2909, 2908, 2923, 2543, 2947, 2896])).
% 2.51/2.22 tff(2955,plain,(hskp26), inference(lemma,lemma(discharge,[]))).
% 2.51/2.22 tff(2956,plain,
% 2.51/2.22 (c0_1(a234)),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[88, 2955])).
% 2.51/2.22 tff(2957,plain,
% 2.51/2.22 (c1_1(a234)),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[77, 2955])).
% 2.51/2.22 tff(2958,plain,
% 2.51/2.22 (c3_1(a234)),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[66, 2955])).
% 2.51/2.22 tff(2959,plain,
% 2.51/2.22 (~c2_1(a234)),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[2738, 2958, 2957, 2956])).
% 2.51/2.22 tff(2960,plain,
% 2.51/2.22 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 2.51/2.22 inference(bind,[status(th)],[])).
% 2.51/2.22 tff(2961,plain,
% 2.51/2.22 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.51/2.22 inference(quant_intro,[status(thm)],[2960])).
% 2.51/2.22 tff(2962,plain,
% 2.51/2.22 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.51/2.22 inference(rewrite,[status(thm)],[])).
% 2.51/2.22 tff(2963,plain,
% 2.51/2.22 (^[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)) | (~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)) | (~c2_1(V)) | (~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)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 2.51/2.22 inference(bind,[status(th)],[])).
% 2.51/2.22 tff(2964,plain,
% 2.51/2.22 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.51/2.22 inference(quant_intro,[status(thm)],[2963])).
% 2.51/2.22 tff(2965,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 2.51/2.22 tff(2966,plain,
% 2.51/2.22 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.51/2.22 inference(modus_ponens,[status(thm)],[2965, 2964])).
% 2.51/2.22 tff(2967,plain,
% 2.51/2.22 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.51/2.22 inference(modus_ponens,[status(thm)],[2966, 2962])).
% 2.51/2.22 tff(2968,plain,(
% 2.51/2.22 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.51/2.22 inference(skolemize,[status(sab)],[2967])).
% 2.51/2.22 tff(2969,plain,
% 2.51/2.22 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.51/2.22 inference(modus_ponens,[status(thm)],[2968, 2961])).
% 2.51/2.22 tff(2970,plain,
% 2.51/2.22 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp22 | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp22 | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.22 inference(rewrite,[status(thm)],[])).
% 2.51/2.22 tff(2971,plain,
% 2.51/2.22 ((hskp22 | (~ndr1_0) | c2_1(a234) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252))) <=> (hskp22 | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.22 inference(rewrite,[status(thm)],[])).
% 2.51/2.22 tff(2972,plain,
% 2.51/2.22 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a234) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp22 | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a252)) | (~c2_1(a252))))),
% 2.51/2.22 inference(monotonicity,[status(thm)],[2971])).
% 2.51/2.22 tff(2973,plain,
% 2.51/2.22 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a234) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp22 | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a252)) | (~c2_1(a252)))),
% 2.51/2.22 inference(transitivity,[status(thm)],[2972, 2970])).
% 2.51/2.22 tff(2974,plain,
% 2.51/2.22 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a234) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)))),
% 2.51/2.22 inference(quant_inst,[status(thm)],[])).
% 2.51/2.22 tff(2975,plain,
% 2.51/2.22 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp22 | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a252)) | (~c2_1(a252))),
% 2.51/2.22 inference(modus_ponens,[status(thm)],[2974, 2973])).
% 2.51/2.22 tff(2976,plain,
% 2.51/2.22 (hskp22),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[2975, 122, 2956, 2957, 2009, 1998, 2023, 2969, 2959])).
% 2.51/2.22 tff(2977,plain,
% 2.51/2.22 (~c2_1(a271)),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[1805, 2976])).
% 2.51/2.22 tff(2978,plain,
% 2.51/2.22 (~c1_1(a271)),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[1811, 2976])).
% 2.51/2.22 tff(2979,plain,
% 2.51/2.22 (~c0_1(a271)),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[1817, 2976])).
% 2.51/2.22 tff(2980,plain,
% 2.51/2.22 (hskp0),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[1824, 122, 2979, 2978, 2977, 1098])).
% 2.51/2.22 tff(2981,plain,
% 2.51/2.22 (~c3_1(a213)),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[810, 2980])).
% 2.51/2.22 tff(2982,plain,
% 2.51/2.22 (~c1_1(a213)),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[816, 2980])).
% 2.51/2.22 tff(2983,plain,
% 2.51/2.22 (c2_1(a213)),
% 2.51/2.22 inference(unit_resolution,[status(thm)],[827, 2980])).
% 2.51/2.22 tff(2984,plain,
% 2.51/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a226)))),
% 2.51/2.22 inference(rewrite,[status(thm)],[])).
% 2.51/2.22 tff(2985,plain,
% 2.51/2.22 (((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c1_1(a234)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226))) <=> (c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a226)))),
% 2.51/2.22 inference(rewrite,[status(thm)],[])).
% 2.51/2.22 tff(2986,plain,
% 2.51/2.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c1_1(a234)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a226))))),
% 2.51/2.23 inference(monotonicity,[status(thm)],[2985])).
% 2.51/2.23 tff(2987,plain,
% 2.51/2.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c1_1(a234)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a226)))),
% 2.51/2.23 inference(transitivity,[status(thm)],[2986, 2984])).
% 2.51/2.23 tff(2988,plain,
% 2.51/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c1_1(a234)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))),
% 2.51/2.23 inference(quant_inst,[status(thm)],[])).
% 2.51/2.23 tff(2989,plain,
% 2.51/2.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a226))),
% 2.51/2.23 inference(modus_ponens,[status(thm)],[2988, 2987])).
% 2.51/2.23 tff(2990,plain,
% 2.51/2.23 ($false),
% 2.51/2.23 inference(unit_resolution,[status(thm)],[2989, 122, 2957, 2958, 2816, 2983, 2841, 2815, 2982, 2981, 878, 2959])).
% 2.51/2.23 % SZS output end Proof
%------------------------------------------------------------------------------